7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Modelling a twophase 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: Twophase thermosyphon, natural circulation loop
Abstract
This paper presents a steadystate 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 finnedcoil 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 twophase flow model is used to predict twophase
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 byproduct, while mCHP is normally
driven by heat demand, with power generation
(electricity) as the byproduct. 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 gasfired 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 30June 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 PF5060 and was in general agreement with
observed trends. Khodabandeh (2004) also presented a
model for twophase flow rate and evaporator heat
transfer in a twophase loop thermosyphon for electronics
cooling. The model was based on mass and energy
balances. Different twophase 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, R11, and
R113 as working fluids of interest, for evaporator heat
fluxes of 0.9952.62 kW/m2, evaporator inner diameters
of 637 mm, evaporator section height of 50609.6 mm,
and vapour temperature of 261352 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 wellseparated, countercurrent 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 Setup
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
Twophase
Vapour
Previous Studies
Most of the available literature on twophase
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
countercurrent 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 twophase
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 smallscale
systems for the passive cooling of electronic components,
or largescale industrial systems. Vincent and Kok (1992)
simulated an oilcooled closedloop thermosyphon using
375 kg water for a 1 MW industrial application. They
applied a controlvolume 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: MinKyun et al. (2001) conducted
experiments to assess a closed loop, twophase
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 twophase
flow and heat transfer in a closed loop, twophase
thermosyphon for another electronics application. The
model was based on mass, momentum, and energy
balances, and the homogeneous twophase flow model
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
,Pressure gauge
and transducer
Fallingtb
Preheater
Expansion
vessel 
Therrnosyphon Circuit thermosyphon
Figure 1: Schematic of the experimental setup for the twophase ;I,, I ,,,. I. .,.
The twophase thermosyphon consists of four major
components: the evaporator, the rising tube, the condenser,
and the falling tube. The evaporator is a finnedtube 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
liquidfilled condenser and falling tube, and the
vapour/1iquidfilled PHE rising tube causes the natural
circulation of water around the loop. The separated two
phase flow model is used to evaluate the twophase
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 twophase 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 singlephase 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 interrelated.
Modelling the Twophase 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 twophase flow model, twophase flow
parameters are crosssection 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 twophase
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 30June 4, 2010
balance the gravitational pressure head and circuit pressure
drops, allowing the thermosyphon to run in steadystate.
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 liquidvapour 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 twophase 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 liquidvapour 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 liquidfilled
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 twophase sections. In the
singlephase 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 30June 4, 2010
0.079 2xG xLlo
drl 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 twophase
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 twophase flow is found using the
separated flow model. The frictional pressure gradient is
expressed as a twophase 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 twophase multiplier qb2 In
this correlation the twophase multiplier is a function of a
constant C and the LockhartMartinelli 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
twophase 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 twophase,
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
trdP ,
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
twophase 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 liquidvapour interface in the
evaporator is:
dPr, ~ +dP,
The Condenser
The condenser model is used to estimate the height of the
liquidvapour interface within the condenser, and to
estimate the pressure drop.
The height of the liquidvapour 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 twophase 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 30June 4, 2010
This can be rearranged to give:
( Tc)'73T5
In tIn 
UX~cond laF Tsat) se TsatT3 (4
T6Tc (T3T5) Tsat3
U is then substituted back into equations 22 and 23 to
calculate Asen and Alat. The lengths of the twophase 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
twophase flows. In order to calculate the drop produced
by the twophase 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 twophase 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 twophase multiplier. The twophase
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 (1xavgav) Pv F
Xt
isen=UxAsenx
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 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 Ushaped 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 outerdiameter 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
singlephase 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 twophase 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 30June 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 underprediction of about 6% for
the 0.9m test, and an overprediction 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 lie 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) twophase 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 30June 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 overprediction 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 XPredictedtot
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 overprediction 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 30June 4, 2010
0.000
11 13 15 17 19 21
0.04
0.080
Heat throughput (kW)
4Actual XPredictedtot
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 overpredicted 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 ,
WEvact HRtact ACondact XFtact XTotact
EvapPr +Rtpr *Condpr Ftpr Totpr
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 twophase 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 twophase 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 thermophysical 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)
QEvact Rtact ACondact xRact xLTotact
EvapPr +Rtpr *CondprPtpr Totpr
Figure 15: Pressure balance around the circuit for H =
0. 92.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 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 TwoPhase
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.
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