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DESIGN POINT ANALYSIS OF THE HIGH PRESSURE REGENERATIVE TURBINE ENGINE CYCLE FOR HIGHSPEED MARINE APPLICATIONS By GEORGE ANAGNOSTIS A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2007 Copyright 2007 By George Anagnostis This thesis is dedicated to my parents, Victor and Linda Anagnostis. Without their emotional and financial encouragement this thesis would not exist. ACKNOWLEDGMENTS I thank the members of my graduate committee members: Dr. William E. Lear, Jr., Dr. S. A. Sherif, and Dr. Herbert Ingley for their support on this thesis. Dr. Lear was especially helpful, providing me with critical advice throughout this project. Next, I would like to thank the Aeropropulsion Systems Analysis Office at the National Aeronautics and Space Administration Glenn Research Center for their assistance on Numerical Propulsion System Simulation program. Two members of that group provided continued technical assistanceScott Jones and Thomas Lavelle. Lastly, I thank two special individuals that have provided me with insight and wisdom concerning matters of engineering and life in general, John Crittenden and William Ellis. TABLE OF CONTENTS page A C K N O W L E D G M E N T S ................................................................................................. iv LIST OF TA BLES ............. ...... ...... .. ........ .......... .. ............. vii LIST OF FIGURES ............. .. ..... ...... ........ ....... .......................... viii N O M EN C L A TU R E ........................................................................ ........................... x CHAPTER 1 INTRODUCTION ............... ................. ........... ................. ... .... 1 2 LITERA TURE REVIEW .......................................................... ..............4 Brief History of Turbine Engine Development ...........................................................4 Gas Turbine Engine Examples in Marine Applications ............................................5 Advantages of Gas Turbine Engines in Marine Applications ....................................6 Recuperation and Intercooling ............................................................................. 7 SemiClosed Cycles................... .. .. ............. ............ ... ... .9 Computer Code Simulators...................... .... .. ..... .. .......................10 Previous Gas Turbine Research at the University of Florida ...............................12 3 NUMERICAL PROPULSION SYSTEM SIMULATION ARCHITECTURE .........16 M o d e l ...................... ... ............... ... ......................... ................ 1 6 E le m e n ts ........................................................................... 1 7 Flow Station.................... .. ............................... ........ .. ...... .......... 18 F low StartE n d ............................ ...................................... ....................18 Therm odynam ic Properties Package ........................................ ....... ............... 20 Solver ............ .............. ......... ..............................................21 4 CYCLE CONFIGURATIONS AND BASE POINT ASSUMPTIONS...................25 M major M o d el F eatu res .............. ........................................................ ..................... 2 5 Flow Path D descriptions & Schem atics ............................................ ............... 26 Simple Cycle Gas Turbine Engine M odel................................... .................26 High Pressure Regenerative Turbine Engine Efficiency Model .......................26 High Pressure Regenerative Turbine Engine with Vapor Absorption Refrigeration System Efficiency M odel .........................................................27 Simple Cycle Gas Turbine Engine Design Assumptions and HPRTE Cycles Base P point A ssum options .......................................... ................... .. ...... 28 5 THERMODYNAMIC MODELING AND ANALYSIS ........................................... 33 T herm odynam ic E lem ents ............................................................... .....................33 H eat Exchangers .................. .............................. ........ .......... .... 33 M ix e rs .......................................................................................3 4 S p little r ........................................................................................................... 3 5 W after E x tracto r ............................................................................................. 3 6 C o m p resso rs ................................................................3 7 T u rb in e s ......................................................................................................... 3 9 B u rn e r .....................................................................................................4 0 Sen sitivity A naly sis ..............................................................4 1 6 RESULTS AND DISCUSSION .............................. .................... 43 Cycle Code Com prison ............................................................................... 43 Sensitivity A analysis .............. ...........................44 Simple Cycle Gas Turbine Engine Model ....................................................... 44 Simple Cycle Gas Turbine Engine Model Sensitivity Analysis.......................48 High Pressure Regenerative Turbine Engine Efficiency Model ......................50 High Pressure Regenerative Turbine Engine Efficiency Model Sensitivity A n a ly sis ...................................................................................................... 5 3 C ycle C om prison A naly sis ................................................................................. 6 1 Extreme Operating Conditions .......................... ... .................................. 65 High Pressure Compressor Inlet Temperature Comparison for HV Efficiency M o d el ................... .. .............................. ...................... .. .. 6 7 Final Design Point Parameter Comparison ........................................ ...68 7 CONCLUSIONS AND RECOMMENDATIONS ............................................ 83 C o n c lu sio n s ........................................................................................................... 8 3 Recommendations................................................... .. ......... 86 LIST OF REFEREN CES .... .............................................................. ............... 88 BIO GR A PH ICA L SK ETCH ........................................... ................................. 91 LIST OF TABLES Table pge 41 Comparison of major configuration features .........................................................29 42 Simple Cycle Gas Turbine engine design point parameters.............................. 32 43 Base case model assumptions for HPRTE cycles [3], [26], [27] ...........................32 61 Cycle codes comparison: NPSS verses spreadsheet code for HPRTE Efficiency m odel data run. All tem peratures are in R....................................................... 70 62 Summary of the HPRTE Efficiency sensitivity analysis ...................................77 63 Comparison of the thermal efficiency maximums and their corresponding overall pressure ratios (O PR s)............. ......................................... ................78 64 Comparison of the specific power maximum values and their corresponding OPRs .............. ....... ........................... ............. ....... 78 65 Comparison of exhaust temperature maximum values for the three engine configurations .............. .. ...... ............... ............. ... .... ........ 79 66 Engine cycles comparison for four extreme operating conditions .........................81 67 High pressure compressor (HPC) inlet temperature comparison for the HV E efficiency engine m odel................................................ ............................... 81 68 Final performance design point comparison for the engine configurations.............82 LIST OF FIGURES Figure pge 31 Exam ple N PSS engine m odel [19]................................. ........................ .. .......... 23 32 State 7 of HPRTE engine cycle ............ .... ........ ....................... 24 41 Simple Cycle Gas Turbine (SCGT) engine model configuration ..........................29 42 High Pressure Regenerative Turbine Engine model, both efficiency and power configurations represented .............................................. ............................. 30 43 High Pressure Regenerative Turbine EngineVapor Absorption Refrigeration System, both efficiency and power model configurations represented ..................31 44 Vapor Absorption Refrigeration Cycle with HPRTE flow connections...............32 61 Thermal efficiency comparison is plotted with respect to OPR. NPSS results (with turbine inlet temperature (TIT) set to 25000R) are compared to the derived and the ideal Brayton cycle expressions. ..................................... ............... 70 62 Thermal efficiency vs. OPR with sensitivity to TIT .............................................71 63 Specific power vs. OPR with TIT sensitivity ........................................................71 64 Thermal efficiency vs. ambient temperature with OPR sensitivity..........................72 65 Demonstrates agreement between NPSS and developed theory that describes the low press re sp ool ................................................................. .. ....... ........ 72 66 High pressure spool pressure ratio (HPPR) vs. ambient temperature with low pressure spool pressure ratio (LPPR) sensitivity ........ ......................................73 67 Thermal efficiency vs. HPPR showing sensitivity to TIT ....................................73 68 Thermal efficiency vs. HPC inlet temperature for recirculation ratio sensitivity ....74 69 Thermal efficiency vs. turbine exit temperature (TET) with cooler pressure drop se n sitiv ity ......................................................................... 7 4 610 Specific power vs. TET for HPC efficiency sensitivity .......................................75 611 Specific power vs. HPPR for HPT efficiency sensitivity...................................75 612 Exhaust temperature vs. OPR for TIT sensitivity ......................................... 76 613 Thermal efficiency vs. HPPR for turbocharger efficiency sensitivity ...................76 614 Thermal efficiency vs. LPPR for TIT sensitivity .................. ...............77 615 Engine cycles comparison of thermal efficiency vs. OPR.............. ............ 78 616 Engine cycles comparison of specific power vs. OPR .................. ................79 617 Engine cycles comparison of exhaust temperature vs. OPR...............................80 618 Engine cycles comparison of thermal efficiency vs. ambient temperature.............80 NOMENCLATURE DepV Dependent variable in a Jacobian matrix IndV Independent variable in a Jacobian matrix E Heat exchanger effectiveness AP/Po Pressure drop as a percentage of the inlet stream pressure Q Heat flow rate (Btu/sec) h1, Mass flow rate at station "n" (lbm/sec) C Specific heat at constant pressure at flow station "n" (Btu/lbmR) TO ,, Stagnation temperature at the inlet to a physical cycle component (R) To o.t Stagnation temperature at the exit to a physical cycle component (R) P0 ,, Stagnation pressure at the inlet to a physical cycle component (psi) Po o.t Stagnation pressure at the exit to a physical cycle component (psi) h0 ,, Mass specific stagnation enthalpy at the inlet to a physical cycle component (Btu/seclbm) ho o., Mass specific stagnation enthalpy at the inlet to a physical cycle component (Btu/seclbm) FAR, Fueltoair ratio at state point "n" htot n For splitters and separators, total mass flow rate at state point "n" (lbm/sec) BPR Flow bypass ratio for splitter elements hH20_ hquzd Mass flow rate of liquid water being extracted in separator (lbm/sec) hH2o hquid Mass specific enthalpy of liquid water being extracted (Btu/seclbm) PRcomp Pressure ratio any compressor rlomp _ad Adiabatic efficiency of any compressor S. n Mass specific stagnation entropy at flow station "n" (Btu/lbmR) R Ideal gas constant (Btu/lbmR) dh, Mass specific enthalpy change for an isentropic process (Btu/seclbm) RComp, Ideal gas constant at a compressor inlet state point (Btu/lbmR) r7b Burner efficiency QR Lower heating value of the fuel (Btu/lbm) WAR Water to air ratio, mass basis TIT Turbine inlet temperature OPR Overall pressure ratio of a system Cp 7 Ratio of specific heats,  C, SpPw Specific Power (HPsec/lbm) Tamb Ambient Temperature (R), also Tab,ent LPPR Low pressure compressor pressure ratio HPRR High pressure compressor pressure ratio 7LPC ad Low pressure compressor adiabatic efficiency rLPT ad Low pressure turbine adiabatic efficiency Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science DESIGN POINT ANALYSIS OF THE HIGH PRESSURE REGENERATIVE TURBINE ENGINE CYCLE FOR HIGHSPEED MARINE APPLICATIONS By George Anagnostis May 2007 Chair: William E. Lear, Jr. Major Department: Mechanical and Aerospace Engineering A thermodynamic sensitivity and performance analysis was performed on the High Pressure Regenerative Turbine Engine (HPRTE) and its combined cycle variation, the HPRTE with a vapor absorption refrigeration system (VARS). The performance analysis consisted of a comparison of three engine configurations, the two HPRTE variants and a simple cycle gas turbine engine (SCGT), modeled after the production marine gas turbine engine, ETF40B. The engine cycles were optimized using a parametric analysis; a sensitivities study was completed to establish which design parameters influence individual engine model performance. The NASA gas turbine cycle code Numerical Propulsion System Simulation (NPSS) was the software platform used to complete this analysis. The comparison was performed at sea level with an ambient temperature of 5440R. The results for the SCGT predict a designpoint optimized thermal efficiency of 33.4% and an overall pressure ratio (OPR) of 10.4 with a specific power of 180 HPsec/lbm. The HPRTE engine, called HPRTE Efficiency for this thesis, had an expected design thermal efficiency of 37.2% (OPR of 32.2) with a specific power rating of 593 HP sec/lbm229% larger than the SCGT specific power. The combinedcycle HPRTE VARS, called HV Efficiency in the analysis, had a predicted design thermal efficiency of 45.0% (OPR of 32) with a specific power of 629 HPsec/lbm. The HV Efficiency thermal efficiency was 34.7% higher than that of the SCGT designed for maximum specific power. Exhaust gas temperatures varied significantly between the SCGT and the HPRTE variants. The model engine exhaust for the SCGT was 15800R while the exhaust temperatures of the HPRTE Efficiency and HV Efficiency were 801R and 837R, respectively. On average, the HPRTE calculated exhaust temperature was 7610R less than that of the SCGT. High pressure compressor (HPC) inlet temperature sensitivity was considered for the HV Efficiency. Two operating cases were consideredthe HPC inlet held constant at 4990R and 5090R. The 4990R case operated with a thermal efficiency higher by 1.56% and a specific power higher by 1.62%. The results of the analysis imply that HPRTE duct sizes will be smaller due to the engine having significantly higher specific power. Since specific fuel consumption is inversely proportional to thermal efficiency, the HV Efficiency engine cycle will require a smaller fuel tank to allow for additional cargo (or if the tank size is unchanged, the ship range is increased). Future project considerations include an offdesign performance analysis using NPSS or another software package, additional NPSS model benchmarking with a reputable cycle simulation code, and an analysis of the effects of moist ambient air on evaporator water flow extraction rates. CHAPTER 1 INTRODUCTION Before the marine gas turbine, naval ships clipped through the water propelled by sooty coalfired steam turbines or diesel engines. The 1940s advent of the gas turbine jet engine introduced a similar technology shift in the marine propulsion industry a decade later. And now for the last 60 years marine gas turbine engine propulsion advancements have derived mainly from aeronautical research and development programs. However, there have been some instances where the marine propulsion industry has led the way in developmentmost notably by the introduction of the WestinghouseRollsRoyce 21st century (WR21) ICR program in the early 1990s. Intercooled compressors and exhaust heat recuperation set the WR21 gas turbine engine apart. Ironically, the same ingenuity that steered the Navy to develop the WR21 program was nowhere to be found during the decisionmaking process time for the propulsion system for the 21st century speed ship toshore transport. The ETF40B, a workhorse and variant of the original TF40 that powered the Navy landing craft aircushion (LCAC) vessel for the last two decades will provide the propulsion and lift thrust for the new JMAC shiptoshore transport. Despite interest in new engine technologies, such as the High Power Regenerative Turbine Engine (HPRTE), funding constraints prevented the Navy from further investigating novel systems. This thesis will make the case for the HPRTE as an alternative engine concept to the ETF40B for the JMAC program. The motivation to compare the HPRTE to the ETF40B is a result of previous experimental and computational modeling efforts completed at the University of Florida (UF) Energy and Gas Dynamics Laboratory to develop alternate engine technologies. There other design considerations besides cost that drive engine development; the HPRTE will outperform the ETF40B, having a higher specific power ratio, improved offdesign performance, and a considerably lower infrared heat signature. The HPRTE is a semiclosed, compressor intercooled, recuperative system. A demonstration engine has been build and performance tested at UF, and the proof of concept has been met. The laboratory demonstrator uses engine exhaust heat to power a vapor absorption refrigeration system (VARS). This is representative of the combined cycle system, one of the two HPRTE configurations, that is considered in this modeling and analysis project. The base HPRTE is the other. The combined cycle variant is expected to outperform the base HPRTE because the VARS unit provides additional cooling to the high pressure compressor inlet of the engine. The analysis in this thesis includes a parametric optimization and sensitivity studies that determine designcritical parameters. There are three engine models total that are consideredthe two HPRTE variants (HPRTE Efficiency and HV Efficiency) and a simple cycle gas turbine engine (SCGT). The SCGT is modeled to represent the ETF 40B engine configuration. Only two of the three engines examined are considered in the sensitivity analysis; they are the SCGT and HPRTE Efficiency engine models. Sensitive parameters for the HPRTE Efficiency are expected to be the similar for the HV Efficiency cycle, and therefore the exercise was deemed redundant. The second part of the project is the cycle comparison analysis which will examine the performance parameters such as thermal efficiency, specific power, exhaust gas temperature, and high pressure compressor inlet temperature. Mission specifications and material and component limitations provide the scope for many of engine variables that are to be optimized. Being for a military application, the engine is expected to have robust performance capabilities; therefore, run cases were analyzed representing a wide range of ambient operating conditions for all cycle configurations. The model processes were based on thermodynamics relationships. The complete set of equations used to close the cycle model is discussed later. The flows were all considered steadystate and incompressible, and the turbomachinery components and ducting were all represented as adiabatic processes. These considerations are built in to the cycle code called Numerical Propulsion System Simulation (NPSS). This is a DOS driven, objectoriented program that has design, offdesign, and transient run operation capabilities. Technical support for this program was provided by the ASAO group at the NASA Glenn Research Facility. CHAPTER 2 LITERATURE REVIEW Brief History of Turbine Engine Development Between 15050 B.C., a Greek named Hero, living in Alexandria, Egypt, boiled water in a sealed container that had two spouts extending from the top and slightly curved [1]. As the water boiled, steam billowed from the spouts, rotating the entire container. At the time it was considered a toy, but today history remembers Hero as the inventor of the steam turbine. Despite this early application, the first documented use of the turbine engine for propulsion purpose was not until 1791; John Barber, a British inventor designed a simple steam engine with a chaindriven compressor to power an automobile [1]. Then in 1872, nearly 100 years after Barber engine, steampowered automobile was designed, Franz Stolze designed the first axial gas turbine engine [2]. The practicality of the engine was suspect and it never ran unassisted. Interest in gas turbine engines continued to increase, and developmental breakthroughs were made in the 1930s. Great Britain and Germany were the spearhead of these efforts as tension between the European heavyweights mounted. Faster, more agile aircraft were being conceived, and the air forces of both nations noticed the advantages of the jet engine over conventional piston engines. Frank Whittle of Great Britain worked out a concept for a turbojet engine and won a patent for it in 1930 [3]. Five years later in Germany Hans van Ohaim, working independently of Whittle, patented his own gas turbine engine system [3]. Ohaim and his colleagues witnessed the first flight of their turbojet engine on August 27, 1939, powering the He.S3B aircraft [3]. The Whittle concept was shelved until mid 1935 when finally with the help of two ex Royal Air Force pilots the engine was built and tested by Power Jets Ltd [3]. After working through design setbacks, including fuel control issues, the first British designed turbojetpowered aircraft flew in May 1941 [3]. Even though the Germans could claim the first turbojet powered flight, the British built the first production turbojet engine, the RollRoyce de Haviland [3]. Turbojet development skyrocketed in the 1940s and 1950s; a Whittle design provided the blueprints for the first American made turbojet engine, the General Electric IA [7]. Gas Turbine Engine Examples in Marine Applications The British were using simple gas turbine engines to power gun boats as early as 1947 [4]. The HMS Grey Goose was the first marine vessel to be powered by a turboshaft engine with an intercooled compressor and exhaust heat recuperation (ICR) [5]. In 1956, the U.S. Navy contracted with Westinghouse to develop a gas turbine engine for submersible operation [6]. They designed a two shaft semiclosed ICR engine; a novel concept that but was limited by fueltype availability. The use of heavy sulfur fuels triggered sulfuric acid buildup in the intercoolers which degraded the metal components in the heat exchanger. A direct effect heat exchanger was tried with sea water, but this only succeeded in introducing salt into the engine which deposited on the turbomachinery parts [6]. At the same time the Westinghouse engine was under development, General Electric was looking to convert their profitable J79 engine into a marine gas turbine. In 1959 they introduced the LM1500. It was a simple cycle gas turbine that produced 12,500 SHP [7]. The General Electric LM2500, introduced in 1968, ushered in the second generation marine of marine turboshaft engines. Like the LM1500, the LM2500 was a derivate of a proven aero engine that powered over 300 U.S. Naval ships [8, 7]. Moreover, thermal efficiency was improved on the LM2500 to 37 percent [8]. Advantages of Gas Turbine Engines in Marine Applications Gas turbine engines have overtaken diesels as the power plant of choice for ferries, cruise liners and fastattack military ships. This trend exists because gas turbines offer higher power outputtoweight ratios, significantly higher compactness, higher availability, and they produce fewer emissions than marine diesels [9, 4]. The powerto weight advantage is best realized with an example comparing a diesel engine to a gas turbine engine of similar power rating. The 7FDM16 marine diesel offered from General Electric produces 4100 BHP and weighs 48,800 lbs [10]. In comparison the Lycoming TF40 turboshaft marine engine, produces 4,000 BHP and weighs only 1,325 lbs [11]. The significant weight disparity favoring the TF40 is a prime reason gas turbines are being chosen to power marine vessels requiring agility and speed. Similarly, the compactness that gas turbine engines offer greatly improves vessel versatility and crew and cargo capacity optimization. As an example, the 7FDM16 diesel has a volume of 920 cubic feet, whereas the TF40 has a volume of less than 43 cubic feet [10, 11]. Subsequently, the compact, lightweight gas turbines are easier to transport and switch out of ships. With skilled professionals available from the aviation industry trained on gas turbines engines, there is an abundance of mechanics and support crew able to maintain and operate these systems [4]. Moreover, the emission reductions achieved by gas turbine engines over comparable diesels make them more attractive to commercial and military forces needing to placate environmental agencies such as the EPA and other international bodies. A simple opencycle gas turbine engine produces 1/3 to /4 the emissions of a diesel engine of comparable technology [9]. Recuperation and Intercooling Simple, opencycle turboshaft engines exhaust hot gas products to the atmosphere wasting highquality heat energy; an increasingly common use of this available heat energy in gas turbine engines is to preheat the compressed gas flow before the combustion stage. This process is called exhaust heat recuperation. As a result of raising the combustor inlet temperature, less fuel is required to achieve the desired turbine inlet temperature and desired power output. This directly impacts the thermal efficiency and specific power of the engine, raising thermal efficiency but dropping specific power in most cases. Any instance in which fuel use can be decreased has a direct positive impact on the cycle thermal efficiency. It is important to note that gas turbine engine recuperators generally work better in engines with only moderate pressure ratios [12]. Qualitatively, one can see that as the engine pressure ratio rises, the compressor exit temperature and turbine exit temperature approach each other. In practice this would drop the capacity of the recuperator to preheat the compressed air before combustion, thus rendering it ineffective. A second improvement on the simple gas turbine engine is the addition of an inter cooler. Intercoolers are placed between the low pressure and high pressure compressors to reduce the air temperature exiting the last stage of the compressor. Assuming the process is adiabatic and the air is a calorically perfect gas, the power required to drive the compressor is written as Wcomp = mpAT. This assumes a control volume analysis around the entire compressor for all stages [3]. The intercooler delivers a lower temperature fluid to the high pressure compressor stage. If the same pressure ratio is applied to the high pressure stage, the exhausting fluid temperature would be lower than if no intercooling had been performed. The outcome is that AT for the entire compressor has been decreased, and subsequently, the total power requirement for the compressor has also been decreased. The net effect on the cycle thermal efficiency is the same as raising the adiabatic efficiency of the entire compressor. The outcome is a net available power increase of 25 to 30% [5]. Coolants exist for both sea and air applications. Jet aircraft have 500C ambient air available and naval ships have the abundant salt water reserves of the oceans. Additionally, combining both compressor intercooling and exhaust gas recuperation provides a further improvement to cycle thermal efficiency. Engines that employ this technology are referred to as intercooling recuperation (ICR) engines. With the intercooler cooling the compressor discharge, the temperature difference between it and the turbine discharge increasesthe outcome is an improved recuperator performance [12]. In 1953 Rolls Royce introduced the RM60 ICR engine which powered the gunboat HMS Grey Goose [5]. Though innovative and more efficient than the steam engine it replaced, the RM60 was too complex to operate using existing controls technology. A further example reviewed for this project compares two gas turbine engines, a simple opencycle and an ICR, for a marine destroyer application. The study noted that fuel use is reduced by 30% with the ICR engine [5, 13]. In 1990, General Electric began retrofitting their midsize turboshaft engine, the LM2500, in hopes of improving its thermal efficiency by 30% [13]. This project was sidelined in 1991 when a team led by Northrop Grumman won a $400 million, 9year development contract to develop and build a replacement for the LM2500 marine gas turbine [14]. Program leaders Northrop Grumman and RollsRoyce chose an ICR engine design, called the WR21, for the navies of the United States, Canada, Great Britain, and France [14]. John Chiprich, who managed the ICR development program, noted that the new engine will reduce the fuel consumption for the entire marine turbine powered fleet of the United States by 27 to 30% [14]. One negative aspect to the ICR concept is that it has a lower power limit for it to be considered effective. Blade tip leakage for gas turbine engines that have a nominal power rating below 1.5MW overrides any efficiency gained from the implementation of ICR technology [15]. SemiClosed Cycles A semiclosed gas turbine cycle is one in which hot exhaust products are recirculated, combined with fresh air, and then burned again in the combustion chamber. Example configurations can include intercooling and recuperation, and some are turbocharged to boost core engine pressures. Despite the added complication of engine components and weight addition; many semiclosed cycle configurations have significant performance related benefits. For instance, semiclosed cycles that are turbocharged, have higher specific power, reduced recuperator size (if a recuperator is present) which improves heat transfer coefficients, and higher partload performance characteristics [13]. All semiclosed cycles benefit from reduced emissions since reduced oxygen concentrations reduce flame temperatures [13]. Some of the earliest semiclosed gas turbine engine configurations were proposed by the Sulzer Brothers in the late 1940s [16]. Their 20 MW gas turbine system for the Weinfelden Station was a complex system that achieved a cycle thermal efficiency of 32% for full load capacity and 28 % for half load capacity [16]. The earliest example of a semiclosed gas turbine system for naval propulsion was the Wolverine engine developed by Westinghouse [6]. The submarine engine program which began in 1956 called for a twoshaft, semiclosed, ICR turboshaft engine [6]. It was never a production engine because of sulfuric acid buildup that degraded the metallic intercooler components. This was attributed to the high concentration of sulfur in early diesel fuels. More recent research projects on semiclosed gas turbine cycles conducted by the University of Florida, Energy and Gas Dynamics Laboratory will be highlighted in the final section of this chapter. Computer Code Simulators Because of the complexity of the cycles that need to be simulated and the iterative nature of semiclosed cycle modeling, it is convenient to employ the use of a computational code to perform the numerous calculations. There were several computational thermodynamic cycle programs that were potential platforms for this project. Below is a brief overview of the programs surveyed. Gas turbine Simulation Program (GSP) is a product of the National Aerospace LaboratoryThe Netherlands (NLR) [17]. The GSP website boasts of a user friendly platform with draganddrop components ready for building engines models. The code can be used for steadystate as well as transient simulation. Material specifications and lifecycle information can be incorporated for failure and deterioration analysis. Unknown, however, is whether or not GSP can model semiclosed engine cycles. A second code called GASCAN was reviewed by Joseph Landon. This code models fluid movement as well as thermodynamic state variables for engine simulations. Semiclosed operation is not explicitly discussed but simple and complex cycles are apparently easily modeled. A third modeling program reviewed was Navy/NASA Engine Program (NEPP); it was developed to perform gas turbine cycle performance analysis forget aircraft engines. NEPP is an older componentbased engine modeling program that has design and off design modeling capabilities with performance map integration. User instantiated variables can be controlled to hold specific parameters constant while the program converges to its solution. This program was eliminated because it can not model recirculated flows [13]. NEPP was only the first of three NASA programs evaluated for this modeling project. The second NASA code was ROCket Engine Transient Simulation (ROCETS) developed at Marshall Space Flight Center. This program provides a suite of engine component modules to assist users in building their models; it also allows users to create their own modules to model more exotic engine cycles [18]. Like NEPP, ROCETS gives the developer the ability to vary certain parameters until other constraints are satisfied and a converged solution is determined [18]. Users have the option of operating in design or offdesign mode as the program has the capability of reading performance maps for compressors and turbines. ROCETS was used in modeling efforts at the University of Florida in the 1990s. The program is capable of modeling recirculation in gas turbines and water particulate extraction. Being somewhat antiquated, the program was dismissed as a possible platform for the project considering the unlikely availability of user support. A commercial software package option was the versatile ASPEN PLUS. The ASPEN PLUS engineering suite is a robust package of software programs that can handle all of the modeling requirements for this project. Once again, here is a program that provides users with the option of running their cycle in design, offdesign, or transient modes. Their website displays screen shots of a pleasant graphic user interface with dragndrop engine components [19]. The third software program from NASA, Numerical Propulsion System Simulation (NPSS) is a product of the Aeropropulsion Systems Analysis Office (ASAO) at the Glenn Research Center. NPSS is set up to operate similar to the earlier programs NEPP and ROCETS. Accordingly, NPSS offers users the convenience of objectoriented engine components for building cycle models [20]. Offdesign and transient modeling are options in addition to running in the design point mode [20]. The model developer has control of convergence through constraint handling. Since this program became the platform of choice for this project, its capabilities will be discussed in further detail in Chapter 2. Previous Gas Turbine Research at the University of Florida In 1995 Todd Nemec performed a thermodynamic design point analysis on a semi closed ICR gas turbine engine with a Rankine bottoming cycle [21]. Nemec developed his model using the ROCETS program discussed earlierhis analysis concluded that the combined cycle with superheated steam in the bottoming cycle resulted in an overall efficiency of 54.5% [21]. The next body of work on semiclosed cycles was performed by Joseph Landon. Landon performed design and offdesign point analysis of two separate regenerative feedback turbine engines (RFTE) [13]. The turbocharger configuration resembled the topping cycle that Nemec modeled. The other configuration sent the combustion products through a power turbine before the recuperation heat exchanger. The analysis predicted that the power turbine configuration produced the highest thermal efficiency, 48.2%, compared to 46% for the turbocharger case [13]. Off design analysis revealed that the turbocharger model was the most efficient between 20% and 80% power capacity [13]. Russell MacFarlane used the ROCETS program to model water extraction and injection on the RFTE engine [12]. MacFarlane found that water removal caused a decrease in specific fuel consumption and a slight increase of specific power [12]. He surmised that water removal was particularly influenced by "recirculation ratio, cooler effectiveness, and first stage pressure ratio" [12]. George Danias extended the study of the RFTE cycle and investigated design and offdesign performance of three separate configurations for a helicopter engine application [18]. His conclusions stated that the three RFTE configurations were 30 to 35% more efficient than the T700701C, baseline engine [18]. Currently, a research project is underway to design and develop a combined cycle, powerrefrigeration cycle called the HPRTEVARS. The High Power Regenerative Turbine Engine (HPRTE) uses exhaust gas heat to power the vapor absorption refrigeration system (VARS). A design point performance study was carried out by Joseph Boza analyzing two HPRTEVARS engine sizes, a small 100 kW engine and a larger 40 MW engine. Boza calculated the performance parameters based on a constant high pressure compressor (HPC) inlet temperature of 5 o C. Excess refrigeration capacity (that capacity not used to cool the HPC inlet stream) was considered in the combined cycle efficiency value. The larger engine analysis predicted a combined cycle efficiency of 63% while the small engine efficiency was determined to be 43% [22]. He determined that increasing ambient temperature limits the excess refrigeration capacity, and at an ambient temperature of 45 C the combinedcycle system has no excess refrigeration. For his analysis, Boza used a spreadsheet cycle code to predict the performance of the HPRTE; this was in conjunction with a VARS model that he created. In Chapter 6 the spreadsheet model has been used to benchmark the NPSS program used in this project. The spreadsheet HPRTE model is not configured to consider the low pressure spool of the engine as a turbochargerin the comparison in Chapter 6, the spreadsheet cycle model will be constrained manually for the turbocharger configuration. Life cycle cost analyses of the HPRTEVARS was performed and compared to a microturbine engine by Viahbav Malhatra. Using a standard life cycle cost analysis procedure, Malhatra determined that the HPRTEVARS system exhibited a life cycle cost savings of 7% over the competing microturbine system [23]. One primary reason for the cost savings was associated with the HPRTE being turbochargedthis enabled smaller and less expensive engine components to be considered. The other reason for the cost savings was directly related to fuel consumption. HPRTE fuel costs were partially compensated by the proceeds from available refrigeration capacity of the VARS unit [23]. To obtain his results Malhatra used a Fortran model of the HPRTEVARS created by Jameel Khan. Khan performed his dissertation study on the design and optimization of the HPRTEVARS combined cycle developing a high fidelity, thermodynamic model for both the engine and the refrigeration systems. He used the optimization package LSGRG2 to determine the best designpoint engine parameters considering such outputs as power, refrigeration, and water. His results for the combined cycle with the NH3 /H20 refrigeration system predicted a cycle thermal efficiency of 40.5% with a ratio of water production to fuel (propane) consumption of 1.5 [24]. Including the excess 15 refrigeration produced by the cycle, a combined cycle thermal efficiency was evaluated as 44%. CHAPTER 3 NUMERICAL PROPULSION SYSTEM SIMULATION ARCHITECTURE Numerical Propulsion System Simulation (NPSS) was developed by Aeropropulsion Systems Analysis Office (ASAO) at the National Aeronautics and Space Administration (NASA) Glenn Research Center, Cleveland, OH in conjunction with the Department of Defense and leaders in the aeropropulsion industry. The purpose of the code was to speed the development process of new gas turbine engine concepts for military and civilian applications. It is a componentbased engine cycle simulation program that can model design and offdesign point operation in steadystate or transient mode [20]. The code can be used as a standalone analysis program or it can be coupled in conjunction with other codes to produce higher fidelity models. Model Engine models are created using any standard text editor such as Microsoft Wordpad. The model file contains the instructions and commands required by NPSS to build an engine model. The engine model file combines the engine components (elements) in a systematic manner that is consistent with the engine cycle the user is modeling. Here, elements are connected to create the flow stations of the engine; these flow stations are created by linking the flow ports between elements. In the model the thermodynamic package, solver solution method, and model constraints should also be specified if different than the defaults. These subjects will be discussed in further detail later in the Chapter 3. Figure 31 is a schematic representation of an example engine modeled using NPSS. The elements are plainly listed; there is an inlet, compressor, burner, turbine, shaft, duct, and exhaust. The working fluid properties are passed through flow ports from one element to the next. Shaft ports connect the compressor and turbine with the shaft element in order to perform the power balance for the engine. The interaction of a subelement, CompressorMap with its parent element, Compressor, is shown with its socket link. This particular model has an assembly for the major engine components. The assembly compartmentalizes any processes or calculations performed by these components from the rest of the model. Elements Elements are the corer stones of the engine model. Although NPSS comes with a full suite of engine component modules, users are encouraged to create their own elements to model their unique circumstances using the C++ type syntax of NPSS. As mentioned above, elements are responsible for performing the individual thermodynamic processes that simulate the physical engine components. The modules use standard thermodynamic relationships to simulate these processes. The level of modeling sophistication is entirely user driven as loss coefficients and scalars may be applied to variables. Mach number effects are calculable. For higher fidelity models heat and frictional energy dissipation may be considered. For the purpose of this analysis the cycle models were kept as simple as possible to shorten computing runtimes. Nevertheless, even simple models require a certain level of complexityfor those cases there are supplemental routines added to elements called subelements and functions. Subelements are subroutines that can be called by elements to perform calculations or performance table lookups. For instance, the turbine element for a model that is operating in offdesign mode would use a subelement to determine the efficiency value from data tables. Functions are a type of subroutine that is user instantiated in a particular element that requests particular calculations be performed. Function calculations take precedence over the solver driven calculations. They may be performed before, after, or during solver runtime depending on the desire of the user. FlowStation For an element to perform its calculations, properties and state information must be known as initial conditions. These initial conditions are set by the user or the computer and passed to the element through a flow port. When flow ports are used to link two elements, this bridge is called a FlowStation. There is a main FlowStation subroutine and then there are the specific FlowStation subroutines unique to each thermodynamic model. The main FlowStation subroutine is responsible for linking the model to the appropriate subroutines that handle the subroutine lookups. When NPSS uses the Chemical Equilibrium with Applications (CEA) thermodynamic software, the main FlowStation subroutine links the model file/files with the CEA program allowing the passage of species and state information between the two programs. FlowStartEnd There are elements in NPSS specifically designed to either begin or end a fluid flow path. Semiclosed gas turbine engine modeling in NPSS makes use of these flow start/end elements to obtain converged solutions. The solution solver in NPSS requires a single initial pass through the model elements to create the flow path and flow stations and essentially build the engine model. For open cycle gas turbine engines this task requires no extra consideration by the modeler. The solution solver can logically step through the engine from the inlet element to the exhaust element for the preprocess pass. However, all of the HPRTE configurations have mixing junctions upstream of the core engine components adding a further level of complexity that the solution solver must negotiate. The solution requires added components, FlowStart and FlowEnd elements, and additional constraints added to the solution solver. For convenience and brevity the ASAO developed the element FowStartEnd to replace the FlowStart/FlowEnd elementsthis element also contains the additional constraints required, eliminating the necessity to initialize these in the main model file. To be complete it is best to describe the coding required to gain convergence of a regenerative gas turbine model using FlowStart, FlowEnd, and FlowStartEnd elements. When the solver is stepping through the HPRTE it expects to have a hotside flow station already instantiated when it reaches the recuperator inlet after the highpressure compressor exit. Therefore, a FlowStart element is created and added to the solver sequence (responsible for the order of element preprocess loading) before the high pressure recuperator flow station is created. Initial conditions are given to the stream including temperature, pressure, mass flow rate, fueltoair ratio, waterairratio, and fuel type. This flow station is 7a. Now the solver can continue to load the model to the point of the highpressure turbine exit flow station. This is the point where the 'bridge' is made with the FlowStart element instantiated earlier. Here, a FlowEnd element is created and the state of the flow exiting the highpressure turbine is stored in this element. The flow station here is 7b. Since the flow conditions cannot be directly passed from the FlowEnd element to the FlowStart element, the solver is given the task of iterating on all the flow station 7 parameters until the conditions match in both elements. To make this happen the user sets up five variables, which NPSS considers 'independents', to iterate on until their five counterpart constraints, which NPSS deems the 'dependents', are satisfied. These five independent variables are listed as: stagnation temperature and pressure, mass flow rate, fuelairratio, and waterairratio. The constraints are generally written as equations that must be satisfied for solver convergence to be recognized. One example of a dependent constraint from the FlowStartEnd element is given below in NPSS syntax. Dependent dep P{ eq lhs = "Fl I.Pt"; eq rhs = "Fl O.Pt"; autoSetup = TRUE; } The constraint variable is 'dep_P'. The left hand side of the equation is set equal to the stagnation pressure of the flow entering FlowStartEnd, and the right hand side is set equal to the exiting stagnation pressure. This constraint is added to the solver along with four others corresponding to the variables listed above. Figure 32 shows the schematic representation of the procedure that was just described. Thermodynamic Properties Package Chemical Equilibrium with Applications (CEA), obtains chemical equilibrium compositions for predefined thermodynamic states. Two thermodynamic state properties must be known for the rest to be calculated or obtained from table subroutines. This requires two input files: 1. Thermo.inpContains thermodynamic property data in least squares coefficients. These data can be used to calculate referencestate molar heat capacity, enthalpy, and entropy at a given temperature. 2. Trans.inpContains the transport property coefficients for the species CEA uses the Gibbs freeenergy minimization method to calculate chemical equilibrium at each state point. Chemical reaction equations are unnecessary when using the freeenergy minimization method and chemical species can be treated individually. For a detailed description of the theory and methods used in CEA please see reference [25]. CEAFlowstations are responsible for passing constituent and state point temperature and pressure from NPSS to CEA. Solver The NPSS solver is responsible for bringing the model to a converged solution. In order to accomplish this task the user must choose which engine parameters to constrain. Constrained parameters are called model "dependent variables". To satisfy the dependent variables a set of"independent variables" must be defined and iterated. This iterative approach to find a solution begins with an initial state guess, and that is subsequently refined until a satisfactory solution is found. The solver solution method is a quasiNewton method. For a simple description assume there is only one constraint on the model, and as a result only one variable to iterate to meet it. The initial value of the independent variable is user specified, and with that the initial value of the variable desired to be constrained can be found. Then the independent variable is perturbed a certain amount chosen by the solver and a new value for the dependent variable is found. The solver now must decide if this new value of the variable to be constrained is a satisfactory one. A partial derivative error term is calculated, ErorTerm (DependentValue+1 DependentValue) )(3.1) ErrorT erm = (r^     '^ (3.1) (IndedependentValue+ _ IndependentValue' ) where I denotes the iteration number. If it is outside the acceptable tolerance region, the process is begun again. With a system of constraints a Jacobian matrix would be created to hold all the error terms. The new perturbation terms would be calculated from the previous Jacobian matrix: (DepV, DepVj) (DepV, DepVDj) IndV1 1IndV 1 IndV,' 1IndV, = I] (3.2) (DepVm DepVm') IndV 1IndV1 ) Here there are "n" number of independents and "m" number of dependents. The Jacobian can be related to the independent variables with the expression [J ]. x ]= [F(x')], (3.3) where [Ax' is the matrix composed of the independent perturbation values. The [F(x)] matrix holds the values of the dependent constraints at the I'th iteration. The new independent values may now be calculated with the following: x '] [J_ I1 ]I F x )]. (3.4) With [x"' ] now determined, [Axi ] and [F(ll )]can be found and a new Jacobian matrix created. The process continues until the Jacobian error values are within the acceptable tolerance limits of the solver. I Sg Figure 31 Example NPSS engine model [19] HPT Recuperator NPSS Code/Element Representation of Above Engine State HPT FlowStart FlowStart 1 FlowEnd Recuperator 7a I I 7b 7temp Simplified Code Representation HPT FlowStartEn Recuperator I 7a 7b Figure 32 State 7 of HPRTE engine cycle CHAPTER 4 CYCLE CONFIGURATIONS AND BASE POINT ASSUMPTIONS Before discussing the thermodynamics relationships used in the analysis, it is necessary to give an overview of the cycles from a systems standpoint. This analysis compares the design point performance of three engine configurations. The first engine is a simple cycle gas turbine engine (SCGT). It has been modeled to predict the performance of the production engine, ETF40B, which powers the military LCAC for the United States Navy. The SCGT will be compared to two variations of the HPRTE engine, the base HPRTE and a variant that uses refrigeration capacity to cool the high pressure compressor inlet stream. Major Model Features When comparing engine systems, it is convenient to understand the major features of each model. Listed in Table 4.1 is a breakdown of the features that distinguish the engine configurations from one another. The HPRTE cycles are two spool engines with exhaust gas product heat recuperation. Both are semiclosed and have compressor inter cooling. The HV Efficiency has additional cooling capacity provided by a vapor absorption refrigeration system (VARS). The additional cooling enables exhausted water vapor to be condensed and collected for use elsewhere or for injection after the high pressure compressor. Flow Path Descriptions & Schematics Simple Cycle Gas Turbine Engine Model As mentioned earlier, the SCGT is a simple, open cycle gas turbine engine. For this analysis the model with have a total of five flow stations (Figure 41). State 1 is the inlet stream. From State 1 to 2 the flow undergoes an adiabatic compression process in compressor, Cl. From State 2 to 3 there is a constant area, premixed burner, B. The process from State 3 to 4 is an adiabatic expansion process through the turbine, T1. Mechanical work generated by the turbine drives the compressor and supplies power for the ship propellers or lift fans. State 5 is the fuel flow station. JP4 was the fuel of choice for this analysis because it is widely used in industry and has a high availability. High Pressure Regenerative Turbine Engine Efficiency Model Figure 42 is a schematic representation for the Efficiency and Power modes of the HPRTE cycle. The Power mode concept incorporates a flow splitter to bypass some exhaust from the high pressure turbine and send it directly to the low pressure turbine. Initially, the Power mode had been considered for this project to give additional boost capabilities to the low pressure spool. However, while completing the analysis it was determined that the Efficiency mode predicts sufficient boost for the system and any additional boost pressure would result in a turbocharger design outside of modern technology limits. There are 14 states for the basic HPRTE (the Power mode has 16). Air enters at State 1 and undergoes an adiabatic compression process in the low pressure compressor, LPC, before reaching State 2. Next, the fresh air from State 2 is combined with the recirculated exhaust gas products from State 10 in an isobaric, adiabatic mixing process. The resultant State is 2.9. Now the combined flow passes through a sea water cooled heat exchanger called the main gas cooler (MGC). The effectiveness, pressure drop, and process fluid temperature are all given. The resulting State is 3.0. After the gas has been cooled it goes through another adiabatic compression process in the high pressure compressor, HPC. The resultant State 4 has the maximum system pressure. Following the HPC there is a heat recuperation process (RHX) in which hightemperature exhaust gas product stream preheats the State 4 flow resulting is State 5. From state 5 to 6 the gas is mixed with fuel and ignited in the combustion chamber, B. A small pressure drop is applied before State 6 to simulate friction losses in the combustor. The high pressure turbine inlet temperature, or TIT, was chosen to be 25000Ran acceptable value for a medium size engine. The expansion across the high pressure turbine, HPT, produces the power to drive the HPC and the net BHP is available power for the vessel. State 7 is State 7.11 in the Efficiency mode, and that flow passes through the RHX, rejecting heat to State 4. The only flow splitter for the Efficiency cycle comes at State 9. Here, a user defined recirculation ratio determines the mass flow rates at State 7.15 and 10. State 10 recombines with fresh air flow from the LPC exit. State 7.2 is also State 7.3 in Efficiency mode. The final expansion process across the low pressure turbine, or LPT, exhausts to the environment at State 8. High Pressure Regenerative Turbine Engine with Vapor Absorption Refrigeration System Efficiency Model Figure 43 is a schematic representation of the HV Efficiency. The HPRTE VARS modes differs from the HPRTE modes only by the addition of two heat exchangers in the flow path after the recirculated gas products combine with the fresh inlet air at State 2.9. The generator (GEN) and the evaporator (EVP) are two of the heat exchangers that make up part of the VARS. A schematic of the VARS is also included as Figure 44 for clarification. It was not modeled since the scope of this analysis only included modeling the gas path side of the combined cycle system. The point of water collection is shown on the figure, as well. The computational model of this cycle required the addition of a separator element to perform the water extraction. The separator is discussed in Chapter 5, Thermodynamic Modeling and Analysis. Notice that the HPRTE cycles require an iterative solution method to obtain model convergence because of the semiclosed operation. For the first iteration of the engine cycle an initial guess for the temperature at StatelO is given. Simple Cycle Gas Turbine Engine Design Assumptions and HPRTE Cycles Base Point Assumptions The SCGT is a medium size, opencycle gas turbine engine modeled after the ETF 40B. The ETF40B has a seven stage axial compressor followed by a single stage centrifugal compressor yielding an overall pressure ratio of 10.4 [Robert Cole]. The nominal output shaft horsepower is 4000 SHP. Turbine inlet temperature was assumed to be 25000R. Turbomachinery efficiency information was provided by Dan Brown of Brown Turbine Technologies. All other engine design parameters were chosen based on conservative current technology limits. See Table 42 for complete details. The base point HPRTE component parameters are listed in Table 43. The same methodology used to determine the design parameters for SCGT was considered when deciding baseline design values for the HPRTE engine cycle configurationssize and technology limitations were applied. There were material and computational limitations that existed and needed to be accounted for to preserve the fidelity of the engine model. They are as follows: TIT maximum was 25000R, hot side recuperator inlet temperature maximum was 20590R, turbocharger pressure ratio maximum was 7.5, and HPC inlet temperature minimum was 4910R (NPSS limitations). Table 41 Comparison of major configuration features Model Features Turbocharger Intercooled VARS Water SemiClosd Recuperatored Model Pressurized Compressors cooling Extraction SCGT HPRTE Efficiency * HV Efficiency * Figure 41 Simple Cycle Gas Turbine (SCGT) engine model configuration Air 1 I (0 0)T LO aI o(1) Figure 42 High Pressure Regenerative Turbine Engine model, both efficiency and power configurations represented 31 CO) o U Ua) a, j C N, Figure 43 High Pressure Regenerative Turbine EngineVapor Absorption Refrigeration System, both efficiency and power model configurations represented Figure 44 Vapor Absorption Refrigeration Cycle with HPRTE flow connections Table 42 Simple Cycle Gas Turbine engine design point parameters Parameter Value C1 Adiabatic Efficiency 0.858 Burner Efficiency 0.99 Burner Pressure Drop 0.03 Turbine Inlet Temperature 2500R T1 Adiabatic Efficiency 0.873 Table 43 Base case model assumptions for HPRTE cycles [3], [26], [27] Parameter Value Ambient Temperature 544.67R Sea Water Temperature 544.67R Ambient Pressure 14.7 PSI LPC Adiabatic Efficiency 0.83 GEN Effectiveness 0.85 GEN Pressure Drop 0.03 MGC Effectiveness 0.85 MGC Pressure Drop 0.03 EVP Effectiveness 0.85 EVP Pressure Drop 0.03 HPC Adiabatic Efficiency 0.858 RHXEffectiveness 0.85 RHX Pressure Drop State 45 0.04 RHX Pressure Drop State 7.119 0.04 B Efficiency 0.99 B Pressure Drop 0.03 HPT Inlet Temperature 2500R HPT Adiabatic Efficiency 0.873 Recirculation Ratio 3 LPT Adiabatic Efficiency 0.87 Fuel Hydrogen to Carbon Ratio 1.93:1 2.9 2.91 Pump 2.92 CHAPTER 5 THERMODYNAMIC MODELING AND ANALYSIS Chapters 3 and 4 addressed the computational structure of NPSS and the cycle configurations of the models including the design point assumptions. While top level NPSS calculations are performed by the solution solver, the intermediate operations performed during every iterative pass to calculate the thermodynamic states are discussed next. Chapter 5 develops the theory for these auxiliary thermodynamic relations that drive the model elements (subroutines). These relations are developed using fundamental thermodynamic concepts. Thermodynamic Elements Heat Exchangers Heat exchangers are an important component in HPRTE cycles. The base HPRTE Efficiency model mode has two heat exchangers, MGC and RHX; and the combined cycle, HV Efficiency, has four heat exchanger elements including three for compressor intercooling. Those for the intercooling have defined process inlet flow states. Mass is conserved by setting the exit mass flow rate equal to the entrance mass flow rate. User defined inputs include effectiveness, E, and AP/Po n Let effectiveness be defined as (1ihotCp hot) V0_ hot in TO hot out ( in1 pl 01 _( ln1 TO outl) (. E (5.1) 0max (imim np _mm l) ( hot in cold in) (rnr Cml pi ) o n1 TO in2) C hot is the hot side specific heat at constant pressure, and C ml is the specific heat of the minimum capacity flow stream. (k 0 nl 0 outl) Therefore, E = T (5.2) T n TO n2 The only unknown in Equation 5.2 is To o ,,. The capacity of the process fluid is set such that it is always the maximum capacity stream. This ensures that it is not used in the calculation above. The exit pressure is determined using the following equation: Po outl = Po n,.( AP/P _nl). (5.3) Know known are the parameters To ou,,, Pt otl, and ooutl The exit state is set. Mixers The mixer is modeled as an adiabatic, constant static pressure process. Because there is no consideration given for Mach number effects, the stagnation pressures of the two flows entering the mixer must be identical. This requires a model constraint be set up by the user for each HPRTE model and satisfied by the solution solver. All HPRTE models have recirculation mixers which are tasked with combing the recirculated exhaust gas products with fresh air discharged from the low pressure compressor. A mass balance requires: ihout = mi + rn2 (5.4) Assuming adiabatic mixing, the energy balance is as follows: nlhO miA + lin2ho in2 (. ho o= (5.5) 111out Constant pressure mixing implies: Po0 iml Po m2 0 Po out. (5.6) Other parameters such as the FAR,,, and the mass fractions are mass averaged. For example: 2Ih,1FAR,, + ilh2FAR,2 FARot = lFAR + FR (5.7) mout With h0 out, P0 out, Mhou, and the exit state mass fractions all known, all other thermodynamic properties can be found. Splitter In Chapter 4 the cycle schematics for the HPRTE cycle models showed flow splitting occurring at State 9. To accomplish this feature with a computer model a splitter component must be defined to separates flow into two streams before exhausting to the environment. The recirculation splitter is tasked with the job of splitting the flow stream on a mass basis after the high temperature recuperation process (State 9). A portion of the flow is reconstituted with fresh air before heading back through the core engine components while the rest is directed to the low pressure turbine (LPT) to power the turbocharger. A bypass ratio, BPR, is user defined to represent the mass basis split of the flow streams. The recirculation splitter inlet state is defined by the following know parameters: T, ,,, P0 ,,, htot ,,, FAR,,, h, ,,, and mass fractions for all species. In general BPR is defined as BPR = nto ou2 (5.8) Mtot outl For this application the bypass ratio is defined as BPR tot recrc (5.9) intot exhausted htot recr.c is the mass flow rate recirculated and mixed with fresh air. ihto exhausted is the mass flow rate that passes directly to the low pressure turbine and be exhausted from the system at State 8. The user also reserves the option of applying flow pressure drops to either or both of the split streams, but for this analysis the splitter is modeled as an isobaric process. Similarly, the process is adiabatic, as there is no heat transfer. The mass fractions are unchanged; therefore, the exit state of each flow is defined. P0 out =PO out2 =Pr In (5.10) To outl T out2 =T ,,n (5.11) Water Extractor The water extraction component is only present in the HV Efficiency configuration. Because water vapor is present in the recirculated mixed gases and the cooling capacity of the three heat exchangers is significant to cause condensation to occur in the flow stream, it is desirable to separate the liquid water from the gas flow before the inlet to the high pressure compressor. The separation of liquid water from the flow stream is modeled as an isentropic process. The inlet state is completely defined; therefore, iH20 lquid and hH20 lquid are readily available from CEA. The exit state is defined by first setting the inlet and exit temperatures and pressures equal. Po o.t =Pi (5.12) To out =To n (5.13) Then the exit mass flow rate and enthalpy are set. mtot out = mtot ,, H20_hqud (5.14) ho ot =h,,n hH20 _quid (5.15) The exit state of the water extractor is now defined. Compressors Compressors inlet states are defined with the following parameters passed to the element: To ,n, P ,, Ihtot n,, FARn, h0 ,,, and mass fractions for all species. The performance of the compressor is determined by the following parameters: pressure ratio (PRcomp) and adiabatic efficiency (Conmp ad) Exit pressure is determined first with the equation Po ot = PRcomP .P _n (5.16) The other thermodynamic parameter, the adiabatic efficiency, is used to calculate the exit state point parameters in the NPSS Compressor module. Define the adiabatic compressor efficiency as ideal compressor work ho out ideal ho , Compad (5.17) Cp d adiabatic _compressor_ work ho out ho i Determining the ideal exit state enthalpy is straight forward knowing P0, o, and so out ideal if So i, = so _out ideal Since entropy and enthalpy are only functions of temperature; the exit state ideal temperature is quickly found along with enthalpy. Now, rearrange and directly solve Equation 5.17 for h0 o,,. With the exit pressure and enthalpy know known, all exit state thermodynamic parameters are readily calculated by CEA. The power required by the compressor is also calculated. Wicon = iOn hono ot* ,,ho ou t (5.18) The power is converted from Btu/sec to HP: 778ft lbf W 1BTU. (5.19) Comp 550ftlbf s " /sec/ 1HP Polytropic efficiency, omp_ poy, is an output parameter calculated from the entrance and exit entropies and pressures. The derivation is as follows: The definition of the polytropic efficiency is dh, rComp _poy h (5.20) Comp _poly =dh To arrive at this equation, first consider a reversible form of the energy equation. Since dh = du +vdP + Pdv, (5.21) Tds = du + Pdv = (dh Pdv vdP) + Pdv = dh vdP (5.22) dh v dh dP Therefore, ds = dP = R (5.23) T T T P dh Solving Equation 5.23 for yields T dh dP = ds + R (5.24) T P For an isentropic process ds = 0. Therefore, dh dP S= R (5.25) T P Combining Equations 5.24 and 5.25 results in the following: dh, Rd dh /T P p py = dh dh dP IT ds +R P Integrating Equation 5.26 from the inlet state to the exit state yields: RConp ,7 log(PRConp ) 77Comp poly Romp Rn log(PRCOMP (5.27) S out S in + RComp_ log(PRcomp Turbines Turbines provide the power to drive the compressors as well as the net power for the ship propellers and lift fans (if LCAC is the mission). The NPSS model Turbine element requires a defined entrance state to include such parameters as T, ,, PI,, htot, ,,, FAR,,, h0 ,,, and mass fractions for all species present. As was the case with the compressors, the performance of the turbine components is determined by the defined parameters: pressure ratio (PRurb) and adiabatic efficiency (Urub ad). NPSS defines PR,,,b differently than most turbomachinery reference texts. Here it is defined as: P , PRTub (5.28) Po out The exit state can be determined by first applying the turbine pressure ratio. PO in PO out n Po out O= PO ,,,/ PRT,,,b (5.29) PRTrb As was the case for the compressor, h0o o, is the other thermodynamic parameter necessary to in order to define the exit state. The turbine adiabatic efficiency is defined as: adiabatic turbine work ho 0n ho out rTurb ad =  = (5.30) ideal _turbine _work h0 ,, h, out ideal The power generated by the turbine is also calculated. WTurb = .h0 ,n h0 n o t* ho out (5.31) 40 This power is converted to horsepower as it is in the compressor. The polytropic efficiency is an output parameter calculated using the same approach described in the compressor section. The final equation is given below. so out so In +RRr,, n, "log(1/PRrb,) lTurb poy , +RTurb n log I/ Prb (5.32) pr pRTur~ in *log(i / PRb) Burner The Burner element is a constant volume burner. The entrance state is completely defined; those parameters include: To ,,, P ,,, itot n,,, FAR,,, ho ,,, and mass fractions for all species. Also specified are the rb and burner AP/Po n,. The exit stagnation pressure, Po o,,, is found with the equation: Po o,,t = (, 'AP/Po n,). (5.33) To ou must be specified by the user in order to determine the incoming fuel flow rate, Mfue, In order to determine the exit state, the burner subroutine makes an initial guess for the fuel flow rate, m1fue,, using a straightforward energy balance. r T T 1 To out 0 in m =2 fuel ar" 18400/0.285 T ot (5.34) The model assumes a lower heating value, QR, of 18400 Btu / Ibm. It also assumes a constant specific heat, Cp, of 0.285 Btu / lbmR. The inlet conditions and the first fuel flow rate iteration, mi<,e, are then passed to CEA from the NPSS subroutine calcBurn. CEA calculates the burner exit state point including: equilibrium composition and the new burner exit temperature iteration, To o,. The burner exit conditions (To' ., P o,, FARout WARot o o,, and mass fractions for all species) are then passed back to calcBurn where the burner efficiency is applied to determine the actual burner exit temperature, To1 act T0 out = r1b _out _n +TO n, (5.35) Then, T Oact is used to determine the next fuel flow rate iteration, th2fuel, with the energy balance described above (Equation 5.34). An error check is performed on the fuel flow rate values every iteration to determine when the loop can be exited. mfuelerr = e er fue ue < Error Tolerance (5.36) Once hfuel is determined, the exit state point is completely defined. Sensitivity Analysis No formal optimization program was used for this project; instead, each engine cycle model was roughly optimized manually starting from base case assumptions listed in Chapter 4. The sensitivity analyses were performed on the SCGT and HPRTE Efficiency models to determine the influences of particular design parameters. The HV Efficiency model was not included in these studies because the results would mirror those for the HPRTE Efficiency model analysis. Two primary dependent parameters investigated in the sensitivity analysis include thermal efficiency and specific power. The thermal efficiency is defined as: 7th (5.37) fuel QR where QR is the lower heating value of the fuel and W is the net power. The specific power is defined as: SP = (5.38) air in Influence coefficients are use to quantify the sensitivity of resultant parameters as they relate to perturbed input parameters. The dimensional influence coefficient is defined as a(Resultant) O(Input Parameter) To relate the magnitudes of influence coefficients to one another, they must be non dimensionalized is required. This is accomplished by dividing the perturbed value by its base case quantity: a(Resultant) npu t Paameter)Resultant Base Value (5.40) d(lnput Parameter)/ (540) Input Parameter Base Value Such an example of a nondimensional influence coefficient is given below. Here, the HPC inlet temperature is perturbed from its base value and the resultant change to 7th is expressed in the following form. A value of 1 suggests that a 1% perturbation in HPC inlet temperature results in a 1% change in qth. In this way the sensitivity of input parameters is determined. S( 7 th base (5.41) 8(HPC _Tin) /HPC Tinbase CHAPTER 6 RESULTS AND DISCUSSION The results and discussion of the analysis performed using the cycle code NPSS are presented in Chapter 6. The first section in this chapter, Cycle Code Comparison, compares results from the spreadsheet code (used by Boza [22]) and the NPSS program for one operating point of the HPRTE Efficiency model. Next, sensitivity studies were performed on the SCGT and HPRTE Efficiency cycles and influence coefficients were calculated. Engine model results are given and compared to derived thermodynamic expressions. Finally, plots and tables are presented that compare the performance parameters of the three engine configurations. Cycle Code Comparison Before initiating the sensitivities studies, it is important to benchmark the NPSS program and compare results of one model configuration to those results obtained from running a proven cycle analysis program. One operating point for the HPRTE Efficiency model was chosen for the comparison, and the results from the two cycle codes are presented in Table 61. The third column in the table lists the absolute differences of the two data sets parameters in percentages. Agreement of the data between the two codes is high; values for rh,, OPR, HPT exit temperature (TET), THP ,,, and Texhat,, are all within acceptable limits. The SpPw calculated by the spreadsheet model was 12.5% higher than that calculated in NPSS. There are three possible reasons for the disparity in the output values. First, it is impossible to implicitly balance the low pressure spool specific work; therefore the turbine specific work is never properly matched to the specific power of the compressor. This could very easily result in a different za,,. Two, different fuels are used in the codes. The hydrogentocarbon ratio is 1.93 in NPSS and 2.03 in the spreadsheet code. Because the fuels are different, the curvefit coefficients used to calculate the enthalpies for the spreadsheet code could be different than the ones used by NPSS. Sensitivity Analysis Simple Cycle Gas Turbine Engine Model Of particular interest for this project is the sensitivity of the opencycle engine thermal efficiency and specific power to variations in turbine inlet temperature and ambient temperature. Figures 62 through 64 show the results of the analysis. Unless otherwise specified the following parameters remained constant throughout the analysis: ambient temperature is 5440R, TIT is 25000R, and nominal power output is 4000 BHP. Figure 62 displays the thermal efficiency as a function of the overall cycle pressure ratio (OPR). The TIT variations have a strong influence on the outcome of the thermal efficiency value. Raising TIT has a positive effect on rth which also implies that the total heat added to the system has been reduced since the power output remains steady. Let rth be defined by the following relationship: 7th (6.1) fuel QR Since, QR, the fuel lower heating value, is constant; hfuel has to decrease in order to reduce the total heat added to the system in order to raise the r7,. For all run cases in the SCGT analysis, variations in r7,h are the direct result of variations in izfuel. To better understand the relationship between 7r/, and the input parameters in this sensitivity study, the following derivation has been included. The State numbers in the equations correspond to those for the SCGT cycle schematic given in the Configurations chapter (Figure 41). Figure 61 shows the comparison between the theoretical expression below, the run data from NPSS, and ideal thermal efficiency expression for an air standard Brayton cycle available in any thermodynamic text. The derived expression predicts a curve with higher efficiency than the NPSS output; this is expected because the pressure losses in the combustor are not accounted for, as it was assumed that the turbine pressure ratio is equal to the compressor pressure ratio. That and the fact that the specific heat ratio (y) was averaged for the entire cycle may explain the discrepancy between the results from NPSS and the derived curvefit expression. There are several assumptions exercised in this derivation to develop the final T03 expression in terms of only the following parameters: T0 7, PR, r,7, b. and rcomp ad. They are as follows: infuel is much less than iha h = h(T) Cp constant ratio of specific heats, y constant P P P02 = PR P P 01 '04 Beginning with the definition of thermal efficiency: W Cpl,, T[(oT3 fuel QR Factoring out To, gives: C pirJT01 r T3 Sfuel QR Now the adiabatic turbomachinery efficiencies derived in the previous chapter may be rewritten in the form: C PR IComp ad lTurb ad 1 (To TO 1 T03 1 K04 \PR 1 (6.4) (6.5) T Solving the compressor Equation 6.4 for 2 and Equation 6.5 for T04 yields the T0, following two expressions. T 1 (P T2 1+ 1 PRd 1 TO1 Comp ad T04  PR \.\ T / l Turb ad + ) (6.6) (6.7) Substituting Equations 6.6 and 6.7 into Equation 6.3 gives the following expression: fuel QR (6.2) TO4 TO2 T04 02 +1 (6.3) TO4) (To2 TO] T3 T3 1 1 /1 CP air1To1 T 0 PR 1 TO, TO PR 1ITurbad omp ad ,th = (6.8) ihfuel QR T03 The denominator can be rewritten in terms of 0, y, PR, and r7Comp ad The energy balance of the combustor is as follows: larrCpT2 + QR fuel = (lar + fuel )pT03 = Ma, pTO3 (6.9) Now, solving for h fueQR gives: rfueiQR = arC o3 2 arCP T03T 2]012 (6.10) T Substituting in the expression for 02 in Equation 6.6 results in the following: T01 m =febCR mar rCp T1 TF3 (PR r 1 1. (6.11) T To,1 rComp _ad The final expression for 7,t is T T03 1 1 1 103 J03 PR T O T PR l 17Turb +ad rCom+p ad rth 1 (6.12) T03 P T PR 1 1 1 STo1 d Comp ad As mentioned above, the ideal thermal efficiency for an air standard Brayton is also plotted on Figure 6.1. rth ,deal = 1 (6.13) PR / Simple Cycle Gas Turbine Engine Model Sensitivity Analysis Figure 6.2 is a plot of the thermal efficiency as a function of OPR with separate curves for TITs. These curves peak at certain OPR values; continuing to increase pressure ratio will continue to decrease the heat added per unit mass to the cycle, however, the thermal efficiency will drop because the recuperator capacity to exchange heat is being neutralized. When this happens the thermal efficiency begins to drop again. The influence coefficients were determined for Figure 6.2. The base case engine chosen had a TIT of 25000R with an OPR of 24. These numbers imply that changes in TIT effect greater change in /th than changes in OPR. One other point to note is the fact that no matter what the TIT is for the engine model, the maximum thermal efficiency always occurs when the compressor power is about twice as large as the net BHP. base= 0.898 th base= 0.0322 S(TIT) (OPR) STITb / OPRbase Figure 63 displays specific power sensitivity to changes in TIT over a pressure range from 8 to 18. The drop in specific power for increasing OPRs can be explained as follows. Consider the engine as a control volume that produces a constant power output. Ignoring the small effects to thermal efficiency that increasing OPR produces, the heat energy added to the engine must be constant. However, as OPR increases the heat rate per unit mass added in the combustor drops. Therefore, more air must be brought into the combustor to maintain the total heat energy input required to produce a constant power engine output. The other trend visible has to do with increasing TIT and its influence on specific power. Drawing two cycles, with different TITs, on the same TS diagram clearly demonstrates this phenomenon. Influence coefficients were calculated using the base case parameters from the last section. Specific power is more affected by changes in TIT than changes in OPR. In fact, there is 1 order of magnitude difference between the two parameters. The negative sign quantifies the drop in specific power with increasing OPR that was discussed earlier. (QSpPw) (OSpPw) SpPwbe 3.36 SpPbae = 0.339 8(TIT) 8 (OPR)/ /TIT OPRb, base base Figure, 64 examines operating temperature variation as it influences cycle thermal efficiency and OPR. The OPR curves are nearly linear and the slopes become more negative as OPR increases. Notice that the thermal efficiencies approach 40% as ambient temperature falls to 5090R. Cold day operation translates to good thermal efficiency for the SCGT. Notice the effect of changing OPR for the case when Tamben is 5720R. The higher OPR curves collapse on each other implying that thermal efficiency maximums are at or near their peak values here, and any further boost in OPR drops the thermal efficiency off the other side of the curve that would appear if this was a three dimensional figure. For example, at Tambent 5540R, the maximum thermal efficiency corresponds to an OPR of 24. A further boost to an OPR of 28 results in a reduced thermal efficiency. The influence coefficients corresponding to Figure 64 for thermal efficiency and specific power are calculated assuming the base case cycle where ambient temperature is 5180R and OPR is 24. (a th) (a th) 7thbase 77th base th bae = 0.669 Pth bse = 0.0682 a(Tamb) 8(OPR) Tambbs /OPRbas The thermal efficiency coefficients suggest that drops in ambient operating temperature impact thermal efficiency more so than variations in pressure ratio. This implies that OPR is a secondary issue if the engine is being designed with the intent to optimize thermal efficiency. (aSpPw) (0SpPw)/ SpPwbase 1.76 /SPPWbase = 0.2676 O(Tamb) /(OPR)/ Tambbase OPRbase The specific power influence coefficients quantify the negative impact on specific power when either ambient temperature or OPR is increased. Of course, the effect of ambient temperature is much more significantalmost an order of magnitude greater. High Pressure Regenerative Turbine Engine Efficiency Model Before beginning the sensitivity analysis of the HPRTE Efficiency, it is important to examine the validity of the data output from NPSS. To accomplish this task an expression has been derived to test the validity of NPSS output. After the derivation is complete, the resulting expression is normalized; and it is only a function of the following parameters: 072 LPPR, y, rLPC and rLPT ad. The plotted NPSS data T01 should agree with the derived expression. The ten points in Figure 65 represent ten distinct converged operating points from NPSS runs. The standard deviation of the set of points is 0.00398, signifying close conformity with the derived thermodynamic expression. The development uses the following assumptions: fuell< har h = h(T) C, constant Ratio of specific heats, y7 constant P P o02 P7 2 =LPPR P P 01 08 The development begins with the adiabatic efficiency expressions for the low pressure compressor and turbine: LPPR /Y 1 7LPC ad = R (6.14) TO 2 T0721 7LPT ad TO8 I (6.15) LPPR / 1 Solving Equation 6.14 for 2To yields T Ic 02 1= L LPPR / 1 (6.16) TO1 LPC ad Now, introducing the power balance for the turbocharger gives (p (T02 1 (im + nfuel)Cp (072 T8). (6.17) And simplifying Equation 6.17 using the assumptions provided above results in (T2 r T)= (72 TO8). (6.18) Rearranging Equation 6.18 and solving for T02 1 = T72 T08 TO, TO, TO Setting Equation 6.16 equal to Equation 6.19 gives 1 LPPR 1 = rlLPC ad \iP TO T,, Solving Equation 6.20 for To, produces Tos = To 072 TO1 L ad1LPPR 17LPC ad Next, rearranging Equation 6.15 and solving for To8 yields (6.22) rLPT d LPPR Setting Equation 6.21 equal to Equation 6.22 results in the following expression: T07 2 rLPT_ ad LPPR Rearranging, ) + T072 T o LPC ad L T,= 1 LPPR TL T, 17LPC ad LP 1]. L7LPT ad *LPPR 1)]. 1) +11. T Then dividing both sides by 072 yields the final expression plotted in Figure 65. TO1 (6.19) (6.20) (6.21) (6.23) (6.24) 1 produces S1)+1 1 t072 K LPC adLPPR 2 1 LLPT ad LPPR 1 +1 1 TO I 1LPC ad 6.25 T07 2 T01 High Pressure Regenerative Turbine Engine Efficiency Model Sensitivity Analysis Figure 66 shows low pressure spool pressure ratio (LPPR) variation influences on the high pressure compressor pressure ratio (HPPR) as ambient temperature varies. For these run cases the TIT and the nominal shaft power output were held constant at 25000R and 4000 BHP, respectively. There are three important features represented by Figure 6 6. First, there is the interaction between LPPR and HPPR. Monotonically increasing LPPR results in a similarly increasing HPPR. Examining the raw data shows that that mass flow rate drops with increasing LPPR; this drop in mass flow rate requires a greater expansion on the high pressure turbine to produce the nominal power output. The second trend to notice is that raising ambient temperature results in raising HPPR. Raising ambient temperature decreases air density which in turn causes a decrease in mass flow rate. With less mass flow rate to the core components, the heat added per unit mass to the combustor must be increased in order to maintain the constant power output. The way to accomplish this task with an HPRTE engine is to increase the HPPR. Increasing HPPR drops the hot side recuperator inlet temperature and as a result the combustor inlet temperature drops, too. Thermal efficiency increases with increasing HPPR until HPPR is about 5.1. Then, any further increasing of HPPR results in a drop in thermal efficiency. Figure 66 can be used to find the operating lines for a properly designed HPRTE. An HPRTE with wastegating capabilities would have operating curves of constant HPPR; therefore, the horizontal grid lines on the Figure 66 could be called operating curves as well. Moreover, the line corresponding to a HPPR of 5.1 would represent the highest thermal efficiency operating curve. The influence coefficients for Figure 66 are listed below. The base case has an ambient temperature of 5280R and a LPPR of 6.0. Tambe,,t and LPPR variations both have significant resultant effects on HPPR. Operationally speaking, Tambent is related to miza which can cause large changes to the specific power of the system. ( HHPPR) ( HPPR) HPPRba H1.63 PPRbase = 6.15 8(LPPR) O (Tamb) /LPPRbae /Tambbase Figure 67 shows cycle thermal efficiency sensitivity to TIT variation for a range of HPPRs. The analysis holds R, ambient temperature, output shaft horse power, and all component efficiencies constant. NPSS convergence is difficult to achieve if HPPR is changed manually by the user; instead, to effect change in HPPR, the LPPR is controlled by the modeler. As LPPR was increased, the model solver reduced fresh air flow rate to the engine. The mass flow rate reduction caused the HPPR to rise for the same reason discussed in the previous section. Figure 66 shows that the thermal efficiency peaks very close to an HPPR of 5.1. Along a curve, TET and the stoichiometry change because R is held constant. The influence coefficients for rth and SpPw were produced by making perturbations around the base run case where TIT was 25000R and HPPR was 5.12. h e = 0.847 7h base = 0.0106 ((TIT)/ (HPPR) TIT HPPR 11 base / base The interpretation of these influence coefficients suggests that changing TIT by 1% causes a 0.847% change in rh. The second coefficient was calculated with data taken from the right side of the plot where HPPR is monotonically increasing and r7th continues to decrease. The small coefficient value suggests that a large change in HPPR has only limited effect on rh This is expected when the influence coefficient is calculated near an optimum r7,h point on the curve. Below, notice that TIT perturbations cause significant resultant changes to the value of specific power. (OSpPw / (SpPw)/ SpPwbas" = 2.59 SpPWbse = 0.318 baTIIT N base Figure, 68 shows the importance with respect to thermal efficiency of reducing the HPC inlet temperature for HPRTE engine cycles. Sensitivity to BPRRetc, is shown and its value is varied from 2.0 to 3.5. Those parameters held constant for the analysis are as follows: output BHP, Tamben,,, TIT, LPPR, all turbomachinery efficiencies, and the sea water temperature. The HPC inlet temperature was varied by changing the effectiveness of the main cooler. The trend toward higher thermal efficiencies for lower HPC inlet temperatures is the same phenomenon seen in Figure 64. A lower inlet temperature to the high pressure core results in an increase in predicted thermal efficiency. Examination of the model data used to produce Figure 68 shows that as HPC inlet temperature drops, HPPR increases. As a result the temperature change across the HPT increases and the mass flow requirements drop. This in turn means that the fuel flow requirement is less. As shown by Equation 6.1, the drop in fuel flow directly affects thermal efficiency since power output is constant. Lower BPRRe,,, helps thermal efficiency because TIT must be maintained at 25000R. The more inert combustion products that are mixed with fresh air act to drive down TIT making it necessary to burn more fuel to keep TIT constant. However, higher recirculation boosts specific power as less fresh air is required to produce the desired power output. The ultimate choice is the designer'sif weight and compactness are important, BPRRe cr would be maximized. However, on a naval vessel, weight might not be the paramount consideration. The influence coefficients for /th and SpPw are calculated using the base case BPRRec,,r of 3 and a HPC inlet temperature of 6220R. S 1hbase = 1.58 1th = 0.0610 a(HPC Tin) / (R) /HPC Tinbase Rbas (aSpPw)/ (aSpPw) /SpPba = 3.66 Sp base = 0.624 8(HPC _Tin)/ '(R)/ (HPC HPCTin) /R HPC Tinbase Rbase The influence coefficients based on variations to BPRRec,,, help to quantify the effects on thermal efficiency and specific power that were discussed above. Moreover, reducing the HPC inlet temperature boosts both thermal efficiency and specific power. This is an observed behavior in recuperated gas turbine engines. Figure 69 displays the thermal efficiency sensitivity to pressure drops in the coolers. To obtain the curves below, HPT exit temperature variations were created by the modeler. This was done in the same manner as it was for the Figure 67. LPPR was manually controlled to effect change in HPC pressure ratio which caused the HPT exit temperature to change. The general trends are consistent with the results of Figure 67. The curve of Figure 67 corresponding to that of a TIT of 25000R is the same as the curve in Figure 6 9 for a cooler AP/P of 3%. There the HPT exit temperature is 18840R. The propensity to see a lowered thermal efficiency when the cooler AP/P is raised has a straightforward explanation. Increasing cooler AP/P results in a drop in the OPR of the cycle. Since the net output power remains constant, mass flow must be increased. This in turn causes a rise in fuel flow rate and a drop in thermal efficiency. Influence coefficients for cooler AP/P and HPT exit temperature are listed below for the base cycle case where cooler AP/P is 3% and HPT exit temperature is 18840R. Specific power influence coefficients are included. The results show that neither cooler AP/P nor HPT exit temperature affect significant change in thermal efficiency. However, the specific power is positively influenced by decreasing HPT exit temperature. ( Tth base = 0.0258 7/ th base= 0.0617 (AP / P)/ 8(HPT Texit) (Op / ) (SpHPT)/ / SPPwbase = 0.0407 /iSPWbase = 1.86 (APP) / (HPT _Texit) /AP / se HPT Texitbase Figure 610 considers specific power sensitivity to HPC adiabatic efficiency. For an engine with constant power output and TIT, raising TET also results in core mass flow increasing. That is because a higher low pressure recuperator inlet temperature drives the combustor inlet temperature up. The effect of driving that temperature up is similar to what happens for SCGT when OPR is increased. While the total heat added to the engine may be remain almost constant, the heat added per unit mass drops off as combustor inlet temperature rises. Consequently, the mass flow coming into the combustor must go up. The result is a drop in specific power. The other noteworthy trend here is the positive effect on specific power that comes from raising HPC adiabatic efficiency. Raising HPC adiabatic efficiency decreases the power requirement of the HPC thereby increasing the specific power of the cycle. Influence coefficients are considered for a base engine with HPC adiabatic efficiency of 86 % and HPT exit temperature of 18830R. Both thermal efficiency and SpPw influence coefficient are given. Compare these results with the influence coefficients for the cooler AP/P discussed above. The rC,,p ad has a stronger effect on the performance of the cycle than does AP/P. (a th ) (OSpPw) 171th base 1.06 SPPWbase =1.74 0(7comp _ad)/ (Comp _ad) / Comp _ad base / Com _adbase Figure 611 is a sister plot to Figure 610. It describes the same specific power trends, however, now they are in terms of HPC pressure ratio (HPPR). HPT adiabatic efficiency ( rb ad ) is varied to show specific power sensitivity to this parameter. The expectation for high r/,b ad to result in an improved specific power is met. From a thermodynamic standpoint, higher 7rb ad means a greater temperature drop across the turbine for the same HPPR. Therefore, less mass flow is required to produce the same powerresulting in a boosted specific power. Influence coefficients for SpPw and 7th were calculated from the base cycle case where urb ad was 87% and HPPR was roughly 5.1. Note: since HPPR is an output, it can not be explicitly set. The coefficient values imply significant influence of 7Turb ad on 7th and SpPw. Similarly, notice that the coefficients calculated based on HPPR variation are very close to those same coefficients calculated for Figure 67 when TIT was the sensitivity parameter. In fact, there is less than a 1% difference between the values. 7th base 0.0105 7rth base = 1.46 8(HPPR)/ a(7Turb ad /HPPRbase /Turb adbase (OSPw)/ (SpPw)/ SPPbase SPPWbase 2.36 ..Spp wby= 0.316 /SpPw = 2.36 O(HPPR) /(Turb ad) /HPPRbae /7Turb ad base Figure 612 displays exhaust gas temperature sensitivity to OPR with TIT variations included. Cycle constants included: output BHP, LPPR, ambient temperature, R, and all component efficiencies except for MCG effectiveness. Since LPPR was held constant, MCG effectiveness was varied to effect HPPR change. The results indicate that exhaust gas temperature is not sensitive to either OPR or TIT variation. This should be expected in an intercooled recuperated system. The heat exchangers act to damp exhaust temperature variations that may result from parametric tweaking. The influence coefficients further illustrate this phenomenon. The base case cycle had an OPR of 24 and a TIT of 25000R. The computed values being small and negative imply that significant manipulation of TIT or OPR is necessary before any change in exhaust temperature is noticed. (aTexhaust) (aTexhaust) Th .t. = 0.0683 Texhaustb"e =0.0201 O(TIT)/ (OPR) TTbase OPRbase Figure 613 examines the 7rurbo impact on 7th as it relates to HPPR. Here, the parameter driving convergence will be LPPR. This means that LPPR is controlled by the modeler and both, LPPR and HPPR, will be varying. Most noteworthy about Figure 613 is that rurbo alone does not significantly affect 7th. The influence coefficient affirms this assertion. Figure 613 likewise gives a clear indication that an HPPR of 5.1 produces the maximum rth this optimum HPPR value agrees with the earlier optimum predicted in the plot of thermal efficiency verses HPPR with TIT sensitivity. 'th base = 0.0228 (IlTurbo) / lTurbobase Figure 614 is the last figure of the sensitivity analysis for the HPRTE Efficiency cycle, and it examines LPPR variations and their effect on thermal efficiency. Thermal efficiency sensitivity to TIT perturbations has previously been analyzed for Figure 67. However, this plot is useful in that it gives optimum LPPRs for particular TITs. Particularly interesting is the curve for a TIT of 25000R since this is the base and design optimum TIT. A quick regard of the curve reveals that the best LPPR is about 6.2. That value is high but within the limits of single stage centrifugal compressor technology. Taking a look at the influence coefficient suggests that perturbing LPPR does not significantly cause change to the resultant, /th. Again, this is most likely because the influence coefficient was evaluated near a design optimum and the curve was flat. (arth , h base = 0.0645 8(LPPR)/ LPPRbase Table 62 summarizes the results of the sensitivity analysis. The perturbed parameters are listed in the left hand column and a value between 1 and 3 (1 being the most important) was assigned to indicate the degree of importance that a particular parameter had on the resultant in the top row. Below are the definitions for the values assigned to the sensitivity parameters listed in summary (Table 62). * 1: 1% fluctuation from parameter produces >1% fluctuation in resultant) * 2: 1% fluctuation of parameter produces between 0. l% Cycle Comparison Analysis Three engine configurations are included in the comparison analysis: the SCGT, the HPRTE Efficiency, and the third engine configuration, HV Efficiency. The rough optimization of the SCGT and the HPRTE Efficiency cycles has been completed in the sensitivity analysis, and now those optimized results will be compared to the predicted performance results from HV Efficiency analysis. Not explicitly shown in this analysis was the iterative process used to determine the best low and high spool pressure ratios for the HV Efficiency cycle. For Figures 6.16 through 6.18, LPPR was held at 3.5. This value proved to be the best LPPR value for the largest number of HV Efficiency data runs. As was the case with HPRTE Efficiency, LPPR was controlled by the modeler and HPPR was controlled by the solution solver. Since heat signature is a serious design consideration for military vessels, an exhaust gas temperature comparison will be included and discussed. Next, performance comparisons will be made considering different air and sea water temperatures. The last table will list the performance details for the optimized engine configurations side by side. Figure 615 provides a clear indication of the thermodynamic advantage that the H V Efficiency cycle enjoys over the other two cycles in the comparison. The HPC inlet temperature of the HV Efficiency engine was maintained at 5090R by the refrigeration system. Contrast that against the HPC inlet temperatures of the HPRTE Efficiency engine. The results reveal that the HV Efficiency HPC inlet temperature was between 991070R below that of the HPRTE Efficiency. Table 63 highlights key features of Figure 615. Considering the results, it is easy to make a case for the HV Efficiency engine configuration. It has the highest 7rh max by 17.1% over the SCGT and 17.2% over the standard HPRTE without refrigerator. Its rth mean is 44.2% which indicates that the curve is very flat. This implies that the HV Efficiency design point is not significantly sensitive to the OPR choice; therefore, existing, off the shelf turbomachinery components can be used to save on capital investment costs. Moreover, the 7th mea for HPRTE Efficiency is 3.08% higher than that of the SCGT configuration, indicating that the HPRTE Efficiency configuration is also less sensitive to OPR choice than SCGT. The second data point for SCGT on Table 63 is the case where the engine is designed for optimum specific power (SCGT SpPw cycle mode). Here, the r7, is only 33.4%a full 10.2% less than the maximum design 7,h for the HPRTE Efficiency cycle. Figure 616 compares SpPw performance characteristics for the three cycle configurations. Here it can be shown that a sizable advantage is enjoyed by the HPRTE cycles over the SCGT. Since the three cycles have the same output BHP requirements, this implies that the HPRTE Efficiency and HV Efficiency engine cycles operate at much reduced mh,, levels. This disparity can be attributed to the three main differences between the HPRTE and SCGT cycles: exhaust gas recirculation, intercooling of the compressors, and recuperative heating before the combustor. Closer examination of the two HPRTE engine configurations reveals that compressor intercooling boosts specific power significantly by itself, especially at lower OPRs. This can be shown from an examination of the run data for an OPR of 14.5. The HV Efficiency cycle has a calculated specific power of 560 HP sec/lbm (units are industry standard) compared to the HPRTE Efficiency specific power of 458 HP sec/lbm for the same OPR. That computes to a specific power increase of 22.2% for the HV Efficiency over the standard HPRTE Efficiency. Table 64 further illustrates that gap in specific power between the two HPRTE engine cycles and the standard SCGT. Now notice the divergence of the SCGT curve from the HPRTE curve. The SCGT mass flow rate requirement increases as OPR increases in order to maintain constant power BHP output. This is because even though the heat added per unit mass drops the total heat input must remain nearly unchanged to produce the same power output. Meanwhile, increasing the OPR for either HPRTE cycle improves specific power because the recuperator has less available heat to drive up the combustor inlet temperature. Reviewing the analysis for Figures 610 and 611 may provide additional clarity. Figure 617 shows the operating exhaust gas temperatures for various OPR design points for the three engine configurations. There are three features to the plot that are worth noting. First, as expected, the SCGT exhaust gas temperature drops in a weak exponential manner as the design OPR increases. The ETF40B engine was designed to optimized specific power, and it had an OPR of 10.4. Assuming the SCGT model is a good representation of the ETF40B engine, it implies that its exhaust gas temperature is about 15800R. The second point brought to light by Figure 617 is the fact that the HPRTE cycles have constant exhaust temperatures for a broad range of design OPRs. Third, the HPRTE Efficiency cycle has lower exhaust gas temperatures than the combined cycle HV Efficiency. The reason for this is that for the same OPR, the HV Efficiency has a lower LPPR than the HPRTE Efficiency, and less expansion across the LPT means the exhaust gas temperature will be higher. Following that logic suggests that the presence of a VARS unit actually raises the exhaust gas temperature slightly. Table 65 is a list of the maximum exhaust gas temperature cases for each cycle with their corresponding OPR values from Figure 617. The mean exhaust temperatures are also given to indicate the flatness of the plotted curves for the HPRTE cycles. Figure 618 compares ,th values of the three engine configurations under different Tambient operating conditions. While LPPRs were held constant, OPRs could not be held constant because ofNPSS operational limitations on the HPRTE models discussed above for Figure 67. The parabolic shape of the HPRTE engine curves resembles the thermal efficiency plots produced in the sensitivity analysis for the HPRTE Efficiency model. Similarly, notice the linear trend of the SCGT as ambient temperature drops. Eventually, the HV Efficiency and SCGT curves will intersect at an ambient temperature of 4910R (32 0 F). The most likely operational scenario for the HV Efficiency will be in a desert environment where the environment temperatures are above 5440R (850F). The engines will also be performance rated at or above 518R (590F). At 518R the HV Efficiency 7,h is 14.0% higher than the SCGTs r7,. Moreover, above 5470R (880F), the r7,h of the HPRTE Efficiency surpasses that of the SCGT. Above 5470R 7th mean for the HPRTE Efficiency engine is 36.9% compared to 36.1% for the SCGT. Extreme Operating Conditions Four extreme operating cases were chosen for this examination of how the engine configurations would perform in the severest of environments. Ambient temperature and sea water temperature were the dependent inputs. Two extreme cases were chosen for each dependent input resulting in a total of four operating casescold day/cold water, cold day/warm water, hot day/cold water, and hot day/warm water. NPSS limited the ability to compare the engine cycles with constant OPRs. While the LPPRs for the engine configurations were chosen from approximated design points maximizing thermal efficiency from the analysis in the last section, it is necessary to let mass flow rates and HPPRs float to obtain convergence from the solution solver. The OPR for the SCGT remained constant at 24. OPRs are listed in the Table 66. Notice that for the 5690R day, the OPRs for the HPRTE engine cycles are very high. High temperature days decrease the air density and NPSS drops the mass flow rates as a result. This in turn requires the HPRTE cycles to increase their pressure ratios to maintain constant power output. Case 1 is the cold day with warm sea water condition. These conditions loosely represent night operations in a dry desert climate. A key comparison for this case includes the r7,h values for the HV Efficiency and SCGT cycles. Table 66 shows that the 7th for the SCGT model is higher than that of the HV Efficiency cycle. This operating point represents a case described during the discussion of Figure 618 when ambient temperature drops to the point where the 7th values of HV Efficiency and SCGT converge. That analysis showed that if the ambient temperature curves were extended down to 4890R, the curves of the SCGT and HV Efficiency would eventually meet. Another key observation from case 1 data is the wide bridge between the specific power values for the HPRTE cycles in comparison to the SCGT. The HPRTE Efficiency configuration enjoys a 104% improvement in specific power over the SCGT. This theme runs through the whole analysis, and as the operating conditions get warmer the disparity becomes more pronounced. Case 2 is the cold day/cold water temperature condition. In a North Atlantic mission, conditions similar to these might exist. Cold water operating points improve the qth and specific power of the HPRTE engine cycles by improving compressor inter cooling. The most significant example is in the change of the 77h of the HPRTE Efficiency engine between case 1 and 2. It increases by 13.2% and achieves its maximum value for any of the four operating points examined. From a specific power standpoint, the HPRTE Efficiency cycle bests the other two configurations in case 2 beating the HV Efficiency by 17.3% and the SCGT by 168%. Unaffected by the drop in water temperature, the 7th of the SCGT continues to hold steady at a sporty 40.1%. The argument for choosing the HV Efficiency cycle strengthens under case 2 operating conditions because it displays the highest 7th of the three configurations at 40.9%. Case 3 is the hot day/hot sea water temperature condition. This operating point is characteristic of a desert day scenariothe most likely mission conditions for the ETF 40B and its replacement. Hot day design points drive up predicted specific power performance values for the HPRTE engine models. The cause of this is described in the introduction to this section. From a thermodynamic standpoint the HV Efficiency outperforms the other two configurations. Here, the 7th of the HV Efficiency cycle is 20.4% better than HV Efficiency and 23.5% better than SCGT. The specific power of the HV Efficiency cycle is 12.1% higher than HPRTE Efficiency and 358% higher than the SCGTs. The rise in 7th from case 1 to 3 for the HV Efficiency is directly indicative of the ambient temperature rise which caused a noteworthy rise in OPR from 10.2 to 30.7. The 7th rise constitutes an 11.3% jump between the case points 1 and 3. Case 4 is an unlikely operating pointwhen ambient temperature is high and water temperature is very cold. A summer day in the North Atlantic is the closest example of this condition. Here the qth of the HV Efficiency cycle bests the HPRTE Efficiency by 15.3% and the SCGT by 24.1%. If the engines were design based on specific power alone, the HPRTE Efficiency is a considerable threat to the HV Efficiency engine mode. Its specific power of 675 HPsec/lbm, respectively, is the highest of the three engines for case 4. However, this is an improbable engine design with an OPR of 55.4. High Pressure Compressor Inlet Temperature Comparison for HV Efficiency Model Up until this point in the analysis the HPC inlet temperature for the HV Efficiency cycle has been held at a conservative 5090R. This section compares the same engine at two different HPC inlet temperatures, 509R and 4990R, respectively (Table 67). In other words, careful consideration was taken to ensure that the HPPRs for both model cases were the same. This was a time intensive consideration that could not be used for other parts of the comparison studies. Other parameters held constant include: nominal output BHP, TIT, Tambent all turbomachinery q values, and R. The results of the analysis conclude that there are performance improvements that result from decreasing HPC inlet temperature but they are not stunning. The 7th increases by 1.56% and the specific power increases by 1.62% for the lower HPC inlet temperature case. LPPR is also 5.14% lower when HPC inlet temperature is 4990R. Essentially, from a computer model handling standpoint, the lower HPC inlet temperature is achieved by lowering the LPPR slightly. This causes OPR to be 5.45% less, as well. Additionally, there is very little influence on Ta,,,,, which drops only 20R when HPC inlet is lowered 100R. In summary, the performance parameters are positively affected by decreasing HPC inlet temperatures, but it is unclear whether or not the difference is significant enough to warrant implication. Moreover, the refrigeration capacity used to cool the HPC inlet could be used elsewhere in applications not examined in this analysis. Final Design Point Parameter Comparison While the extreme operating conditions section provides key insight into offdesign point performance of the three engine cycles, it is necessary to compare the cycles with their optimized design parameters at the most likely operating condition. Two versions of the SCGT cycle are comparedthe SCGT Efficiency is the open cycle optimized for maximum thermal efficiency and the SCGT SpPw is the open cycle optimized for maximum specific power. For this analysis the ambient temperature and the sea water temperature were both set to 5440R. The engine output requirement was unchanged, at 4000 BHP. TIT was held to a maximum of25000R. TET was restricted below 20590R. The turbocharger pressure ratio was limited to 7.5. Table 68 results are consistent with the comparative analysis plots. * From a thermodynamic stance, the HV Efficiency engine cycle has a higher design point thermal efficiency besting the SCGT Efficiency by 20.6%, the SCGT SpPw cycle version by 34.7%, and the HPRTE Efficiency engine cycle by 21.0%. The SCGT Efficiency thermal efficiency has an expected thermal efficiency that is 10.2% higher than the SCGT SpPw engine configuration. When comparing the specific power results of the HPRTE cycles the performance gap isn't quite as large. For that parameter, the HV Efficiency has a predicted specific power that is only 6.08% better than the HPRTE Efficiency. The SCGT SpPw cycle has a predicted specific power that is 13.2% greater than the SCGT Efficiency configuration. * TET for the HV Efficiency is 1100R less than the HPRTE Efficiency providing some leeway in material selection. * Equivalence ratios are all within the reasonable limit (0.9 was maximum allowable). As the equivalence ratio value approaches a value of 1, the oxygen concentration in the gas is being limited. Limiting the excess oxygen helps to reduce the soot and harmful emissions production. * Both HPRTE engine cycles have R values of 3 or above. This directly affects equivalence ratio. Increasing R limits the fresh air dilution into the combustion chamberthe net effect is an increase in the equivalence ratio value. * The extra cooling capacity of the HV Efficiency cycle causes water vapor from the combustion products to condense to liquid. That mass flow rate has been included in the table, as well. It is also convenient to relate that value to the mass flow rate of fuel used by the engine. The mass basis ratio of fuel burned to water extracted from the flow path was 1.13. Note: for simplicity, the ambient air was considered dry with a %RH of 0. * Exhaust gas temperatures for both HPRTE cycles are approximately 5000R less than the exhaust temperature of the SCGT Efficiency configuration and nearly 8000R less than the exhaust temperature of the SCGT SpPw configuration. Naval forces are concerned with IR signatures produced by engine exhaust coming from their ships, the 8000R difference represents a significant stealth advantage over the SCGT. Moreover, reduced exhaust temperatures suggests that air density is higher; and as a result, the exhaust duct size can be smaller. Table 61 Cycle codes comparison: NPSS verses spreadsheet code for HPRTE Efficiency model data run. All temperatures are in R. SpreadSheet HPRTE Eff. NPSS HPRTE Eff. ABS % Difference rth 37.0% 37.2% 0.54 SpPw (HPsec/Ibm) 519 593 12.5 OPR 32.0 32.2 0.621 TET 1880 1880 0.00 R 3.30 3.30 0.00 Equivalence Ratio 0.827 0.894 7.51 ambient 544 544 0.00 LPPR 6.25 6.25 0.00 HPPR 5.29 5.31 0.377 THPC in 632 614 2.93 TIT 2500 2500 0.00 Exhaust 790 801 1.37 All Temperatures are in R 0.65 0.6 0.55 0.5 0.45 0.4 0.35 AIdeal Eta  Deried Eta  NPSS OPR Figure 61 Thermal efficiency comparison is plotted with respect to OPR. NPSS results (with turbine inlet temperature (TIT) set to 25000R) are compared to the derived and the ideal Brayton cycle expressions. , U U U 71 SCGT 0.38 0.36 o W 0.34 xTIT= 2500R SE TIT= 2400R e TIT= 2300R 0.32 TIT=2200R 0.3 7 10 13 16 19 22 25 28 31 34 37 OPR Figure 62 Thermal efficiency vs. OPR with sensitivity to TIT SCGT 200 E 180 _ S TIT= 2500R 160 TIT= 2400R TIT= 2300R 0 140 TIT= 2200R I 120 u, 100 6 8 10 12 14 16 18 20 OPR Figure 63 Specific power vs. OPR with TIT sensitivity 72 SCGT 520 540 560 Ambient Temperature (OR) 0.4 0.39 0.38 0.37 0.36 0.35 0.34 0.33 580 Figure 64 Thermal efficiency vs. ambient temperature with OPR sensitivity HPRTE Efficiency 1.10 1.05 1.00 0.95 0.90 * Model Data Points LPPR Figure 65 Demonstrates agreement between NPSS and developed theory that describes the low pressure spool OPR = 28 OPR = 24 OPR = 20 OPR = 16 OPR = 12 500 ... '. HPRTE Efficiency 520 540 560 Ambient Temperature (OR)  LPPR = 6.4  LPPR = 6.0  LPPR = 5.5  LPPR = 5.0  LPPR = 4.5 580 Figure 66 High pressure spool pressure ratio (HPPR) vs. ambient temperature with low pressure spool pressure ratio (LPPR) sensitivity HPRTE Efficiency 0.375 0.37 > 0.365 .TIT = 2500R o TIT = 2450oR w 0.355 / TIT = 2400R 0.35 ~ TT = 2350R 0.345 I 0.34 0.335 0.33 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 HPPR Figure 67 Thermal efficiency vs. HPPR showing sensitivity to TIT 8 7 6 5 C. a 4 I 3 2 1 0 m 4. 500  RecircRatio = 2.0  RecircRatio = 2.5 A RecircRatio = 3.0 * RecircRatio = 3.5 HPC Inlet Temperature (OR) Figure 68 Thermal efficiency vs. HPC inlet temperature for recirculation ratio sensitivity HPRTE Efficiency 1825 1900 TET (0R) Cooler dP/P = 3%  Cooler dP/P = 4%  Cooler dP/P = 5% \ Cooler dP/P = 6% 1975 2050 Figure 69 Thermal efficiency vs. turbine exit temperature (TET) with cooler pressure drop sensitivity HPRTE Efficiency 0.38 0.36 0.34 0.32 0.3 0.28 0.26 600 650 700 0.375 0.37 0.365 0.36 0.355 0.35  1750 ~i HPRTE Efficiency * 1825 1900 1975 2050 TET (R) Figure 610 Specific power vs. TET for HPC efficiency sensitivity HPRTE Efficiency  HPTeff = 0.88 HPT eff = 0.87 uHPTeff = 0.86 A HPT eff = 0.85 3 4 5 6 7 HPPR Figure 611 Specific power vs. HPPR for HPT efficiency sensitivity  HPCeff = 0.86  HPCeff = 0.85 HPCeff = 0.84  HPC eff = 0.83 620 580 540 500 460 420 380 ! 1750 625 575 525 475 425 HPRTE Efficiency 812 810 808 806 804 802 800  TIT = 2350R  TIT = 2400R ATIT = 2450R TIT = 2500R 27 OPR Figure 612 Exhaust temperature vs. OPR for TIT sensitivity HPRTE Efficiency 0.375 0.37 o 0.365 S0.36 Turbo Eff = 0.7138 36 Turbo Eff = 0.6970 0.355 Turbo Eff = 0.6804 S0.35 0.345 0.34 0.335 2.5 4.5 6.5 8.5 HPPR Figure 613 Thermal efficiency vs. HPPR for turbocharger efficiency sensitivity A 11L 77 HPRTE Efficiency 0.38 0.37 0.36 0.35 0.34 0.33 4 4.5 5 5.5 6 6.5 7 7.5 LPPR Figure 614 Thermal efficiency vs. LPPR for TIT sensitivity Table 62 Summary of the HPRTE Efficiency sensitivity analysis Resultant Parameter Perturbed Parameter 7th Specific Power HPPR Texhaust TIT 2 1 3 TET 3 1 T 1 ambient THPC n 1 1 trCompad 1 1 rTurb ad 1 1 rTurbo 3 1 HPPR 3 2 LPPR 3 1 OPR 3 R 3 2 CoolerAP 3 3  TIT= 2500R  TIT= 2450R TIT= 2400R  TIT= 2350R 78 Table 63 Comparison of the thermal efficiency maximums and their corresponding overall pressure ratios (OPRs) Parameter Configuration t7rh max OPR r7 th mean HV Eff. 45.0% 23.6 0.442 HPRTE Eff. 37.2 32.2 0.368 SCGT 37.3 24.0 0.361 SCGT SpPw 33.4 10.4 0.46 0.44 0.42 0.4 0.38 0.36 0.34 0.32 0.3 HV Eff. SHPRTE Eff. SCGT 5 10 15 20 25 30 35 40 45 5 10 15 20 25 30 35 40 45 r OPR Figure 615 Engine cycles comparison of thermal efficiency vs. OPR Table 64 Comparison of the specific power maximum values and their corresponding OPRs Parameter SpPwnx OPR SpPw ... Configuration Sp OPR S HV Eff. 665 35.0 586 HPRTE Eff. 624 42.6 565 SCGT 180 10.5 155 SpPw units are industry standard (HPsec/Ibm) 700 600 E 500 0. S400 0. o o 300 200 100 5 10 15 20 25 OPR 30 35 40 45 Figure 616 Engine cycles comparison of specific power vs. OPR Table 65 Comparison of exhaust temperature maximum values for the three engine configurations Parameter T PR T Configuration exhaust mx OPR Texhaust mean HV Eff. 855 49.0 832 HPRTE Eff. 805 42.6 799 SCGT 1660 8.00 1360 Temperatures have units of R SHV Eff.  HPRTE Eff. SCGT 1800 1600 0 1400 SCGT 1200 HV Eff. S HPRTE Eff. 1000 L 800  600 5 10 15 20 25 30 35 40 45 50 OPR Figure 617 Engine cycles comparison of exhaust temperature vs. OPR 520 540 560 580 Ambient Temperature (OR) * HV Eff.  HPRTE Eff.  SCGT 600 Figure 618 Engine cycles comparison of thermal efficiency vs. ambient temperature 0.46 0.44 0.42 0.4 0.38 0.36 0.34 500 Table 66 Engine cycles comparison for four extreme operating conditions Engine Type Operating Point HV Efficiency HPRTE Efficiency SCGT Case Tambient Twater rlth SpPw OPR rlth SpPw OPR lth SpPw OPR 1 4890R 5440R 0.397 411 10.2 0.341 390 17.8 0.401 191 24.0 2 489 499 0.409 436 10.8 0.386 512 23.7 0.401 191 24.0 3 569 544 0.442 659 30.7 0.367 588 42.0 0.358 144 24.0 4 569 499 0.444 670 32.3 0.385 675 55.4 0.358 144 24.0 All Specific Power calculations have industry standard units of HPsec/Ibm Table 67 High pressure compressor (HPC) inlet temperature comparison for the HV Efficiency engine model T THPC in Design Point Parameter 509R 499R lth 45.0% 45.7% SpPw (HPsec/Ibm) 629 639 OPR 23.6 22.3 TET 1768 1769 R 3.00 3.00 Equivalence Ratio 0.799 0.799 mair (Ibm/sec) 6.36 6.26 mH20_hquid (Ibm/sec) 0.306 0.306 Tambient 545 545 LPPR 3.5 3.32 HPPR 7.37 7.35 THPC in 509 499 TIT 2500 2500 Texhaust 837 835 Temperatures are in R Table 68 Final performance design point comparison for the engine configurations Design Parameter Engine Configuration SCGT Eff. SCGT SpPw HPRTE Eff. HV Eff. rth 37.3% 33.4% 37.2% 45.0% SpPw (HPsec/Ibm) 159 180 593 629 OPR 24 10.4 32.2 23.6 TET 1330 1580 1880 1770 R N/A N/A 3.30 3.00 Equivalence Ratio 0.240 0.303 0.894 0.799 mair (Ibm/sec) 25.2 22.2 6.75 6.36 mH 20 lquid (Ibm/sec) N/A N/A N/A 0.306 Tambient 544 544 544 544 LPPR N/A N/A 6.25 3.50 HPPR N/A N/A 5.31 7.37 T HPC in 544 544 614 509 TIT 2500 2500 2500 2500 Texhaust 1330 1580 801 837 Temperatures are in R CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS Conclusions The analysis performed for this thesis project consisted of parametric studies to establish design point parameters, sensitivity studies to examine specific parameter/resultant interactions, and design point comparisons of the performance characteristics of the three gas turbine engine configurations. The engine models were developed using a steadystate, incompressible thermodynamic approach with the engine cycle code NPSS developed by NASA Glenn Research Center. The mission requirement for the engine was produce continuous nominal power output of 4000 BHP. To refrain from investing capital in exotic material development for the engine components, the TIT maximum was limited to 25000R and the hot side recuperator inlet temperature was constrained to not exceed 20590R. The turbocharger pressure ratio was designed to not exceed a value of 7.5this was a design limitation determined for singlestage centrifugal compressors. Moreover, NPSS and CEA do not have thermodynamic properties for solids; therefore, to prevent icing before the in the HPRTE engines, the high pressure compressor (HPC) inlet temperature minimum value was 4920R (330F). The dependent variables optimized during the parametric performance comparison of the engine cycles are listed in their order of significance: rth, specific power, and exhaust gas temperature. The conclusions are as follows: S Comparison output from a NPSS run case of the HPRTE Efficiency matched well with output from a similarly configured engine cycle using the spreadsheet code. Those parameters whose values from NPSS agreed with the counterpart values from the spreadsheet code included: ,,, OPR, TET, THpc ,,, and Texh,,,. The specific power outputs from the two codes did not match well. Their values differed by 12.5%. The difference in these output values can be associated to three causes. The operational handling of the spreadsheet code was such that it was impossible to model the HPRTE in the proper turbocharger configuration. Moreover, the codes modeled the engine using different fuels and thermodynamic curvefit equations. * For the SCGT sensitivity analysis, the results showed that the cycle thermal efficiency and specific power were both particularly sensitive to TIT and Tambent variations but were not very sensitive to OPR changes. This is not surprising when considering the dominance of the temperature ratio in the development of the theoretical thermal efficiency expression in the first section in Chapter 6. The three most noteworthy influence coefficients from this section are (OSpPw)/ (8SpPw) S/PPWb&e SPPWb&he 1.76 base =3.36  base = 1.76 S(TIT)3.36 (Tamb) TITse Tambba /rth ae = 0.898. (TIT) bTITase * Two design points were considered for the SCGT engine configuration. One was optimized for maximum rth (SCGT Efficiency ) and the other was optimized for maximum specific power (SCGT SpPw). The SCGT SpPw best predicts the ETF 40B design point. The SCGT Efficiency had a predicted rth value of 37.3% 10.2% higher than the 7th predicted for the SCGT SpPw engine configuration. The SCGT SpPw had a predicted specific power of 180 HPsec/lbm13.2% greater than the SCGT Efficiency configuration. * HPRTE Efficiency sensitivity analysis was performed next. Variations in the following parameters affected the rth resultant by a proportional amount: THPC , 7Turb ad, rWCompad, and TIT to a lesser extent. Specific power was decidedly sensitive to these input parameters: TIT, TET, THc ,, r7Turbad rCompad, and r7urbo. The HPPR was sensitive to the following parameter inputs: Tambent and LPPR. * A byproduct of the sensitivity analysis for the HPRTE Efficiency was that the optimized pressure ratios for the two spools were determined. The optimization was based on maximizing 7th rather than specific power. The turbocharger pressure ratio was chosen to 6.25, and the HPPR was chosen to be 5.31. * Exhaust gas temperature (Texhaust) was an important consideration in the engine cycles comparison studies. T'xhaut values for the HPRTE cycles were an average of 550R less than the Texhast values of the SCGT Efficiency design point. When compared to the SCGT SpPw design point, the T'hhaut values for the HPRTE cycles were almost 8000R less. Cooler exhaust temperatures directly impact the survivability of the ship. Naval ships powered by HPRTE engines instead of SCGT engines would have a greatly reduced infrared detection signature. Moreover, an 8000R reduction in temperature would increase the density of the exhausted gases implying that the exhaust ducting would be smaller in diameter for the HPRTE system. * The 7th values for both HPRTE cycles remain consistently high through a wide operating range of pressure ratio designs. The q7th me for HV Efficiency is 44.2% and for HPRTE Efficiency it is 36.8%. The r7th mea of the SCGT was 36.1%. The HPRTE cycle curves for this part of the analysis were very flat meaning that the qth value is not greatly affected by OPR variations. The implication here is that existing turbomachinery components could most likely be used to design a production HPRTE system. * The four extreme operating cases analyze the performance characteristics of the competing engine cycles headtohead. Many conclusions can be drawn from this section of work. First, the HV Efficiency has better thermal performance in hot weather than in cold weather. Second, thermal performance of the HV Efficiency is not significantly affected by water temperature. Third, raising air temperature positively impacts the thermal performance and specific power of both HPRTE cycles while negatively affecting both performance characteristics of the open cycle SCGT. Under hot conditions (cases 3 and 4) the HV Efficiency performed with an average thermal efficiency of 44.3%. That is an average of 17.8% higher than the HPRTE Efficiency cycle and 23.7% higher than the SCGT. * The effects of decreasing HPC inlet temperature on a HV Efficiency configured engine were analyzed. The data reveals that there are minor increases (less than 2%) in the performance variables 7th and specific power when HPC inlet temperature is dropped from 509R to 4990R; however, those increases are not significant enough to make a recommendation for this concept. * For their optimized design point parameters, the HV Efficiency has a 7th of 45.0%besting the SCGT Efficiency by 20.6%, the SCGT SpPw cycle version by 34.7%, and the HPRTE Efficiency engine cycle by 21.0%. Thermal efficiency is inversely related to the specific fuel consumption. For the same ship platform, the HV Efficiency engines would allow for increased cargo if the mission range is unchanged. The HPRTE cycles should also be considered if the important design issue is mission range. Having lower specific fuel consumption than the SCGT SpPw design point suggests that the HPRTE cycles would exhibit an increased mission range capability if the fuel tank size is a constant parameter. * There are significant specific power differences between the HPRTE engine cycles and the SCGT. The mean specific power of the HV Efficiency cycle is nearly four times larger than that of the SCGT. Since specific power is directly proportional to the area of the ducting in the engine, the core HPRTE engine would be almost four times smaller than a SCGT of the same power capacity (of course some additional space would be needed to house the VARS unit). Currently, it is unknown if the size and performance tradeoffs would cancel each other. Recommendations * An offdesign point analysis should be completed on the engine cycle configurations reported on in this analysis because over 93% of naval ship operation time is spent operating at or below 35% engine power [Landon]. NPSS would be the obvious software choice for this next step since it has offdesign point modeling capabilities. Moreover, the engine models have already been created in NPSS and the output has been benchmarked to a certain degree. Performance map integration and scaling is a critical competency that must be addressed before this next step is taken; and it is unknown how the performance map lookups would affect model computing times. Of course, any added sophistication to a model increases the expectation that it will lengthen the model runtime. Currently, for the HV Efficiency model, the runtimes range from 4 to 12 minutes, depending on the model its constraints. A comprehensive offdesign study should include range and propeller analysis, as well. * Further benchmarking of the results of this analysis is a necessary next step to guarantee the accuracy of the work. The accuracy of NPSS is not in question; it was developed by NASA in conjunction with leading United States aeropropulsion companies. However, checking the fidelity of the HPRTE models against other thermodynamic cycle codes, such as the code created by Jameel Kahn, is a useful next step to give confidence to this work. Furthermore, comparing NPSS model results against experimental test data from the laboratory demonstrator should be considered. * A more robust model would include the VARS unit, at least to the extent that the HPC inlet temperature is set by calculations representative of having the VARS unit in the model. Thus far, excess cooling capacity of the VARS has not been addressed, but there are obvious uses for additional refrigeration on a naval ship. 
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PAGE 1 DESIGN POINT ANALYSIS OF THE HIGH PRESSURE REGENERATIVE TURBINE ENGINE CYCLE FOR HIGHSPEED MARINE APPLICATIONS By GEORGE ANAGNOSTIS A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2007 PAGE 2 Copyright 2007 By George Anagnostis PAGE 3 This thesis is dedicated to my parents, Victor and Linda Anagnostis. Without their emotional and financial encouragemen t this thesis would not exist. PAGE 4 iv ACKNOWLEDGMENTS I thank the members of my graduate co mmittee members: Dr. William E. Lear, Jr., Dr. S. A. Sherif, and Dr. Herb ert Ingley for their support on this thesis. Dr. Lear was especially helpful, providing me with critic al advice throughout th is project. Next, I would like to thank the Aeropropulsion Sy stems Analysis Office at the National Aeronautics and Space Administration Glenn Research Center for their assistance on Numerical Propulsion System Simulation progra m. Two members of that group provided continued technical assistanceScott Jones a nd Thomas Lavelle. Lastly, I thank two special individuals that have provided me with insight and wisdom concerning matters of engineering and life in general, John Crittenden and William Ellis. PAGE 5 v TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES............................................................................................................vii LIST OF FIGURES.........................................................................................................viii NOMENCLATURE............................................................................................................x CHAPTER 1 INTRODUCTION........................................................................................................1 2 LITERATURE REVIEW.............................................................................................4 Brief History of Turbine Engine Development............................................................4 Gas Turbine Engine Examples in Marine Applications...............................................5 Advantages of Gas Turbine Engi nes in Marine Applications......................................6 Recuperation and Intercooling....................................................................................7 SemiClosed Cycles......................................................................................................9 Computer Code Simulators.........................................................................................10 Previous Gas Turbine Research at the University of Florida.....................................12 3 NUMERICAL PROPULSION SYSTEM SIMULATION ARCHITECTURE.........16 Model..........................................................................................................................16 Elements.....................................................................................................................17 FlowStation.................................................................................................................18 FlowStartEnd..............................................................................................................18 Thermodynamic Properties Package..........................................................................20 Solver......................................................................................................................... .21 4 CYCLE CONFIGURATIONS AND BASE POINT ASSUMPTIONS.....................25 Major Model Features.................................................................................................25 Flow Path Descriptions & Schematics.......................................................................26 Simple Cycle Gas Turbine Engine Model...........................................................26 High Pressure Regenerative Turb ine Engine Efficiency Model.........................26 PAGE 6 vi High Pressure Regenerative Turbin e Engine with Vapor Absorption Refrigeration System Efficiency Model..........................................................27 Simple Cycle Gas Turbine Engine Desi gn Assumptions and HPRTE Cycles Base Point Assumptions.................................................................................................28 5 THERMODYNAMIC MODELING AND ANALYSIS............................................33 Thermodynamic Elements..........................................................................................33 Heat Exchangers..................................................................................................33 Mixers..................................................................................................................34 Splitter.................................................................................................................35 Water Extractor...................................................................................................36 Compressors........................................................................................................37 Turbines...............................................................................................................39 Burner..................................................................................................................40 Sensitivity Analysis....................................................................................................41 6 RESULTS AND DISCUSSION.................................................................................43 Cycle Code Comparison.............................................................................................43 Sensitivity Analysis....................................................................................................44 Simple Cycle Gas Turbine Engine Model...........................................................44 Simple Cycle Gas Turbine Engine Model Sensitivity Analysis..........................48 High Pressure Regenerative Turb ine Engine Efficiency Model.........................50 High Pressure Regenerative Turbine Engine Efficiency Model Sensitivity Analysis............................................................................................................53 Cycle Comparison Analysis.......................................................................................61 Extreme Operating Conditions............................................................................65 High Pressure Compressor Inlet Temperature Comparison for HV Efficiency Model...............................................................................................................67 Final Design Point Parameter Comparison.........................................................68 7 CONCLUSIONS AND RECOMMENDATIONS.....................................................83 Conclusions.................................................................................................................83 Recommendations.......................................................................................................86 LIST OF REFERENCES...................................................................................................88 BIOGRAPHICAL SKETCH.............................................................................................91 PAGE 7 vii LIST OF TABLES Table page 41 Comparison of major configuration features...........................................................29 42 Simple Cycle Gas Turbine engine design point parameters.....................................32 43 Base case model assumptions for HPRTE cycles [3], [26], [27].............................32 61 Cycle codes comparison: NPSS verses sp readsheet code for HPRTE Efficiency model data run. All temperatures are in R .............................................................70 62 Summary of the HPRTE Efficiency sensitivity analysis.........................................77 63 Comparison of the thermal efficiency maximums and their corresponding overall pressure ratios (OPRs)..................................................................................78 64 Comparison of the specific power maxi mum values and their corresponding OPRs.........................................................................................................................78 65 Comparison of exhaust temperature ma ximum values for the three engine configurations...........................................................................................................79 66 Engine cycles comparison for four extreme operating conditions...........................81 67 High pressure compressor (HPC) inlet temperature comparison for the HV Efficiency engine model...........................................................................................81 68 Final performance design point compar ison for the engine configurations.............82 PAGE 8 viii LIST OF FIGURES Figure page 31 Example NPSS engine model [19]...........................................................................23 32 State 7 of HPRTE engine cycle................................................................................24 41 Simple Cycle Gas Turbine (SCGT) engine model configuration............................29 42 High Pressure Regenerative Turbine Engi ne model, both efficiency and power configurations represented.......................................................................................30 43 High Pressure Regenerative Turbine E ngineVapor Absorption Refrigeration System, both efficiency and power m odel configurations represented....................31 44 Vapor Absorption Refrigeration Cycle with HPRTE flow connections..................32 61 Thermal efficiency comparison is plotted with respect to OPR. NPSS results (with turbine inle t temperature (TIT) set to 2500R ) are compared to the derived and the ideal Brayton cycle expressions..................................................................70 62 Thermal efficiency vs. OPR with sensitivity to TIT................................................71 63 Specific power vs. OPR with TIT sensitivity...........................................................71 64 Thermal efficiency vs. ambient te mperature with OPR sensitivity..........................72 65 Demonstrates agreement between NPSS and developed theory that describes the low pressure spool....................................................................................................72 66 High pressure spool pressure ratio (H PPR) vs. ambient temperature with low pressure spool pressure ratio (LPPR) sensitivity......................................................73 67 Thermal efficiency vs. HPPR showing sensitivity to TIT.......................................73 68 Thermal efficiency vs. HPC inlet temperat ure for recirculation ratio sensitivity....74 69 Thermal efficiency vs. turb ine exit temperature (TET) w ith cooler pressure drop sensitivity.................................................................................................................74 610 Specific power vs. TET for HPC efficiency sensitivity...........................................75 PAGE 9 ix 611 Specific power vs. HPPR for HPT efficiency sensitivity.........................................75 612 Exhaust temperature vs. OP R for TIT sensitivity....................................................76 613 Thermal efficiency vs. HPPR for turbocharger efficiency sensitivity.....................76 614 Thermal efficiency vs. LPPR for TIT sensitivity.....................................................77 615 Engine cycles comparison of thermal efficiency vs. OPR.......................................78 616 Engine cycles comparison of specific power vs. OPR.............................................79 617 Engine cycles comparison of exhaust temperature vs. OPR....................................80 618 Engine cycles comparison of thermal efficiency vs. ambient temperature..............80 PAGE 10 x NOMENCLATURE DepV Dependent variable in a Jacobian matrix IndV Independent variable in a Jacobian matrix Heat exchanger effectiveness inP P_ 0 Pressure drop as a percentage of the inlet stream pressure Q Heat flow rate (Btu/sec) nm Mass flow rate at station n (lbm/sec) n pC_ Specific heat at constant pressure at flow station n (Btu/lbmR) inT_ 0 Stagnation temperature at the inle t to a physical cycle component (R) outT_ 0 Stagnation temperature at the ex it to a physical cycle component (R) inP_ 0 Stagnation pressure at the inlet to a physical cycle component (psi) outP_ 0 Stagnation pressure at the exit to a physical cycle component (psi) inh_ 0 Mass specific stagnation enthalpy at the inlet to a physical cycle component (Btu/seclbm) outh_ 0 Mass specific stagnation enthalpy at the inlet to a physical cycle component (Btu/seclbm) nFAR Fueltoair ratio at state point n PAGE 11 xi n totm_ For splitters and separators, total mass flow rate at state point n (lbm/sec) BPR Flow bypass ratio for splitter elements liquid O Hm_ 2 Mass flow rate of liquid water bei ng extracted in separator (lbm/sec) liquid O Hh_ 2 Mass specific enthalpy of liquid wa ter being extracted (Btu/seclbm) CompPR Pressure ratio any compressor ad Comp Adiabatic efficiency of any compressor ns_ 0 Mass specific stagnation entropy at flow station n (Btu/lbmR) R Ideal gas constant (Btu/lbmR) idh Mass specific enthalpy change for an isentropic process (Btu/seclbm) in CompR_ Ideal gas constant at a compresso r inlet state point (Btu/lbmR) b Burner efficiency RQ Lower heating value of the fuel (Btu/lbm) WAR Water to air ratio, mass basis TIT Turbine inlet temperature OPR Overall pressure ratio of a system Ratio of specific heats, v pC C SpPw Specific Power (HPsec/lbm) ambT Ambient Temperature (R), also ambientT LPPR Low pressure compressor pressure ratio HPRR High pressure compressor pressure ratio PAGE 12 xii ad LPC_ Low pressure compressor adiabatic efficiency ad LPT Low pressure turbine adiabatic efficiency PAGE 13 xiii Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science DESIGN POINT ANALYSIS OF THE HIGH PRESSURE REGENERATIVE TURBINE ENGINE CYCLE FOR HIGHSPEED MARINE APPLICATIONS By George Anagnostis May 2007 Chair: William E. Lear, Jr. Major Department: Mechanic al and Aerospace Engineering A thermodynamic sensitivity and performan ce analysis was performed on the High Pressure Regenerative Turbine Engine (HPR TE) and its combined cycle variation, the HPRTE with a vapor absorption refrigeration system (VARS). The performance analysis consisted of a comparison of three engine c onfigurations, the two HPRTE variants and a simple cycle gas turbine engine (SCGT), m odeled after the production marine gas turbine engine, ETF40B. The engine cycles were optimized using a parametric analysis; a sensitivities study was completed to esta blish which design parameters influence individual engine model performance. The NASA gas turbine cycle code Numerical Propulsion System Simulation (NPSS) was the software platform used to complete this analysis. The comparison was performed at sea level with an ambient temperature of 544R. The results for the SCGT predict a designpoi nt optimized thermal efficiency of 33.4% and an overall pressure ratio (OPR) of 10.4 with a specifi c power of 180 HPsec/lbm. PAGE 14 xiv The HPRTE engine, called HPRTE Efficiency for this thesis, had an expected design thermal efficiency of 37.2% (OPR of 32.2) with a specific power rating of 593 HPsec/lbm% larger than the SCGT speci fic power. The combinedcycle HPRTEVARS, called HV Efficiency in the analysis had a predicted design thermal efficiency of 45.0% (OPR of 32) with a specific power of 629 HPsec/lbm. The HV Efficiency thermal efficiency was 34.7% higher than that of the SCGT designed for maximum specific power. Exhaust gas temperatures va ried significantly between the SCGT and the HPRTE variants. The model engine exhaus t for the SCGT was 1580R while the exhaust temperatures of the HPRTE Efficiency and HV Efficiency were 801R and 837R, respectively. On average, the HPRTE cal culated exhaust temperature was 761R less than that of the SCGT. High pressure co mpressor (HPC) inlet temperature sensitivity was considered for the HV Efficiency. Tw o operating cases were consideredthe HPC inlet held constant at 499R and 509R. The 499R case operated with a thermal efficiency higher by 1.56% and a sp ecific power higher by 1.62%. The results of the analysis imply that HP RTE duct sizes will be smaller due to the engine having significantly higher specific power. Since specific fuel consumption is inversely proportional to thermal efficiency, th e HV Efficiency engine cycle will require a smaller fuel tank to allow for additional car go (or if the tank size is unchanged, the ship range is increased). Future project consid erations include an offdesign performance analysis using NPSS or another software package, additional NPSS model benchmarking with a reputable cycle simulation code, and an analysis of the effects of moist ambient air on evaporator water flow extraction rates. PAGE 15 1 CHAPTER 1 INTRODUCTION Before the marine gas turbine, naval sh ips clipped through the water propelled by sooty coalfired steam turbines or diesel engi nes. The 1940s advent of the gas turbine jet engine introduced a similar technology shift in the marine propulsion industry a decade later. And now for the last 60 years marine gas turbine engine propulsion advancements have derived mainly from aeronautical rese arch and development programs. However, there have been some instances where the ma rine propulsion industr y has led the way in developmentmost notably by the introduc tion of the WestinghouseRollsRoyce 21st century (WR21) ICR program in the early 1990s Intercooled compressors and exhaust heat recuperation set the WR21 gas turbine engi ne apart. Ironically, the same ingenuity that steered the Navy to develop the WR21 program was nowhere to be found during the decisionmaking process time for the propulsion system for the 21st century speed shiptoshore transport. The ETF40B, a workhorse and variant of the original TF40 that powered the Navy landing craft aircushion (LCAC) vessel for the last two decades will provide the propulsion and lift thrust for the new JMAC shiptoshore tr ansport. Despite interest in new engine technologies, such as the Hi gh Power Regenerative Turbine Engine (HPRTE), funding constraints prevented the Navy from further investigating novel systems. This thesis will make the case fo r the HPRTE as an alternative engine concept to the ETF40B for the JMAC program. PAGE 16 2 The motivation to compare the HPRTE to the ETF40B is a result of previous experimental and computational modeling effort s completed at the University of Florida (UF) Energy and Gas Dynamics Laboratory to develop alternate engine technologies. There other design considerat ions besides cost that drive engine development; the HPRTE will outperform the ETF40B, having a higher specific power ratio, improved offdesign performance, and a considerab ly lower infrared heat signature. The HPRTE is a semiclosed, compressor intercooled, recuperative system. A demonstration engine has been build and pe rformance tested at UF, and the proof of concept has been met. The laboratory demonstr ator uses engine exhaust heat to power a vapor absorption refrigeration system (VARS). This is representative of the combined cycle system, one of the two HPRTE configurat ions, that is considered in this modeling and analysis project. The ba se HPRTE is the other. The combined cycle variant is expected to outperform the base HPRTE because the VARS unit provides additional cooling to the high pressure compressor inlet of the engine. The analysis in this thesis includes a pa rametric optimization and sensitivity studies that determine designcritical parameters. Th ere are three engine models total that are consideredthe two HPRTE variants (HPR TE Efficiency and HV Efficiency) and a simple cycle gas turbine engine (SCGT). The SCGT is modeled to represent the ETF40B engine configuration. Only two of the three engines examined are considered in the sensitivity analysis; they are the SCGT and HPRTE Efficiency engine models. Sensitive parameters for the HPRTE Efficiency are expected to be the similar for the HV Efficiency cycle, and therefore the exercise was deemed redundant. PAGE 17 3 The second part of the project is the cycl e comparison analysis which will examine the performance parameters such as therma l efficiency, specific power, exhaust gas temperature, and high pressure compressor inle t temperature. Missi on specifications and material and component limitations provide th e scope for many of engine variables that are to be optimized. Being for a military ap plication, the engine is expected to have robust performance capabilities; therefore, run cases were analyzed representing a wide range of ambient operating conditions fo r all cycle configurations. The model processes were based on thermodynamics relationships. The complete set of equations used to clos e the cycle model is discussed later. The flows were all considered steadystate and incompressibl e, and the turbomachinery components and ducting were all represented as adiabatic processes. These considerations are built in to th e cycle code called Numerical Propulsion System Simulation (NPSS). This is a DOS driven, objectoriented program that has design, offdesign, and transient run operation capabilities. Technical support for this program was provided by the ASAO group at the NASA Glenn Re search Facility. PAGE 18 4 CHAPTER 2 LITERATURE REVIEW Brief History of Turbine Engine Development Between 15050 B.C., a Greek named Her o, living in Alexan dria, Egypt, boiled water in a sealed container that had two spout s extending from the top and slightly curved [1]. As the water boiled, steam billowed from the spouts, rotating the entire container. At the time it was considered a toy, but today history remembers Hero as the inventor of the steam turbine. Despite this early application, the first documented use of the turbine engine for propulsion purpose was not until 1791; John Barber, a British inventor designed a simple steam engine with a chaindriven compressor to power an automobile [1]. Then in 1872, nearly 100 years after Barber engine, steampowered automobile was designed, Franz Stolze designed the first axial gas turbine engi ne [2]. The practicality of the engine was suspect and it never ran unassisted. Interest in gas turbine engines con tinued to increase, and developmental breakthroughs were made in the 1930s. Gr eat Britain and Germany were the spearhead of these efforts as tension between the European heavywei ghts mounted. Faster, more agile aircraft were being c onceived, and the air forces of both nations noticed the advantages of the jet engine over conventional piston engine s. Frank Whittle of Great Britain worked out a concept fo r a turbojet engine and won a patent for it in 1930 [3]. Five years later in Germany Hans van Ohaim, working independently of Whittle, patented his own gas turbine engine system [3]. Ohaim and his colleagues witnessed the PAGE 19 5 first flight of their turbojet engine on August 27, 1939, powering the He.S3B aircraft [3]. The Whittle concept was shelved until mid 1935 when finally with the help of two exRoyal Air Force pilots the engine was built and tested by Power Jets Ltd [3]. After working through design setbacks, including fu el control issues, the first British designed turbojetpowered aircraft flew in May 1941 [3]. Even though the Germans could claim the first turbojet powered flight, the British built the first production turbojet engine, the RollRoyce de Haviland [3]. Tur bojet development skyrocketed in the 1940s and 1950s; a Whittle design provided the blueprints for the first American made turbojet engine, the General Electric IA [7]. Gas Turbine Engine Examples in Marine Applications The British were using simple gas turbine engines to power gun boats as early as 1947 [4]. The HMS Grey Goose was the fi rst marine vessel to be powered by a turboshaft engine with an intercooled co mpressor and exhaust heat recuperation (ICR) [5]. In 1956, the U.S. Navy contracted with Westinghouse to develop a gas turbine engine for submersible operation [6]. They designed a two shaft semiclosed ICR engine; a novel concept that but was limited by fueltype availability. The use of heavy sulfur fuels triggered sulfuric acid buildup in the intercoolers which degraded the metal components in the heat exchanger. A direct effect heat exchange r was tried with sea water, but this only succeeded in introduci ng salt into the engine which deposited on the turbomachinery parts [6]. At the same time the Westinghouse engine was under development, General Electric was looking to convert their profitabl e J79 engine into a marine gas turbine. In 1959 they introdu ced the LM1500. It was a simple cycle gas turbine that produced 12,500 SHP [7]. The General Electric LM2500, introduced in 1968, ushered in the second genera tion marine of marine turb oshaft engines. Like the PAGE 20 6 LM1500, the LM2500 was a derivate of a proven aero engine that powered over 300 U.S. Naval ships [8, 7]. Moreover, thermal e fficiency was improved on the LM2500 to 37 percent [8]. Advantages of Gas Turbine Engi nes in Marine Applications Gas turbine engines have overtaken diesels as the power plant of choice for ferries, cruise liners and fastattack military ships. This trend exists because gas turbines offer higher power outputtoweight ratios, si gnificantly higher compactness, higher availability, and they produce fewer emissions than marine diesels [9, 4]. The powertoweight advantage is best realized with an example comparing a diesel engine to a gas turbine engine of similar power rating. Th e 7FDM16 marine diesel offered from General Electric produces 4100 BHP and weighs 48,800 lbs [10]. In comparison the Lycoming TF40 turboshaft marine engine, produces 4,000 BHP and weighs only 1,325 lbs [11]. The significant weight disparity favoring th e TF40 is a prime reason gas turbines are being chosen to power marine vessels re quiring agility and speed. Similarly, the compactness that gas turbine engines offer gr eatly improves vessel versatility and crew and cargo capacity optimization. As an exam ple, the 7FDM16 diesel has a volume of 920 cubic feet, whereas the TF40 has a volum e of less than 43 cubic feet [10, 11]. Subsequently, the compact, lightweight gas tu rbines are easier to transport and switchout of ships. With skilled professionals available from the aviation industry trained on gas turbines engines, there is an abundance of mechanic s and support crew able to maintain and operate these systems [4]. Moreover, the emission reductions achieved by gas turbine engines over comparable diesels make them more attractive to commercial and military forces needing to placate envir onmental agencies such as the EPA and other PAGE 21 7 international bodies. A simple opencycle gas turbine engine produces 1/3 to the emissions of a diesel engine of comparable technology [9]. Recuperation and Intercooling Simple, opencycle turboshaft engines exha ust hot gas products to the atmosphere wasting highquality heat energy; an increa singly common use of this available heat energy in gas turbine engines is to preheat the compressed gas flow before the combustion stage. This process is called exhaus t heat recuperation. As a result of raising the combustor inlet temperature, less fuel is required to achieve the desired turbine inlet temperature and desired power output. This directly impacts the thermal efficiency and specific power of the engine, raising therma l efficiency but dropping specific power in most cases. Any instance in which fuel use can be decreased has a direct positive impact on the cycle thermal efficiency. It is im portant to note that gas turbine engine recuperators generally work be tter in engines with only mode rate pressure ratios [12]. Qualitatively, one can see that as the engine pressure ratio rises, the compressor exit temperature and turbine exit temperature appr oach each other. In practice this would drop the capacity of the rec uperator to preheat the comp ressed air before combustion, thus rendering it ineffective. A second improvement on the simple gas turb ine engine is the addition of an intercooler. Intercoolers are placed between the low pressure and high pressure compressors to reduce the air temperature exiting the last stage of the compressor. Assuming the process is adiabatic and the air is a calorically perfect gas, the power required to drive the compressor is written as T c m Wp comp This assumes a control volume analysis around the entire compressor for all stages [3 ]. The intercooler delivers a lower PAGE 22 8 temperature fluid to the high pressure compresso r stage. If the same pressure ratio is applied to the high pressure st age, the exhausting fluid temp erature would be lower than if no intercooling had been performed. The outcome is that T for the entire compressor has been decreased, and subseque ntly, the total power requirement for the compressor has also been decreased. The net effect on the cycle thermal efficiency is the same as raising the adiabatic efficiency of the entire compressor. The outcome is a net available power increase of 25 to 30% [5]. Coolants exist for both sea and air applications. Jet aircraft have 50C ambient air availa ble and naval ships have the abundant salt water rese rves of the oceans. Additionally, combining both compresso r intercooling and exhaust gas recuperation provides a further improvement to cycle thermal efficiency. Engines that employ this technology are referred to as intercooling recuperation (ICR) engines. With the intercooler cooling the compressor discharge, the temperature difference between it and the turbine discharge increasesth e outcome is an improved recuperator performance [12]. In 1953 Rolls Royce intr oduced the RM60 ICR engine which powered the gunboat HMS Grey Goose [5]. Though innova tive and more efficient than the steam engine it replaced, the RM60 was too comp lex to operate using existing controls technology. A further example reviewed for this project compares two gas turbine engines, a simple opencycle and an ICR, fo r a marine destroyer a pplication. The study noted that fuel use is reduced by 30% with the ICR engine [5, 13]. In 1990, General Electric began retrofitting their midsize turboshaft engine, the LM2500, in hopes of improving its thermal effi ciency by 30% [13]. This project was sidelined in 1991 when a team led by No rthrop Grumman won a $400 million, 9year PAGE 23 9 development contract to develop and build a replacement for the LM2500 marine gas turbine [14]. Program leaders Northrop Gr umman and RollsRoyce chose an ICR engine design, called the WR21, for the navies of th e United States, Canada Great Britain, and France [14]. John Chiprich, who managed th e ICR development program, noted that the new engine will reduce the fuel consumption fo r the entire marine turbine powered fleet of the United States by 27 to 30% [14]. One negative aspect to the ICR concept is that it has a lower power limit for it to be considered effective. Blade tip leakage fo r gas turbine engines that have a nominal power rating below 1.5MW overrides any effici ency gained from the implementation of ICR technology [15]. SemiClosed Cycles A semiclosed gas turbine cycle is on e in which hot exhaust products are recirculated, combined with fr esh air, and then burned again in the combustion chamber. Example configurations can include inte rcooling and recuperation, and some are turbocharged to boost core engine pressures. Despite the added complication of engine components and weight addition; many semiclo sed cycle configurations have significant performance related benefits. For instance, semiclosed cycles that are turbocharged, have higher specific power, redu ced recuperator size (if a recuperator is present) which improves heat transfer coefficients, and higher partload performance characteristics [13]. All semiclosed cycles benefit from reduced emissions since reduced oxygen concentrations reduce flame temperatures [13]. Some of the earliest semiclosed gas turb ine engine configurations were proposed by the Sulzer Brothers in the late 1940s [ 16]. Their 20 MW gas turbine system for the Weinfelden Station was a complex system that achieved a cycle thermal efficiency of PAGE 24 10 32% for full load capacity and 28 % for half lo ad capacity [16]. The earliest example of a semiclosed gas turbine system for na val propulsion was the Wolverine engine developed by Westinghouse [6]. The subm arine engine program which began in 1956 called for a twoshaft, semiclosed, ICR turbosha ft engine [6]. It was never a production engine because of sulfuric acid buildup that degraded the metallic intercooler components. This was attributed to the high conc entration of sulfur in early diesel fuels. More recent research projects on semiclo sed gas turbine cycles conducted by the University of Florida, Energy and Gas Dyna mics Laboratory will be highlighted in the final section of this chapter. Computer Code Simulators Because of the complexity of the cycles th at need to be simulated and the iterative nature of semiclosed cycle modeling, it is convenient to employ the use of a computational code to perform the nume rous calculations. There were several computational thermodynamic cycle programs that were potential platforms for this project. Below is a brief overview of the programs surveyed. Gas turbine Simulation Program (GSP) is a product of the National Aerospace LaboratoryThe Netherlands (NLR) [17]. Th e GSP website boasts of a user friendly platform with draganddrop components re ady for building engines models. The code can be used for steadystate as well as transi ent simulation. Material specifications and lifecycle information can be incorporated for failure and deterioration analysis. Unknown, however, is whether or not GSP can model semiclosed engine cycles. A second code called GASCAN was reviewed by Joseph Landon. This code models fluid movement as well as thermodynamic state vari ables for engine simulations. Semiclosed PAGE 25 11 operation is not explicitly disc ussed but simple and complex cy cles are apparently easily modeled. A third modeling program reviewed wa s Navy/NASA Engine Program (NEPP); it was developed to perform gas turbine cycle perf ormance analysis for jet aircraft engines. NEPP is an older componentbased engine modeling program that has design and offdesign modeling capabilities with performan ce map integration. User instantiated variables can be controlled to hold specifi c parameters constant while the program converges to its solution. This program was eliminated because it can not model recirculated flows [13]. NEPP was only the first of thr ee NASA programs evaluated for this modeling project. The second NAS A code was ROCket Engine Transient Simulation (ROCETS) developed at Marsha ll Space Flight Center. This program provides a suite of engine component modules to assist users in building their models; it also allows users to create th eir own modules to model more exotic engine cycles [18]. Like NEPP, ROCETS gives the developer the ability to vary certain parameters until other constraints are satisfied and a converged solution is de termined [18]. Users have the option of operating in design or offdesign mode as the program has the capability of reading performance maps for compressors and turbines. ROCETS was used in modeling efforts at the University of Florid a in the 1990s. The program is capable of modeling recirculation in gas turbines and wa ter particulate extrac tion. Being somewhat antiquated, the program was dismissed as a pos sible platform for the project considering the unlikely availability of user support. A commercial software package option was the versatile ASPEN PLUS. The ASPEN PLUS engineering suite is a robust pack age of software programs that can handle PAGE 26 12 all of the modeling requirements for this pr oject. Once again, here is a program that provides users with the option of running thei r cycle in design, o ffdesign, or transient modes. Their website displays screen shot s of a pleasant graphic user interface with dragndrop engine components [19]. The third software program from NASA, Numerical Pr opulsion System Simulation (NPSS) is a product of the Aeropropulsion Syst ems Analysis Office (ASAO) at the Glenn Research Center. NPSS is set up to operate similar to the earlie r programs NEPP and ROCETS. Accordingly, NPSS offers users the convenience of obj ectoriented engine components for building cycle models [20] Offdesign and transient modeling are options in addition to running in the design point mode [2 0]. The model developer has control of convergence through constraint handling. Since this program became the platform of choice for this project, its capabil ities will be discussed in further detail in Chapter 2. Previous Gas Turbine Research at the University of Florida In 1995 Todd Nemec performed a thermodynamic design point analysis on a semiclosed ICR gas turbine engine with a Ranki ne bottoming cycle [21]. Nemec developed his model using the ROCETS program discusse d earlierhis analysis concluded that the combined cycle with superheated steam in the bottoming cycle resulted in an overall efficiency of 54.5% [21]. The next body of work on semiclosed cycles was performed by Joseph Landon. Landon performed design an d offdesign point analysis of two separate regenerative feedback turbine e ngines (RFTE) [13]. The turbocharger configuration resembled the t opping cycle that Nemec modele d. The other configuration sent the combustion products through a power turbine before the recuperation heat exchanger. The analysis pr edicted that the power turbin e configuration produced the PAGE 27 13 highest thermal efficiency, 48.2% compared to 46% for the tu rbocharger case [13]. Offdesign analysis revealed that the turbocharg er model was the most efficient between 20% and 80% power capacity [13]. Russell MacFarlane used the ROCETS pr ogram to model water extraction and injection on the RFTE engine [12]. MacF arlane found that water removal caused a decrease in specific fuel consumption and a slight increase of specific power [12]. He surmised that water removal was particularly influenced by recirculation ratio, cooler effectiveness, and first stage pressure ratio [12]. George Danias extended the study of the RFTE cycle and investigated design and offdesign performance of three separate configurations for a helicopter engine application [18]. Hi s conclusions stated that the three RFTE configurations were 30 to 35% mo re efficient than the T700701C, baseline engine [18]. Currently, a research project is underway to design and develop a combined cycle, powerrefrigeration cycle called the HPR TEVARS. The High Power Regenerative Turbine Engine (HPRTE) uses exhaust ga s heat to power the vapor absorption refrigeration system (VARS). A design point performance study was carried out by Joseph Boza analyzing two HPRTEVARS engi ne sizes, a small 100 kW engine and a larger 40 MW engine. Boza calculated the pe rformance parameters based on a constant high pressure compressor (HPC) inlet temper ature of 5 C. Excess refrigeration capacity (that capacity not used to cool th e HPC inlet stream) was considered in the combined cycle efficiency value. The larger engine analysis predicted a combined cycle efficiency of 63% while the small engine effi ciency was determined to be 43% [22]. He determined that increasing ambient temperature limits the excess refrigeration capacity, PAGE 28 14 and at an ambient temperature of 45 C the combinedcycle system has no excess refrigeration. For his analysis, Boza used a spreadsheet cycle code to predict the performance of the HPRTE; this was in c onjunction with a VARS m odel that he created. In Chapter 6 the spreadsheet model has been used to benchmark the NPSS program used in this project. The spreadsheet HPRTE m odel is not configured to consider the low pressure spool of the engine as a turboc hargerin the comparison in Chapter 6, the spreadsheet cycle model will be constrained manually for the turbocharger configuration. Life cycle cost analyses of the HPRT EVARS was performed and compared to a microturbine engine by Viahba v Malhatra. Using a standard life cycle cost analysis procedure, Malhatra determined that the HP RTEVARS system exhibited a life cycle cost savings of 7% over the competing microturbine system [23]. One primary reason for the cost savings was associated with the HPR TE being turbochargedthis enabled smaller and less expensive engine components to be c onsidered. The other reason for the cost savings was directly related to fuel cons umption. HPRTE fuel costs were partially compensated by the proceeds from available refrigeration capacity of the VARS unit [23]. To obtain his results Malhatra used a Fortran model of the HPRTEVARS created by Jameel Khan. Khan performed his disse rtation study on the design and optimization of the HPRTEVARS combined cycle develo ping a high fidelity, thermodynamic model for both the engine and the refrigeration sy stems. He used the optimization package LSGRG2 to determine the best designpoint engine parameters considering such outputs as power, refrigeration, and water. His results for the combined cycle with the O H NH2 3/ refrigeration system predicted a cycl e thermal efficiency of 40.5% with a ratio of water production to fuel (propane) consumption of 1.5 [24]. Including the excess PAGE 29 15 refrigeration produced by the cycle, a combin ed cycle thermal efficiency was evaluated as 44%. PAGE 30 16 CHAPTER 3 NUMERICAL PROPULSION SYSTEM SIMULATION ARCHITECTURE Numerical Propulsion System Simu lation (NPSS) was developed by Aeropropulsion Systems Analysis Office (ASAO) at the National Aeronautics and Space Administration (NASA) Glenn Research Center, Cleveland, OH in conjunction with the Department of Defense and leaders in the ae ropropulsion industry. The purpose of the code was to speed the development process of new gas turbine engine concepts for military and civilian applications. It is a componentbased engine cycle simulation program that can model design and offdesign poi nt operation in stea dystate or transient mode [20]. The code can be used as a sta ndalone analysis program or it can be coupled in conjunction with other codes to produce higher fidelity models. Model Engine models are created using any sta ndard text editor such as Microsoft Wordpad. The model file contains the in structions and commands required by NPSS to build an engine model. The engine m odel file combines the engine components (elements) in a systematic manner that is c onsistent with the engine cycle the user is modeling. Here, elements are connected to cr eate the flow stations of the engine; these flow stations are created by linking the flow ports between elements. In the model the thermodynamic package, solver solution met hod, and model constraints should also be specified if different than the defaults. These subjects will be discussed in further detail later in the Chapter 3. PAGE 31 17 Figure 31 is a schematic representation of an exam ple engine modeled using NPSS. The elements are plainly listed; there is an inlet, compressor, burner, turbine, shaft, duct, and exhaust. The working fluid properties are passed through flow ports from one element to the next. Shaft ports connect the compressor and turbine with the shaft element in order to perform the power bala nce for the engine. The interaction of a subelement, CompressorMap with its parent element, Compressor, is shown with its socket link. This particular model has an assembly for the major engine components. The assembly compartmentalizes any pro cesses or calculations performed by these components from the rest of the model. Elements Elements are the corner stones of the engi ne model. Although NPSS comes with a full suite of engine component modules, users are encouraged to create their own elements to model their unique circumstances using the C++ type syntax of NPSS. As mentioned above, elements are responsible for performing the individual thermodynamic processes that simulate the physical engine components. The modules use standard thermodynamic relationships to simulate th ese processes. The level of modeling sophistication is entirely user driven as loss coef ficients and scalars may be applied to variables. Mach number effects are calculable. For higher fidelity models heat and frictional energy dissipation ma y be considered. For the purpose of this analysis the cycle models were kept as simple as possible to shorten computing runtimes. Nevertheless, even simple models require a certain level of complexityfor those cases there are supplemental routines added to elements called subelements and functions. Subelements are subroutines th at can be called by elements to perform calculations or performance table lookups. For instance, the turbine element for a model PAGE 32 18 that is operating in offdesign mode would us e a subelement to determine the efficiency value from data tables. Functions are a type of subroutine that is us er instantiated in a particular element that requests particul ar calculations be performed. Function calculations take precedence over the solver driv en calculations. They may be performed before, after, or during solver runtim e depending on the desire of the user. FlowStation For an element to perform its calculations, properties and state information must be known as initial conditions. Thes e initial condit ions are set by the user or the computer and passed to the element through a flow port. When flow ports are used to link two elements, this bridge is calle d a FlowStation. There is a ma in FlowStation subroutine and then there are the specific FlowStation subr outines unique to each thermodynamic model. The main FlowStation subroutine is responsib le for linking the model to the appropriate subroutines that handle th e subroutine lookups. When NPSS uses the Chemical Equilibrium with Applicati ons (CEA) thermodynamic software, the main FlowStation subroutine links the model file/files with the CEA program allowing the passage of species and state informati on between the two programs. FlowStartEnd There are elements in NPSS specifically de signed to either begin or end a fluid flow path. Semiclosed gas turbine engine modeling in NPSS makes use of these flow start/end elements to obtain converged solutions The solution solver in NPSS requires a single initial pass through the model elements to create the flow path and flow stations and essentially build the engine model. Fo r open cycle gas turbine engines this task requires no extra consideration by the modeler. The solution solver can logically step through the engine from the inlet element to the exhaust element for the preprocess pass. PAGE 33 19 However, all of the HPRTE configurations have mixing junctions upstream of the core engine components adding a further level of complexity that the solution solver must negotiate. The solution requires added components FlowStart and FlowEnd elements, and additional constraints added to the solution solver. Fo r convenience and brevity the ASAO developed the element FowStart End to replace the FlowStart/FlowEnd elementsthis element also contains the add itional constraints required, eliminating the necessity to initialize these in the main model file. To be complete it is best to describe the coding required to gain convergence of a regenerative gas turbine mode l using FlowStart, FlowEnd, and FlowStartEnd elements. When the solver is stepping through the HPRTE it expects to have a hotside flow station already instantiated when it reaches the r ecuperator inlet after the highpressure compressor exit. Therefore, a FlowStart el ement is created and added to the solver sequence (responsible for the order of elem ent preprocess loading) before the highpressure recuperator flow sta tion is created. Initial condit ions are given to the stream including temperature, pressure, mass flow ra te, fueltoair ratio, wa terairratio, and fuel type. This flow station is 7a. Now the solver can continue to load the model to the point of the highpressure turbine exit flow station. Th is is the point where the bridge is made with the FlowStart element instantiated earlier. Here, a FlowEnd element is created and the state of the flow exiting the highpressure turbine is stored in th is element. The flow station here is 7b. Since the flow conditions cannot be directly passed from the FlowEnd element to the FlowStart element, the solver is given the task of iterating on a ll the flow station 7 PAGE 34 20 parameters until the conditions match in both elements. To make this happen the user sets up five variables, which NPSS considers i ndependents, to iterate on until their five counterpart constraints, whic h NPSS deems the dependents, are satisfied. These five independent variables are listed as: stagnati on temperature and pre ssure, mass flow rate, fuelairratio, and waterairratio. The constraints are generally written as equa tions that must be satisfied for solver convergence to be recognized. One exam ple of a dependent constraint from the FlowStartEnd element is given below in NPSS syntax. Dependent dep_P{ eq_lhs = "Fl_I.Pt"; eq_rhs = "Fl_O.Pt"; autoSetup = TRUE; } The constraint variable is dep_P. The left hand side of the equation is set equal to the stagnation pressure of the flow enteri ng FlowStartEnd, and the ri ght hand side is set equal to the exiting stagnation pressure. This constraint is added to the solver along with four others corresponding to the variables listed above. Fi gure 32 shows the schematic representation of the procedur e that was just described. Thermodynamic Properties Package Chemical Equilibrium with Applications (CEA), obtains chemical equilibrium compositions for predefined thermodynamic states. Two thermodynamic state properties must be known for the rest to be calc ulated or obtained fr om table subroutines. This requires two input files: PAGE 35 21 1. Thermo.inpContains thermodynamic property data in least squares coefficients. These data can be used to calculate referencestate mo lar heat capacity, enthalpy, and entropy at a given temperature. 2. Trans.inpContains the transport property coefficients for the species CEA uses the Gibbs freeenergy minimi zation method to calculate chemical equilibrium at each state point Chemical reaction equations are unnecessary when using the freeenergy minimization method and chemi cal species can be tr eated individually. For a detailed descriptio n of the theory and methods used in CEA please see reference [25]. CEAFlowstations are responsible fo r passing constituent and state point temperature and pressure from NPSS to CEA. Solver The NPSS solver is responsible for bringi ng the model to a conve rged solution. In order to accomplish this task the user must choose which engine parameters to constrain. Constrained parameters are called model depen dent variables. To satisfy the dependent variables a set of independent variables mu st be defined and iterated. This iterative approach to find a solution begins with an in itial state guess, and th at is subsequently refined until a satisfactory solution is found. The solver solution method is a quasiNew ton method. For a simple description assume there is only one constraint on the model, and as a result only one variable to iterate to meet it. The initial value of the i ndependent variable is user specified, and with that the initial value of the variable desired to be constr ained can be found. Then the independent variable is pertur bed a certain amount chosen by the solver and a new value for the dependent variable is found. The solver now must decide if this new value of the variable to be constrained is a satisfactory one. A partia l derivative error term is calculated, PAGE 36 22 I I I ItValue Independen tValue Independen alue DependentV alue DependentV ErrorTerm 1 1, (3.1) where I denotes the iteration number. If it is outside the ac ceptable tolera nce region, the process is begun again. With a system of cons traints a Jacobian matrix would be created to hold all the error terms. The new pert urbation terms would be calculated from the previous Jacobian matrix: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1IndV IndV DepV DepV IndV IndV DepV DepV IndV IndV DepV DepV JI I m I m n I n I I I I I I (3.2) Here there are n number of independe nts and m number of dependents. The Jacobian can be related to the in dependent variables with the expression I I Ix F x J (3.3) where Ix is the matrix composed of the i ndependent perturbation values. The Ix F matrix holds the values of th e dependent constraints at the th I iteration. The new independent values may now be calculated with the following: I I I Ix F J x x 1 1. (3.4) With 1 Ix now determined, 1 Ix and 1 Ix Fcan be found and a new Jacobian matrix created. The process continues until the Jacobian error va lues are within the acceptable tolerance limits of the solver. PAGE 37 23 Figure 31 Example NPSS engine model [19] PAGE 38 24 HPT Recuperator NPSS Code/Element Representation of Above Engine State HPT FlowStart Recuperator Recuperator FlowEnd HPT FlowStartEn Simplified Code Representation 7a 7b 7a 7b 7temp Figure 32 State 7 of HPRTE engine cycle PAGE 39 25 CHAPTER 4 CYCLE CONFIGURATIONS AND BASE POINT ASSUMPTIONS Before discussing the thermodynamics rela tionships used in the analysis, it is necessary to give an overview of the cycles from a systems standpoint. This analysis compares the design point performance of thr ee engine configurations. The first engine is a simple cycle gas turbine engine (SCGT). It has been modeled to predict the performance of the production engine, ETF40B, which powers the military LCAC for the United States Navy. The SCGT will be co mpared to two variations of the HPRTE engine, the base HPRTE and a variant that us es refrigeration capacity to cool the high pressure compressor inlet stream. Major Model Features When comparing engine systems, it is c onvenient to understand the major features of each model. Listed in Table 4.1 is a br eakdown of the features that distinguish the engine configurations from one another. The HPRTE cycles are two spool engines with exhaust gas product heat recupe ration. Both are semiclose d and have compressor intercooling. The HV Efficiency has additio nal cooling capacity provided by a vapor absorption refrigeration system (VARS). Th e additional cooling enables exhausted water vapor to be condensed and collected for us e elsewhere or for injection after the high pressure compressor. PAGE 40 26 Flow Path Descriptions & Schematics Simple Cycle Gas Turbine Engine Model As mentioned earlier, the SCGT is a simp le, open cycle gas turbine engine. For this analysis the model with have a total of fi ve flow stations (Figure 41). State 1 is the inlet stream. From State 1 to 2 the flow undergoes an adiabatic compression process in compressor, C1. From State 2 to 3 there is a constant area, premixed burner, B. The process from State 3 to 4 is an adiabatic expansion process through the turbine, T1. Mechanical work generated by the turbine dr ives the compressor and supplies power for the ship propellers or lift fans. State 5 is th e fuel flow station. JP4 was the fuel of choice for this analysis because it is widely us ed in industry and has a high availability. High Pressure Regenerative Turbine Engine Efficiency Model Figure 42 is a schematic re presentation for the Efficiency and Power modes of the HPRTE cycle. The Power mode concept inco rporates a flow splitter to bypass some exhaust from the high pressure turbine and send it directly to the low pressure turbine. Initially, the Power mode had been considered for this project to give additional boost capabilities to the low pressure spool. Ho wever, while completing the analysis it was determined that the Efficiency mode pred icts sufficient boost for the system and any additional boost pressure woul d result in a turbocharger design outside of modern technology limits. There are 14 states for the basic HPRTE (t he Power mode has 16). Air enters at State 1 and undergoes an adiabatic compression process in the low pressure compressor, LPC, before reaching State 2. Next, the fres h air from State 2 is combined with the recirculated exhaust gas products from State 10 in an isobaric, adiabatic mixing process. The resultant State is 2.9. Now the combin ed flow passes through a sea water cooled PAGE 41 27 heat exchanger called th e main gas cooler (MGC). The effectiveness, pressure drop, and process fluid temperature are all given. The resulting State is 3.0. After the gas has been cooled it goes through another adiabatic compression process in the high pressure compressor, HPC. The resultant State 4 has the maximum system pressure. Following the HPC there is a heat recuperation proce ss (RHX) in which hightemperature exhaust gas product stream preheats the State 4 flow resu lting is State 5. From state 5 to 6 the gas is mixed with fuel and ignited in the combus tion chamber, B. A small pressure drop is applied before State 6 to simulate friction lo sses in the combustor. The high pressure turbine inlet temperature, or TIT, was chosen to be 2500Ran acceptable value for a medium size engine. The expansion across the high pressure turb ine, HPT, produces the power to drive the HPC and the net BHP is available power fo r the vessel. State 7 is State 7.11 in the Efficiency mode, and that flow passes through the RHX, rejecting heat to State 4. The only flow splitter for the Efficiency cycl e comes at State 9. Here, a user defined recirculation ratio determines the mass flow rates at State 7.15 and 10. State 10 recombines with fresh air flow from the LPC ex it. State 7.2 is also State 7.3 in Efficiency mode. The final expansion process across the lo w pressure turbine, or LPT, exhausts to the environment at State 8. High Pressure Regenerative Turbine Engine with Vapor Absorption Refrigeration System Efficiency Model Figure 43 is a schematic representation of the HV Efficiency. The HPRTEVARS modes differs from the HPRTE m odes only by the addition of two heat exchangers in the flow path after the reci rculated gas products combine with the fresh inlet air at State 2.9. The gene rator (GEN) and the evaporator (EVP) are two of the heat PAGE 42 28 exchangers that make up part of the VARS. A schematic of the VARS is also included as Figure 44 for clarification. It was not mode led since the scope of this analysis only included modeling the gas path side of the co mbined cycle system. The point of water collection is shown on the figure, as well. The computational model of this cycle required the addition of a separator elem ent to perform the water extraction. The separator is discussed in Chapter 5, Thermodynamic Modeling and Analysis. Notice that the HPRTE cycles require an iterative solution method to obtain model convergence because of the semiclosed operation. For the first iteration of the engine cycle an initial guess for the temper ature at State10 is given. Simple Cycle Gas Turbine Engine Design Assumptions and HPRTE Cycles Base Point Assumptions The SCGT is a medium size, opencycle ga s turbine engine modeled after the ETF40B. The ETF40B has a seven stage axia l compressor followed by a single stage centrifugal compressor yielding an overall pre ssure ratio of 10.4 [Robert Cole]. The nominal output shaft horsepower is 4000 SHP. Turbine inlet temperature was assumed to be 2500R. Turbomachinery efficiency in formation was provided by Dan Brown of Brown Turbine Technologies. All other engine design parameters were chosen based on conservative current technology limits. See Table 42 for complete details. The base point HPRTE component paramete rs are listed in Table 43. The same methodology used to determine the design parameters for SCGT was considered when deciding baseline design values for the HP RTE engine cycle conf igurationssize and technology limitations were applied. There were material and computational limitations that existed and needed to be accounted for to preserve the fidelity of the engine model. They are as follows: TIT PAGE 43 29 maximum was 2500R, hot side recuperato r inlet temperature maximum was 2059R, turbocharger pressure ratio maximum was 7.5, and HPC inlet temperature minimum was 491R (NPSS limitations). Table 41 Comparison of majo r configuration features SCGT HPRTE Efficiency **** HV Efficiency ****** Model Features Intercooled Compressors VARS cooling Water Extraction Model SemiClosd Turbocharger Pressurized Recuperatored 1 2 3 4 B C1 T1 5 Fuel Air Figure 41 Simple Cycle Gas Turbine (SCGT) engine model configuration PAGE 44 30 Figure 42 High Pressure Regenerative Turbin e Engine model, both efficiency and power configurations represented 7 7.12 7.2 7.3 8 6 5 4 3 2.9 2 1 10 9 7.11 LPC RH X HP C MG C HPT B LPT Fuel Air Sea Water PAGE 45 31 Figure 43 High Pressure Regenerative Turb ine EngineVapor Abso rption Refrigeration System, both efficiency and power model configurations represented 7 7.12 7.2 7.3 8 6 5 4 3 2 1 10 9 7.11 2.91 2.92 2.9 LPC MG C HP C RH X B HPTLPT GENEVP Fuel Air Wate Sea Water HP Refrigerant LP Refrigerant PAGE 46 32 GEN EVP CND CND 2.9 2.91 2.92 3 Pump Expander Figure 44 Vapor Absorption Refrigerati on Cycle with HPRTE flow connections Table 42 Simple Cycle Gas Turbin e engine design point parameters ParameterValue C1 Adiabatic Efficiency0.858 Burner Efficiency0.99 Burner Pressure Drop0.03 Turbine Inlet Temperature 2500R T1 Adiabatic Efficiency0.873 Table 43 Base case model assumptions for HPRTE cycles [3], [26], [27] Paramete r Value Ambient Temperature544.67R Sea Water Temperature544.67R Ambient Pressure14.7 PSI LPC Adiabatic Efficiency0.83 GEN Effectiveness0.85 GEN Pressure Drop0.03 MGC Effectiveness0.85 MGC Pressure Drop0.03 EVP Effectiveness0.85 EVP Pressure Drop0.03 HPC Adiabatic Efficiency0.858 RHXEffectiveness0.85 RHX Pressure Drop State 45 0.04 RHX Pressure Drop State 7.1190.04 B Efficiency0.99 B Pressure Drop0.03 HPT Inlet Temperature2500R HPT Adiabatic Efficiency0.873 Recirculation Ratio3 LPT Adiabatic Efficiency0.87 Fuel Hydrogen to Carbon Ratio1.93:1 PAGE 47 33 CHAPTER 5 THERMODYNAMIC MODELING AND ANALYSIS Chapters 3 and 4 addressed the computational structure of NPSS and the cycle configurations of the models including the design point a ssumptions. While top level NPSS calculations are performed by the soluti on solver, the intermediate operations performed during every iterative pass to calcu late the thermodynamic states are discussed next. Chapter 5 develops the theory for these auxiliary therm odynamic relations that drive the model elements (subroutines). Thes e relations are developed using fundamental thermodynamic concepts. Thermodynamic Elements Heat Exchangers Heat exchangers are an im portant component in HPRTE cycles. The base HPRTE Efficiency model mode has two heat exchangers, MGC and RHX; and the combined cycle, HV Efficiency, has four heat exch anger elements including three for compressor intercooling. Those for the inte rcooling have defined process inlet flow states. Mass is conserved by setting the exit mass flow ra te equal to the entrance mass flow rate. User defined inputs include effectiveness, and 1 0 inP P Let effectiveness be defined as 2 0 1 0 1 1 1 0 1 0 1 1 _ 0 _ 0 min min _ 0 _ 0 max in in p in out in p in in cold in hot p out hot in hot hot p hotT T C m T T C m T T C m T T C m Q Q (5.1) hot pC_ is the hot side specific heat at constant pressure, and min pC is the specific heat of the minimum capacity flow stream. PAGE 48 34 Therefore, 2 0 1 0 1 0 1 0 in in out inT T T T (5.2) The only unknown in Equation 5.2 is 1 0 outT. The capacity of the process fluid is set such that it is always the maximum capacity stream. This ensures that it is not used in the calculation above. The exit pressure is determined using the following equation: 1 0 1 0 1 01in in outP P P P (5.3) Know known are the parameters 1 0 outT, 1 0 outP, and 1 outm The exit state is set. Mixers The mixer is modeled as an adiabatic, cons tant static pressure process. Because there is no consideration given for Mach numbe r effects, the stagnation pressures of the two flows entering the mixer must be identical. This requir es a model constraint be set up by the user for each HPRTE model and satis fied by the solution solver. All HPRTE models have recircula tion mixers which are tasked with combing the recirculated exhaust gas products with fresh air discharged from the low pressure compressor. A mass balance requires: 2 1 in in outm m m (5.4) Assuming adiabatic mixing, the energy balance is as follows: out in in in in outm h m h m h 2 0 2 1 0 1 0 (5.5) Constant pressure mixing implies: out in inP P P_ 0 2 0 1 0 (5.6) PAGE 49 35 Other parameters such as the outFAR and the mass fractions are mass averaged. For example: out in in in in outm FAR m FAR m FAR 2 2 1 1 (5.7) With outh_ 0, outP_ 0, outm and the exit state mass fractions all known, all other thermodynamic properties can be found. Splitter In Chapter 4 the cycle schematics for the HPRTE cycle models showed flow splitting occurring at State 9. To accomplish this feature with a computer model a splitter component must be defined to separates flow into two streams before exhausting to the environment. The recirculation splitter is ta sked with the job of splitting the flow stream on a mass basis after the high temperature rec uperation process (State 9). A portion of the flow is reconstituted w ith fresh air before heading back through the core engine components while the rest is directed to th e low pressure turbin e (LPT) to power the turbocharger. A bypass ratio, BPR, is user defi ned to represent the ma ss basis split of the flow streams. The recirculation splitter inlet state is defined by the following know parameters: inT_ 0, inP_ 0, in totm_, inFAR, inh_ 0, and mass fractions for all species. In general BPR is defined as 1 2 out tot out totm m BPR (5.8) For this application the b ypass ratio is defined as exhausted tot recirc tot circm m BPR_ Re (5.9) PAGE 50 36 recirc totm_ is the mass flow rate recirculat ed and mixed with fresh air. exhausted totm_ is the mass flow rate that passes directly to th e low pressure turbine and be exhausted from the system at State 8. The user also reserves the option of applyi ng flow pressure drops to either or both of the split streams, but for this analysis the splitter is modeled as an isobaric process. Similarly, the process is adiabatic, as there is no heat transfer. The mass fractions are unchanged; therefore, the exit st ate of each flow is defined. in out outP P P_ 0 2 0 1 0 (5.10) in out outT T T_ 0 2 0 1 0 (5.11) Water Extractor The water extraction component is onl y present in the HV Efficiency configuration. Because water vapor is pres ent in the recirculated mixed gases and the cooling capacity of the three heat exchangers is significant to cause condensation to occur in the flow stream, it is desirable to separate the liquid water from the gas flow before the inlet to the high pressure compressor. Th e separation of liquid water from the flow stream is modeled as an isentropic process. The inlet state is completely defined; therefore, liquid O Hm_ 2 and liquid O Hh_ 2 are readily available from CEA. The exit state is defined by first setting the inlet and ex it temperatures and pressures equal. in outP P_ 0 0 (5.12) in outT T_ 0 0 (5.13) Then the exit mass flow rate and enthalpy are set. liquid O H in tot out totm m m_ 2 _ (5.14) PAGE 51 37 liquid O H in outh h h_ 2 0 0 (5.15) The exit state of the water extractor is now defined. Compressors Compressors inlet states are defined with the following parameters passed to the element: inT_ 0, inP_ 0, in totm_, inFAR, inh_ 0, and mass fractions for all species. The performance of the compressor is determined by the following parameters: pressure ratio (CompPR) and adiabatic efficiency (ad Comp ). Exit pressure is determined first with the equation in Comp outP PR P_ 0 0 (5.16) The other thermodynamic parameter, the adia batic efficiency, is used to calculate the exit state point paramete rs in the NPSS Compressor modul e. Define the adiabatic compressor efficiency as in out in ideal out ad Comph h h h work compressor adiabatic work compressor ideal_ 0 0 0 _ 0 __ _ (5.17) Determining the ideal exit state en thalpy is straight forward knowing outP_ 0 and ideal outs_ 0 if ideal out ins s_ 0 0 Since entropy and enthalpy are only functions of temperature; the exit state ideal temperatur e is quickly found along w ith enthalpy. Now, rearrange and directly solve Equation 5.17 for outh_ 0. With the exit pressure and enthalpy know known, a ll exit state thermodynamic parame ters are readily calculated by CEA. The power required by the compressor is also calculated. out out in in Comph m h m W_ 0 0 0 0 (5.18) PAGE 52 38 The power is converted from Btu/sec to HP: HP lbf ft BTU lbf ft WComp1 sec 550 1 778 (5.19) Polytropic efficiency, poly Comp_ is an output parameter calculated from the entrance and exit entropies and pressures. The derivation is as follows: The definition of the polytropic efficiency is dh dhi poly Comp_. (5.20) To arrive at this equation, first consider a reversible form of the energy equation. Since Pdv vdP du dh (5.21) vdP dh Pdv vdP Pdv dh Pdv du Tds ) ( (5.22) Therefore, P dP R T dh dP T v T dh ds (5.23) Solving Equation 5.23 for T dh yields P dP R ds T dh (5.24) For an isentropic process0 ds. Therefore, P dP R T dhi. (5.25) Combining Equations 5.24 and 5. 25 results in the following: P dP R ds P dP R T dh T dh dh dhi i poly Comp _. (5.26) Integrating Equation 5.26 from the in let state to the exit state yields: PAGE 53 39 Comp in Comp in out Comp in Comp poly CompPR R s s PR Rlog log_ 0 0 _ (5.27) Turbines Turbines provide the power to drive the compressors as well as the net power for the ship propellers and lift fans (if LC AC is the mission). The NPSS model Turbine element requires a defined entrance st ate to include such parameters as inT_ 0, inP_ 0, in totm_, inFAR, inh_ 0, and mass fractions for all species pr esent. As was the case with the compressors, the performance of the turbin e components is determined by the defined parameters: pressure ratio (TurbPR) and adiabatic efficiency (ad Turb ). NPSS defines TurbPR differently than most turbomachinery refe rence texts. Here it is defined as: out in TurbP P PR_ 0 0. (5.28) The exit state can be determined by first applying the turbin e pressure ratio. Turb in outPR P P_ 0 0. Turb in outPR P P_ 0 0 (5.29) As was the case for the compressor, outh_ 0 is the other thermodynamic parameter necessary to in order to define the exit state. The turbine adiabatic efficiency is defined as: ideal out in out in ad Turbh h h h work turbine ideal work turbine adiabatic_ 0 0 0 0 __ _ (5.30) The power generated by the tu rbine is also calculated. out out in in Turbh m h m W_ 0 0 0 0 (5.31) PAGE 54 40 This power is converted to horsepower as it is in the compressor. The polytropic efficiency is an output parameter calculated using the same approach described in the compressor section. The final equation is given below. Turb in Turb Turb in Turb in out poly TurbPR R PR R s s/ 1 log / 1 log_ _ 0 0 (5.32) Burner The Burner element is a constant volume bur ner. The entrance state is completely defined; those parameters include: inT_ 0, inP_ 0, in totm_, inFAR, inh_ 0, and mass fractions for all species. Also specified are the b and burner inP P_ 0 The exit stagnation pressure, outP_ 0, is found with the equation: in in outP P P P_ 0 0 01 (5.33) outT_ 0 must be specified by the user in order to determine the incoming fuel flow rate, fuelm. In order to determine the exit state, the burner subroutine makes an initial guess for the fuel flow rate, 1 fuelm, using a straightforward energy balance. (5.34) The model assumes a lower heating value, RQ, of 18400 Btu / lbm. It also assumes a constant specific heat, pC, of 0.285 Btu / lbmR. The inlet conditions and the first fuel flow rate iteration, 1 fuelm, are then passed to CEA from the NPSS subroutine calcBurn. CEA calculates the burner exit state point including: equilibrium composition and the new burner exit temperature iteration, 1 0 outT. The burner exit conditions (1 0 outT,outP_ 0, out in out in air fuelT T T m m_ 0 0 0 1285 0 / 18400 PAGE 55 41 outFAR outWAR, outh_ 0, and mass fractions for all spec ies) are then passed back to calcBurn where the burner efficiency is applied to determine the actual burner exit temperature, act outT_ 1 0. in in out b act outT T T T_ 0 0 1 0 1 0 (5.35) Then, act outT_ 1 0 is used to determine the next fuel flow rate iteration, 2 fuelm, with the energy balance described above (E quation 5.34). An error ch eck is performed on the fuel flow rate values every iteration to de termine when the loop can be exited. Tolerance Error m m mfuel fuel error fuel_1 2 (5.36) Once fuelm is determined, the exit state point is completely defined. Sensitivity Analysis No formal optimization program was used for this project; instead, each engine cycle model was roughly optimized manually st arting from base case assumptions listed in Chapter 4. The sensitivity analyses were performed on the SCGT and HPRTE Efficiency models to determine the influences of particular design parameters. The HV Efficiency model was not included in these studies because the results would mirror those for the HPRTE Efficiency model analysis Two primary dependent parameters investigated in the sensitivity analysis in clude thermal efficiency and specific power. The thermal efficiency is defined as: R fuel thQ m W (5.37) where RQ is the lower heating value of the fuel and Wis the net power. PAGE 56 42 The specific power is defined as: in airm W SP_ (5.38) Influence coefficients are use to quantify the sensitivity of resultant parameters as they relate to perturbed input parameters. The dimensional influence coefficient is defined as Parameter Input Resultant (5.39) To relate the magnitudes of influence coeffi cients to one another, they must be nondimensionalized is required. This is accomp lished by dividing the perturbed value by its base case quantity: Value Base Parameter Input Parameter Input Value Base Resultant Resultant (5.40) Such an example of a nondimensional influe nce coefficient is given below. Here, the HPC inlet temperature is perturbed from its base value and the resultant change to th is expressed in the following form. A value of 1 suggests that a 1% perturbation in HPC inlet temperature results in a 1% change in th In this way the sensitivity of input parameters is determined. base base th thTin HPC Tin HPC ) (_ (5.41) PAGE 57 43 CHAPTER 6 RESULTS AND DISCUSSION The results and discussion of the analysis performed using the cycle code NPSS are presented in Chapter 6. The first section in this chapter, Cycle Code Comparison, compares results from the spreadsheet c ode (used by Boza [22]) and the NPSS program for one operating point of the HPRTE Efficiency model. Next, sensitivity studies were performed on the SCGT and HPRTE Efficiency cycles and influence coefficients were calculated. Engine model results are give n and compared to derived thermodynamic expressions. Finally, plots and tables are presented that compare the performance parameters of the three engine configurations. Cycle Code Comparison Before initiating the sensitivities studies, it is important to benchmark the NPSS program and compare results of one model c onfiguration to those results obtained from running a proven cycle analysis program. On e operating point for the HPRTE Efficiency model was chosen for the comparison, and the results from the two cycle codes are presented in Table 61. The third column in the table lists the absolute differences of the two data sets parameters in percentages. Agreement of the data between the two codes is high; values for th OPR, HPT exit temperature (TET), in HPCT_, and exhaustT are all within acceptable limits. The SpPw calculated by the spreadsheet model was 12.5% higher than that calculated in NPSS. There are three possible reasons for the disparity in the output values. First, it is impossible to implicitly balance the low pressure spool PAGE 58 44 specific work; therefore the turbine specific work is never properly matched to the specific power of the compressor. This could very easily result in a different airm. Two, different fuels are used in the codes. Th e hydrogentocarbon ratio is 1.93 in NPSS and 2.03 in the spreadsheet code. Because the fu els are different, the curvefit coefficients used to calculate the enthalpies for the spread sheet code could be different than the ones used by NPSS. Sensitivity Analysis Simple Cycle Gas Turbine Engine Model Of particular interest for this project is the sensitivity of the opencycle engine thermal efficiency and specific power to va riations in turbine inlet temperature and ambient temperature. Figures 62 through 64 show the results of the analysis. Unless otherwise specified the followi ng parameters remained consta nt throughout the analysis: ambient temperature is 544R, TIT is 2500 R, and nominal power output is 4000 BHP. Figure 62 displays the thermal efficiency as a function of the overall cycle pressure ratio (OPR). The TIT variations have a str ong influence on the outcome of the thermal efficiency value. Raising TIT has a positive effect on th which also implies that the total heat added to the system has been re duced since the power output remains steady. Let th be defined by the following relationship: R fuel thQ m W (6.1) Since, RQ, the fuel lower heating value, is constant; fuelm has to decrease in order to reduce the total heat added to the system in order to raise the th For all run cases in the SCGT analysis, variations in th are the direct result of variations in fuelm. PAGE 59 45 To better understand th e relationship between th and the input parameters in this sensitivity study, the following derivation has been included. The State numbers in the equations correspond to those for the SCGT cy cle schematic given in the Configurations chapter (Figure 41). Figure 61 shows the comparison between the theoretical expression below, the run data from NPSS, a nd ideal thermal efficiency expression for an air standard Brayton cycle available in a ny thermodynamic text. The derived expression predicts a curve with higher efficiency than the NPSS output; this is expected because the pressure losses in the combustor are not accoun ted for, as it was assumed that the turbine pressure ratio is equal to the compressor pressure ratio. That and the fact that the specific heat ratio ( ) was averaged for the entire cycle may explain the discrepancy between the results from NPSS and the derive d curvefit expression. There are several assumptions exercised in this derivation to develop the final expression in terms of only the following parameters: 01 03T T, PR ad Turb and ad Comp They are as follows: fuelm is much less than airm T h h constantpC ratio of specific heats, constant PR P P P P 04 03 01 02 Beginning with the definition of thermal efficiency: PAGE 60 46 R fuel air p R fuel thQ m T T T T m C Q m W 01 02 04 03. (6.2) Factoring out 01T gives: R fuel air p thQ m T T T T T T T m C 101 02 01 04 01 03 01. (6.3) Now the adiabatic turbomachinery efficiencies derived in the previous chapter may be rewritten in the form: 1 101 02 1 _T T PRad Comp (6.4) 1 11 04 03 PR T Tad Turb (6.5) Solving the compressor Equation 6.4 for 01 02T T and Equation 6.5 for 04T yields the following two expressions. 1 1 11 01 02 PR T Tad Comp (6.6) 1 1_ 1 03 04 ad TurbPR T T (6.7) Substituting Equations 6.6 and 6.7 into E quation 6.3 gives the following expression: PAGE 61 47 R fuel ad Comp ad Turb air p thQ m PR PR T T T T T m C 1 1 1 1 11 _ 1 01 03 01 03 01 (6.8) The denominator can be rewritten in terms of 01 03T T, PR, and ad Comp The energy balance of the combustor is as follows: 03 03 02T C m T C m m m Q T C mp air p fuel air fuel R p air (6.9) Now, solving for R fuelQ m gives: 01 02 01 03 01 02 03T T T T T C m T T C m Q mp air p air R fuel (6.10) Substituting in the expression for 01 02T T in Equation 6.6 results in the following: 1 1 11 01 03 01 PR T T T C m Q mad Comp p air R fuel (6.11) The final expression for th is 1 1 1 1 1 1 1 11 01 03 1 _ 1 01 03 01 03 PR T T PR PR T T T Tad Comp ad Comp ad Turb th. (6.12) As mentioned above, the ideal thermal efficien cy for an air standard Brayton is also plotted on Figure 6.1. PAGE 62 48 1 _1 1 PRideal th (6.13) Simple Cycle Gas Turbine Engine Model Sensitivity Analysis Figure 6.2 is a plot of the thermal effici ency as a function of OPR with separate curves for TITs. These curves peak at certain OPR values; c ontinuing to increase pressure ratio will continue to decrease the heat added per unit mass to the cycle, however, the thermal efficiency will drop becau se the recuperator capacity to exchange heat is being neutralized. When this happens th e thermal efficiency begins to drop again. The influence coefficients were determined for Figure 6.2. The base case engine chosen had a TIT of 2500R with an OPR of 24. These numbers imply that changes in TIT effect greater change in th than changes in OPR. One ot her point to note is the fact that no matter what the TIT is for the engi ne model, the maximum thermal efficiency always occurs when the compressor power is about twice as large as the net BHP. 898 0 ) (_ base base th thTIT TIT 0322 0 ) (_ base base th thOPR OPR Figure 63 displays specific power sensitivity to changes in TIT over a pressure range from 8 to 18. The drop in specific pow er for increasing OPRs can be explained as follows. Consider the engine as a control vo lume that produces a constant power output. Ignoring the small effects to thermal effici ency that increasing OPR produces, the heat energy added to the engine must be constant. However, as OPR increases the heat rate per unit mass added in the combustor drops. Th erefore, more air must be brought into the combustor to maintain the total heat energy input required to pr oduce a constant power engine output. The other trend visible has to do with increasing TI T and its influence on PAGE 63 49 specific power. Drawing two cycles, with different TITs, on the same TS diagram clearly demonstrates this phenomenon. Influence coefficients were calculated usi ng the base case parameters from the last section. Specific power is more affected by changes in TIT than changes in OPR. In fact, there is 1 order of magnitude differen ce between the two parameters. The negative sign quantifies the drop in specific power with increasing OPR that was discussed earlier. 36 3 ) ( base baseTIT TIT SpPw SpPw 339 0 ) ( base baseOPR OPR SpPw SpPw Figure, 64 examines operating temperature variation as it influences cycle thermal efficiency and OPR. The OPR curves are nearly linear and the slopes become more negative as OPR increases. Notice that the th ermal efficiencies approach 40% as ambient temperature falls to 509R. Cold day operati on translates to good thermal efficiency for the SCGT. Notice the effect of changing OPR for the case when ambientT is 572R. The higher OPR curves collapse on each other impl ying that thermal efficiency maximums are at or near their peak values here, a nd any further boost in OPR drops the thermal efficiency off the other side of the curve that would appear if this was a three dimensional figure. For example, at ambientT 554R, the maximum thermal efficiency corresponds to an OPR of 24. A further boost to an OPR of 28 results in a reduced thermal efficiency. The influence coefficients corresponding to Figure 64 for thermal efficiency and specific power are calculated assuming the base case cycle where ambient temperature is 518R and OPR is 24. PAGE 64 50 669 0 ) (_ base base th thTamb Tamb 0682 0 ) (_ base base th thOPR OPR The thermal efficiency coefficients s uggest that drops in ambient operating temperature impact thermal efficiency more so than variations in pressure ratio. This implies that OPR is a secondary issue if the engine is being designe d with the intent to optimize thermal efficiency. 76 1 ) ( base baseTamb Tamb SpPw SpPw 2676 0 ) ( base baseOPR OPR SpPw SpPw The specific power influence coefficients quantify the negative impact on specific power when either ambient temperature or OPR is increased. Of course, the effect of ambient temperature is much more significan talmost an order of magnitude greater. High Pressure Regenerative Turbine Engine Efficiency Model Before beginning the sensitivity analysis of the HPRTE Efficiency, it is important to examine the validity of the data output from NPSS. To accomplish this task an expression has been derived to test the valid ity of NPSS output. After the derivation is complete, the resulting expression is nor malized; and it is onl y a function of the following parameters: 01 2 07T T, LPPR , ad LPC and ad LPT The plotted NPSS data should agree with the derived expression. The ten points in Figure 65 represent ten distinct converged operating poin ts from NPSS runs. The standa rd deviation of the set of points is 0.00398, signifying close conf ormity with the derived thermodynamic expression. The development uses the following assumptions: PAGE 65 51 fuelm<< airm T h h constant pC Ratio of specific heats, constant LPPR P P P P 08 2 07 01 02 The development begins with the adiabatic e fficiency expressions for the low pressure compressor and turbine: 1 101 02 1 _T T LPPRad LPC (6.14) 1 11 08 2 07 LPPR T Tad LPT. (6.15) Solving Equation 6.14 for 01 02T T yields 1 1 11 01 02 LPPR T Tad LPC. (6.16) Now, introducing the power balanc e for the turbocharger gives 08 2 07 01 02) ( T T C m m T T C mp fuel in p in (6.17) And simplifying Equation 6.17 using the as sumptions provided above results in 08 2 07 01 02T T T T (6.18) PAGE 66 52 Rearranging Equation 6.18 and solving for 101 02 T T produces 01 08 01 2 07 01 021T T T T T T. (6.19) Setting Equation 6.16 equal to Equation 6.19 gives 01 08 01 2 07 1 _1 1 T T T T LPPRad LPC (6.20) Solving Equation 6.20 for 08T produces 1 11 01 2 07 01 08 LPPR T T T Tad LPC. (6.21) Next, rearranging Equation 6.15 and solving for 08T yields 1 11 2 07 08 LPPR T Tad LPT. (6.22) Setting Equation 6.21 equal to Equation 6. 22 results in the following expression: 1 1 1 11 01 2 07 01 1 2 07 LPPR T T T LPPR Tad LPC ad LPT. (6.23) Rearranging, 1 1 1 11 1 01 2 07 01 2 07 LPPR LPPR T T T Tad LPT ad LPC. (6.24) Then dividing both sides by 01 2 07T T yields the final expressi on plotted in Figure 65. PAGE 67 53 01 2 07 1 1 01 2 071 1 1 1 1 T T LPPR LPPR T Tad LPT ad LPC 6.25 High Pressure Regenerative Turbine Engine Efficiency Model Sensitivity Analysis Figure 66 shows low pressure spool pressu re ratio (LPPR) variation influences on the high pressure compressor pressure ratio (HPPR) as ambient temperature varies. For these run cases the TIT and th e nominal shaft power output we re held constant at 2500R and 4000 BHP, respectively. There are three important features re presented by Figure 66. First, there is the in teraction between LPPR and H PPR. Monotonically increasing LPPR results in a similarly increasing HPPR Examining the raw data shows that that mass flow rate drops with increasing LPPR; this drop in mass flow rate requires a greater expansion on the high pressure turbine to produce the nominal power output. The second trend to notice is that raising ambient temp erature results in raising HPPR. Raising ambient temperature decreases air density wh ich in turn causes a decrease in mass flow rate. With less mass flow rate to the core components, the heat added per unit mass to the combustor must be increased in order to main tain the constant power output. The way to accomplish this task with an HPRTE engine is to increase the HPPR. Increasing HPPR drops the hot side recuperato r inlet temperature and as a result the combustor inlet temperature drops, too. Thermal efficiency increases with incr easing HPPR until HPPR is about 5.1. Then, any further increasi ng of HPPR results in a drop in thermal efficiency. Figure 66 can be used to find the operati ng lines for a properly designed HPRTE. An HPRTE with wastegating capabilities w ould have operating curves of constant PAGE 68 54 HPPR; therefore, the horizontal grid line s on the Figure 66 coul d be called operating curves as well. Moreover, the line corresponding to a HPPR of 5.1 would represent the highest thermal efficiency operating curve. The influence coefficients for Figure 66 are listed below. Th e base case has an ambient temperature of 528R and a LPPR of 6.0. ambientT and LPPR variations both have significant resultant effects on HPPR. Operationally speaking, ambientT is related to airm which can cause large changes to the specific power of the system. 63 1 ) ( base baseLPPR LPPR HPPR HPPR 15 6 ) ( base baseTamb Tamb HPPR HPPR Figure 67 shows cycle thermal efficiency se nsitivity to TIT variation for a range of HPPRs. The analysis holds R, ambient temperature, output shaft horse power, and all component efficiencies consta nt. NPSS convergence is difficult to achieve if HPPR is changed manually by the user; instead, to eff ect change in HPPR, the LPPR is controlled by the modeler. As LPPR was increased, the model solver reduced fr esh air flow rate to the engine. The mass flow rate reduction ca used the HPPR to rise for the same reason discussed in the previous sect ion. Figure 66 shows that the thermal efficiency peaks very close to an HPPR of 5.1. Along a curv e, TET and the stoichiometry change because R is held constant. The influence coefficients for th and SpPw were produced by making perturbations around the base run case where TIT was 2500R and HPPR was 5.12. 847 0 ) (_ base base th thTIT TIT 0106 0 ) (_ base base th thHPPR HPPR PAGE 69 55 The interpretation of these influence coe fficients suggests that changing TIT by 1% causes a 0.847% change in th The second coefficient was calculated with data taken from the right side of the plot wher e HPPR is monotonica lly increasing and th continues to decrease. The small coefficient value s uggests that a large change in HPPR has only limited effect on th This is expected when the infl uence coefficient is calculated near an optimum th point on the curve. Below, no tice that TIT perturbations cause significant resultant changes to the value of specific power. 59 2 ) ( base baseTIT TIT SpPw SpPw 318 0 ) ( base baseHPPR HPPR SpPw SpPw Figure, 68 shows the importance with respec t to thermal efficiency of reducing the HPC inlet temperature for HPRTE engine cycles. Sensitivity to circBPRRe is shown and its value is varied from 2.0 to 3.5. Those pa rameters held constant for the analysis are as follows: output BHP, ambientT, TIT, LPPR, all turbomachinery efficiencies, and the sea water temperature. The HPC inlet temperat ure was varied by changing the effectiveness of the main cooler. The trend toward highe r thermal efficiencies for lower HPC inlet temperatures is the same phenomenon seen in Figure 64. A lower inlet temperature to the high pressure core results in an increase in predicted thermal efficiency. Examination of the model data used to produce Figure 68 shows that as HPC inlet temperature drops, HPPR increases. As a result the temperatur e change across the HPT increases and the mass flow requirements drop. This in turn mean s that the fuel flow requirement is less. As shown by Equation 6.1, the drop in fuel flow directly affects thermal efficiency since PAGE 70 56 power output is constant. Lower circBPRRe helps thermal efficiency because TIT must be maintained at 2500R. The more inert combus tion products that are mixed with fresh air act to drive down TIT making it necessary to burn more fuel to keep TIT constant. However, higher recirculation boosts specific power as less fresh air is required to produce the desired power output. The ultima te choice is the desi gnersif weight and compactness are important, circBPRRe would be maximized. However, on a naval vessel, weight might not be the para mount consideration. The influence coefficients for th and SpPw are calculated using the base case circBPRRe of 3 and a HPC inlet temperature of 622R. 58 1 ) (_ base base th thTin HPC Tin HPC 0610 0 ) (_ base base th thR R 66 3 ) ( base baseTin HPC Tin HPC SpPw SpPw 624 0 ) ( base baseR R SpPw SpPw The influence coefficients based on variations to circBPRRe help to quantify the effects on thermal efficiency and specific power that were discussed above. Moreover, reducing the HPC inlet temperature boosts bot h thermal efficiency and specific power. This is an observed behavior in recuperated gas turbine engines. Figure 69 displays the thermal efficiency sensitivity to pressure drops in the coolers. To obtain the curves below, HPT ex it temperature variations were created by the modeler. This was done in the same manne r as it was for the Figure 67. LPPR was manually controlled to effect change in HP C pressure ratio which caused the HPT exit temperature to change. PAGE 71 57 The general trends are consistent with th e results of Figure 67. The curve of Figure 67 corresponding to that of a TIT of 250 0R is the same as the curve in Figure 69 for a cooler P P of 3%. There the HPT exit temp erature is 1884R. The propensity to see a lowered thermal efficiency when the cooler P P is raised has a straightforward explanation. Increasing cooler P P results in a drop in the OPR of the cycle. Since the net output power remains constant mass flow must be increase d. This in turn causes a rise in fuel flow rate and a drop in thermal efficiency. Influence coefficients for cooler P P and HPT exit temperature are listed below for the base cycle case where cooler P P is 3% and HPT exit temperature is 1884R. Specific power influence coefficients are include d. The results show that neither cooler P P nor HPT exit temperature affect signif icant change in thermal efficiency. However, the specific power is positively influenced by decreasing HPT exit temperature. 0258 0 / ) / (_ base base th thP P P P 0617 0 ) (_ base base th thTexit HPT Texit HPT 0407 0 / ) / ( base baseP P P P SpPw SpPw 86 1 ) ( base baseTexit HPT Texit HPT SpPw SpPw Figure 610 considers specific power sensitivity to HPC adiabatic efficiency. For an engine with constant power output and TIT, rais ing TET also results in core mass flow increasing. That is because a higher low pressure recuperator inlet temperature drives the combustor inlet temperature up. The effect of driving that temperature up is similar to what happens for SCGT when OPR is increased. While the total heat added to the engine PAGE 72 58 may be remain almost constant, the heat a dded per unit mass drops off as combustor inlet temperature rises. Consequently, the mass fl ow coming into the combustor must go up. The result is a drop in specific power. The other noteworthy trend here is the positive effect on specific power that comes from rais ing HPC adiabatic effi ciency. Raising HPC adiabatic efficiency decreases the power re quirement of the HPC thereby increasing the specific power of the cycle. Influence coefficients are considered for a base engine with HPC adiabatic efficiency of 86 % and HPT exit temperature of 1883R. Both thermal efficiency and SpPw influence coefficient are given. Co mpare these results with the influence coefficients for the cooler P P discussed above. The ad Comp has a stronger effect on the performance of the cycle than does P P 06 1 ) (_ _ base ad Comp ad Comp base th th 74 1 ) (_ base ad Comp ad Comp baseSpPw SpPw Figure 611 is a sister plot to Figure 610. It descri bes the same specific power trends, however, now they are in terms of HPC pressure ratio (H PPR). HPT adiabatic efficiency (ad Turb ) is varied to show specific power sensitivity to this parameter. The expectation for high ad Turb to result in an improved speci fic power is met. From a thermodynamic standpoint, higher ad Turb means a greater temperature drop across the turbine for the same HPPR. Therefore, less mass flow is required to produce the same powerresulting in a b oosted specific power. PAGE 73 59 Influence coefficients for SpPw and th were calculated from the base cycle case where ad Turb was 87% and HPPR was roughly 5.1. Note: since HPPR is an output, it can not be explicitly set. The coefficient values imply significant influence of ad Turb on th and SpPw. Similarly, notice that the coe fficients calculated based on HPPR variation are very close to those same coe fficients calculated for Figure 67 when TIT was the sensitivity parameter. In fact, there is less than a 1% difference between the values. 0105 0 ) (_ base base th thHPPR HPPR 46 1 ) (_ _ base ad Turb ad Turb base th th 316 0 ) ( base baseHPPR HPPR SpPw SpPw 36 2 ) (_ base ad Turb ad Turb baseSpPw SpPw Figure 612 displays exhaust gas temp erature sensitivity to OPR with TIT variations included. Cycle c onstants included: output BHP, LPPR, ambient temperature, R, and all component efficien cies except for MCG effectiveness. Since LPPR was held constant, MCG effectiveness was varied to eff ect HPPR change. The results indicate that exhaust gas temperature is not sensitive to ei ther OPR or TIT varia tion. This should be expected in an intercooled recuperated system The heat exchangers act to damp exhaust temperature variations that may result from parametric tweaking. The influence coefficients further illustrate this phenome non. The base case cycle had an OPR of 24 and a TIT of 2500R. The computed valu es being small and negative imply that PAGE 74 60 significant manipulation of TI T or OPR is necessary before any change in exhaust temperature is noticed. 0683 0 ) ( base baseTIT TIT Texhaust Texhaust 0201 0 ) ( base baseOPR OPR Texhaust Texhaust Figure 613 examines the Turbo impact on th as it relates to HPPR. Here, the parameter driving convergence will be LPPR. This means that LPPR is controlled by the modeler and both, LPPR and HPPR, will be va rying. Most noteworthy about Figure 613 is that Turbo alone does not significantly affect th The influence coefficient affirms this assertion. Figure 613 likewise gives a clear indication that an HPPR of 5.1 produces the maximum th this optimum HPPR value agrees with the earlier optimum predicted in the plot of thermal efficiency ve rses HPPR with TIT sensitivity. 0228 0 ) (_ base Turbo Turbo base th th Figure 614 is the last figure of the sensit ivity analysis for the HPRTE Efficiency cycle, and it examines LPPR variations and their effect on thermal efficiency. Thermal efficiency sensitivity to TIT perturbations has previously been analyzed for Figure 67. However, this plot is useful in that it gives optimum LPPRs for particular TITs. Particularly interesting is the curve for a TI T of 2500R since this is the base and design optimum TIT. A quick regard of the curve reveals that the best LPPR is about 6.2. That value is high but within the limits of si ngle stage centrifugal compressor technology. Taking a look at the influence coefficien t suggests that perturbing LPPR does not PAGE 75 61 significantly cause change to the resultant, th Again, this is most likely because the influence coefficient was evaluated near a design optimum and the curve was flat. 0645 0 ) (_ base base th thLPPR LPPR Table 62 summarizes the results of the sensitivity analysis. The perturbed parameters are listed in the left hand colu mn and a value between 1 and 3 (1 being the most important) was assigned to indicate th e degree of importance that a particular parameter had on the resultant in the top row. Below are the definitions for the values assigned to the sensitivity parameters listed in summary (Table 62). 1: 1% fluctuation from parameter pr oduces >1% fluctuation in resultant) 2: 1% fluctuation of parameter produ ces between 0.1% PAGE 76 62 consideration for military vessels, an exhaust gas temperature comparison will be included and discussed. Next, performan ce comparisons will be made considering different air and sea water temperatures. Th e last table will list the performance details for the optimized engine confi gurations side by side. Figure 615 provides a clear indication of the thermodyna mic advantage that the HV Efficiency cycle enjoys over the other two cycles in the comparison. The HPC inlet temperature of the HV Efficiency engine was maintained at 509R by the refrigeration system. Contrast that against the HPC in let temperatures of the HPRTE Efficiency engine. The results reveal that the HV Efficiency HPC inlet temperature was between 99107R below that of the HPRTE Efficiency. Table 63 highlights key featur es of Figure 615. Consider ing the results, it is easy to make a case for the HV Efficiency engi ne configuration. It has the highest max th by 17.1% over the SCGT and 17.2% over the sta ndard HPRTE without refrigerator. Its mean th is 44.2% which indicates that the curve is very flat. This implies that the HV Efficiency design point is not significantly sensitive to the OPR choice; therefore, existing, off the shelf turbomachinery com ponents can be used to save on capital investment costs. Moreover, the mean th for HPRTE Efficiency is 3.08% higher than that of the SCGT configuration, indicating that the HPRTE Efficiency configuration is also less sensitive to OPR choice than SCGT. Th e second data point for SCGT on Table 63 is the case where the engine is designed for optimum specific pow er (SCGT SpPw cycle mode). Here, the th is only 33.4%a full 10.2% less than the maximum design th for the HPRTE Efficiency cycle. PAGE 77 63 Figure 616 compares SpPw performance characteristics for the three cycle configurations. Here it can be shown that a sizable advantage is enjoyed by the HPRTE cycles over the SCGT. Since the three cycles have the same output BHP requirements, this implies that the HPRTE Efficiency and HV Efficiency engine cycles operate at much reduced airm levels. This disparity can be attr ibuted to the three main differences between the HPRTE and SCGT cycles: exhaus t gas recirculation, intercooling of the compressors, and recuperative he ating before the combustor. Closer examination of the two HPRTE engine configurations reveals that compressor intercooling boosts sp ecific power signifi cantly by itself, especially at lower OPRs. This can be shown from an examinati on of the run data for an OPR of 14.5. The HV Efficiency cycle has a cal culated specific power of 560 lbm HPsec (units are industry standard) compared to the HP RTE Efficiency specific power of 458 lbm HP sec for the same OPR. That computes to a specific power increase of 22.2% for the HV Efficiency over the standard HPR TE Efficiency. Table 64 further illustrates that gap in specific power between the tw o HPRTE engine cycles and the standard SCGT. Now notice the divergence of the SCGT cu rve from the HPRTE curve. The SCGT mass flow rate requirement increases as OPR increases in order to maintain constant power BHP output. This is because even though the heat added per unit mass drops the total heat input must remain nearly unc hanged to produce the same power output. Meanwhile, increasing the OPR for either HP RTE cycle improves specific power because the recuperator has less availa ble heat to drive up the combustor inlet temperature. Reviewing the analysis for Figures 610 and 611 may provide additional clarity. PAGE 78 64 Figure 617 shows the operating exhaust ga s temperatures for various OPR design points for the three engine conf igurations. There are three fe atures to the plot that are worth noting. First, as expected, the SCGT exhaust gas temperature drops in a weak exponential manner as the design OPR increas es. The ETF40B engine was designed to optimized specific power, and it had an OPR of 10.4. Assuming the SCGT model is a good representation of the ETF40B engine, it im plies that its exhaust gas temperature is about 1580R. The second point brought to light by Figure 617 is the fact that the HPRTE cycles have constant exhaust temper atures for a broad range of design OPRs. Third, the HPRTE Efficiency cycle has lo wer exhaust gas temperatures than the combined cycle HV Efficiency. The reason fo r this is that for the same OPR, the HV Efficiency has a lower LPPR than the HPRTE Efficiency, and less expansion across the LPT means the exhaust gas temperature will be higher. Following that logic suggests that the presence of a VARS unit actually rais es the exhaust gas temperature slightly. Table 65 is a list of the maximum exhaus t gas temperature cases for each cycle with their corresponding OPR va lues from Figure 617. The mean exhaust temperatures are also given to indicate the flatness of the plotted curves for the HPRTE cycles. Figure 618 compares th values of the three engine configurations under different ambientT operating conditions. While LPPRs were he ld constant, OPRs could not be held constant because of NPSS operational limita tions on the HPRTE models discussed above for Figure 67. The parabolic shape of the HPRTE engine curves resembles the thermal efficiency plots produced in the sensitivity analysis for the HPRTE Efficiency model. Similarly, notice the linear trend of the SCGT as ambient temperature drops. Eventually, the HV Efficiency and SCGT curves will in tersect at an ambient temperature of 491R PAGE 79 65 (32 F). The most likely operational scenario for the HV Efficiency will be in a desert environment where the environment temperat ures are above 544R (85F). The engines will also be performance rate d at or above 518R (59F). At 518R the HV Efficiency th is 14.0% higher than the SCGTs th Moreover, above 547R (88F), the th of the HPRTE Efficiency surpasses th at of the SCGT. Above 547R mean th for the HPRTE Efficiency engine is 36.9% compared to 36.1% for the SCGT. Extreme Operating Conditions Four extreme operating cases were chosen for this examination of how the engine configurations would perform in the severest of environments. Ambient temperature and sea water temperature were the dependent inputs. Two extreme cases were chosen for each dependent input resulting in a total of four operating casescold day/cold water, cold day/warm water, hot da y/cold water, and hot day/warm water. NPSS limited the ability to compare the engine cycles with constant OPRs. While the LPPRs for the engine configurations were chosen from approximated design points maximizing thermal efficiency from the analysis in the last sec tion, it is necessary to let mass flow rates and HPPRs float to obtain convergence from the solution solver. The OPR for the SCGT remained constant at 24. OPRs are listed in the Table 66. Notice that for the 569R day, the OPRs for the HPRTE engine cycles are very high. High temp erature days decrease the air density and NPSS drops the mass flow rate s as a result. This in turn requires the HPRTE cycles to increase their pressure ratios to maintain constant power output. Case 1 is the cold day with warm sea wa ter condition. Thes e conditions loosely represent night operations in a dry desert climate. A key comparison for this case includes the th values for the HV Efficiency and SCGT cycles. Table 66 shows that PAGE 80 66 the th for the SCGT model is higher than that of the HV Efficiency cycle. This operating point represents a case described during the discussion of Figure 618 when ambient temperature drops to the point where the th values of HV Efficiency and SCGT converge. That analysis showed that if the ambient temperature curves were extended down to 489R, the curves of the SCGT and HV Efficiency would eventually meet. Another key observation from case 1 data is the wide bridge between the specific power values for the HPRTE cycles in comp arison to the SCGT. The HPRTE Efficiency configuration enjoys a 104% improvement in specific power over the SCGT. This theme runs through the whole analysis, and as the operating conditions get warmer the disparity becomes more pronounced. Case 2 is the cold day/cold water temp erature condition. In a North Atlantic mission, conditions similar to these might exis t. Cold water operating points improve the th and specific power of the HPRTE engi ne cycles by improving compressor intercooling. The most significant example is in the change of the th of the HPRTE Efficiency engine between case 1 and 2. It increases by 13.2% and achieves its maximum value for any of the four operati ng points examined. From a specific power standpoint, the HPRTE Efficien cy cycle bests the other tw o configurations in case 2 beating the HV Efficiency by 17.3% and the SCGT by 168%. Unaffected by the drop in water temperature, the th of the SCGT continues to hold st eady at a sporty 40.1%. The argument for choosing the HV Efficiency cycle streng thens under case 2 operating conditions because it displays the highest th of the three configurations at 40.9%. Case 3 is the hot day/hot s ea water temperature condition. This operating point is characteristic of a desert day scenariothe most likely mission conditions for the ETF PAGE 81 67 40B and its replacement. Hot day desi gn points drive up predicted specific power performance values for the HPRTE engine models The cause of this is described in the introduction to this section. From a thermodynamic standpoint the HV Efficiency outperforms the other two configurations. Here, the th of the HV Efficiency cycl e is 20.4% better than HV Efficiency and 23.5% better than SCGT. The specific power of the HV Efficiency cycle is 12.1% higher than HPRTE Efficiency and 358% higher than the SCGTs. The rise in th from case 1 to 3 for the HV Efficiency is directly indicative of the ambient temperature rise which caused a notewort hy rise in OPR from 10.2 to 30.7. The th rise constitutes an 11.3% jump between the case points 1 and 3. Case 4 is an unlikely operating pointwhen ambient temperature is high and water temperature is very cold. A summer day in the North Atlantic is the closest example of this condition. Here the th of the HV Efficiency cycle bests the HPRTE Efficiency by 15.3% and the SCGT by 24.1%. If the e ngines were design based on specific power alone, the HPRTE Efficiency is a considerable threat to the HV Effi ciency engine mode. Its specific power of 675 HPsec/lbm, respectivel y, is the highest of the three engines for case 4. However, this is an improbabl e engine design with an OPR of 55.4. High Pressure Compressor Inlet Temperatu re Comparison for HV Efficiency Model Up until this point in the analysis the HP C inlet temperature for the HV Efficiency cycle has been held at a conservative 509R. This section compares the same engine at two different HPC inlet temperatures, 509R and 499R, respectively (Table 67). In other words, careful consider ation was taken to ensure th at the HPPRs for both model PAGE 82 68 cases were the same. This was a time intensive consideration that could not be used for other parts of the comparison studies. Other parameters held constant include: nominal output BHP, TIT, ambientT, all turbomachinery values, and R. The results of the analysis conclude that there are performance improvements that result from decreasing HPC inlet temper ature but they are not stunning. The th increases by 1.56% and the specific power increases by 1.62% for the lower HPC inlet temperature case. LPPR is also 5.14% lo wer when HPC inlet temperature is 499R. Essentially, from a computer model handling standpoint, the lower HPC inlet temperature is achieved by lowering the LPPR slightly. This causes OPR to be 5.45% less, as well. Additionally, there is very little influence on exhaustT which drops only 2R when HPC inlet is lowered 10R. In summary, the performance parameters are positively affected by decreasing HPC inlet temperatures, but it is unclear whether or not the difference is significant enough to warrant imp lication. Moreover, the refr igeration capacity used to cool the HPC inlet could be used elsewhere in applications not examined in this analysis. Final Design Point Parameter Comparison While the extreme operating conditions sect ion provides key insi ght into offdesign point performance of the three engine cycles it is necessary to compare the cycles with their optimized design parameters at the mo st likely operating condi tion. Two versions of the SCGT cycle are comparedthe SCGT Efficiency is the open cycle optimized for maximum thermal efficiency and the SCGT SpPw is the open cycle optimized for maximum specific power. For this analysis the ambient temperature and the sea water temperature were both set to 544R. The e ngine output requirement was unchanged, at 4000 BHP. TIT was held to a maximum of 2500R. TET was restricted below 2059R. PAGE 83 69 The turbocharger pressure ratio was limited to 7.5. Table 68 results are consistent with the comparative analysis plots. From a thermodynamic stance, the HV Effi ciency engine cycle has a higher design point thermal efficiency besting the SC GT Efficiency by 20.6%, the SCGT SpPw cycle version by 34.7%, and the HPRTE Ef ficiency engine cycle by 21.0%. The SCGT Efficiency thermal efficiency has an expected thermal efficiency that is 10.2% higher than the SCGT SpPw engine configuration. When comparing the specific power results of the HPRTE cycl es the performance gap isnt quite as large. For that parameter, the HV Effici ency has a predicted specific power that is only 6.08% better than the HPRTE Effici ency. The SCGT SpPw cycle has a predicted specific power that is 13.2% greater than the SCGT Efficiency configuration. TET for the HV Efficiency is 110R less than the HPRTE Efficiency providing some leeway in material selection. Equivalence ratios are all within th e reasonable limit (0.9 was maximum allowable). As the equivalence ratio va lue approaches a value of 1, the oxygen concentration in the gas is being lim ited. Limiting the excess oxygen helps to reduce the soot and harmful emissions production. Both HPRTE engine cycles have R values of 3 or above. This directly affects equivalence ratio. Increasing R limits th e fresh air dilution into the combustion chamberthe net effect is an increase in the equivalence ratio value. The extra cooling capacity of the HV Effici ency cycle causes water vapor from the combustion products to condense to liquid. That mass flow rate has been included in the table, as well. It is also convenien t to relate that value to the mass flow rate of fuel used by the engine. The mass basi s ratio of fuel burned to water extracted from the flow path was 1.13. Note: for simplicity, the ambient air was considered dry with a %RH of 0. Exhaust gas temperatures for both HPR TE cycles are approximately 500R less than the exhaust temperature of the SCGT Efficiency configuration and nearly 800R less than the exhaust temperature of the SCGT SpPw conf iguration Naval forces are concerned with IR signatures produced by engine exhaust coming from their ships, the 800R difference represents a significant stealth advantage over the SCGT. Moreover, reduced exhaust temperatur es suggests that air density is higher; and as a result, the exhaust duct size can be smaller. PAGE 84 70 Table 61 Cycle codes comparison: N PSS verses spreadsheet code for HPRTE Efficiency model data run. All temperatures are in R. SpreadSheet HPRTE Eff.NPSS HPRTE Eff. A BS % Difference 37.0%37.2%0.54 (HPsec/lbm)51959312.5 OPR32.032.20.621 TET188018800.00 R3.303.300.00 Equivalence Ratio0.8270.8947.51 5445440.00 LPPR6.256.250.00 HPPR5.295.310.377 6326142.93 TIT250025000.00 7908011.37 All Temperatures are in R th SpPw ambientT in HPCT_ exhaustT 0.35 0.4 0.45 0.5 0.55 0.6 0.65 1520253035 OPRThermal Efficiency Ideal Eta Derived Eta NPSS Figure 61 Thermal efficiency comparison is pl otted with respect to OPR. NPSS results (with turbine in let temperature (TIT) set to 2500R) are compared to the derived and the ideal Bray ton cycle expressions. PAGE 85 71 0.3 0.32 0.34 0.36 0.38 710131619222528313437 OPRThermal Efficiency TIT = 2500R TIT = 2400R TIT = 2300R TIT = 2200R SCGT Figure 62 Thermal efficiency vs. OPR with sensitivity to TIT 100 120 140 160 180 200 68101214161820 OPRSpecific Power (HPsec/lbm) TIT = 2500R TIT = 2400R TIT = 2300R TIT = 2200R SCGT Figure 63 Specific power vs. OPR with TIT sensitivity PAGE 86 72 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 500520540560580 Ambient Temperature (R)Thermal Efficiency OPR = 28 OPR = 24 OPR = 20 OPR = 16 OPR = 12 SCGT Figure 64 Thermal efficiency vs. ambi ent temperature with OPR sensitivity 0.90 0.95 1.00 1.05 1.10 4567 LPPRRHS of Equation 6.25 Model Data Points HPRTE Efficiency Figure 65 Demonstrates agreement between NPSS and developed theory that describes the low pressure spool PAGE 87 73 0 1 2 3 4 5 6 7 8 500520540560580 Ambient Temperature (R) HPPR LPPR = 6.4 LPPR = 6.0 LPPR = 5.5 LPPR = 5.0 LPPR = 4.5 HPRTE Efficiency Figure 66 High pressure spool pressure ra tio (HPPR) vs. ambient temperature with low pressure spool pressure ratio (LPPR) sensitivity 0.33 0.335 0.34 0.345 0.35 0.355 0.36 0.365 0.37 0.375 33.544.555.566.577.58 HPPRThermal Efficiency TIT = 2500R TIT = 2450R TIT = 2400R TIT = 2350R HPRTE Efficiency Figure 67 Thermal efficiency vs. HPPR showing sensitivity to TIT PAGE 88 74 0.26 0.28 0.3 0.32 0.34 0.36 0.38 600650700 HPC Inlet Temperature (R )Thermal Efficiency RecircRatio = 2.0 RecircRatio = 2.5 RecircRatio = 3.0 RecircRatio = 3.5 HPRTE Efficiency Figure 68 Thermal efficiency vs. HPC inlet te mperature for recirculation ratio sensitivity 0.35 0.355 0.36 0.365 0.37 0.375 17501825190019752050 TET (R)Thermal Efficiency Cooler dP/P = 3% Cooler dP/P = 4% Cooler dP/P = 5% Cooler dP/P = 6% HPRTE Efficiency Figure 69 Thermal efficiency vs. turbine ex it temperature (TET) w ith cooler pressure drop sensitivity PAGE 89 75 380 420 460 500 540 580 620 17501825190019752050 TET (R)Specific Power (HPsec/lbm) HPC_eff = 0.86 HPC_eff = 0.85 HPC_eff = 0.84 HPC_eff = 0.83 HPRTE Efficiency Figure 610 Specific power vs. TET for HPC efficiency sensitivity 425 475 525 575 625 345678 HPPRSpecific Power (HPsec/lbm) HPT_eff = 0.88 HPT_eff = 0.87 HPT_eff = 0.86 HPT_eff = 0.85 HPRTE Efficiency Figure 611 Specific power vs. HPPR for HPT efficiency sensitivity PAGE 90 76 800 802 804 806 808 810 812 1722273237 OPRExhaust Temperature (R) TIT = 2350R TIT = 2400R TIT = 2450R TIT = 2500R HPRTE Efficiency Figure 612 Exhaust temperature vs. OPR for TIT sensitivity 0.335 0.34 0.345 0.35 0.355 0.36 0.365 0.37 0.375 2.54.56.58.5 HPPRThermal Efficiency Turbo Eff = 0.7138 Turbo Eff = 0.6970 Turbo Eff = 0.6804 HPRTE Efficiency Figure 613 Thermal efficiency vs. HPPR for turbocharger efficiency sensitivity PAGE 91 77 0.33 0.34 0.35 0.36 0.37 0.38 44.555.566.577.5 LPPRThermal Efficiency TIT = 2500R TIT = 2450R TIT = 2400R TIT = 2350R HPRTE Efficiency Figure 614 Thermal efficiency vs. LPPR for TIT sensitivity Table 62 Summary of the HPRTE E fficiency sensitivity analysis Perturbed Parameter Specific PowerHPPR TIT213 TET31 1 11 11 11 31 HPPR32 LPPR31 OPR3 R32 Cooler 33 Resultant Parameter P ambientT in HPCT_ ad Comp ad Turb Turbo th exhaustT PAGE 92 78 Table 63 Comparison of the thermal efficiency maximums and their corresponding overall pressure ratios (OPRs) Configuration OPR HV Eff.45.0%23.60.442 HPRTE Eff.37.232.20.368 SCGT37.324.00.361 SCGT SpPw33.410.4 Parameter max th mean th 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 5101520253035404550 OPRThermal Efficiency HV Eff. HPRTE Eff. SCGT Figure 615 Engine cycles comparis on of thermal efficiency vs. OPR Table 64 Comparison of the specific power maximum values and their corresponding OPRs Configuration OPR HV Eff.66535.0586 HPRTE Eff.62442.6565 SCGT18010.5155 Parameter SpPw units are industry standard (HPsec/lbm) maxSpPw meanSpPw PAGE 93 79 100 200 300 400 500 600 700 51015202530354045 OPRSpecific Power (HPsec/lbm) HV Eff. HPRTE Eff. SCGT Figure 616 Engine cycles comp arison of specific power vs. OPR Table 65 Comparison of exhaust temperatur e maximum values for the three engine configurations Configuration OPR HV Eff.85549.0832 HPRTE Eff.80542.6799 SCGT16608.001360 Parameter Temperatures have units of R max exhaustT mean exhaustT_ PAGE 94 80 600 800 1000 1200 1400 1600 1800 5101520253035404550 OPRExhaust Temperature (R) SCGT HV Eff. HPRTE Eff. Figure 617 Engine cycles comparison of exhaust temperature vs. OPR 0.34 0.36 0.38 0.4 0.42 0.44 0.46 500520540560580600 Ambient Temperature (R )Thermal Efficiency HV Eff. HPRTE Eff. SCGT Figure 618 Engine cycles comparison of th ermal efficiency vs. ambient temperature PAGE 95 81 Table 66 Engine cycles comparison fo r four extreme operating conditions CaseSpPwOPRSpPwOPRSpPwOPR 1489R544R0.39741110.20.34139017.80.40119124.0 24894990.40943610.80.38651223.70.40119124.0 35695440.44265930.70.36758842.00.35814424.0 45694990.44467032.30.38567555.40.35814424.0 Operating PointHV EfficiencyHPRTE EfficiencySCGT Engine Type All Specific Power calculations have industry standard units of HPsec/lbm th th th ambientT waterT Table 67 High pressure compressor (HPC) inlet temperature comparison for the HV Efficiency engine model Design Point Parameter 509R 499R 45.0%45.7% (HPsec/lbm)629639 OPR23.622.3 TET17681769 R3.003.00 Equivalence Ratio0.7990.799 (lbm/sec)6.366.26 (lbm/sec)0.3060.306 545545 LPPR3.53.32 HPPR7.377.35 509499 TIT25002500 837835 Temperatures are in R airm liquid O Hm_ 2 th SpPw ambientT in HPCT_ exhaustT in HPCT_ PAGE 96 82 Table 68 Final performance design point co mparison for the engine configurations Design Parameter SCGT Eff.SCGT SpPwHPRTE Eff HV Eff. 37.3%33.4%37.2%45.0% (HPsec/lbm)159180593629 OPR2410.432.223.6 TET1330158018801770 RN/AN/A3.303.00 Equivalence Ratio0.2400.3030.8940.799 (lbm/sec)25.222.26.756.36 (lbm/sec)N/AN/AN/A0.306 544544544544 LPPRN/AN/A6.253.50 HPPRN/AN/A5.317.37 544544614509 TIT2500250025002500 13301580801837 Temperatures are in R Engine Configuration airm liquid O Hm_ 2 th SpPw ambientT in HPCT_ exhaustT PAGE 97 83 CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS Conclusions The analysis performed for this thesis pr oject consisted of parametric studies to establish design point parameters, sensitivity studies to examine specific parameter/resultant interactions, and desi gn point comparisons of the performance characteristics of the three gas turbine engine configurations. The engine models were developed using a steadystate, incompressibl e thermodynamic approach with the engine cycle code NPSS developed by NASA Glenn Re search Center. The mission requirement for the engine was produce continuous nomin al power output of 4000 BHP. To refrain from investing capital in exotic material de velopment for the engine components, the TIT maximum was limited to 2500R and the hot si de recuperator inlet temperature was constrained to not exceed 2059R. The turboc harger pressure ratio was designed to not exceed a value of 7.5this was a desi gn limitation determined for singlestage centrifugal compressors. Moreover, N PSS and CEA do not have thermodynamic properties for solids; therefore, to prevent icing before the in the HPRTE engines, the high pressure compressor (HPC) inlet temper ature minimum value was 492R (33F). The dependent variables optimized during the parametric performance comparison of the engine cycles are listed in their order of significance: th specific power, and exhaust gas temperature. PAGE 98 84 The conclusions are as follows: Comparison output from a NPSS run case of the HPRTE Efficiency matched well with output from a similarly configured e ngine cycle using the spreadsheet code. Those parameters whose values from NPSS agreed with the counterpart values from the spreadsheet code included: th OPR, TET, in HPCT_, and exhaustT. The specific power outputs from the two code s did not match well. Their values differed by 12.5%. The difference in these ou tput values can be associated to three causes. The operational handling of the spreadsheet code was such that it was impossible to model the HPRTE in the proper turbocharger configuration. Moreover, the codes modeled the engine using different fuels and thermodynamic curvefit equations. For the SCGT sensitivity analysis, the results showed that the cycle thermal efficiency and specific power were both particularly sensitive to TIT and ambientT variations but were not very sensitive to OPR changes. This is not surprising when considering the dominance of the temperat ure ratio in the development of the theoretical thermal efficiency expression in the first section in Chapter 6. The three most noteworthy influence coeffi cients from this section are 36 3 ) ( base baseTIT TIT SpPw SpPw 76 1 ) ( base baseTamb Tamb SpPw SpPw 898 0 ) (_ base base th thTIT TIT Two design points were considered for the SCGT engine configuration. One was optimized for maximum th (SCGT Efficiency ) and the other was optimized for maximum specific power (SCGT SpPw). The SCGT SpPw best predicts the ETF40B design point. The SCGT Efficiency had a predicted th value of 37.3% 10.2% higher than the th predicted for the SCGT SpPw engine configuration. The SCGT SpPw had a predicted specific power of 180 HPsec/lbm13.2% greater than the SCGT Efficiency configuration. HPRTE Efficiency sensitivity analysis wa s performed next. Variations in the following parameters affected the th resultant by a proportional amount: in HPCT_, ad Turb ad Comp and TIT to a lesser extent. Specific power was decidedly sensitive to these input parameters: TIT, TET, in HPCT_, ad Turb ad Comp and Turbo The HPPR was sensitive to th e following parameter inputs: ambientT and LPPR. PAGE 99 85 A byproduct of the sensitivity analysis fo r the HPRTE Efficiency was that the optimized pressure ratios for the two s pools were determined. The optimization was based on maximizing th rather than specific power. The turbocharger pressure ratio was chosen to 6.25, and th e HPPR was chosen to be 5.31. Exhaust gas temperature (exhaustT) was an important consideration in the engine cycles comparison studies. exhaustT values for the HPRTE cycles were an average of 550R less than the exhaustT values of the SCGT Efficiency design point. When compared to the SCGT SpPw design point, the exhaustT values for the HPRTE cycles were almost 800R less. Cooler exhaus t temperatures directly impact the survivability of the ship. Naval ship s powered by HPRTE engines instead of SCGT engines would have a greatly re duced infrared detection signature. Moreover, an 800R reduction in temperat ure would increase the density of the exhausted gases implying that the exhaust ducting would be smaller in diameter for the HPRTE system. The th values for both HPRTE cycles remain consistently high through a wide operating range of pressure ratio designs. The mean th for HV Efficiency is 44.2% and for HPRTE Efficiency it is 36.8%. The mean th of the SCGT was 36.1%. The HPRTE cycle curves for this part of the an alysis were very flat meaning that the th value is not greatly affected by OPR vari ations. The implication here is that existing turbomachinery components coul d most likely be used to design a production HPRTE system. The four extreme operating cases analyze the performance characteristics of the competing engine cycles headtohead. Many conclusions can be drawn from this section of work. First, the HV Efficien cy has better thermal performance in hot weather than in cold weather. Second, thermal performance of the HV Efficiency is not significantly affected by water temper ature. Third, raising air temperature positively impacts the thermal performa nce and specific power of both HPRTE cycles while negatively affecting both perf ormance characteristics of the open cycle SCGT. Under hot conditions (cases 3 and 4) the HV Efficiency performed with an average thermal efficiency of 44.3%. That is an average of 17.8% higher than the HPRTE Efficiency cycle and 23.7% higher than the SCGT. The effects of decreasing HPC inlet temp erature on a HV Efficiency configured engine were analyzed. The data reveals that there are minor increases (less than 2%) in the performance variables th and specific power when HPC inlet temperature is dropped from 509R to 499 R; however, those increases are not significant enough to make a recommendation for this concept. For their optimized design point pa rameters, the HV Efficiency has a th of 45.0%besting the SCGT Efficiency by 20. 6%, the SCGT SpPw cycle version by PAGE 100 86 34.7%, and the HPRTE Efficiency engine cycle by 21.0%. Thermal efficiency is inversely related to the speci fic fuel consumption. For the same ship platform, the HV Efficiency engines would allow for increased cargo if th e mission range is unchanged. The HPRTE cycles should also be considered if the important design issue is mission range. Having lower spec ific fuel consumption than the SCGT SpPw design point suggests that the HP RTE cycles would exhibit an increased mission range capability if the fuel tank size is a constant parameter. There are significant specific power differe nces between the HPRTE engine cycles and the SCGT. The mean specific power of the HV Efficiency cycle is nearly four times larger than that of the SCGT. Sin ce specific power is di rectly proportional to the area of the ducting in the engine, the co re HPRTE engine would be almost four times smaller than a SCGT of the same power capacity (of course some additional space would be needed to house the VARS unit). Currently, it is unknown if the size and performance tradeoffs would cancel each other. Recommendations An offdesign point analysis shoul d be completed on the engine cycle configurations reported on in this anal ysis because over 93% of naval ship operation time is spent operating at or be low 35% engine power [Landon]. NPSS would be the obvious software choice for th is next step since it has offdesign point modeling capabilities. Moreover, the engine models have already been created in NPSS and the output has been benchmarked to a certain degree. Performance map integration and scaling is a critical compet ency that must be addressed before this next step is taken; and it is unknown how the performance map lookups would affect model computing times. Of cour se, any added sophistication to a model increases the expectation that it will le ngthen the model runtime. Currently, for the HV Efficiency model, the runtime s range from 4 to 12 minutes, depending on the model its constraints. A comprehens ive offdesign study should include range and propeller analysis, as well. Further benchmarking of the re sults of this analysis is a necessary next step to guarantee the accuracy of the work. The accu racy of NPSS is not in question; it was developed by NASA in conjunction wit h leading United St ates aeropropulsion companies. However, checking the fideli ty of the HPRTE models against other thermodynamic cycle codes, such as the c ode created by Jameel Kahn, is a useful next step to give confidence to this work. Furthermore, comparing NPSS model results against experimental test data from the laborat ory demonstrator should be considered. A more robust model would include the VARS unit, at least to the extent that the HPC inlet temperature is set by calculat ions representative of having the VARS unit in the model. Thus far, excess co oling capacity of the VARS has not been addressed, but there are obvious uses for additional refrigeration on a naval ship. PAGE 101 87 Other software modeling programs should be considered for future performance analysis of the power and refrigeration cycles being examined by the University of Florida (UF). One commerci al software package currently being explored by the Energy and Gas Dynamics Laboratory at UF is ASPEN Plus. ASPEN Plus is an industry leader in process flow modeli ng and has proven capabilities modeling gas turbine power and refrigeration cycles Not only can it model design point performance, but offdesign analysis is available. There are other HPRTE layout designs being explored by UF. Even the current test rig in the Energy and Gas Dynamics Laborat ory has a slightly different gas flow path than the HPRTEs in th is analysis. Instead of in troducing the fresh air before the evaporator, the current test engine rig has the air inlet ducted into the entrance to generator heat exchanger of the VARS unit. Since the analysis was done assuming dry ambient air, perhaps more cases should be run on the HV Efficiency to determin e how the added moisture of humid air would affect the water extraction rate. 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[26] Hill, P., and Peterson, C., Mechanics and Thermodynamics of Propulsion, AddisonWesley Publishing Company, Reading, MA, 1992, pp. 173. [27] Turns, S. R., An Introduction to Combustion: Concepts and Applications, McGrawHill Book Company, Boston, MA, 2000. PAGE 105 91 BIOGRAPHICAL SKETCH The author is a native of Flagler Beach, Florida. He earned a bachelor of science degree in aerospace engineering from the Univer sity of Florida in 2004. For the past 2 years he has been a member of the Energy and Gas Dynamics Laboratory at the University of Florida. His graduate emphasis was firmly focused in the thermal sciences with selective coursework including gas turbine propulsi on systems, combustion, and entrepreneurship for engineers. His futu re plans include working in nuclear power generation in Crystal River, FL. 