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'3 NATIONAL ADVISORY COMMITTEE F'OR AERONAUTICS ADVANCE CONFIDENTIAL REPORT i" PHB :MIINARY INVESTIGATION OF SUPERSONIC DIFPSERS AT: Art: ur Kantrowlts and Coleman duP. Donaldson I .*" o :; ... .,*. :.. i.. .. : '.: : i" J iw .: '. . . S. SUMMARY i..: .i . i. 'j; 1 dee leration of air from supersonic velocities S la i sannelsh has been. studied. It has become apparent tha: a normal ahook in the diverging part of the diffuser s' s.pehaibay. necessary for stable flow, and ways of min'i m sing. the intensity of this shook have been developed. : The frfet of various geometrical parameters, especially eantac tion ratio in the entrance region, on the performs A. e of.supersonic diffusers has been investigated. :By the use of these results, diffusers were designed itoehi starting without initial boundary layer, recovered 90 percent of the kinetic energy in supersonic air streams, uai4to a Mach number of 1.85. INTRODUCTION .The deceleration of air from supersonic to subsonic Vicitieas is a problem that is encountered in the design ofhighwapeed rotary compressors and supersonic air intakes. Th&effictency of the supersonic diffusers used to accom plish third deceleration has an important effect on the :performance of these machines. The present study is i Qltaded to provide information upon whioh to design. eflaoient spersonic diffusers for use in cases in which theflow starts without initial boundary layer. S The available .data on supersonic diffusers are very lheager and are reviewedd by Crocco in reference 1. This Sreiew indicates that, in the deceleration of air from supersonia velocities, the totalheed losses are:so large as to: aimpa a seriously the efficiency of machines employing this: rodes.. The experiments reported in reference 1 were primarily daspgned to serve the needs of supersonic wind Stabel, l Ae therefore only diffusers starting with initial boundary layer were considered. CONFIDENTIAL 2 CONFIDENTIAL NACA ACR No. L5D20 FLOW IN A SUPERSOIIODIFFUSER Stability. In a Lavalnozzle the gases start at a low velocity, are accelerated to the velocity of soubiain the converging part of the nozzle, and are accelerated to supersonic velocities in the divergingpart.of th. noathle. The supersonic velocities reached can be calculated approx imately from the isentropicmassflow curve of figure 1 and the geometry of the nozzle. It is well known that, for shockfree flow, experiment is in good agreement with this onedimensional isentropic theory although, since the boundary layer thickens in the diverging part. of thesozsle, the Mach numbers'reached may be a little lower thbat..tWE% ,l values calculated. (For example, see referenc.e'2.) (wf:ih dimensional nozzles can be designed by the PrandtlB3~Aeafn method (reference 3) to give essentially shockfefree s apfl sions, which can be obtained experimentally providdt'.O asf" moisturecondensation effects are present (tefsreneeid"t:40 It might be supposed that the flow in a nozzle designed by the Prandtl*Busemann method could be reversed. atdif proper allowance were made for.boundarylayer dieplmeoftl thickness, a smooth deceleration through the speed. ;. ;:.i ? sound obtained. A flow of this type is, however, uinatefla in the sense that it is unattainable in practice. Consider that a flow of this type has been established. (See fig. 2(a),) In this flow pattern the mass flow per unit area through the throat is the maximum possible for the given state and velocity of the gas entering the diffusers As long as the flow entering the diffuser is supers.eaito,: the entering mass flow would be unaffected by even4taiJ4ai. .stream. A transient disturbance propagated upstreamE:iltdm:: 'the subsonic region would, however, reduce the masa "Itft~ r at least temporarily in the velocityofsound regieozt fIJ. Thus, a disturbance would result in an acduiulation saf:.i:l1 air ahead of the throat. The 'perturbation of the. oritgbjlt isentropic flow produced by this accumulation of alr t:ll9tt.; prevent the mass flow from returning to its initial..mntl imum value; thus, air would continue to accumulate ahead of the throat until the mass flow entering.the:dtffu* i r was reduced. In the case of a supersonic diffuser..immea.se in a supersonic stream as in the experimental arrangemeGq't described later, this would.necessitate the formation :.I ar: a normal shock ahead of thb diffuser and, in other f'r'tg*0 ments, would likewise necessitate drastic changes &snj*h'U'Ii. flow pattern. From the .discussion of the .tear itg,: ,?*ti.": supersonic flows in diffusers given later, it will be *d . CONFIDENTIAL :. .. ." that these changes are irreversible (certainly in the experimental arrangement described later and probably in mbst other arrangements). It therefore appears that isentrople deceleration through the speed of sound in channels is unstable end unattainable in practice. In a series of preliminary attempts to produce an approximation to isentropic deceleration through the speed of sound, it was found that supersonic flow could not be started into diffusers designed to produce this flow. In diffusers with a larger throat area, the normal shock jumped from a position ahead of the diffuser to a position in the diverging part.of the diffuser. Flows of the type shown in figure 2(b), which involve a normal shock in the diverging part of the diffuser, were found to be stable. S Contraction ratio and losses. An important part of the losses in. a supersonic diffuser are associated with the dissipation accompanying the normal shock in the div:erging part of the diffuser. It is therefore important "'~o consider the factors that determineits intensity. As in a Laval nozzle, the position of the shock wave is controlled by the back pressure on the diffuser and moves upstream as the back pressure is increased. When the back pressure forces the shock to a point close to the minimum area of the diffuser, the shock Mach number approaches its lowest value and the associated losses are minimized. The magnitude of these minimum losses depends upon how much the air entering the diffuser is slowed up by the 'time it reaches the minimum cross section. The more the entrance area of the diffuser can be contracted, the lower the :ach number of the normal shock and the greater the efficiency of the diffuser. It is therefore valuable to .npiider what determines the maximum contraction ratio that can be used. (Contraction ratio is defined as the "ratio of the area at the entrance of a diffuser to the area at its minimum section. See fig. 2(b).) In most applications, the establishment of supersonic flow is preceded by a normal shock traveling downstream.,. If this normal shock is to move into the diffuser at a given entrance Mech number and thus establish supersonic flow, the throat of the diffuser must be large enough to permit the passage of the mass flow in a stream tube having an area that corresponds to the entrance area of the diffuser and a total head that corresponds to the value behind a normal shock at the entrance Mach number. Thus, if the throat areahas .minimum value for a given CONFIDENTIAL NAOA 'AR .N. L5DRO CONFIDENTIAL NACA ACR No. L5D20., entrance Mach.number, the Mach'number at the. throat will be close to 1 when there is a normal shock ahead of the diffuser. An approximation"td the contraction ratt.' that produces this condition can be found from conventional . onedimensionalflow theory. The conditions after th4 normal shock are known from the usual normalshock equations and it is necessary merely to find.the stream tube eentrac tion, which increases the Mach numberat the .throat .t'l. Since the mass flow per unit area at th.e. Mach..numbeP.'f 1 ` for a given stagnation temperature is proportional 6; the total head,.the maximum permissible contraction rati IsV.'' equal to the contraction ratio that would be require,.:fa :' an isentropic compression to the Mach number of ,1 (frji'i' the initial supersonic conditions) multiplied by the. totalhead ratio across the normal shock. The maxiamlJ'L theoretical contraction ratio that permits starting of''' supersonic flow is computed in this way in appendix .A and is shownin figure 3. If the throat area were redudWi after supersonic flow had been established or if the ilo' throughthe diffuser were started by temporarily incbansNig the entrance Mach number to a value greater than t&. " design value, a less intense shock and lower losses "mcid ; probably be obtained. In these cases, the lowest limit of the shock intensity would be provided by stability considerations. For diffusers in which the geometry (particularly the throat area) cannot be variad..and in which the.'`per sonic flow cannot be started by temporarily. increa'sfn'g tlh entrance Mach number, the minimumwloss diffusion occuivra with the shock just downstream fron the minimum seclt'dbon.. The .Mach number preceding such a.shock (with isantrp. d. flow assumed) can be found fromthe computed contraf6tiS ratio (fig. 3) and equation (2):of .appendix.A., ~el tdtiBl6 heed loss across a normal shock at this Mech.number, (equation (4), appendix A) is then an approximation to the minimum losses (with boundarylayer losses neglected) in a supersonic diffuser subject to the foregoing'starting restrictions. The performances of diffusers obtained in this way are given in figure 4. . It should be pointed out that these theoretical ' considerations are derived with the tacit assumption thatL conditions in a plane perpendicular to the axis of the'..: channel are constant; that is, onedimensional flow is,"" assumed.. For example, the occurrence.of oblique shocks at the entrance of a diffuser would lightly a4ter thes4i;:. conditions; in'particular, the normal shock.in'the diver tag CONFIDENTIAL.: CONFIDENTIAL NAtA kCRNo. LSD20O CONFIDENTIAL 5 part of the diffuser would have a somewhat reduced intensity and the theoretical efficiency would be some what higher. It is considered, however, that the general features would not be much altered by the departures from onedimensional flow that would occur in diffusers such as those discussed in the experimental part of this report, EXPERIMENTAL TECHNIQUE In order to investigate experimentally the properties of constantgeometry supersonic diffusers, the apparatus shown schematically in figure 5 was designed .and con structed. The settling chamber was connected to a supply of dry compressed air controlled by a valve in such a way that the chamber pressure could be held constant at any desired value, The air left the chamber through inter changeable twodimensional nozzles that were designed to give parallel flow at various desired Mach numbers. The featheredge tip of the diffuser (fig. 6) was held in the center of, the supersonic jet at the exit of the nozzle. The experimental arrangement was designed to study the operation of supersonic diffusers that started without initial boundary layer. This condition was studied for two reasons: (1) It is the simplest defined boundary layer condition to obtain experimentally, and (2)'it is considered to approximate more closely than any other the boundarylayer conditions that occur at the entrance to supersonic diffusers used in compressors. A long sub, sonic diffuser cone behind the supersonic diffuser tip was provided to complete the diffusion process. The valve behind'the cone was used to control the back pressure in the subsonic portion of the diffuser and an orifice was used to measure the mess flow through the diffuser. The surface in the supersonic diffuser tips was machined steel, whereas the cone in the subsonic portion was rolled and finished heavy sheet steel. In order to compare the efficiencies of the various diffuser combinations tested, two quantities were required: (1) the percentage of the total head that the diffuser recovered and (2) the entrance Mech number at which the diffuser attained this recovery. Because the losses in welldesigned supersonic nozzles are small, the absolute pressure in the settling chamber was assumed to be the total heed before diffusion. CONFIDENTIAL m j ... NACA ACR No, ;]ia, This pressure was measured with a large mercury manometer. The total head after diffusion can be assumed equal to tbh static pressure'at the end bf the subsonic diffuser cone. without appreciable error, inasmuch as the kinetic energy at the end of the cones was of the order of 0.16 percent of the entering kinetic energy. A mercury manometer was... used to measure the difference between the total heads before and after diffusion. These two measurements were sufficient to determine the percentage of total head recovered. The mass flow per unit area and the stagnation con ditions are sufficient to determine the Mach number at. any point. (See equation (2), appendix A.) The Mach number at which a diffuser was operating was determined by measuring the mass flow through the diffuser, which had a known entrance areas, and by measuring the settling chamber pressure and temperature that correspond to stagnation conditions. Two other observations were made. The pressure just inside the supersonic tip of the diffuser was measured to make sure that the shock had passed down the diffuser and that supersonic flow existed in the contracting portion. The flow in the nozzle and into the diffuser was observed with a schlieren system to check visually whether the shock had entered the diffuser. In order to make a test, the nozzle was brought up" to design speed by increasing the pressure in the settling. chamber po to some value that was held constant thtftAjgh out the test. The throttling valve behind the diffuser' cone was open and the shock passed down the .diffuser, if the contraction ratio permitted, and stopped at someplioe in the diffuser cone. The throttling valve was then slowly closed, thus increasing the pressure at the end of the cone pf and pushing the shock upstream to lower and lower Mach numbers. When the shock had been moved upstream as far as possible, that is, just downstream from the minimum section of the diffuser, pf reached its maximum, value. Although pf was increased during this process, the mass flow through the diffuser was not affected be.%uae the flow was supersonic into the diffuser tip, When theI valve was closed farther, the shock wave passed the mini mum section and suddenly moved out in front of the diffqser. CONFIDENTIAL CONFIDENTIAL NJA AiR.N6. 5 20O CONFIDENTIAL 7 .r steass flow immediately dropped (and continued to drop as Jhe valve was closed farther) and the pressure' inside the diffuser tip immediately jumped to a subsonic value. .The results of a typical test are presented in fig .ui: 7. The breaks in the massflow and tippressure curves give an excellent indication'of when the diffuser was operating at maximum efficiency and when it failed to ant as a supersonic diffuser. The slight change in mass flow while the diffuser was operating was due to the fact that the pressure in the settling chamber Varied slightly. from the beginning to the end of the test run. The curves indicate that a given diffuser may have any ,WjaLue of totalhead recovery, up to a certain maximum, depending upon the position of the shock. Therefore, the e' .,bous method of comparing the performance of a number . slo:diffusers is to compare their maximum recoveries. :. RESULTS AND DISCUSSION ',"The primary design parameterof a supersonic diffuser is Its contraction rptio, which determines the minimum K4a0..number.~ which the supersonic diffuser operates and the nounti.of compression that the entering air undergoes before it must.negotiate the normal shock. If the con . traction ratio of a diffuser is increased, the minimum Mach.number at which it operates theoretically increases as shown in figure 3. The minimum Machnumbers at which a number of diffusers were observed to operate and the Mach numbers at which they first failed to operate are shown in figure 3. The points so plotted give excellent agreement with the theoretical contractionratio curve. As was pointed out previously, the effect of contrac tioa ratio uoon the performance of a supersonic diffuser should be approximately as shown in figure 4. The observed performances of three diffusers with different contraction ratios are plotted in figure 8. The effect of contraction ratio is very similar to the approximate theoretical results shown in figure 4. The indicated discrepancy betw.ween experimental and theoretical results is probably chiefly due to losses in the subsonic portion of the diffuseer.. ,. Aftdr, the contraction .ratio of a supiersonic diffuser Shas been:fixed according to the minimum Mach number at CONFIDENTIAL NACA ACR No. L5~iE : which it must operate, two other parameters the entraiob cone angle and the exitcone angle may be considered :f Owing to the difficulty of measuring the exact entrance angles .on the small diffusers tested, the data evaluating the effect of the entrancecone angle arenot" considered quantitative and are not presented herein,*'./ The trend observed, however, was that the larger the entrancecone angle, the better the performance of tht . diffuser. Further experiment is needed to determine the. optimum entrancecone angles although, for the three diffusers of figure 8, the entrancecone angles are probably so close to the optimum that no large gain inh recovery could be expected from a change in this paramef~r . In the diffusers tested, the internal shape was faired@  a smooth curve between the entrance cone and the exit n0i. The curve was close to a circular arc and started ve9r nSter the leading edge of the entrance cone. Two diffusers of equal contraction ratio and entrance cone angle but different exitcone angle were tested, The performances of the two diffusers with exitcone angles of 50 and 30 are plotted in figure 9. The diffuser With an exitecone angle of 30 was found to give consistently higher recoveries. As is pointed out in reference 14 the' boundary layer.is thick after a normal shock and th*efl06 the pressure recovery in the subsonic cone must be s~tW"~1' to prevent separation. The slightly different shepe.t .. the performance curve of these diffusers when compa*bd: with the other diffusers reported (fig. 8) may be dB to':: the fact that, although the two diffusers correspond ' closely to each other except for exitcone angles, they do not correspond to the other three diffusers. The totalhead recoveries measured in the experiments were transformed into energy efficiencies. The energy efficiency n is defined as the percentage of available kinetic energy recovered in the diffusion process or the kinetic energy of an expansion from the pressure at Vest after diffusion pf to the pressure at the entrance :of the diffuser Pe divided by the kinetic energy of an expansion from the initial chamber pressure po to g.i:. Because no external work is done, the whole process of i.; expansion and diffusion is a throttling process' and the 1J' stagnation temperature To is the same after diffusion CONFIDENTIAL CONFIDENTIAL NAOBath 1,4 Z0 ... *CONFIDSMTIAL 9 as ,a ....t.he settling Sasmber4 The equation for the energy et~o&siseny may be. written. ,p/P' R/c *2op [To T " 20 Sp The symbols are defined in appendix B. When = 5.5, R 5 p/11/35.5 where M is the Mach number of the flow entering the diffuser. The efficiencies obtained by equEtion (1) are compared in figure 10 with the typical efficiencies (converted to efficiency as defined in equation (1))of the work previously done with supersonic diffusers presented by Crocco in reference 1, the efficiency of a normal shock (combined with compression to rest without further loss), and the approximate maximum theoretical efficiency .for constant geometry diffusers previously derived. Figure 10 shows that the normalshock efficiency may be exceeded and that energy recoveries of over 90 percent can be obtained up to a Mach number of 1.85; thus, the results presented for supersonic diffusers in reference 1 are far too conservative for diffusers that have no initial boundary layer. CONCLUDING REMARKS An investigation of the deceleration of air in channels from supersonic to subsonic velocities was conducted. A channel flow involving the shockfree deceleration of a gas stream through the local speed of sound was found to be unstable. A stable flow probably involves a normal shock in the diverging part of the diffuser. The losses CONFIDENTIAL 10 CONFIDENTIAL NACA AOR No. LSDW S . involved in this normal shock can be minimized by makingl the throat area as small as possible for a given entrana.i : Mach number. The maximum contraction ratio that permits starting of supersonic flow at a given entrance Mach number has been calculated and checked very closely by experiment. With the use of these results, diffusers were designed which, starting without initial boundary layer, recovered over 90 percent of the kinetic energy in supersonic air streams up to a Mach number of 1.85. Langley Memorial Aeronautical Laboratory National Advisory Committee for Aeronautics Langley Field, Va. S.. . CONFIDENTIAL NAWA AR W~. L5D20 APPENDIX A CALCULATION OF MAXIMUM PERMISSIBLE CONTRACTION RATIO It can be shown that the mass flow per unit area at Mach number M is = M + 2M) (2) poao 2 where the symbols are defined in appendix B. The isentropic areacontraction ratio from a Mach number M to the local velocity of sound is then (PV)M= (3) (pV)M where pV is computed from equation (2). When air crosses a shock wave, its stagnation temperature is unchanged; hence, the reduction in possible mass flow per unit area, from equation (2) and the perfect gas law, is proportional to the totalhead loss across the shock. The totalhead ratio p3/Po across a normal shock wave can be shown to be P3 (\ 1) Po Y 1 + .M2 1) 0 1 1  Multiplying equation (4) by expression (3) gives the maximum contraction ratio that permits supersonic flow to start in a diffuser. This, quantity is plotted in figure 2. CONFIDENTIAL CONFIDENTIAL NACA ACR.No. L5DiQ APPENDIX B SYMBOLS y ratio of specific heat at constant pressure to specific heat at constant volume p density a velocity of sound V velocity M Mach number Cp specific heat at constant pressure R gas constant T efficiency pe pressure at entrance of diffuser pf pressure at rest after diffusion Po initial chamber pressure p3 total head after normal shock wave '' '' Pd pressure at internal leadingedge of supersanic diffuser (see fig. 7) Md design Mach number of supersonic diffuser; that is, minimum starting Mach number of diffuser with given contraction ratio T entrance angle of diffuser (see fig. 6) 8 exit angle of diffuser b, c dimensions used in .ig. '2 CR contraction ratio (see fig. 2(b)) C CUFIDENTIAL CONFIDENTIAL NACA ACR No. L5D20 S passage area T temperature The subscript o refers to initial stagnation conditions. REFERENCES 1. Crocco, Luigi: Gallerie aerodynamiche oer alte velocity. L'Aerotecnica, vol. XV, fasc. 5, March 1955, pp. 237 275 end vol. XV, fasc. 7 and 8, July and Aug. 1935, pp. 755778. 2. Kantrowitz, Arthur, Street, Robert E., and Erwin, John R.: Study of the TwoDimensional Flow through a ConvergingDiverging Nozzle. NACA CB No. 3D24, 1943. 3. Busemann, A.: Oasdynamik. Handb. d. Experimentalphys., Bd. IV, 1. Tail, Akad. Verlrgsgesellschaft m. b. H. (Leipzig), 1951, pp. 421541 end 447449. 4. Doneldson, Coleman duP.: Effects of Interaction between Normrl Shock and Boundary Leyer. NACA CB No. 4A27, 1944. CON IDENTICAL CONFIDENTIAL I I ri 0'0dS 'oiP mOiJ s9l3o0Tdoa1uasI MOTJ ssVW NACA ACR No. L5D20 Fig. 1 * m C O IC 00 a) a0 o m OC 0 0 i u Ld *0 C 03 a) S .I4 OLi 3 L. ! o i d ed  , *^a bp) NACA ACR No. L5D20 CONFIDENTIAL Sonic boundary NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS (a) Reversed Laval nozzle with isentropic flow (unstable). AT [ Subsonic flow Shock CONFIDENTIAL (b) Stable supersonic diffuser flow. (For circular diffuser = CR, where CR is contraction ratio.) Figure 2. Flow in a convergingdiverging diffuser. Fig. 2a,b NACA ACR No. L5D20 Fig. 3 0 ou I mm 3i Li.) 1 10) 4 0 ot >d ce 0 Id E 4 0 m 1 So i E E0 O 0l I 0 U 4 4m  Sw 0 ooo 0 a0 o0o SH 0)0) 3 og .to o o U (d"mmt+H~rt~trm~ d ~m~U Z RRTRRRRRFRRRRFIf lOU Ir Li.3L hli*r C 4'0 '.i ' NACA ACR No. L5D20 o oa < Od/Ud 'OTIVJ Rj9Aooajp'Be4Te0oj 0 0 100 r#4 ..4 .2 ULa U ow 0 0.E 0 .I B) 0 IC ** 4 Li E 4 0 Si 0 C 14 ra c * 0E 0 : bo CU A LO 5 .. N 4 0 0 L r .C CD EOc I 0 r4 40 0 0 ^ o oJE 3 L E u i l0 1 X5 00X 3 *^e Fig. 4 NACA ACR No. L5D20 Fig. 5 o u I 5 z o o 030 o C 0 8 O 6  *. I I CDD W O W rJ m I t e N 1 t N "I "T' ^ 03 r  I v il 03 0 43 a bo3 I1 bD a H .3 o (d 0) ( .3 *I43 ib \ a 'C \ 107 \\1 t ^1,____^ sn 1  I M ? a NACA ACR No. L5D20 CONFIDENTIAL ,0 t CONFIDENTIAL OZ __ _ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS Figure 6. Interchangeable circular diffuser tips for which performances are shown in figures 8 and 10. These different tips were screwed into a permanent cone having an exit angle of 30. r, entrancecone angle. Fig. 6 n,' NACA ACR No. L5D20 Fig. 7 d/Pd 'dia jasnjjTp Iv ainssajd ****.. %a N cm o O ol H O  3 I _____0 [* 0 (4 d Ea 0 0Q ci E S. HE Q N H 0 0 D. H ) *S. rr N Tu 91 on~     ya NACA ACR No. L5D20 0 co o *0 '1 0d/Jd 'olTqB AJa9oosapveq'TloJ Fig. 8 L, 10 .4 I w 0 00 Sb (" icd O I Le  n a3 O (0 C 4 Sa) C O r.. c o La . bac * *c NACA ACR No. L5D20 O c o' CM d/0d 'OTlISJ tJ9AOOajpBaqtT.elo 0 bo on 0) i1 i * c to 0 0t o o r. o4 t o c a, 0 0 *4 o SI C t0 E a si 3 a, CIi 0 +. +3 'I C Xo .3 Li U C a, 4 Cr Fig. 9 NACA ACR No. L5D20 Fig. 10 0 . 4 m e a( C 0 Ld 3 0 w O 0 01 O 04.l m 3 eco 4im S .' m o c u 4 0 .O 0. U i .. . 0 0 id * o bo C ( * 0 3 d r; l Bc u [S fc * nS; t *^ rl .. JI: UNIVERSITY OF FLORIDA I IIIIII 11 111111 01 3 1262 08105 007 11 
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