Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: P1.50 - Modelling a two-phase thermosyphon for heat transfer in micro CHP
ALL VOLUMES CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00102023/00453
 Material Information
Title: P1.50 - Modelling a two-phase thermosyphon for heat transfer in micro CHP Industrial Applications
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Metcalf, P.
Benstead, R.
Owen, I.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: two-phase thermosyphon
natural circulation loop
 Notes
Abstract: This paper presents a steady-state model for the prediction of mass flow rate and vapour quality created within a 22kW twophase thermosyphon. Thermosyphons of this type are used for heat transfer in micro- combined heat and power (mCHP) applications, and the model presented is being used in the development of a system that can achieve higher thermal throughput. The thermosyphon consists of a finned-coil evaporator and plate heat exchanger condenser, connected with copper tubing. The model is based on mass and energy balances in the evaporator, rising tube, condenser and falling tube, with the total pressure drop around the system in equilibrium with the static head available. Models of each element are used to predict liquid levels and component pressure drops. The separated two-phase flow model is used to predict two-phase frictional pressure drop in the evaporator and rising tube, whilst a model specific to plate heat exchangers is used to predict pressure drop in the condenser. Results are compared with experimental data for water at different heat throughputs for distinct circuit geometries, and are in general agreement with the observed trends - flow rate and pressure drop predictions correlate well with experimental results. Pressure, temperature and flowrate oscillations were observed at low heat throughputs.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
 Record Information
Bibliographic ID: UF00102023
Volume ID: VID00453
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: P150-Metcalf-ICMF2010.pdf

Full Text



7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010



Modelling a two-phase thermosyphon for heat transfer in micro CHP


Paul Metcalf, Russell Benstead and leuan Owen


Department of Engineering
University of Liverpool,
Liverpool, United Kingdom
Email: p aulmetcalf @hotmail.com

Keywords: Two-phase thermosyphon, natural circulation loop

Abstract

This paper presents a steady-state model for the prediction of mass flow rate and vapour quality created within a 22kW two-
phase thermosyphon. Thermosyphons of this type are used for heat transfer in micro- combined heat and power (mCHP)
applications, and the model presented is being used in the development of a system that can achieve higher thermal
throughput. The thermosyphon consists of a finned-coil evaporator and plate heat exchanger condenser, connected with
copper tubing. The model is based on mass and energy balances in the evaporator, rising tube, condenser and falling tube,
with the total pressure drop around the system in equilibrium with the static head available. Models of each element are used
to predict liquid levels and component pressure drops. The separated two-phase flow model is used to predict two-phase
frictional pressure drop in the evaporator and rising tube, whilst a model specific to plate heat exchangers is used to predict
pressure drop in the condenser. Results are compared with experimental data for water at different heat throughputs for
distinct circuit geometries, and are in general agreement with the observed trends flow rate and pressure drop predictions
correlate well with experimental results. Pressure, temperature and flowrate oscillations were observed at low heat
throughputs.


Introduction


In a Combined Heat and Power system (CHP), the
primary energy source is used to produce both power,
from an engine, and heat, by using the heat rejected from
the engine. The same principle applies in Micro
Combined Heat and Power (mCHP) but the scale is
smaller and usually applies to domestic or office
dwellings. Another important difference is that in large
scale CHP systems the primary output is that of the engine
with heat as the by-product, while mCHP is normally
driven by heat demand, with power generation
(electricity) as the by-product. This paper reports on an
aspect of the development of a mCHP system that has
evolved from a domestic hot water / central heating boiler
to include a power unit based on the Rankine Cycle. The
primary heat source is a gas-fired boiler which transfers
its heat through a thermosyphon to the both the heating
system and the Rankine cycle. This paper proposes a
model for this thermosyphon-

Nomenclature


Latent heat of vaporisation
Characteristic length
Mass flow rate
Number of plates
Pressure
Heat transfer rate
Reynolds number
Temperature
Overall heat transfer coefficient
Volume
Characteristic width
Mass fraction
Lockhart Martinelli parameter


kJ/kg
m
kg/s

Pa
W

ag
J/m .K
m
m


Greek letters

a Void fraction
p Density
p Viscosity

Subscript


kg/m3
kg/m/s


Area
Chisholm factor
Specific heat capacity
Pressure difference
Hydraulic diameter
Friction factor
Acceleration due to gravity
Mass flux
Vertical height
Gravitational pressure head


J/kg.K
Pa
m


Due to acceleration
Average
Condenser
Evaporator
Friction
Falling tube
Due to gravity
Into the system


acc
avg
cond
evap
fr
ft
gr
in


9.81 m /s
kg/m2.s
m
Pa







7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

was used to evaluate the friction pressure drop of the two-
phase flow. Thermodynamic constraints were applied to
model the saturation temperature. The model was
compared with experimental data for dielectric working
fluid PF-5060 and was in general agreement with
observed trends. Khodabandeh (2004) also presented a
model for two-phase flow rate and evaporator heat
transfer in a two-phase loop thermosyphon for electronics
cooling. The model was based on mass and energy
balances. Different two-phase flow models were trialled
for evaluating the frictional pressure drop of the two-
phase flow the separated flow model was eventually
selected based on good agreement with experimental data.
Further information is contained within Khodabandeh
(2005) and Khodabandeh and Palm (2000).

The selection of a suitable working fluid is of critical
importance, as density, specific heat capacity, latent heat
of vaporisation and viscosity all significantly influence
the way the thermosyphon behaves. An analysis by El-
Genk and Saber (1998) shows ethanol, acetone, R-11, and
R-113 as working fluids of interest, for evaporator heat
fluxes of 0.99-52.62 kW/m2, evaporator inner diameters
of 6-37 mm, evaporator section height of 50-609.6 mm,
and vapour temperature of 261-352 K. The length and
temperature scales evaluated are smaller than in the
present thermosyphon arrangement.

The modelling of the saturation temperature is also of
importance to the present system Harley and Faghri
(1994) modelled a closed thermosyphon arrangement
using the mass, momentum, and energy balances, and
solving them for the well-separated, counter-current liquid
and vapour flows due to a Nusselt type condensation on
the wall. The maximum temperature variation in their
thermosyphon is only 60C over the test range. They
modelled the saturation temperature as the falling
condensate film interface temperature that drives heat
transfer across the film and the wall. They solved the
vapour momentum balance and the velocity field by using
an estimated pressure field, and used the Clasius-
Clapeyron equation to find the new saturation temperature
corresponding to the new pressure, and applied the
general gas law to find the new vapour density. The
coupling between the heat transfer and the flow geometry
was used to determine the correct saturation pressure and
temperature fields on the interface.

Experimental Set-up

A thermosyphon is a circulating fluid system in which a
heat sink is positioned above a heat source and fluid
buoyancy drives circulation. The present study details a
thermosyphon design that allows not only large, self-
regulated heat throughputs, but also removes the
requirement for a circulating fluid pump.

A circuit schematic is shown in Figure 1.


Latent
Liquid
Liquid only
Liquid vapour
Out of the system
Rising tube
Saturation
Sensible
System
Two-phase
Vapour


Previous Studies

Most of the available literature on two-phase
thermosyphons is concerned with the analysis of wick-
less thermosyphon heat pipes, whose lower and upper
sections serve as the evaporator and condenser,
respectively. The working fluid absorbs heat in the
evaporator section: the vapour rises through the centre of
the pipe to the condenser, and rejects heat by condensing
on the vertical pipe wall. The liquid then flows downward
on the wall under the effect of gravity as a thin film. The
liquid and vapour streams are usually well separated,
although large flow rates are inherently limited by the
counter-current nature of the flow. A thorough analysis of
the working principles of such thermosyphons is found in
Lock (1992).

A need was felt to develop a model for a loop two-phase
thermosyphon capable of transferring a heat load of
between 9 and 22 kW a thermal load utilised in mCHP
applications. Most of the literature that does evaluate loop
thermosyphons is concerned with either very small-scale
systems for the passive cooling of electronic components,
or large-scale industrial systems. Vincent and Kok (1992)
simulated an oil-cooled closed-loop thermosyphon using
375 kg water for a 1 MW industrial application. They
applied a control-volume based energy and momentum
balance, but did not deal with the thermodynamics of the
thermosyphon. The saturation temperature was treated as
an independent parameter in their parametric study,
although it varied from 90oC to 250oC.

Recently, research has focused on developing systems for
cooling electronics: Min-Kyun et al. (2001) conducted
experiments to assess a closed loop, two-phase
thermosyphon for this purpose. A separated flow model
was employed to predict the mass flux and the pressure
drop in the condenser, and average convective boiling
heat transfer coefficients and corresponding wall
superheat were calculated using the Chen's correlation.
The effect on thermal performance of condenser size and
charge fluid quantity was evaluated experimentally.

Haider et al. (2002) presented a model for the two-phase
flow and heat transfer in a closed loop, two-phase
thermosyphon for another electronics application. The
model was based on mass, momentum, and energy
balances, and the homogeneous two-phase flow model







7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


----,Pressure gauge
and transducer



Fallingtb
Preheater

Expansion
vessel -
Therrnosyphon Circuit thermosyphon


Figure 1: Schematic of the experimental set-up for the two-phase ;I,, I ,,,. I. .,.


The two-phase thermosyphon consists of four major
components: the evaporator, the rising tube, the condenser,
and the falling tube. The evaporator is a finned-tube copper
coil, with a preheater plate heat exchanger, used to transfer
heat from the combustion products of natural gas and air to
the water this component is referred to as the Primary
Heat Exchanger (PHE). The terms "riin" n "alin"
describe the general fluid flow direction through the
connecting copper tubes in a thermosyphon where the
condenser is placed at a higher elevation than the
evaporator. The preheater inlet port on the PHE serves as
the reference plane with which the various elevations of
the thermosyphon are measured to reflect different
gravitational heads. Flue gas temperatures within the
combustion chamber can rise to 6000C, but the temperature
of the coil wall in contact with the working fluid is
typically between 150 and 1800C.

After rejecting heat in the condenser, the condensate then
flows vertically downward through the falling tube, turns
through 90 degrees, and enters the evaporator. The model
assumes that the copper tubes, PHE casing and condenser
casing are adiabatic, and so the vapour quality, void
fraction, and temperature remain constant along the rising
and falling tubes. The tubing is heavily insulated.

The difference between the gravitational heads of the
liquid-filled condenser and falling tube, and the
vapour/1iquid-filled PHE rising tube causes the natural
circulation of water around the loop. The separated two-
phase flow model is used to evaluate the two-phase
frictional pressure drop through the PHE, rising tube and
falling tube. A correlation proposed in Wang, et al. (1999)


is used to calculate the pressure drop produced in the plate
heat exchanger,

If the condensation is not complete in the condenser, the
falling tube experiences two-phase flow, a higher frictional
pressure drop and will yield a smaller gravitational head
due to vapour presence. Furthermore, the evaporator will
receive both vapour and liquid, and the entire
thermosyphon would operate at a constant saturation
temperature/pressure, all the heat transfer in the evaporator
being latent. On the other hand, if the condensation is
complete, partial flooding would deteriorate the
condenser's heat transfer performance, while the falling
tube would experience single-phase pressure drop and
would give a maximum gravitational head at the
evaporator, and some of the heat addition in the evaporator
would be sensible. The mechanisms of heat transfer and
fluid flow in the thermosyphon are inter-related.

Modelling the Two-phase Thermosyphon

A thermosyphon model was developed by satisfying mass,
momentum and energy balances, in conjunction with a set
of thermodynamic constraints, on the PHE, rising tube,
condenser and falling tube. A number of assumptions were
based on observations of the flow made using the
visualisation glasses installed within the circuit. Steady-
state thermosyphon operation was assumed for the
construction of the component models. The pressure drops
in the rising and falling tubes are calculated using the
separated two-phase flow model, two-phase flow
parameters are cross-section averaged, with vapour
assumed to be an ideal gas in thermodynamic equilibrium











with the liquid phase this follows the assumption of
adiabatic rising and falling tubes. Constant liquid/vapour
thermophysical properties are assumed. The saturation
pressure and temperature of the system is treated as
independent parameter.

Figure 2 shows the structure of the two-phase
thermosyphon model. The flow rate is iterated until a
balance is achieved between circuit pressure drops and the
available gravitational head.



Model Inputs: Circuit
dimensions, working fluid
properties, heat load


Flowrate m,, calculated El Iterate ms, p


PHE & Condenser models
used to calculate liquid-
vapour interfaces and mass
fractions

Static head H calculated


Pressure drop dP,,, around
system calculated using
component models


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

balance the gravitational pressure head and circuit pressure
drops, allowing the thermosyphon to run in steady-state.

Mlodelling the Evaporator

The evaporator model is applicable to the finned coil
primary heat exchanger and preheater. The model performs
three actions: calculation of the phase and quality of the
fluid entering and leaving the evaporator, calculation of the
height of the liquid-vapour interface within the evaporator,
and calculation of evaporator pressure drop.

The phases of the fluid leaving the evaporator, and the
height of the liquid/vapour interface, are calculated by
performing an energy balance on the evaporator:


ei,; = se,,* + la

Q,,,, = nSys x Cp x (Tsar T4)


Is the heat transfer due to the sensible heating of the liquid
to T,,,


eiar = msysxhxxifg


Is due to the vaporization of the liquid.

Mass fraction x: is calculated initially using the heat input
and an estimated flow rate. In subsequent iterations it is
calculated using equation 3. By assuming a constant heat
flux and knowing the dimensions of the heat exchanger,
the position of the liquid/vapour interface relative to the
pipe inlet can be calculated, providing the lengths of the
single and two-phase flow sections. This is then converted
into a height using the ratio of the vertical height of the
evaporator with its tube length.

The average mass fraction within the evaporator, xc,,4, is
used for pressure drop calculations:


Figure 2: Logic J,..nI ,/,, ,. I e ,,, for the thermosvphon
model.

Within each iteration there are mass, momentum and
energy balances. Models of the evaporator, rising tube,
condenser and falling tube are used to calculate the
positions of the liquid-vapour interfaces in the evaporator
and condenser, the mass fraction within the rising tube, and
the total pressure drop around the entire thermosyphon
loop. The pressure drop must be equal to the available
gravitational pressure head, which is the liquid-filled
falling tube gravitational head minus the liquid/vapour
gravitational head of the evaporator and the rising tube.
The calculation yields a system mass flow rate whose
circulation through the circuit would satisfy the overall
pressure balance around the circuit.

Overall, the model calculates the total mass flow rate, two-
phase mass fraction and liquid/vapour interface position
that, for a given heat load and circuit geometry, would


The calculation of the evaporator pressure drop is broken
down into contributions from friction, gravity and
acceleration. The loss due to friction is calculated
separately for the single and two-phase sections. In the
single-phase section, a method from Khodabandeh and
Palm (2000) is used. For fully developed laminar flow
(Re<2300) in circular tubes, the frictional pressure drop
was calculated using:


16 2xG xLlo
dPg =-x~
Relo D7,x P1


For the turbulent flow regime, the Blasius correlation for
the friction factor was used:


Solution







7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


0.079 2xG xLlo
d-rl Re2L5x Dhxpl


1 2/

1+x


The flow is determined to be laminar or turbulent
depending on Reynolds number:


The total gravitational pressure drop produced in the
evaporator is the sum of the single- and two-phase
components.

Pressure drops are also caused by flow acceleration. A
correlation from Carey (1992) is used to predict the
magnitude:


Relo G x D 2300


Pressure drop from the two-phase flow is found using the
separated flow model. The frictional pressure gradient is
expressed as a two-phase multiplier multiplied by the
single phase pressure gradient for the total flow as a liquid.
Lockhart and Martinelli (1949) proposed a generalised
correlation for determining the two-phase multiplier qb2 In
this correlation the two-phase multiplier is a function of a
constant C and the Lockhart-Martinelli parameter X,,:


dPacc = Gtmla(1X2 x~ + a


The total pressure drop produced in the evaporator is due
to friction, gravity and acceleration:


dPfw 2 xdPfr


dPevap = dPfr. + dPgr + dPacc


The Rising Tube


Where,


The rising tube is modelled as an adiabatic, isothermal
two-phase flow, with vertical and horizontal sections. The
total pressure drop is divided into two components -
friction and gravity. The mass fraction x: is taken from the
evaporator calculation.

Flow through the rising tube is assumed to be two-phase,
and the frictional pressure drop is calculated using the
separated flow model, as used in the evaporator.

Pressure drop due to gravity is calculated using equation
12 the average void fraction is calculated using equation
13.

The total pressure drop produced by the rising tube is then
calculated using:


C2 1 + i
Xtt Xtt


Xt-
tr-dP ,


Values for dPf, and dPf,, are calculated using equations 5
and 6, depending on whether the flow is laminar or
turbulent the Re number is individually calculated using
equation 6 for both the liquid and vapour phases. The
constant C varies from 5 to 20 and depends on the flow
regime and hydraulic diameter. Further details can be
found in Carey (1992). The total frictional pressure drop
produced in the evaporator is the sum of the single- and
two-phase components.

As with the frictional pressure drop, the pressure drop due
to gravity is calculated separately for the single and two-
phase regions of flow. The pressure drop produced by the
liquid upstream of the liquid-vapour interface in the
evaporator is:


dPr, ~ +dP,


The Condenser

The condenser model is used to estimate the height of the
liquid-vapour interface within the condenser, and to
estimate the pressure drop.

The height of the liquid-vapour interface is calculated
using the Log Mean Temperature Difference (LMTD)
method:

Applying the principle of conservation of energy, the heat
transfer across the condenser is:


dPgrz = p xg xhl


Where hiv is the height of the interface above the inlet to
the evaporator. The pressure drop in the two-phase section
is calculated using a correlation from Carey (1992):


dPgr = [(axp, )+((1- ~xpl )Ixg xhtp

Where the void fraction is calculated using:


Gin = eour


An analysis of figure 3 reveals that heat transfer from
sensible cooling is:























Tat

IThermosyphon





Colt Ostenm YT



Length


Figure 3: Temperature distribution along the I. :. I of the
condensing heat exchanger.

In order to use the LMTD method, the temperature of the
cooling circuit fluid at condensation (Te) needs to be
known. An analysis of figure 3 allows Tc to be calculated:


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


This can be re-arranged to give:

( Tc)'73T5
In tIn -
UX~cond laF Tsat) se Tsat-T3 (4
T6-Tc (T3-T5)- Tsat-3



U is then substituted back into equations 22 and 23 to
calculate Asen and Alat. The lengths of the two-phase and
COndensate sections are then:


esen = mess x Cp x (Tsat T3


And heat transfer from condensation is therefore:


Qzar = eout- en


Al,
n plate x wcond



IndnplateA en cond


The pressure drop in the condenser is composed of
contributions from friction, acceleration and gravity. The
method used for calculating the pressure drops produced
by the condenser has been taken from Wang, et al. (1999).

As in the evaporator, the condenser contains single- and
two-phase flows. In order to calculate the drop produced
by the two-phase section, the average quality of the vapour
inside the condenser is required. This is calculated using:


xa 2


As outlined in Wang, et al. (1999), the two-phase liquid-
only pressure drop is calculated using a friction factor f:


Lt Gt
dPfo fx f x P
Dhcond 2P1
Where


The total heat transfer area within the
approximated using:

Acond = cond Xcond X plate




ela, =v UAlat x atT)

In(Tsat -T6


heat exchanger is


0.56
Re01


Dhcond is twice the gap between the heat exchanger plates.
The Martinelli correction is calculated using:


(T3 -T5) (sat Tc)
In (3 -T5)
(Tsat -T3) ,


As detailed in Wang, et al. (1999), C = 16, allowing
calculation of the two-phase multiplier. The two-phase
frictional drop can then be calculated using equation 8. The
pressure drop from the condensate section is calculated
usmng:


Tc = 76 6 T5

--.P i~ Out


X (1-xavgav) Pv F
Xt


isen=UxAsenx







7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

expected at the evaporator inlet. Conversely, the same
balances on the condenser require knowledge of heat
addition in the evaporator. Furthermore, the evaporator and
condenser balances require the mass flow rate that is not
known until the pressure balances are applied, which in
turn require the vapour qualities that are not known until
the evaporator/condenser mass and energy balances have
been applied. The commercially available MATLABTM
software was used to solve this system of coupled non-
linear equations.

The model predictions were compared with experimental
data, using the test rig displayed in Figure 1.

The thermosyphon was operated by boiling water inside
the primary heat exchanger. The primary heat exchanger
consists of two finned tubes a preheater and a 6 V/2 tuTH
coil. The preheater is a 200mm long U-shaped aluminium
tube, immersed in the flue gas stream from the burner.
Heat is transferred using an array of 17 aluminium fins, 85
mm wide by 140 mm tall by 0.8mm thick, with a 6mm gap
between the fins. Flue gas temperatures are between 130 -
150 OC. The finned coil is positioned inside the combustion
chamber it is made from 18mm inner diameter copper
tubing with an array of circular fins, 3mm in height and 0.4
mm thick. The gap between fins is 2mm. Combustion
products pass over the finned coil at approximately 5500C.

The brazed plate heat exchanger used for the condenser is
an Alfa Laval CB18 with 20 plates, cooled by water
circulated using a Wilo RS60 centrifugal pump at a rate of
12 L/min. The temperature of the cooling water at the inlet
of the condenser was maintained at 800C.

The rising and falling tubes are made from 22mm and
15mm outer-diameter copper tubing respectively, with a
minimum number of swept bends to reduce pressure
losses; both tubes were insulated using Armaflex insulating
foam. Borosilicate glass tubes, 100mm in length, were
used in the vertical and horizontal sections of the rising
tube for flow visualisation.

The following figures show predictions by the circuit
model over the tested heat throughput range of 9.6 to 20.3
kW chosen based on current steam circuit design heat
loads. These predictions, were experimental data was
available, were used in the development and validation of
the model. Tested condenser elevations, measured from the
top of the primary heat exchanger to the top of the
condenser, were 900mm and 1000mm.


L G1-
lPf, = fx x ,
Dhcond ~ '


Where f is calculated using equation 29-

The total drop due to friction within the condenser is then:


dPfr = dPyf + dPfr;


The pressure drop due to gravity can be calculated using
equation 11, where the height of the liquid column is Li,,
derived from equation 26. This drop has a negative value,
indicating a gain in pressure.

The pressure drop due to acceleration is calculated using
equation 13, with equation 14 used to calculate the void
fraction in the plate heat exchanger. This drop also has a
negative value.

The total pressure drop produced in the condenser is then:


clPeond dfi + Pgr dPace


The Falling Tube

The falling tube is modelled as an adiabatic, isothermal
single-phase flow, with vertical and horizontal sections.
The total pressure drop is caused by friction and gravity.
The fluid is assumed to be a subcooled liquid.

The frictional pressure drop is calculated using equations 5
or 6 depending on flow regime, with the flow Re number
calculated using equation 7.

The pressure drop due to gravity is calculated using
equation 11. The height value used is simply the height of
the falling tube. This drop has a negative value, indicating
the presence of a gravitational head.

The falling tube pressure drop is therefore:


clPf = clP +dP ,


Total Pressure Drop

The pressure drop around the circuit is equal to zero
(pressure losses are balanced with the gravitational head
generated), therefore:


O = clPevap + Prr +Pcond +Pft


Results and Discussion

As illustrated in Figure 2, the steam circuit model is
coupled through mass, momentum and energy balances,
creating an iterative procedure. For example, to perform
the mass and energy balances on the evaporator, one needs
to know whether the condensation is complete or not and
whether subcooled liquid or a two-phase flow should be





-A


I .- Y -3Y L'W S~-


' mm


.~~~


9 11 13 15 17 19 21


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


0.08




0.00
9 11 13 15 17 19 21

Heat input (kW)

-Actual flow, H=0.9m -Actual flow, H=1.0m
-Predicted flow, H=0.9m -Predicted flow, H=1.0m

Figure 6: Mass fow rate for both geometries at different
heat inputs.

Figure 6 displays predicted and actual mass flow, for both
geometries tested, as a function of heat input. There is a
good agreement between the flow rates at heat inputs
below 17 kW there is an under-prediction of about 6% for
the 0.9m test, and an over-prediction of about 6% for the
1.0m test.

Above 17 kW, the actual mass flow rate peaks and then
declines with increasing heat input. This is because of the
combined effect of increased flow resistance around the
circuit and decreasing gravitational head due to the
decrease in liquid density at increased temperature. The
discrepancy between predicted and actual may be because
at increasing heat input the additional flow resistance
present in the circuit is not accounted for by the model as
the vapour quality within the rising tube increases, the
influence of bends and ports, which are not modelled,
become more significant.


21




11
9 I I


2000 2500 3000 3500 4000 4500

Burnerfan speed (rpm)

-Heat Input (H=0.9m) -Heat Output (H=0.9m)


Figure 4: H. l i,ar l,.. .I li-e I: different fan speeds.

Figure 4 displays an energy balance applied to the circuit
for the 900mm test. The heat input figure is calculated by
multiplying the measured gas flow into the PHE and
multiplying it by the calorific value of the gas. The heat
output is calculated by measuring the energy uptake by the
cooling circuit water across the condensing heat
exchanger. The figure shows that as the heat throughput of
the steam circuit increases, losses from the circuit also
increase this would be explained by increased evaporator
and rising tube temperatures at higher heat throughputs,
leading to higher convective and radiation heat losses.
Identical behaviour was found for the 1000mm test, which
would be expected as the heat throughput was the same.


g


0.0ss
0.oso
0.025


0.010
0.005
0.000


0.02
0.01 -
-~o


0.05


9 11 13 15 17 19 21


Heat throughput (kW)

AH=0.9m XH=1.0m

Figure 5: Steam circuit mass fraction across heat input for
both geometries.

Figure 5 shows predicted rising tube vapour qualities as a
function of heat input, and shows a substantially liquid (by
mass) two-phase flow, which becomes drier as heat input
increases. Very low vapour quality in the rising tube is in
accordance with visual observations at a heat input below
11kW, bubbly flow was observed, whilst at higher heat
inputs the flow became plug and then annular (above 15
kW). Due to the large density difference between liquid
and steam, the formation of even a very small mass of
vapour creates a large void fraction. For example, the
model calculated that for a mass fraction of 0.101 at 11.1
kW, the volume fraction would be 59%. Because of the
dynamic boiling activity within the finned coil, the
generated vapour may drag some of the saturated liquid
inside the evaporator into the rising tubing in effect
acting as a 'bubble pump'. A major component of the heat
throughput within both evaporator and condenser is due to
sensible heat transfer.


9 11 13 15 17


19 21


Heat throughput (kW)


XActual XPredicted tot

Figure 7: Predicted and actual pressure drop across the
evaporator for H=0O. 9n.


Heat throughput (kW)

xActual XPredicted -tot



Figure 8: Predicted and actual pressure drop across the
evaporator for H=1.0n2.












S11 13 15 17 19 21







Heat throughput (kW)


9 1Helatthroulghput(k7W)19 2


~c;lbc--


i.


11 13 ,15 ~7 19 2







Heat throughput (kW)


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Figures 7 and 8 display predicted and actual pressure drops
in the evaporator for H=0.9m and H=1.0m respectively.
There is a slight over-prediction of pressure drop which
increases with heat throughput in both tests. The present
model assumes a constant fluid density an analysis of the
results shows that the majority is produced by gravity,
which would reduce further at higher heat inputs if density
varied with fluid temperature. The acceleration drop
increases with heat throughput in conjunction with Figure
5, as mass fraction increases, a greater acceleration drop is
produced-


MActual XPredicted tot

Figure 11: Predicted and actual pressure drop across the
condenser for H=0O. 9n.


AActual XPredicted-tot


Heat throughput (kW)

mActual XPredicted tot


Figure 9: Predicted and actual pressure drop ;ln .I. I.1 the
rising tube for H=0. 92.


0.06
0.0s
0.04
0.03
0.02


YYY


Figure 12: Predicted and actual pressure drop across the
COndenser for H=1.0n2.

Figures 11 and 12 display predicted and actual pressure
drops in the condenser for H=0.9m and H=1.0m. There is a
good correlation between predicted and actual for both
tests. The pressure gain (head) produced decreases with
increasing heat throughput as the condenser fills with
vapour instead of liquid, and the influence of friction at
higher flow speeds becomes more pronounced.


9 11 13 15 17 19 21


Heatthroughput(kW)

AActual *Predicted -fr HPredicted -gr XPredicted -tot

Figure 10: Predicted and actual pressure drop ;I1 .I the
TISmng tube for H=1.0T.

Figures 9 and 10 display predicted and actual pressure
drops in the rising tube for H=0.9m and H=1.0m. There is
a good agreement between predicted and actual for
H=0.9m, although there is an over-prediction that increases
with heat throughput for H=1.0m. As with the evaporator,
gravitational head is the major component, due to the large
mass of liquid within the rising tube, and the net pressure
drop decreases with increasing vapour quality.


-0.052


*Actual XPredicted tot


Figure 13: Predicted and actual pressure drop ;I1 .I the
falling tube for H=0. 9n.


























Heat throughput (kW)


- --~I-


11~ 13 L15 L 21


An 4. & ~8 i


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


0.000


11 13 15 17 19 21


0.04


-0.080


Heat throughput (kW)

4Actual XPredicted-tot


Figure 14: Predicted and actual pressure drop ;I1 .I the
falling tube for H=1.02.

Figures 13 and 14 display predicted and actual pressure
drops through the falling tube for H=0.9m and H=1.0m.
Like the condenser, both the predicted and actual results
show a large pressure gain (negative pressure drop) across
the tube because of the gravitational head produced by the
subcooled liquid. There is a good agreement between
predicted and actual for H=0.9m, however, for H=1.0m the
predicted gain becomes over-predicted with increasing
heat input. Possibly, the influence on friction of the mass
flowmeter and bends at the higher flow rate observed for
H=1.0m are more significant than previously thought. This
may be combined with reduced liquid density (and
therefore reduced head) at higher temperatures, which
again are not accounted for in the calculation,

Finally, the balance of pressure changes around the circuit,
for H1 = 0.9m and H1 = 1.0m, are shown in figures 15 and
16 respectively. An analysis of the results shows that the
sum of both predicted and actual is equal to zero, as
theorised in equation 35. The contributions of different
components can clearly be seen.

0.06 ,


WEv-act HRt-act ACond-act XFt-act XTot-act
Evap-Pr +Rt-pr *Cond-pr -Ft-pr Tot-pr


Figure 16: Pressure balance around the circuit for H =
1.0n2.

Conclusion


The present paper proposes an analytical approach to
modelling the behaviour of a two-phase thermosyphon.
The model uses mass, momentum and energy balances to
predict the vapour quality, mass flow rate and pressure
drop around the circuit. System temperatures are
considered as independent parameters, and the thermo-
physical properties of the fluid are considered constant for
the relevant temperature.

The model is compared with experimental data and is in
general agreement with the observed trends. The
simulation results for the given experimental setup suggest
a primarily liquid two-phase flow across the tested range of
heat throughput and geometry, with vapour quality and
mass flow rate increasing with increasing heat load. The
major component of heat transfer within the system is
sensible.

Test results highlight two possible inaccuracies within the
model. The first is the influence of bends and other
components within the circuit, which will contribute to the
overall pressure drop, especially when a high vapour
quality is observed. More realistic predictions are expected
once better pressure drop correlations are used that are
more sensitive to vapour quality effects.

The second uncertainty stems from treating the
temperature in the system as an independent parameter and
then assuming constant thermo-physical properties for the
Working fluid. In reality there are changes in pressure and
temperature around the circuit, but their affect on the fluid
properties are not significant.

In conclusion, the model is reasonably accurate at
predicting thermosyphon behaviour over the heat
throughput range tested, and has proven to be a useful tool
in mCHP development.


Heat throughput (kW)

QEv-act Rt-act ACond-act xR-act xLTot-act
Evap-Pr +Rt-pr *Cond-pr-Pt-pr Tot-pr

Figure 15: Pressure balance around the circuit for H =
0. 92.







7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Thermosyphon Devices for Cooling MCMs, Heat Transfer
Engineering, Vol. 22 (2001)

Vincent C. C. J. and Kok J. B. W., Investigation of the
Overall Transient Performance of the Industrial Two-Phase
Closed Loop Thermosyphon, International Journal of Heat
& Mass Transfer, Vol. 35 (1992)

Wang L. K., Sunden B. and Yang Q. S., Pressure Drop
Analysis of Steam Condensation in a Plate Heat
Exchanger, Heat Transfer Engineering, Vol. 20 (1999)


Acknowledgements

This conference paper was sponsored by a partnership
between the University of Liverpool, Energetix Genlec Ltd
and the Knowledge Transfer Programme (administered by
AEA Momenta), who are gratefully acknowledged.


References



Carey V. P., Liquid-Vapour Phase-Change Phenomena,
Hemisphere Publishing Corporation, ISBN 1-56032-074-5
(1992)

El-Genk M. S. and Saber H. H., Heat Transfer
Correlations for Liquid Film in the Evaporator of
Enclosed, Gravity-Assisted Thermosyphons, ASME
Journal of Heat Transfer, Vol. 120 (1998)

Haider S. I., Joshi Y. K. and Nakayama W., A Natural
Circulation Model of the Closed Loop, Two-Phase
Thermosyphon for Electronics Cooling, ASME Journal of
Heat Transfer, Vol. 124 (2002)

Harley C. and Faghri A., Complete Transient Two-
Dimensional Analysis of Two-Phase Closed
Thermosyphons Including the Falling Condensate Film,
ASME Journal of Heat Transfer, Vol. 116 (1994)

Khodabandeh R. and Palm B, An experimental and
numerical investigation of pressure drop in a closed loop
two phase thermosyphon system, ITHERM 2000
Conference Proceedings, IEEE (2000)

Khodabandeh Rahmatollah, Heat Transfer and Pressure
Drop in a Thermosyphon Loop for Cooling of Electronic
Components PhD Thesis, Dept. of Applied
Thermodynamics and Refrigeration, KTH University
(2004)

Khodabandeh Rahmatollah, Pressure drop in riser and
evaporator in an advanced two-phase thermosyphon loop,
International Journal of Refrigeration, Vol. 28 (2005)

Lock G. S. H., The Tubular Thermosyphon: Variations on
a Theme, Oxford University Press, ISBN 0-19-856247-0
(1992)

Lockhart R. W. and Martinelli R. C., Proposed
correlation of data for isothermal two-phase, two-
component flow in pipes, Chemical Engineering Progress
(1949)

Min-Kyun N., Jin-Seok J. and Ho-Young K.,
Experimental Study on Closed-Loop Two-Phase




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - Version 2.9.7 - mvs