Towards an optimal design ofheat pipe equipped

heat exchangers

M. H. M. Grooten (Mart)January 2007

Report number WPC2007.01Supervisors:prof.dr.ir. J. J. H. Brouwers TU/edr. C. W. M. van der Geld TU/eS. Brand VDL Klima bv.dr. ir. H. P. van Kemenade TU/edr. ir. J. C. H. Zeegers TU/e

Eindhoven University of TechnologyDepartment of Mechanical EngineeringDivision: Thermo Fluids EngineeringSection: Process Technology

1

Contents

Nomenclature………………………………...…………………………….……….3

Introduction……………………………………………………………………..…..5

1. Air heat exchangers with long heat pipes: experiments and predictions…... 6

1.1 Introduction……………………………………………………………. 61.2 The closed two phase thermosyphon…………………………..………. 61.3 Experimental setup…………………………………………………….. 81.4 Heat transfer performance………………………………………………111.5 Heat transfer phase change…………………………………………….. 151.6 Results………………………………………………………………. …171.7 Analysis…………………………………………………………………211.8 Conclusions……………………………………………………………. 24

2. Single pipe experiments…………………………………………………… 25

2.1 Introduction……………………………………………………………. 252.2 Theory and literature survey…………………………………………… 26

2.2.1 Heat flux limits in thermosyphons…………………………... 262.2.2 Inclination of the thermosyphon…………………………….. 29

2.3 Experimental……………………………………………………………342.4 Experimental results…………………………………………………… 38

2.4.1 Temperature distribution at operating limit…………………. 382.4.2 Saturation temperature………………………………………. 402.4.3 Angle of inclination with the vertical…………………………452.4.4. Filling ratio………………………………………………….. 482.4.5. Heat flux limits……………………………………………… 49

2.5 Analysis………………………………………………………………... 512.6 Conclusions……………………………………………………………. 58

3. Design program for a Heat Pipe Heat Exchanger…………………………. 59

3.1. Introduction…………………………………………………………….593.2. Main HPHE program structure……………………………………….. 60

4. Steady-state numerical model of the single pipe thermosyphon…………... 70

Nomenclature……………………………………………………………….704.1. Introduction…………………………………………………………….71

2

4.2. Model of a single closed two phase thermosyphon………………..….. 72

5. Conclusions and recommendations…………………………………………75

References…………………………………………………………………………..77

Appendices………………………………………………………………………… 81

Summary……………………………………………………………………………117

Samenvatting………………………………………………………………………..118

3

Nomenclature

A surface area, m2

Fe filling degree, -H total channel height, mL length, mM molecular weight, kg/kmolN number of tubes in a row, -Nu Nusselt number, -Pr Prandtl number, -Q heat flow rate, WR heat resistance, K/WRe Reynolds number, -Rn number of rows, -S distance between fins, mT temperature, °CV volume, m3

W distance between pipes, ma distance between tubes in a row, mb distance between rows, mcp heat capacity at constant pressure, J/kgKd diameter, mg acceleration due to gravity, m/s2

h fin distance, m∆h fg enthalpy of evaporation, J/kgj Colburn factor, -m� mass flow rate, kg/sp pressure, Papr reduced pressure, -q heat flux, W/m2

r radius, mv velocity, m/s

Greekα heat transfer coefficient, W/m2Kλ thermal conductivity, W/mKδ thickness, m

finη fin efficiency, -

µ dynamic viscosity, Pasν kinematic viscosity m2/sρ mass density, kg/m3

χ geometric correction factor

Subscripts and superscriptsb boilingc condensationcond condenserevap evaporator

4

f fluidff fluid filmi innerlm logarithmic meanmax maximummin minimumo outersat saturationtot totalv vapourw wallx, y Cartesian coordinates

5

Introduction

Stand-alone electricity power generators are usually cooled with ambient air. In somesituations water is not available or ambient temperatures are too high to use traditionalair cooling. In those cases heat pipes may provide an alternative for cooling powers inexcess of 100 kW, where the heat transfer rate exceeds 5 kW/K. Multiple heat pipesor thermosyphons then connect two plate heat exchangers.

The goal of this study is to develop an operational model for the thermal design of anair-to-air heat exchanger equipped with heat pipes. This type of heat exchanger canserve as an alternative for present air-to-air heat exchangers where these become toolarge / expensive. At the first outset, focus of this study will be on the cooling ofelectricity generators, where the applied heat pipes in the heat exchanger will be filledwith R-134a. Dunn [1] and Vasiliev [57, 58] give an overview of possible otherapplications of heat pipes and thermosyphons.

The heat transfer in the system is based on the continuous cycle of the vaporizationand condensation process. The thermosyphon, or heat pipe if equipped with a wickinside, is heated at the evaporator, which causes evaporation of a part of the fluid. Thevapour flows to the condenser, where the fluid condenses while giving off its latentheat, caused by cooling from the outside. The condensate flows back to the heatedsection along the wall by gravitation, which closes the cycle.Thermosyphons can be used to transfer heat between two gas streams. The advantagesare the high heat recovery effectiveness, compactness, no moving parts, light weight,relative economy, no external power requirements, pressure tightness, no cross-contamination between streams and reliability [1, 2].

Chapter 1 presents experimental data of prototype air-heat pipe-air heat exchangerswith two filling ratios. The results are compared with those of a model that is basedon existing correlations of the literature. Results of this study show which conditionsfoster application of this novel type of heat exchanger.For scaling the prototype to a commercial applicable heat exchanger, knowledge ofthe performance of a single full scale thermosyphon needs to be gained. To obtainmore accurate tools in predicting heat transfer in this single long thermosyphon, adedicated test rig will be built. Operational limits of the thermosyphon, angle ofinclination and filling ratio at different working temperatures are subject of research.This is covered in chapter 2.

From results obtained in chapters 1 and 2, a computer program built in Matlab for thedesign of air-to-air heat pipe heat exchangers is developed. This will be outlined inchapter 3.

Chapter 4 presents a first step towards numerical simulation of the flow in athermosyphon, to gain more understanding of the experimental results obtained inchapter 2 especially with respect to the operating limit in a single heat pipe.

6

Chapter 1: Air heat exchangers with long heat pipes:experiments and predictions••••

1.1. Introduction

This chapter presents the study of a heat pipe-equipped heat exchanger with 1.5 meterlong pipes at two filling ratios of R134a 19% and 59%, respectively. The airflow ratevaries from 0.4 to 2.0 kg/s. The temperatures at the evaporator side of the heat pipevary from 40 to 70°C and at the condenser part from 20 to 50°C. The performance ofthe heat exchanger has been compared with two pool boiling models, Cooper andGorenflo, and two filmwise condensation models, Nusselt and Butterworth. A fairlygood agreement is found for measurements and the model of Cooper at low airflowReynolds number at the evaporator side of the heat exchanger. The result of this studyis that a heat pipe equipped heat exchanger can replace a traditional air to air heatexchanger without loss of performance. The tested process conditions are typical forwarmer countries.

1.2. The closed two phase thermosyphon

A heat pipe without a capillary wick structure is defined as a thermosyphon. Theliquid phase flows from the cold to hot side of the pipe, only driven by gravity. Thefluid circulates in the pipe, based on difference in density of the working fluid, causedby phase change through evaporation and condensation. The system is driven by atemperature difference between a hot and a cold side of the pipe, even if thistemperature difference is often small. The hot side of the pipe is the evaporatorsection, where the vapor pressure is higher then at the condenser section. The pressuredifference drives the vapor to the cold side. Figure 1.1 shows the thermosyphonschematically.

• This chapter is submitted for publication as: Air heat exchangers with long heat pipes: experimentsand predictions, H. Hagens, F. L. A. Ganzevles, C. W. M. van der Geld, M. H. M. Grooten, Appl.Thermal Engng. 1 (1), 1-40 (2007)

7

Figure 1.1: Thermosyphon, schematically

The heat transfer in the system is based on the continuous cycle of the vaporizationand condensation process. The thermosyphon is heated at the evaporator, whichcauses evaporation of a part of the fluid. The vapor flows to the condenser, where thefluid condenses while giving off its latent heat, caused by cooling from the outside.The condensate flows back to the heated section along the wall by gravitation, whichcloses the cycle.

Thermosyphons can be used to transfer heat between two gas streams. The advantagesare the high heat recovery effectiveness, compactness, no moving parts, light weight,relative economy, no external power requirements, pressure tightness, no cross-contamination between streams and reliability [1, 2].The heat transfer being based on evaporation and condensation, the latent heat of thefluid is an important parameter. The higher the latent heat of a fluid is the higher thetransfer of heat at a lower pressure. The working principles of the thermosyphonimply that the fluid should evaporate and condense within the temperature range.Taking the possible application of cooling an electricity generator with ambient airinto account, the working fluid R-134a is an option, considering the expectedtemperature ranges in practice. The hot air will be in a range of 40 – 80°C, theambient air will be in a range of -20 – 50°C. R-134a sublimates at -40°C and 0.51 bar,so phase change from liquid to gas only occurs above this temperature [3]. Thecritical temperature of R-134a is 101.06°C [4], which defines the extremes of thetemperature range of R-134a, with a critical pressure of 40.6 bar.Other possible working fluids are ammonia, pentane or water [1]. All these fluidshave the advantage over R-134a that they have a higher latent heat, which enableshigher heat transfer.Unfortunately, the maximum practical temperature limit of ammonia is 50°C [8],which is too low for the situation at hand. Water has a risk of freezing at the lower

8

temperature range. Pentane could be a useful alternative for R-134a, considering itstemperature range from –20 - 120°C, the higher latent heat and the higher surfacetension [1, 6, 7]. A higher surface tension has the benefit of lowering the risk ofentrainment, which is the most likely occurring limit in the application of thethermosyphon [8]. Possibly, other hydrocarbon refrigerants mentioned by Lee et al.[9]are possible working fluids as well. The type of filling fluid and the operational limitswill be subject of later research.This chapter presents experimental data of air-heat pipe-air heat exchangers with twofilling ratios. The results are compared with those of a model that is based on existingcorrelations of the literature. Results of this study show which conditions fosterapplication of this novel type of heat exchanger.

1.3. Experimental setup

A laboratory scale test rig was designed and built to compare the performances ofconventional plate-type exchangers (with water as intermediate medium) and heatpipe equipped plate heat exchangers. An overview can be seen in figure 1.2.

Figure 1.2: Overview of the test rig at VDL Klima bv, Eindhoven

A range of mass flow rates of ambient air of 0.2–2.5 kg/s is possible. Temperaturedifferences between hot and cold sides of the heat pipe of 60°C are possible. Twofilling degrees, Fe see (1.1), of the heat pipe have been examined (in equilibrium at20°C). Let the volume of the evaporator, Vevap, be defined as the inner volume of thatpart of the heat pipe that is in contact with hot air. It will be quantified, below, as thevolume � ri

2 Levap with ri = 7.2 mm and Levap = 640 mm.

evap

fe V

VF = (1.1)

9

Note that the volume of fluid is the volume that the liquid would have, if all of thefluid would be in the liquid phase.In this study, the overall heat transfer and temperature distribution are assessed undermass flow rates of ambient air varying from 0.4 kg/s to 2.0 kg/s. The ambient airtemperature varies from 20 – 50°C, whereas the hot air flow has temperatures in therange from 40 – 70°C. The heat pipe is filled with R-134a at ratios of 19% and 59%.A schematic overview of the setup can be seen in figure 1.3. The upper side is thecold side, where ambient air enters. Up- and downstream of the heat exchangertemperatures are measured with 16 Pt100’s (IC Istec ME 1009), with an accuracy of0.1°C. The temperatures of four sensors are averaged and they are denoted as T1, T2,T3 and T4 (see figure 1.4) respectively. The sensors are mounted at ¼ and ¾ of thelength of the diagonal cross cut of the 645 × 520 mm2 rectangular duct. The air streamvelocity profile was measured and found to have a homogeneous profile. Downstreamthe hot section, ten Pt-100 temperature sensors are mounted to investigate thetemperature variation in the height of the pipe at the evaporator section. They aremounted vertically at 50 mm apart and 117 mm of the sidewall. The Pt-100 sensorsare all calibrated with accuracy better than 0.1°C for the temperature range of 0 –100°C. The measurement section is thermally insulated to minimize errors in the heatfluxes deduced.

Figure 1.3: Schematic view of the test rig

At the entry, the dynamic pressure measurement with an orifice results in the air massflow rate, at an accuracy of 2%. The uncertainties of all measured and calculatedparameters are estimated according to [10].

The air heater is a water-air heat exchanger, with 3 mm spaced vertical fins, whichallows a uniform velocity profile upstream the evaporator. This neutralizes theinduced swirl in the airflow caused by the radial fan.

10

Figure 1.4: Definition of temperatures in air streams

The heat exchanger consists of 4 rows of alternating 14 and 13 copper pipes. Thepipes have an outer diameter of 16 mm and a wall thickness of 0.8 mm. The totallength of a pipe is 1.5 m, with 0.64 m in the condenser section and the evaporatorsection each. The adiabatic length is 0.22 m. This is the distance between the twosections of the airflow in the wind tunnel. The inner surface of each pipe has smallspiral grooves, to enhance the heat transfer in evaporation and condensation. Thegrooves are 0.2 mm wide and 0.2 mm deep each, separated 1 mm, under an angle of25° with the vertical. The distance between the pipes in a row is 36.5 mm, see figure1.5. Each row is filled with R-134a separately. The rows are 27.5 mm apart and thetotal depth of the aluminium fins including the 4 rows is 114.5 mm. At the top of eachrow, the pressure is measured with a WIKA type RB manometer, at a frequency of100 Hz, with an accuracy of 1% after calibration. The range of the manometers is 0 –100 bar. The saturation temperature of R134a is given by the Antoine relation (1.2)obtained from data from NIST [4] with temperatures in degrees Celsius and pressurein bar

( )ln v

BT C

A p= −

− (1.2)

with A = 10.52, B = 2484, C = 263.1

Over the height of the pipes, aluminum fins are attached. At the evaporator side, thedistance between the fins is 1.6 mm, where the distance at the condenser side is 2.6mm, see LHS of figure 1.5. With the aluminum fins included, the total heattransferring area at the hot side is 38.6 m2 and at the cold side 24.3 m2.

11

36.5 mm

27.5 mm

1.6 or 2.6 mm

Figure 1.5: Fin spacing (LHS) and spacing between tubes (RHS)

1.4. Heat transfer performance

To analyze the performance of the heat pipe equipped heat exchanger, the generalheat flow rate can be expressed by:

TcmQ p ∆= �

� (1.3)

with the temperature differences of the air flows upstream and downstream the 4 rowsof the heat pipe heat exchanger.

The effectiveness of the heat transfer at both the hot and cold side of the heat pipeheat exchanger, the heat transfer coefficient α in W/m2K is defined as [13]:

lmtot TA

Q

∆=

χα

�

(1.4)

with the corresponding Q� from equation (1.3) in W, A the heat transferring area ofwhether the hot or the cold side in [m2], χ a geometrical correction factor, here 1 [11]if each side is seen as a counter flow heat exchanger and

( )

���

����

�

∆∆

∆−∆=∆

min

max

minmax

lnT

T

TTTlm (1.5)

with maxT∆ and minT∆ denote the maximum and minimum temperature differencesbetween the first and last row of the heat pipes and the airflow.

12

To analyze the temperature over the heat pipe in stationary use, the temperaturedifference between the hot air flow at the evaporator side and the cold air flow at thecondenser side, can be divided in a hotoutsideT ,∆ , the temperature difference between the

hot air and the outer wall of the pipe, with a certain area of the pipe and a heat transfercoefficient and coldoutsideT ,∆ the temperature difference between the outer wall and the

cold air. In the heat pipe, a temperature difference at the evaporator between the hotwall and the evaporation temperature of the fluid evapT∆ and a temperature difference

between the condensation temperature of the fluid and the cold wall, condT∆ , exists.So,

coldoutsidecondevaphotoutside TTTTT ,, ∆+∆+∆+∆=∆ (1.6)

with a heat resistance R, it follows:

R

TQ

∆=� (1.7)

Under stationary assumption follows:

QQQ coldhot��� == (1.8)

condfinsaircoldoutsidewallcoldoutside

condfinsaircoldoutsidewallcoldoutsidecold

evapfinsairhotoutsidewallhotoutside

evapfinsairhotoutsidewallhotoutsidehot

RRR

TTTQ

RRR

TTTQ

++∆+∆+∆

=

++∆+∆+∆

=

+

+

+

+

,,,,

,,,,

,,,,

,,,,

�

�

(1.9)

so

R

T

RRRRRR

TTTTTTQ

condfinsairhotoutsidewallcoldoutsideevapfinsairhotoutsidewallhotoutside

condfinsairhotoutsidewallcoldoutsideevapfinsairhotoutsidewallhotoutside ∆=+++++

∆+∆+∆+∆+∆+∆=

++

++

,,,,,,,,

,,,,,,,,�

(1.10)

in which R are the specific heat resistances. As long as the heat resistances at the innerof the heat pipe are much smaller than the outer resistances, the full axial heattransport abilities of the heat pipe are not exploited. The outer heat resistances arecalculated, knowing the material and the fin geometry. The heat resistance in the heatpipe however, is subject of the study and depends among others on the quantity ofworking fluid. See figure 1.6 for an overview of the heat resistances.

13

Figure 1.6: Definition of the heat resistances with the temperatures

The heat resistances of the heat pipe wall is defined by R,w,evap and Rw,cond and givenas:

( )evap

ioevapw L

rrR

πλ2

ln, = and

( )cond

iocondw L

rrR

πλ2

ln, = (1.11)

with ro and ri the outer and inner radius of the pipe [m]. λ is the thermal conductivityof the copper pipe and L in m the length of the evaporator or the condenser sectionrespectively.

Rfin at both sides have to include the heat transfer resistance of the air stream to thealuminum fins and the resistance of the heat transfer through the fins to the coppertube.The heat transfer from the air stream to the fins and from the fins to the tube can bedescribed with a fin efficiency according to [12]:

( )

( )

21

1

2

tanh

�����

�

�

�

��

�

�

��

�

�+

=

=

ff

f

f

fin

f

lm

ml

ml

δλ

δ

α

η

(1.12)

with l = length from fin tip to tube wall in m, finα is the heat transfer coefficient to

the fin in W/m2K, fδ the fin thickness, here 0.2 mm, fλ the thermal conductivity of

the fin material, here aluminum. Every tube in the tube bank is observed as having itsown segment of fins. This leads to a local fin length lf of 18.3 mm from fin tip to tubewall. The heat transfer coefficient finα has to be determined with a Nusselt relation.

14

finα is assumed to be constant over the fin, which can lead to inaccuracies when

observing the total heat exchanger, since finα is dependant on the flow properties.

The total heat transferring area equals the heat transferring area of the fins, so fromthis assumption follows [12]:

evapfinevapfinfevapfin A

R,,

,

1

αη= and

condfincondfinfcondfin A

R,,

,

1

αη= (1.13)

As stated above, finα is determined with the Nusselt theory for convective flow

between fins. Several correlations can be applied, see appendix C.Gray and Webb [13] provide the following correlation:

νovd

=Re (1.14)

031.0502.0328.0Re14.0 ��

�

����

���

���

�=−

−

od

h

b

aj (1.15)

31

PrRejNu = (1.16)

o

airfin d

Nuλα = (1.17)

with h the distance between the fins (evaporator side 1.6 mm, condensor side 2.6mm), a the distance between two pipes in a row, 36.5 mm, and b the distance betweenthe rows, 27.5 mm, and all fluid properties evaluated at the average film temperatureat the inlet:

2,, averagefiningas

f

TTT

−= (1.18)

A difference in finα at the hot and cold side can be explained by a different fin

distance and a different temperature of the inlet air flow.

15

1.5. Heat transfer phase change

The resistance in the thermosyphon at the condenser side is defined as:

( )condcond

cond A

yR

αλδ 1== (1.19)

with δ the thickness of the condensate film in m and λ the thermal conductivity of thefluid.The local thickness of the condensate is yδ [14], assuming laminar flow following

Nusselt theory:

41

2

4��

�

�

��

�

�

∆∆=

fgfy hg

Ty

ρηλδ (1.20)

with fρ the fluid density in kg/m3, g the gravitational constant in m/s2, yδ the

thickness of the condensate in m, η the dynamic viscosity in Ns/m2, id the inner pipe

diameter, λ the local heat transfer coefficient W/mK, T∆ the temperature differencebetween saturation temperature and wall temperature, fgh∆ the latent heat of the fluid

in J/kg.

By draining heat at the condenser from the vapor, a film of condensate forms, whichbecomes thicker in the direction of the adiabatic zone. The film flows down to theevaporator conserving the film thickness in the adiabatic zone. At the evaporator, thefilm starts thinning under influence of the added heat. Under stationary operatingconditions of the thermosyphon, the local heat transfer coefficient over the condensercan be described by:

41

32

4 ��

�

�

��

�

�

∆∆

==condcond

fgf

LT

hg

ηλρ

δλα (1.21)

with condT∆ temperature difference between the wall and the saturation temperature at

the condenser side. condL in m is the position at the condenser.To investigate the heat transfer of thin downward flowing liquid films in a verticaltube, it is convenient to define a film Reynolds number [12]:

f

condf

m

µ�4

Re = (1.22)

with condm� the mass flow rate of liquid per unit of periphery idπ and fµ the liquid

viscosity in Ns/m2. Mention that this is equal to the Reynolds number for liquid flowin the tube only.Depending on Ref , three situation can be defined:

16

Ref < 20-30: A smooth and laminar filmRef > 30-50: Interfacial waves occur, which influence the heat transfer and

hydrodynamical behavior of the film.Ref > 1600: The film becomes turbulent with still present waves.

To analyze condm� , it is convenient to write the total mass flow of the liquid film as [5]:

fgh

Qm

∆=

�

� (1.23)

with fgh∆ the latent heat of the fluid J/kg and Q� obtained from equation (1.3).

Assuming laminar flow, the Nusselt theory can be applied again, now for mean filmthickness of downward flowing films:

3/13

1

2

231

2Re

4

33f

f

f

f

condl

gg

m��

�

�

��

�

�=

��

�

�

��

�

�=

ρµ

ρµδ

�

(1.24)

The mean heat transfer coefficient for a vertical tube is given by:

3/13

1

2

32

Re3

4 −

��

�

�

��

�

�== f

f

fff g

µλρ

δλ

α (1.25)

Another model for filmwise condensation is obtained from Butterworth, as stated byRohsenow et al. [12]:

( )3

12

22.1 2.5Re08.1

Re

��

�

�

��

�

�

−

��

�

�

��

�

�

−=

ggff

f

f

f

ρρρµ

λ

α (1.26)

with ρv the mass density of the vapour.

In the evaporator the condensed film evaporates due to pool boiling. The models ofCooper, see Eq. (1.27), and Gorenflo, see Eq. (1.28) describes this phenomena [15].

( ) ( )( ) 0.550.12 0.4343ln

0.5 0.67

55 0.4343lnpR

r rp P

M q

α −−

−

= − ×(1.27)

with pr the reduced pressure, Rp surface roughness in µm, M molecular weight of thecondensate in kg/kmol and q the heat flux.

17

( )( )

0.30.9 0.3

0.133

4500 20000

0.4

rp

PF

p

F q

R

α −= ×(1.28)

with ( )0.271.2 2.5 1PF r r r rF p p p p= + + − .

The total heat transfer coefficient, see Eqn. (1.29) and (1.30), is found from thesummation of the partial heat resistances, which are given by Eqn. (1.11), (1.13) andthe desired heat transfer coefficient of condensation or pool boiling.

1tot

tot finR Aα = (1.29)

with

finfinfinwwwfftot AAA

Rαηαα

111 ++= (1.30)

1.6. Results

The measurements are performed at steady state, after minimal 1 hour. For stability,each condition lasts 5 minutes. Figure 1.7 shows a typical example of the airflowtemperature histories during a measurement. This figure shows that the variation isless than 0.1°C.

0 60 120 180 240 300

Time [s]

0.00

0.50

1.00

1.50

2.00

2.50

3.00

Air

tem

pera

ture

[°C

]

mair = 0.4 kg/s, F e = 19%

T3

T4

T1

T2

Figure 1.7: Typical histories of temperatures up- and downstream of the evaporator: T3=78.21 ±0.03°C, T4=60.84 ± 0.02°C, T1=24.76 ± 0.03°C and T2=40.13 ± 0.02°C

The heat flow rate is measured from the temperature difference over the heatexchanger at the evaporator and condenser part of the heat pipe. At steady state bothheat flow rates should be equal. Figure 1.8 shows the comparison of the heat flowrates at the evaporator side and condenser part of the experiments. This figure shows

18

that the heat flow rate of evaporator is about 4% larger than the heat flow rate of thecondenser, for which we have no explanation.

0 5 10 15 20 25

Qcond [kW]

0

5

10

15

20

25

Qev

ap[k

W]

Figure 1.8: Comparison of measured heat flow rates at evaporator and condenser side of the heatpipe

In some cases the heat flow rate is that high that the heat pipe can dry out. TenPt100’s were mounted downstream the evaporator to measure the temperaturedistribution along the evaporator. Figure 1.9 shows four distributions at two processconditions for two filling degrees of the heat pipe. A local, nongradual increase intemperature along the evaporator indicates a dry out. The inner wall of thethermosyphon is in this situation not fully covered with liquid. This occurs at lowfilling degree and high heat flow rate (Fig. 1.9). If dry-out occurs, the measurement isskipped from the analysis. Chapter 2 will give a deeper look into the dry-out of thethermosyphon.

Figure 1.9: The effect of filling degree and of mass flow rate on temperature distributiondownstream of the evaporator

19

Figures 1.10 and 1.11 show the performance of the heat pipe at the evaporator side forvarious Reynolds numbers and filling degrees. In figure 1.10 the total heat transfercoefficient at Fe of 19% is shown, whereas Figure 1.11 shows results at the higherfilling degree. The figures show that the performance increase with increasing heatflow rate. An increase of the Reynolds number of the airflow (with the length scalechosen as two times the distance between the fins) leads also to a better performance.Some process conditions have been repeated with a higher filling degree. The resultsare given in figure 1.11. A higher filling degree gives a higher overall heat transfercoefficient at otherwise identical process conditions.

0 5 10 15 20 25

Q [kW]

0

10

20

30

40

50

60

α tot

[W/m

2 K]

Re=250

Re=500

Re=800Re=1400

Re=250

Re=500

Re=800

Re=1400

Figure 1.10: Measured heat transfer coefficient evaporator side for various Reynolds numbers atFe=19%

0 5 10 15 20 25

Q [kW]

0

10

20

30

40

50

60

α tot

[W/m

2 K]

Re=250

Re=500

Re=800

Re=1400

Re=250

Re=500

Re=800

Re=1400

Figure 1.11: Measured heat transfer coefficient evaporator side for various Reynolds numbers atFe=59%

Figures 1.12 and 1.13 show the performance of the heat pipe at the condenser side forvarious Reynolds numbers and filling degrees. Figure 1.12 presents the total heat

20

transfer coefficient at Fe of 19% and that of the filling degree of 59% is shown infigure 1.13. The figures show that the performance improves with increasing heatflow rate. An increase of the Reynolds number of the airflow leads also to a betterperformance. Some process conditions have been repeated with a higher fillingdegree. The results are given in figure 1.13. A higher filling degree gives a higheroverall heat transfer coefficient at some process conditions. The figures 1.10-1.13show that the performance of the condenser is better than that of the evaporator at thesame heat flow rate, if performance is measured in terms of net heat transfercoefficient.

0 5 10 15Q [kW]

0

10

20

30

40

50

60

α tot

[W/m

2 K]

Re = 400

Re = 800

Re = 800

Re = 400

Figure 1.12: Measured heat transfer coefficient condenser side for various Reynolds numbers atFe=19%

0 5 10 15Q [kW]

0

10

20

30

40

50

60

α tot

[W/m

2 K]

Re = 400

Re = 800

Re = 800

Re = 400

Figure 1.13: Measured heat transfer coefficient condenser side for various Reynolds numbers atFe=59%

21

1.7. Analysis

Figures 1.14 and 1.15 show a comparison of the measured total heat transfercoefficient and predictions based on models of pool boiling of Gorenflo and Cooper[15]. Figure 1.14 shows the comparison at airflow Reynolds number of 250 whereasfigure 1.15 presents the comparison at Re 800. In both cases the Gorenflo correlationpredicts a higher transfer coefficient than Cooper. Both correlations have the sametrend with respect to dependency on heat flux as the corresponding measurements.The difference between the two models and the measured ones could be caused by anoverestimate of the Nusselt number for the airflow to the fins. Here it is assumed thatthe fins have a constant temperature due to high thermal conductivity of the fins. Ifthe temperature is not homogenously distributed the Nusselt number is lower. Theheat transfer from the air to the fins has a large influence to the heat transfer, so anyuncertainty in it is directly reflected in discrepancies in comparisons like those ofFig.’s 1.14-1.15.

0 5 10 15Q [kW]

0

10

20

30

40

50

60

α tot

[W/m

2 K]

Re = 250

Gorenflo

Cooper

measured

Figure 1.14: Comparison of measured and predicted total heat transfer coefficient of theevaporator at airflow Reynolds number of 250

22

0 5 10 15 20 25

Q [kW]

0

10

20

30

40

50

60α to

t[W

/m2 K

]Re=800

Gorenflo

Cooper

measured

Figure 1.15: Comparison of measured and predicted total heat transfer coefficient of theevaporator at airflow Reynolds number of 800

Figures 1.16 and 1.17 show a comparison of the measured total heat transfercoefficient and predictions based on models of filmwise condensation of Butterworthand Nusselt [15]. The film Reynolds number has been taken into account (laminar gasand laminar liquid and condensate layer with waves). Figure 1.16 shows thecomparison at airflow Reynolds number of 400 whereas figure 1.17 presents thecomparison at Re 800. Figure 1.16 shows a fairly good agreement between thepredictions and the measurements. At higher airflow Reynolds number the differencebetween prediction and measured heat transfer coefficient becomes large (Fig. 1.17)and in this case the models underpredict the heat transfer. In both cases Butterworthpredicts a higher result than Nusselt. However, in both cases (Fig.’s 1.16,1.17) thepredicted heat flux decreases with increasing heat flow rate, which is a different trendthan the one measured.

23

0 5 10 15Q [kW]

0

10

20

30

40

50

60α to

t[W

/m2 K

]

Re = 400

measured

Butterworth

Nusselt

Figure 1.16: Comparison of measured and predicted total heat transfer coefficient of thecondenser at airflow Reynolds number of 400

0 5 10 15Q [kW]

0

10

20

30

40

50

60

α tot

[W/m

2 K]

Re = 800

measured

ButterworthNusselt

Figure 1.17: Comparison of measured and predicted total heat transfer coefficient of thecondenser at airflow Reynolds number of 800

For the predictions in Fig.’s 1.14-1.17 the Nusselt relation (1.14-1.17) for airflow hasbeen used. Apparently the best predictions are obtained with correlations for boilingin the heat pipe (Gorenflo or –even better- Cooper) and for convective heat transfer onthe gas side (Nusselt-relation (1.14-1.17)), if the last one is corrected slightly. Thereason why this correction is necessary is not fully clear, but might have to do withsome loss of contact between fins and tubes.

24

1.8. Conclusions

The performance of a heat pipe equipped heat exchanger on a laboratory test rig hasbeen measured and analyzed at the most common process conditions: various massflow rates of ambient air, various temperature differences between hot and cold sidesof the heat pipe and various filling degrees of the heat pipe. The heat pipe has nowick, so in fact it is a thermosyphon.The overall heat transfer of the heat exchanger has been assessed. At the evaporatorside 10 to 40 W/m2K has been measured and at the condenser side of the heat pipe 20to 50 W/m2K. The temperature distribution over the evaporator has been found to beindicative of proper filling degree.The results are rewarding, although more research has to be carried out to find themost suitable working fluid, the optimal heat pipe geometry, operating limits andfilling degree.A model to predict the heat transfer and to calculate the performance of the heat pipeequipped heat exchanger has been set up. This model is a first step towards a fullpredictive model to optimize the heat pipe equipped heat exchanger.The result of this study is that a heat pipe equipped heat exchanger can replace an airto air heat exchanger without loss of performance. The tested process conditions aretypical for warmer countries like Bahrain. This study therefore demonstrates that it ispossible to apply heat-pipe-based cooling equipment in practical conditions of warmercountries.

AcknowledgementsThe author is grateful to Harry Hagens for performing measurements.

25

Chapter 2: Single pipe experiments

2.1. Introduction

This chapter presents a study on the performance of a single 3 m thermosyphon with alarge length-to-diameter ratio of 187.5. The length of 3 m is relevant for furthercommercial use in a heat pipe equipped heat exchanger, which provides an alternativefor air-to-air heat exchangers at low air temperature differences High heat transferrates are required for compactness of the heat exchanger. The goals are to:

• Obtain a validation and/or improvement of the heat exchanger model obtainedfor evaporation and condensation in chapter 1. Heat transfer from air to fin isexcluded now, and the phase change heat transfer in the thermosyphon ismeasured. The results of this phase change heat transfer will be compared withresults from the literature.

• Control the heat input at a single tube to measure the temperature distributionover the tube and to determine the operating limits of the thermosyphon.Relationships between filling ratio, inclination angle, performance andoperating limit are to be derived, in order to facilitate future design ofthermosyphons / heat pipe equipped heat exchangers.

First, a theoretical approach with a literature survey concerning the operating limits,liquid inventory and effects of inclination of thermosyphons on the performance arepresented. Next, the test rig with the single 3 m thermosyphon will be described,followed by the experimental results and analysis.

26

2.2. Theory and literature survey

2.2.1. Heat flux limits in thermosyphons

For safe and optimal operation of a thermosyphon, it is important to know theoperating limit. According to [16], the boiling limit and the entrainment limit aredominant in a thermosyphon. The limiting heat flux depends on the working fluidproperties, the fluid temperature operating range and the geometry of thethermosyphon. To calculate this heat flux limit, several correlations were derived [16-24] for the working fluids water, methanol, ethanol and some refrigerants. All thesecorrelations are valid for a minimum filling degree of 40% of the evaporator invertical thermosyphons. These correlations are based on experiments conducted withinner thermosyphon diameters between 3 and 34 mm with the ratio of the evaporatorlength to its diameter up to 325. Results of the correlations from [16-24], calculatedfor the thermosyphon with R-134a as applied in our experiments are gathered infigure 2.1. Some expressions from [16-24] are summarised in appendix B.

Figure 2.1: The dependence of the maximum heat input on the temperature inthe thermosyphon with R-134a, length 3 m and diameter 16 mm according tocorrelations [16-24]

The correlations derived by [16-24] readily predict the heat flux limit of thethermosyphon at varying operation temperatures. The applicability of the mentionedcorrelations must be checked in a test rig before one of these correlations can beapplied to predict the heat flux limit in our specific situation of the thermosyphon of 3m length and with R-134a as working fluid. Unfortunately, this method does not giveany information about how to determine the optimal filling degree. It should be

27

mentioned that the filling degree in combination with the working fluid and the pipegeometry determines the operating limits [5,25,26]. A too low initial filling ratiowould lead to liquid film dry-out, where a too high initial filling ratio would lead toboiling liquid rushing up to the condenser (some authors call this the boiling limit,others the flooding limit). According to El Genk et al. [26], an increase in pipediameter results in a broader range of possible initial filling degrees that ensuresappropriate operation and a higher entrainment limit. An increase of the evaporatorlength decreases the initial filling ratio necessary to avoid dry-out at the same powerthroughput [26]. A minor effect on the possible boiling limit is reported if theevaporator length is changed. A change in the adiabatic or the condenser length hasno effect on the entrainment limit, as long as the filling degree is chosen well; enoughfluid to avoid liquid film dry-out and not too much fluid to avoid liquid rushing up tothe condenser. The initial filling ratio should be slightly increased if the condenserlength increases or the adiabatic length decreases. Abou Ziyan et al. [30] concludethat the adiabatic length in combination with the filling ratio is important for the heattransfer performance of the thermosyphon.

Depending on the working fluid and the geometry, the entrainment limit can bereached at high heat input; the downward flowing liquid film will break underinfluence of the high vapor velocity, flowing upward. If the filling degree is too low, adry-out of the evaporator will occur, before the entrainment limit is reached. Thisimplies that the condensation film thickness reaches below a critical level. On theother hand, the boiling limit is characterized by a bubbly flow reaching into thecondenser section, causing breakdown of the film condensation if the filling degree istoo high.

Reaching the dry-out limit or the entrainment limit is detected by an increasing non-stationary temperature of the evaporator. This was observed in the measurementsdescribed in chapter 1 with a filling ratio of 19%. The temperature gradient rises overthe evaporator length, with a maximum temperature at the evaporator end. The boilinglimit is detected by a temperature peak at the upper side of the evaporator in time,after which the temperature over the whole tube becomes equal [25]. At both limits,the heat transfer coefficient decreases [25]. At the boiling limit, the liquid can rise intothe condenser, causing a breakdown of the film condensation [28]. Collier [29]defines a so called ‘burnout pool boiling critical heat flux’ on which an inner walldry-out occurs, causing the wall surface temperature to jump. A transition fromnucleate pool boiling to film boiling is assumed. This definition of Collier, with acorrelation derived by Zuber [29], is the starting point of the derivation of theentrainment limit as found by Reay [8], as explained in the next alinea.

Another approach to determine the operating limits is derived from [1,8,12] and [27].The results of this approach can be seen in figures 2.2 and 2.3.

28

Figure 2.2: Operating limits of a thermosyphon, derived from [8, 12, 27, 29],

length 3 m, diameter 16 mm, R-134a

The vapour shear forces that entrain liquid droplets from the liquid film flowingdownward cause the entrainment limit. The liquid cannot flow back from thecondenser to the evaporator. The viscous limit can be reached at very lowtemperatures where viscous forces in the working fluid become dominant in the liquidflowing downward. The sonic limit may exist at high temperatures where chokingoccurs at the evaporator. Compressibility effects play a role in the internal fluid flow.From figure 2.2 follows that the entrainment limit is dominant in this case. Theentrainment limit is shown separately in figure 2.3. This performance limit predictionis less strict than most correlations in figure 2.1 suggest. This is probably due toapproach in the derivation of these heat flux limits. As stated before, the starting pointfor derivation of the entrainment limit by [8] is the ‘burnout pool boiling critical heatflux’ as defined by Collier [29]. Here a fundamental difference must be taken intoaccount: entrainment is caused by vapour shear forces in a counter-current annulartwo phase flow, but the critical heat flux of Collier accounts for critical pool boiling,which is a different phenomenon. For this reason, the maximum heat input for athermosyphon as proposed by [8, 12, 27, 29] is not regarded as realistic. It is expectedthat the correlations from [16-24] approximate the heat flux limits in our experimentsbetter, although a large scatter due to large variations in experimental parameters(length, diameter, working fluid, filling ratio etc.) is observed. The correlations from[16-24] do not clarify whether the entrainment or the boiling limit occurs.

29

Figure 2.3: Entrainment limit from [12], length 3 m, diameter 16 mm, R-134a

2.2.2. Inclination of the thermosyphon

It is reported [31], that the inclination angle of the thermosyphon affects heat transferin the condensation process. However:

• Due to large differences in operating conditions, geometries, working fluidand filling ratio, no conclusions can be drawn with regard to the optimuminclination angle from the studies found in the literature [32-35].

• Only the general conclusion that the condensation heat transfer coefficient isdependent on the inclination angle holds.

• The optimum angle is not affected by the heat flux or the temperaturedifference between the wall and the saturation temperature. Probably the flowstructure inside the thermosyphon affects the optimum inclination angle.

In the experimental apparatus in our study, the inclination angle of the thermosyphonwill therefore be varied to find if a certain inclination angle at a specific filling degreewould be advantageous for the maximum heat transfer capacity.

The working of heat pipes, with an internal wick, in for example space applications isbased on capillarity in the wick to bring the liquid in the tube to flow back to theevaporator, even against gravity. The thermosyphon does not have an internal wickand the liquid film flow from condenser to evaporator is based on gravity and wetting.From this point of view it stands to reason to expect that the thermosyphon operatesoptimal when the tube is situated vertically, with the condenser above the evaporator.Some research into the influence of an inclination of the thermosyphon on theperformance was carried out [33, 31, 35, 36]. An inclination (non vertical orientation,

30

angle is non-zero) will change the flow structure within the thermosyphon and couldaffect:

• The maximum heat flow possible.• The heat flow rate at a fixed temperature difference between evaporator and

condenser.• The optimum filling ratio.• The boiling and the condensation process.

To get more insight in this matter, an overview of earlier research on this topic will bepresented first. In the present study, a dedicated test will be carried out to find therelation between filling ratio, inclination angle and maximum heat transfer capacity ofa 3 m thermosyphon with R-134a as working fluid.

Larkin [36] analytically adapted the Nusselt film condensation model forcondensation within a thermosyphon under an angle and showed experimentally therelevance of his model to connect the minimum filling ratio with the operating limit ofthe thermosyphon by calculation of the condensate film flow. His experiments wereexecuted in a 0.61 m pipe with a diameter of 13.7 mm, with R-114 and R-22 asworking fluids. From the results presented, positioning the thermosyphon vertically ismost beneficial. This resulted in the broadest temperature operating range for bothworking fluids. The temperature operating range is limited by the temperature atwhich all working fluid is saturated vapor and the highest temperature at which thethermosyphon has normal conductivity i.e. enough liquid to wet the evaporator walland to sustain the natural cycle of fluid flow in the thermosyphon.Hahne and Gross [33] examined the maximum heat flow rate for a 2 m length and 40mm diameter thermosyphon filled with R-115 at 45% of the total volume. Theyconcluded that the maximum heat flow rate was obtained at an inclination of 40º tothe vertical, though in general the more vertical, the better the heat transfer. It wasalso found that the condensation has the largest thermal resistance in thethermosyphon e.g. the required temperature difference to transport heat. The optimuminclination angle was made plausible from a change in the condensation process. Theboiling process locally varied with varying inclination angle. The boiling heat transferincreased at small inclination due to bubble separating effects exerted by buoyancyand decreased at larger inclinations due to a concentration of bubbles at the upperwall.Negishi and Sawada [35] visualised a water and ethanol flow in a 0.33 m, 13 mmdiameter thermosyphon at filling ratio of 5-100% of the evaporator volume at variousinclination angles. They observed some interesting phenomena. At a 25% filling ratioof water, flooding occurred at an angle of 60º from vertical up to almost horizontalposition; a large amount of liquid rushed up to the condenser due to turbulent motionof the liquid caused by boiling bubbles. At 55% of water filling ratio, the liquid filmeven rose up to the condenser end in vertical position. At a water filling ratio higherthan 70%, bubble dashing and oscillations occurred; the working fluid is pushed up tothe condenser end by an explosive boiling bubble expansion. The vapor in thecondenser is compressed and the vapor bubbles collapse violently. At a small fillingratio of 5%, dryout occurred at 75º and more. A filling ratio of 10% or more andinclinations of less than 50º from vertical resulted in pool boiling at the evaporator. Ingeneral, the more the inclination becomes horizontal, the faster dry-out occurs. Forwater, a filling between 25-60% and an angle of 50-70º to the vertical was advised.Ethanol showed different behaviour. The best heat transfer was reached at small

31

inclination angles, less than 30º from vertical, although stable operation was observedup to inclination angles of 85º with a fluid inventory of 40-70%.Wang and Ma [31] observed that no uniform conclusion for an optimum inclinationangle of a thermosyphon can be drawn due to the varying operating conditions ofearlier research. They derived a model for condensation heat transfer within aninclined thermosyphon and presented a semi-empirical correlation for water asworking fluid. Depending on the filling ratio, the optimal inclination angle was foundto be 40-70º.Lock and Kirchner [37] experimentally studied the heat transfer of a 0.4 m, 20 mmdiameter thermosyphon, filled with water. The optimal inclination angle was found tobe 45-70º from the vertical, which was explained from a change of the flowphenomena at inclination.Zuo and Gunnerson [38] attempted to numerically calculate the minimum requiredmass of working fluid and maximum heat transfer at a specific angle for a tube of 1.5-2 m with a diameter of 17-38 mm, filled with distilled water. Their model assumedsteady state liquid film behaviour. They concluded that the minimum filling ratiorequired to maintain operation increased sharply at near horizontal position, but wasquite constant at lower inclination angles. With a constant heat transfer rate andincreased inclination angle, dry-out occurred faster. A maximum heat transfer ratewas found between 30-45º from vertical. This was due to the equilibrium betweenimproved condensation caused by secondary flows and decreased boiling heat transferat larger angles.Shiraishi et al. [39-41] visualised the internal flow phenomena of severalthermosyphon configurations. One tube of 0.93 m length, 13 mm diameter filled with80% R-113 showed maximum heat transfer capacity at 40º to the vertical. Theimproved heat transfer capacity at this inclination was due to the change of the flowpattern from annular to stratified flow. Two tubes of diameter 12 and 28,5 mm withan aspect ratio Levaporator/D of 30 and 5, with a filling ratio of 50% R-123 showed slugflow at inclination at aspect ratios larger than 10. The Bond number seems to haveless effect on the angle at which the heat transfer is at maximum. The Bond number isdefined as follows:

σρ 24 gRBo l= (2.1)

Typical Bond numbers in our experiments are between 16 and 34.A 11,1 mm tube with a R123 filling ratio of 80% at small inclinations and aspectratios larger than 10 showed heat transfer improving stratified slugs. For comparison:the aspect ratio in our experiment with the single tube 3 m thermosyphon (at VDLKlima) is 75 (evaporator of 1.20 m, diameter 16 mm).Terdtoon et al. [42, 43] reached the same conclusions as Shiraishi with a 10 mmdiameter tube with 80% and 150% R-123. A correlation between the Kutateladzenumber and the optimal inclination angle was proposed. The Kutateladze number isdefined as:

( )[ ]{ }41

21

ghA

QKu

glgfgevap σρρρ −= (2.2)

The Ku number in our experiments typically ranges from 1.9e-3 to 1.2e-1

32

Payakaruk [44] described the effect of dimensionless parameters Bo and Ku on heattransfer characteristics of an inclined copper thermosyphon. The working fluids werewater, ethanol, R-22, R-123 and R-134a with filling ratios of 50, 80 and 100%.Diameters were 7.5, 11.1 and 25.4 mm with aspect ratios varying from 5 to 40.However, for R-134a only two data points at a diameter of 7.5 and 11.1 mm werereported. Major conclusion was that the filling ratio had no effect on the optimalinclination angle and that fluid properties were the most important parametersinfluencing the optimal inclination angle. This influence was mostly visible between20-70º, although the results for R134a were not explicitly presented. The correlationsbased on Kutateladze numbers are rather inaccurate. First a correlation to predict themaximum heat transfer at vertical position was adopted. Then, a correlation to predictthe heat transfer at an angle was derived. These results agreed at best within +/-25%with the experiments.Hahne et al. [45] observed the phenomena occurring in a 0.5 m glass thermosyphonfilled with R115 at critical conditions. A breakdown of the heat transfer was found asa consequence of liquid flooding in the condenser region. An inclination of thethermosyphon prevented the heat transfer breakdown at flooding and the naturalcirculation cycle stayed stable. The advice was to fill the thermosyphon at a rate of20% below critical fill volume, which was defined here as about 0.4-0.5 of the totalthermosyphon volume, and slightly incline the thermosyphon from vertical. Thisenhanced the heat transfer capacity of the thermosyphon, without the risk of floodingthe condenser.Kudritskii [46] investigated internal coaxial inserts in the heating zone. Special insertsin the heating zone ensured the operation of the thermosyphon, even at very smallinclination to the horizontal. In a 0.25 m copper tube, diameter 20 mm, filled withdistilled water, an improved heat transfer was measured both at vertical and atinclined orientation. The improved heat transfer means that the same heat transfer at asmaller temperature difference between the evaporator side and the condenser sidewas observed. Depending on the type of insert, the optimal inclination angle at whichan equal amount of heat was transferred at a lower temperature difference between thehot and cold side of the experimental setup varied.

In general, this literature overview shows that further research is necessary to find anoptimum for the inclination angle, especially for the specific geometry of 3 m lengthand a large aspect ratio of 75. Not much research can be found on this subject withR134a as working fluid, despite the fact that fluid properties seem to influence theoptimum inclination angle with respect to the heat transfer to a large extent. Anotherconclusion is that the heat transfer can be enhanced with an inclination compared tothe vertical situation. This is due to a change in flow phenomena and a better heattransfer at the condenser side. Experiments are necessary to see in which respect theinclination of the thermosyphon can enhance the heat transfer capacity in the specificdesign. To predict the maximum heat transfer at inclination, only one correlation,based on the Kutateladze number and the maximum heat transfer at verticalorientation of the thermosyphon, was derived by Payakaruk [44]. Unfortunately, onlytwo data points for R-134a were reported in the derivation of Payakaruks correlation.These points are also at a smaller diameter (maximum 11.1 mm) and smaller aspectratio (maximum 40) than in our experiments (diameter 16 mm, aspect ratio 75).One has to keep in mind that predictions of the correlations for the maximum heattransfer at vertical can vary as much as 100% after extrapolation to the specific

33

situation in our setup. (See the section 2.2.1. ‘Heat flux limits in thermosyphons’ inthe above)

34

2.3. Experimental

The length of the tube is 3 m, of which the evaporator is 1.20 m and the condenser is1.45 m, the adiabatic section is 0.35 m. The tube is made of copper, 16 mm outerdiameter, wall thickness 0.8 mm, with a smooth inner surface. The length to diameterratio is large: 187.5. The working fluid is R-134a. The filling ratio can be varied;experiments are performed with a filling ratio of 25%, 62% and 100%, determined asdefined in the previous chapter. Before filling of the tube, the tube is at vacuum, soonly R-134a liquid and vapour fill the pipe. The pressure after the evacuation processis less than 6 Pa, due to residual inert gases, see appendix A.A schematic overview of the two phase closed thermosyphon mounted in the test rigis shown in figure 2.4.

Figure 2.4: Schematic overview of the test rig, dimensions in [mm]

35

Figure 2.5: Above: mounting of athermocouple at the wall and mounting of theheater elements with hose clips and thermalpasta (white). At the left: mounting of theheater elements, the fill nipple and thepressure sensor. Insulation is not shown

36

Thermocouples (K-type, appendix A, 0.75 ºC accuracy) are welded at the outer wallof the tube to measure the axial temperature distribution, Fig. 2.5. A thermocouple issoldered at every 190 mm. The K-type thermocouples are coupled with an IOtech 16-bit signal convertor (appendix A). Inclination of the thermosyphon is sideways so thatthe thermocouples, all mounted in the front, are located in the middle at all angles toavoid deviations between thermocouples in almost horizontal position wheretemperature differences over the perimeter of the thermosyphon are to be expecteddue to partially dry-out.At the evaporator end, the pressure is measured with a WIKA type RB manometer, ata frequency of 100 Hz, with an accuracy of 2% after calibration. The manometeroutput is averaged and read at 1 Hz. The range of the manometer is 0 – 100 bar. A 16-bit signal convertor is applied for data acquisition. At the top, a Pt-100 of 0.06 mprobe depth is mounted into the tube, to measure the saturation temperature.Calibrations are given in appendix A.

The experimental apparatus is shown schematically in Fig. 2.6. An electric heater isattached at the evaporator outer wall, consisting of three 4 mm diameter heaterelements, 1.20 m heated length of 650 W each, distributed equally over the perimeterand placed in axial direction, Fig. 2.5. To enhance the thermal contact between theheater elements and the tube, thermal pasta is applied equally over the length of theheaters. Together with equally spaced hose clips around the heater elements, allmounted with a 3 Nm moment, the heat input can be regarded as uniform over theevaporator length, Fig. 2.6. The heat input by the electric heater is controlled by aGossen Wattmeter and measured within 1% accuracy. A 20 mm layer of polyethylenefoam insulation surrounds the condenser section with the water jacket. The evaporatorsection with the heater elements is surrounded by a 40 mm glass wool insulation tominimize heat losses to the environment. The heat losses are measured with a TNOPU55 heat flux sensor at 2% accuracy, positioned on the outside of the insulation. Atthis position with the calibration constant of the heat flux sensor and with themeasured voltage at 0.5% accuracy, the heat loss to the surrounding can be calculatedto be 0.5% of the heat input at worst. The heat flow rate at both the condenser and theevaporator is corrected for these heat losses to the environment.Tap water flows through the water jacket surrounding the condenser for cooling. Thetap water flow is measured by an Altometer 41BNW15 flow meter, suitable for flowvelocities of 0 – 1 m/s and flow rates of 0 – 0.17671 l/s within 0.01 l/s accuracy.The temperature of the water is measured before and after the water jacket with twoPt-100 (IC Istec ME 1009, appendix A) sensors. The Pt-100 sensors are all calibratedwith accuracy better than 0.1°C for the temperature range of 0 – 100°C. The rejectedheat at the condenser is calculated according to Eq. (2.3), after substitution of theappropriate values for tap water.

TcmQ p ∆⋅⋅= (2.3)

The two Pt-100 sensors for measuring tap water inlet and outlet at the condenser havean offset. Values of Q from Eq. (2.3) are calculated with the corrected values of thesetemperatures only. Values of this offset are found in an isothermal run and are givenin appendix A.The angle to the vertical is adjustable up to 16° by rotating the tube in its construction.Any larger angle is possible by rotation of the whole construction to angles over 90°.

37

Measurements are performed at inclination angles from 0° to 87°. The angle isdetermined with a Mitutoyo Pro 360 Digital Protractor at 0.2° accuracy, see appendixA.Within the tap water circuit for cooling of the condenser section, a 2 kW boilerenables preheating of the cooling water. By controlling the cooling water mass flowand temperature at the condenser and the heat input of the heater elements at theevaporator, the saturation temperature inside the thermosyphon can be variedindirectly between 20°C and 75°C. This corresponds with pressures of 5.7 – 20.6 bar.A recirculation tube from the condenser exit to the pump enables mixing of the heatedcooling water from the condenser outlet with tap water from the boiler. In this way weare able to preheat enough water above 60°C to compensate for the too small capacityof the boiler and high cooling water temperatures are achieved, see Fig. 2.6. At thetop of the condenser all air possibly caught in the cooling water system can exit with awater overflow to a sink. A part of the cooling water flows through the recirculationtube back to the pump.

Figure 2.6: Schematic view of the experimental setup

38

2.4. Experimental Results

The following results will be presented:• A typical temperature distribution over the thermosyphon at the operating

limit• The effects of varying the saturation temperature between 20°C and 75°C on

heat transfer for the vertical orientation with a filling ratio of 62%.• The effects of the angle of inclination for constant filling ratio and saturation

temperature on heat transfer.• The effects of changing the filling ratio from 62% to 25% and 100% on heat

transfer.• The operating limits depending on saturation temperature and angle of

inclination.

2.4.1. Temperature distribution at operating limit

Figure 2.7 shows a typical example of the wall temperatures at the heat transfer limit /operating limit. This is clearly the entrainment limit: the temperature at the evaporatorend starts to increase due to a lack of liquid. The liquid does not reach the end of theevaporator because it evaporates before that time and vapour shear forces entrainliquid resulting in film break up. Every time an operation limit was reached, this typeof temperature history has been seen. This is in agreement with the observations of[16, 30]. Park et al. [25] observed a boiling limit at filling ratio of 50% and higher.This is not observed in our experiments. At low filling ratio (in their case 10%), theyobserve the same entrainment limit as seen in all our measurements.Only at almost horizontal orientation and high saturation temperature >75°C, the heatflux limit could be observed as an intermittent dry-out, figure 2.8. All walltemperatures stabilize at a high level, starting with the evaporator end in the directionof the condenser. A temporary drop in evaporator end temperature is observed. In analmost horizontal position, the liquid can easily flood the condenser, causing abreakdown of the condensation process and dry patches in the evaporator section.This is in agreement with the results of Gross [28] as stated for a vertically orientedthermosyphon. From this point of view it is reasonable to conclude that thisintermittent dry-out matches with the effects mentioned as the boiling limit. Although,the time history as measured in our experiments does not agree with the time historyobserved by Park [25]. Shiraishi et al [39, 40] visualised the flow behaviour at almosthorizontal position with a d=13 mm glass tube filled with R-113, figure 2.8 RHS. Theobserved flow patterns by [39, 40] agree with the measured temperature histories ofour measurements.

39

Figure 2.7: LHS: Temperature history at operating limit

RHS: Sketch of flow pattern at entrainment limit

Figure 2.8: LHS: Temperature history at operating limit at large inclination andhigh temperatures. RHS: Flow pattern observed by [39] (d=13 mm, R-113).

40

2.4.2. Saturation temperature

The measurements are performed at steady state and each condition lasts at least 5minutes (one measured point). Fig. 2.9 shows a typical example of the walltemperature history at steady state condition. Maximum standard deviations are 0.2.

Figure 2.9: Typical histories of wall temperatures, Q = 400 W with verticalorientation, Fe = 62%.

Figure 2.10 shows the heat flow rate measured from the temperature difference overwater outlet and water inlet at the condenser side and the electric heater at theevaporator side. The error bars on the measured condenser heat flow rates account forthe accuracies of the cooling water flow meter and cooling water temperaturedifference measurements. At steady state these heat flow rates should be equal. Thisfigure shows that all measurements match within +/- 10%. Deviations are due toinaccuracies in correction for heat losses to the environment. All measurements in thisfigure present the results of the thermosyphon at vertical position with a filling ratioFe of 62% (2.4). The saturation (working) temperatures are 20, 35, 40, 55, 65 and 75°C.

evap

fe V

VF = (2.4)

41

Figure 2.10: Comparison of measured heat flow rates at evaporator andcondenser at Fe=62%, vertical, for various saturation temperatures

Figure 2.11 shows the mean wall temperature difference between the evaporator andthe condenser. The mean condenser temperature is defined as the average of 4thermocouples at the condenser wall, the mean evaporator temperature is the averagedwall temperature of 6 thermocouples at the evaporator wall. The temperaturedifference between condenser and evaporator increases with increased heat flux. Atincreasing saturation temperature, the temperature difference decreases slightly atconstant heat flux, but taking the accuracy of the temperature difference into account,this trend is too weak to draw conclusions. Some data points show a deviation fromthe trend in temperature differences at increasing heat flow rate. These data points areobserved at the highest heat fluxes achievable at the corresponding saturationtemperature. These inconsistencies are due to a jump in evaporator temperatures at theheat flux limit causing a larger temperature difference than would be in the line ofexpectation; see the temperatures in figure 2.7.

42

Figure 2.11: Measured mean temperature differences between evaporator andcondenser for various saturation temperatures at Fe=62%, vertical

Most desirable for analysis is a clear separation between the evaporation and thecondensation process. For example, some research was carried out on condensationinside thermosyphons, as reviewed by Gross [28]. This research focussed on modelsfor heat transfer in film condensation and experimental determination of heat transferin the condensation process.To calculate a heat transfer coefficient for the condensation process, both thecondenser wall temperatures and the saturation temperature need to be known. In ourexperiments, the saturation temperature is measured with an inside Pt-100, but manyauthors take the adiabatic section temperature as the saturation temperature. Fromfigure 2.12 follows that the adiabatic wall temperature not always is the same as theinner saturation temperature. A match is only observed at high heat transfer rates. Themeasured saturation temperature seems to have a systematic error at low heat transferrates. Possibly condensation on the inner Pt-100 occurs, resulting in too lowtemperatures. The saturation temperature is alternatively calculated from themeasured saturation pressure with the Antoine relation (2.5). However, this is lessaccurate taking the accuracy of the pressure measurement into account.

( ) CpA

BT −

−=

ln(2.5)

with A=10.52, B=2484, C=263.1, pressure in bar, T in °C

43

Figure 2.12 gives a typical example of the differences in saturation temperaturedepending on whether the saturation temperature is obtained with the inner Pt-100(called ‘Saturation’), averaged adiabatic wall temperature (called ‘Adiabatic’) or withthe Antoine relation (called ‘Pressure sensor’). The same discrepancies betweensaturation temperature, adiabatic wall temperature and saturation temperatureobtained from pressure measurements can be observed at lower saturationtemperatures, other filling ratio and inclination angles. Care needs to be taken whenzooming in on the evaporation or condensation process separately, because in order tocalculate heat transfer coefficients accurately at the condenser and evaporator, acorrect temperature difference between condenser, saturation and evaporator is ofgreat importance. In view of figure 2.12, the adiabatic wall temperature measuredwith two thermocouples has been selected for further analysis of the condensation andevaporation process.

Figure 2.12: Typical deviation in measuring the saturation temperature withseveral methods, compared with the mean evaporator and condensertemperature

The heat transfer coefficient α at the condenser side is now defined by (2.6) and at theevaporator side by (2.7):

( )condadiabaticcondcond TTA

Q

−=α (2.6)

( )adiabaticevapevapevap TTA

Q

−=α (2.7)

44

This yields the results of Fig.’s 2.13 and 2.14. Heat transfer coefficients forcondensation are around 1500 W/m2K and not very sensitive for heat transfer rate andsaturation temperature. However, a minimum in condensation heat transfer coefficientof 1300 W/m2K exists around a heat transfer rate of 500 W, independent of thesaturation temperature. At heat transfer rates up to 400 W, a higher saturationtemperature is beneficial for condensation heat transfer, for example: 1800 W/m2K at200 W for Tsat = 75°C versus 1400 W/m2K at 200 W for Tsat = 20°C. Also, anincrease in condensation heat transfer coefficient with increasing heat transfer ratesabove 500 W is observed for all saturation temperatures.Heat transfer coefficients for evaporation increase from 1000 to approximately 3000W/m2K with increasing heat transfer rates, figure 2.14. At the heat transport limit, theevaporation heat transfer coefficient levels off. Higher saturation temperaturescorrespond to a slightly higher heat transfer coefficient for evaporation at given heattransfer rate.

Figure 2.13: Measured heat transfer coefficient condenser side for varioussaturation temperatures, Fe=62%, vertical

45

Figure 2.14: Measured heat transfer coefficient evaporator side for varioussaturation temperatures, Fe=62%, vertical

2.4.3. Angle of inclination with the vertical

Similar steady state measurements as shown by Fig’s. 2.9 and 2.10 are performed forconstant saturation temperature of 20 °C, but with variation in inclination angle, seeFig. 2.15. Measurements are performed at a filling ratio of 62% again, at inclinationfrom vertical of 0, 8, 16, 30, 60 and 83°. Not shown, but also performed aremeasurements at 75°C at angles of 0, 60, 83 and 87°, which gave similar results,except for the heat transport limit. Figure 2.16 shows the mean temperature differencebetween condenser and evaporator again. Measurement points at the transport limitcause the scattering at high heat flux. Figure 2.17 shows a slight increase of condα at

low heat flux if the inclination angle increases. Coefficient condα is found to be in therange of 1300 – 2200 W/m2K. Heat transfer coefficients at the evaporator sideincrease from 1000 to almost 4000 W/m2K at increasing heat flow rate, Fig. 2.18.

46

Figure 2.15: Comparison of measured heat flow rates at evaporator andcondenser for various inclination angles, Fe=62%, Tsat=20ºC

Figure 2.16: Measured mean temperature differences between evaporator andcondenser for various inclination angles, Fe=62%, Tsat=20ºC

47

Figure 2.17: Measured heat transfer coefficient condenser side for variousinclination angles, Fe=62%, Tsat=20ºC

Figure 2.18: Measured heat transfer coefficient evaporator side for variousinclination angles, Fe=62%, Tsat=20ºC

48

2.4.4. Filling ratio

A similar steady state procedure as described above is applied to measure at differentfilling ratio, figure 2.19. An easy method to calculate the filling ratios, defined as(2.4), for the thermosyphon at rest at different temperature is found in appendix A.Saturation temperature and orientation are kept constant (20°C, vertical). All previousmeasurements were performed at a filling ratio of 62%, which resulted in a goodworking of the thermosyphon system up to the operating limit. A filling ratio of 100%is chosen to see the sensitivity on overfilling the thermosyphon, where a filling ratioof 25% results in a forced dryout within the working temperature range. Figure 2.20presents the mean temperature difference between the evaporator and condenser invertical orientation at a saturation temperature of 20°C for filling ratios of 25, 62 and100%. Again, with increased heat flux the temperature difference increases. Deviatingpoints at the highest heat flow rates are due to the fact that these measurement pointsare taken at the heat transport limit. At a filling ratio of 25% the temperaturedifference between condenser and evaporator is structurally higher at constant heatflux compared with filling ratio of 62% and 100%.

Figure 2.19: Comparison of measured heat flow rates at evaporator andcondenser for various filling ratios, vertical, Tsat=20ºC

49

Figure 2.20: Measured mean temperature differences between evaporator andcondenser for various filling ratio, vertical, Tsat=20ºC

2.4.5. Heat flux limits

In figure 2.21, the heat transport limit at vertical orientation at various filling ratio canbe observed to decrease with increasing saturation temperature. Only one point at25% filling ratio was measured. At higher temperature, only the gaseous phase ispresent at this underfilled case, see appendix A. At 20°C the operation limit is about900 W, decreasing to 500 W above 80°C.A higher heat transport limit is observed at a higher inclination with respect to thevertical in figure 2.22: from 900 W in vertical orientation at 20°C to 1200 W inalmost horizontal position at 20°C. The trend of a decreasing heat transport limit withincreasing temperature is coherent for all measurements, also when the thermosyphonis inclined.

50

Figure 2.21: Operating limit of the thermosyphon vs. saturation temperature forvarious filling ratios

Figure 2.22: Operating limit of the thermosyphon vs. inclination angle forvarious filling ratios and saturation temperatures

51

2.5. Analysis

The temperature difference between evaporator and condenser is related to the totalheat resistance of the thermosyphon according to (2.8):

QRT ⋅=∆ (2.8)

The heat resistance seems rather constant for increasing power, 0,013 – 0,022 K/Wfor varying saturation temperatures, figure 2.11. This simplifies the design of a heatpipe equipped heat exchanger. The lower the temperature difference per Watt, thelower the total heat resistance. When neglecting the wall heat resistances of thecopper tubing, a lower total heat resistance results in higher combined heat transferrates of boiling and condensation. In general, at a filling ratio of 62% in verticalposition, saturation temperature does not influence the heat resistance of thethermosyphon dramatically, except for the operating limit. This will become clearlater.

No clear correlation can be found between the total heat transfer resistance and theangle of inclination. Again, the combined condensation and evaporation heat transferis rather constant over the heat transfer rate and inclination angle range, see figure2.16.A remarkable result is the constant working of the thermosyphon even up to almosthorizontal orientation. No optimal angle could be detected. This is contradicted to theresults from the literature survey in section 2.2.2., where several authors advised(different) optimal inclination angles depending on operating conditions.

From figure 2.20 it becomes clear that even at non-dryout the lowest filling ratio of25% has a higher heat transfer resistance. Overfilling has no influence on thebehaviour of the thermosyphon.

The saturation temperature and inclination angle do not dramatically influence theheat resistance of the thermosyphon. But both variables do change the heat transportlimit of the thermosyphon as shown in figures 2.23 and 2.24. To gain more generalresults, the heat flux is given in W/m2 evaporator area. Zuo et al. [38] observed dry-out to occur faster at larger inclination from vertical. This is contradicted to thepresent measurements.

52

Figure 2.23: Operating limit in W/m2 evaporator area of the thermosyphon vs.saturation temperature for various filling ratios

Figure 2.24: Operating limit in W/m2 evaporator area of the thermosyphon vs.inclination angle for various filling ratios and saturation temperatures

53

We have no clear explanation for the increased heat transport limit at higherinclination angles. Probably, the orientation influences the fluid flow in thethermosyphon, as well as the condensation process. To gain more understanding, anoptically accessible thermosyphon scale model will be developed, scaled to diameterand static contact angle of the fluid on the wall. This work is still in progress.

The measured values of the heat transport limit as a function of the saturationtemperature agree within 100 W with the correlations of Tien [20] and Nejat [18],described in the section ‘heat flux limits in thermosyphons’, however thosecorrelations are extrapolated to this specific geometry (L/D = 187.5), working fluid(R-134a) and only valid for vertical orientation of the thermosyphon. It seemsnevertheless useful to apply one of the proposed correlations as a design aid for a heatpipe equipped heat exchanger. The data from the operating limit measurement arecompared with correlations from literature in figure 2.25. Both correlations of Tien

and Nejat are in the form of2

21

1

a

evapL

dBoaq

��

�

�

��

�

�⋅⋅=′′ with a1 and a2 constants. It stands

to reason to fit the present measured data in a correlation of the same form. This leadsto the following equations, valid for a thermosyphon with R-134a on saturationtemperatures between 0˚C and the critical temperature:

24

1

02.090.0

21

51

1

101.014.0

���

�

�

���

�

�

��

�

�

��

�

�+

��

���

�

���

����

�−⋅±=

±

f

g

evap

c

Ld

BoT

TKu

ρρ

(2.9)

( )( ) 41

21

gfgfg ghKuq ρρσρ −∆⋅=′′ (2.10)

evapAqQ ⋅′′= (2.11)

with Bo from Eq. (2.1), T in K and Tc the critical temperature of R-134a in K.The datafit from the present measurements is shown in Fig. 2.25 and with the leastsquares error estimate an agreement with data of Fe=100% of F=29.2, r2=0.936 andFe=62% of F=129.8 and r2=0.97. The correlation coefficient r2 is defined by

( ) ( ) ==−−= N

i i

N

i i yyyyr1

2

1

22 ˆ(2.12)

where N is the number of measurements with outcome yi, �i are the corresponding

predictions with the fit function, and�

is the average of the set {yi}. The number ofparameters used in the fit, k, of course affects the quality of the fit. Whereas thecorrelation coefficient should preferably have a value close to 1, the parameter Fshould at the same time have a maximum value:

54

( ) ( ){ } ( ) ( )1ˆˆ1

2

1

2 −−⋅−−= ==kkNyyyyF

N

i ii

N

i i (2.13)

Obviously, the approach to determine thermosyphon operating limits with the theoryderived in [1, 8, 12, 27], for example by Reay, gives no results in agreement with themeasurements presented. Compare figure 2.23 with figure 2.3. Reay [8] overestimatesthe heat transport limit by a factor 4 – 6.

Figure 2.25: Operating limits of a thermosyphon with R-134a, length 3 m,diameter 16 mm, correlations of Tien [20] and Nejat [18] compared with the newmeasured data.

Eq’s (2.9-2.11) hold for a vertical orientation of the thermosyphon. From Fig. 2.24 itwas concluded that an increase of the inclination angle increases the operating limit atall temperatures. Although not enough data points are available for an extensivestatistic fit, it is proposed to add this sensitivity of the operating limit on inclinationangle in the Eq.’s (2.9-2.11). A fit on the data shown in Fig. 2.24 results in thefollowing equation for the operating limit depending on inclination angle:

���

����

�⋅���

����

�++⋅= β210 1 A

T

TAQQ

c

(2.14)

with Q0 the operating limit obtained from (2.11), saturation temperature T in K and Tc

the critical temperature of R-134a in K. A1 is –0.01253+/-10% and A2 is 1.01448+/-10%. Fit parameters of better than F=43.76 and r2=0.879 are obtained. β is denoted

55

as the inclination with the vertical from 0˚ to 90˚. All errors indicated are for a 95 %confidence interval. The fit of (2.14) is obtained from data shown Fig. 2.24, soextrapolation outside the shown temperature area should be done with prudence.

Measured heat transfer coefficients are compared with models described in chapter 1:Nusselt and Butterworth for condensation heat transfer, Fig. 2.26, and Cooper andGorenflo for evaporation, Fig. 2.27. Comparisons are in the case of Fe=62% at verticalorientation of the thermosyphon.Both models for condensation are sensitive to the saturation temperature. Thischanges pressure and fluid properties involved. In the results from measurements, noclear sensitivity on saturation temperature can be observed. Butterworth predicts toohigh heat transfer coefficient in this case. The results of the Nusselt model matchbetter with the measurements. However, Nusselt predicts an overall downward trend.But, above 500 W the measured heat transfer coefficients increase again (Ref >50),Fig. 2.13. This is possibly due to turbulent waves in the liquid film, enhancingcondensation heat transfer. Nusselt does not take this into account and is only valid inthe laminar case. This is probably also the explanation why the Nusselt model doesnot show the increasing trend at high heat transfer rates in chapter 1, Fig’s 1.16 and1.17. It is recommended to enhance the film condensation model of Nusselt to amodel which takes turbulent liquid film flow with countercurrent vapour flow intoaccount, as done by Thumm et al. [47]. This is model is expected to agree better withthe present measurements, but is not implemented (yet) due to time limitations.

Figure 2.26: Comparison of measured and predicted heat transfer coefficientcondenser side at various saturation temperatures, vertical, Fe=62%

56

Similar to the applied models for filmwise condensation, the models for evaporation,Cooper and Gorenflo [15], are sensitive to changes in saturation temperature. This ismainly due to the saturation pressure, which is an important parameter in the models.For example Cooper:

( ) ( )( ) 0.550.12 0.4343ln

0.5 0.67

55 0.4343lnpR

r rp P

M q

α −−

−

= − ×(2.15)

Cooper predicts the heat transfer coefficients for evaporation well, however heattransfer is overestimated at higher temperatures. If the influence of saturationtemperature expressed in the reduced pressure is decreased, a better agreement withpresent measurements is achieved. Our proposal is to apply Cooper’s model forevaporation with an adjustment of the power -0.55 in Eq. (2.15) to –0.25, see Fig.2.28. This still needs to be further optimized. With the momentary adjustment, heattransfer coefficients for evaporation at vertical orientation can be predicted. Themodel accounts for 91.6% of the variability in the data (= r2) up to the operating limitat high temperatures and for 97.2% at low temperatures. Gorenflo overestimates theheat transfer coefficients in all cases. However, higher saturation temperatures resultin a higher heat transfer coefficient at similar heat flow rate. In general, higher heattransferring coefficients are measured at the evaporator side than at the condenserside, except for a heat flux below 200 W. Fig. 2.17 shows that condensation heattransfer at low heat transfer rates increases with an increase of the inclination angle atconstant saturation temperature. This effect vanishes at heat transfer rates above 700W. The heat transfer coefficient at the evaporator side does not show a clearrelationship with the angle of inclination.

57

Figure 2.27: Comparison of measured and predicted heat transfer coefficientevaporator side at various saturation temperatures, vertical, Fe=62%

Figure 2.28: Comparison of measured and predicted heat transfer coefficientevaporator side with the adjusted model of Cooper at various saturationtemperatures, vertical, Fe=62%

58

2.6. Conclusions

In this chapter a study on the performance of a 3 m thermosyphon with a large lengthto diameter ratio of 187.5, filled with R-134a was presented. Heat transfer coefficientsfor condensation resulted to be around 1500 W/m2K, not very sensitive for changes insaturation temperature and inclination angle. Evaporation heat transfer coefficientsincrease from 1000 to over 3000 W/m2K for increasing heat flow rate. The heattransfer coefficients for evaporation are neither sensitive to saturation temperature norinclination angle.

The angle of inclination, varied from 0 - 87º does not affect the heat resistance of thethermosyphon. No optimal angle could be found. However, the heat transport limitincreases with increasing angle at equal process conditions, for which we have noexplanation. Most remarkable is the proven operation up to an angle of 83º withoutany loss of performance.

The heat transport limit depends, besides from angle of inclination, from thesaturation temperature. Measurements show fair agreement with correlations topredict the heat transport limit of a thermosyphon from Tien [20] and Nejat [18].Based on the mentioned correlations and present measured data, a new correlation isconstructed, which takes both saturation temperature and inclination on the operatinginto account.In the experimental temperature range (20 - 85ºC), the operating limit decreases withincreasing saturation temperature. This is due to temperature dependant fluidproperties. The entrainment limit resulted to be dominant.

From measurements we conclude that the filling ratio does not influence the operationof the thermosyphon in any aspect (saturation temperature, inclination and transportlimit) as long as enough fluid is present to avoid dry-out in all process conditions.Overfilling is not advisable taking the risk of flooding of the condenser into account,although this was not observed in the experiments except for almost horizontalorientation of the thermosyphon. Experiments were carried out with filling ratios of25, 62 and 100%. At 25% dry-out occurred.

The model of Cooper is in fair agreement with the measured values to predictevaporation heat transfer, but an overprediction of the heat transfer coefficients occursat high saturation temperatures. To avoid this overprediction, the influence thesaturation is decreased by adjusting the model of Cooper. This results in goodagreement between predictions and present measurements. The model of Nusseltfairly predicts the condensation heat transfer at low heat transfer rates, but predicts toolow values at high heat transfer rates. Nusselt does not take turbulent film heattransfer into account, which is expected to occur at higher heat transfer rates.Enhancement of the model to predict the condensation heat transfer, as done byThumm et al. [47], is seen as necessary to obtain a better agreement with the presentmeasurements.

59

Chapter 3: Design program for a Heat Pipe Heat Exchanger

3.1. Introduction

This text is meant as a manual for the use of the Matlab program HPHE.m, appendixE, to design a heat pipe equipped heat exchanger to cool an air flow. With the aid ofthis computer program, the design for an air-to-air heat exchanger with heat pipes canbe optimised for the process parameters such as air mass flow and temperatures atinlet and outlet.The program is developed for internal use by VDL Klima bv. The quantitiesexpressed in this chapter deviate from the general nomenclature of this report. Thequantities in this chapter refer to the computer code of the HPHE.m design program.In first instant the working fluid in the pipes is R134a. The pipes are made of copper,with aluminium fins. At the upperside, cold air is fed, where at the lower side the hotair comes in as shown in figure 3.1. The designer can easily change geometry andconstruction materials. Other working fluids can be easily implemented in the code.

Figure 3.1: General schematic layout of the Heat Pipe Equipped Heat Exchanger

60

3.2. Main HPHE program structure

At the start of the design process, the customer defines the total cooling power of thedevice Q in kW, the maximum allowable pressure drop over the coil at both the hot(evaporator) and cold (condenser) side, declared as deltapmax and the desired outletair temperature at the hot side, Thu in °C, with the total air volume flow Vwarm inm3/h. Also, an air inlet temperature Tci in °C is defined, see figure 3.2.

Figure 3.2: Fill out screen for customer requirements

As a first choice for the designer, one chooses the air volume flow of cool air at theentry Vkoud in m3/h. The next step is to define a geometry for the heat pipe heatexchanger, containing choices for: distance between the fins at both sides hvinwarmand hvinkoud in m, the length of the pipe in both the hot and cold section Levap andLcond in m, the width of the heat exchanger Bevap and Bcond in m, the depth of thecoil L in m and the thickness of each fin deltafin in m. See figure 3.3

61

Figure 3.3: Fill out screen for the designer (1)

By defining this geometry, one fixes the total number of fins at the hot and cold sideNfinevap and Nfincond respectively:

hvinwarmdeltafin

LevapNfinevap

+= (3.1)

hvinkouddeltafin

LcondNfincond

+= (3.2)

Next, the distances between the pipes should be defined in both the transversaldirection Pt (in width, within one row) and longitudinal direction Pl (distance in depthof the coil, between the rows) in m. Together with the defined depth and width of theheat pipe heat exchanger, the number of pipes in every row Nt and the number ofrows Nl is known:

62

Pt

BevapNt = (3.3)

Pl

LNl = (3.4)

This results in a total number of pipes N in the heat exchanger, taking a staggered tubearrangement into account:

( ) ( )2NlNtNlN −⋅= (3.5)

For further calculations, the designer declares the inner and outer diameter of thepipes Di and Do in m, the heat transfer coefficient of both the fin material lambdavand pipe material lambdabuis in W/mK, the tensile strength of the pipe material Sbuisin Pa and a local finlength lf in m, figure 3.4.

63

Figure 3.4: Fill out screen for the designer (2)

Now, the program will calculate the relevant heat transferring areas in m2, theminimal free flow area in m2, the surface area density m2/m3, the free flow ratio andhydraulic diameter in m. The primary area is the area of the pipe outer diameter in theair flow, at the hot and cold side respectively:

( )NfinevapdeltafinNLevapDoAph ⋅−⋅⋅⋅= π (3.6)

( )NfinconddeltafinNLcondDoApc ⋅−⋅⋅⋅= π (3.7)

The secondary area is the heat transferring surface of the fins at the hot and cold siderespectively:

64

( ) NfinevapNDoLBevapAfh ⋅��

���

� ⋅⋅−⋅⋅= 422π (3.8)

( ) NfincondNDoLBcondAfc ⋅��

���

� ⋅⋅−⋅⋅= 422π (3.9)

This results in a total heat transferring area at the hot and cold side:

AfhAphAh += (3.10)

AfcApcAc += (3.11)

For the calculation of the free flow area it is necessary to check how the pipearrangement limits the flow through the heat exchanger. Therefore, dubbelah,dubbelac, bh, bc, ch and cc are calculated [48]. This results in the free flow area Aohand Aoc.The frontal area of the heat exchanger at the hot and cold side is defined as:

LevapBevapAfrh ⋅= (3.12)

LcondBcondAfrc ⋅= (3.13)

Knowing the frontal areas and the free flow area, the free flow ratio is:

Afrh

Aohffrh = (3.14)

Afrc

Aocffrc = (3.15)

The surface area density is defined by:

LLevapBevap

Ahsadh

⋅⋅= (3.16)

LLcondBcond

Acsadc

⋅⋅= (3.17)

Now, the hydraulic diameter becomes:

sadhffrhDhh ⋅= 4 (3.18)

sadcffrcDhc ⋅= 4 (3.19)

Within the program, temperature dependant data for air are built in. From data ofNIST [4], the Prandtl number, density in kg/m3, viscosity in Pa*s, conductivity in

65

W/mK and specific heat in J/kgK of air are calculated. These are necessary for theheat balance. At the hot side, the temperature Thu and volume flow Vwarm aredefined. The temperature enables the calculation of the air density rholuchth and withthe volume flow, this leads to a mass flow mdoth in kg/s and a mean air velocityvmeanh in m/s at the hot side.

3600VwarmVw = (3.20)

rholuchthVwmdoth ⋅= (3.21)

Afrh

Vwvmeanh = (3.22)

With a prescribed cooling power Q and the calculated mass flow mdoth and specificheat cpluchth, the hot inlet temperature Thi is calculated.

cpluchthmdoth

QdTh

⋅⋅= 1000

(3.23)

dThThuThi += (3.24)

At the cold side, the same technique is applied to calculate the cold outlet temperatureTcu from a known inlet temperature and a volume flow rate prescribed by thedesigner.

dTcTciTcu

cpluchtcmdotc

QdTc

Afrc

Vkvmeanc

rholuchtcVkmdotc

VkoudVk

+=⋅⋅=

=

⋅=

=

1000

3600

(3.25-3.29)

Now, knowing the four temperatures (hot in and out, cold in and out) the logarithmicmean temperature difference LMTD is calculated. This, with a known cooling power,leads to a maximum allowable heat resistance for the total heat pipe heat exchangerRtotaalvereistmax.

��

���

�

−=

−=−=

2

1log

21

2

1

dT

dT

dTdTLMTD

TciThudT

TcuThidT

(3.30-3.32)

66

kAtotaaleistRtotaalver

LMTDQkAtotaal

1max

1000

=

⋅=(3.33-3.34)

.After the evaluation of the heat balance, the heat transfer of the fins, alphahotair andalphacoldair, and the pressure drops dPh and dPc over the coil are calculated. The airproperties at the cold side are calculated at the mean of the inlet and outlettemperature at the cold side, at the hot side of the mean of the hot inlet and outlettemperature respectively. In the end, after calculation of Reynolds numbers Red basedon the pipe outer diameter, free flow velocities vh and vc, Colburn factors j andNusselt numbers Nu, this leads to an air heat transfer coefficient to the fins at both thehot and cold side, calculated with two different correlations as a check. The set ofequations, see the print of the code in appendix E, below is the general procedure.Some correlations are found in appendix C. These calculated heat transfer coefficientsare a little conservative compared to measured values at a test rig at VDL Klima bv.,though these are save values for a design. The applied correlations are based on flatfins around tubes, where the fins of VDL Klima bv. have a special surface for heattransfer enhancement.

Do

tlambdaluchNualpha

luchtdjNu

dj

orDo

hvin

Pl

Ptdj

htdynviscluc

Dovd

AohVwv

⋅=

⋅⋅=

⋅=

��

���

���

���

�⋅=

⋅=

=

−

−−

31

364.0

031.0502.0328.0

PrRe

Re159.0

Re14.0

Re

(3.35-3.40)

The pressure drop over the coil depends on air mass flow, free flow area, air viscosity,air density and the hydraulic diameter. For calculation of the pressure drop throughthe heat exchanger, the air flow based on the free flow area is necessary. This leads toa specific Reynolds number and with a Reynolds based correlation to a friction factorfh and fc [48]. The total pressure drop consists of a frictional part in which the frictionfactor can be found and an acceleration part depending on inlet and outlettemperatures (so differences in densities). The general procedure follows:

67

22

267.0

1112

Re276.0

Re

GrholuchtintrholuchtuiDh

Lrholucht

GfdP

f

htdynviscluc

DhGAo

mdotG

��

���

� −+��

���

�⋅⋅=

⋅=

⋅=

=

−(3.41-3.44)

The calculated pressure drop is compared with the maximum allowable pressure dropdefined at the start of the design process. The extra pressure drop left, that is still leftfor the designer to change the geometry or enlarge the air flow, is displayed asReservedrukval. The calculated pressure drops are slightly less (within 10%)compared to a 4-row test rig at Klima at equal circumstances.After calculation of the air heat transfer coefficients, the fin-efficiency vineff iscalculated with the equivalent annulus method, similar to chapter 1, Eq. (1.12). Thisresults in the heat resistance of the air to fin heat transfer at both the hot and cold sideRvinh and Rvinc. In general:

AairalphavineffRvin

⋅⋅=

_

1(3.45)

Two other heat transfer resistances are easily calculated: the heat transfer resistancesRwallh and Rwallc of the pipe depend only on pipe geometry and material properties,similar to chapter 1, Eq (1.11). What remains is the heat transfer resistance of theprocesses within the pipe: evaporation and condensation of the working fluid. Forthis, the saturation temperature of the working fluid is calculated as:

( ) ( ) ( ) 210002

10002 �

�

�

� +⋅++++⋅−��

���

� += RvincRwallcQTcuTci

RwallhRvinhQThuThi

Tsat

(3.46)

Two other calculation methods for Tsat are applied in the code (appendix E) as acheck.

All fluid properties are taken dependant on the saturation temperature and fitted fromdata of NIST [4]. Now, liquid viscosity muf, latent heat hfgf, densities rhogf and rhoff,liquid heat conductivity lambdaf, liquid specific heat cpf, surface tension surftf andinternal pressure Pfit are known. Critical pressure pcrit and molar mass M are knowntoo, since they are material specific. Knowing the cooling power, total number ofpipes and latent heat, the total mass flow of working fluid mdotf in each pipe is knownas well as the averaged cooling power per pipe Qpijp. This results in a certain in-pipeReynolds number Ref. Reduced pressure Preduced and the heat transferring area forevaporation and condensation Aevap and Acond in the pipe are calculated. With aknown critical pressure pcrit, pipe inner and outer diameter and pipe material tensilestrength, minimum pipe wall thickness and a pipe safety factor are calculated,deltaPijpwand_min and Pijp_safety_factor.

68

( )min_

21

__

2

51min_

Pr

2

2

4Re

1000

anddeltaPijpw

DiDofactorsafetyPijp

Sbuis

eDopcritanddeltaPijpw

pcrit

Pfiteduced

rLcondNAcond

rLevapNAevap

muf

mdotff

hfgfN

Qmdotf

N

QQpijp

−=

⋅⋅⋅=

=

⋅⋅⋅=⋅⋅⋅=

⋅=

⋅=

⋅=

ππ

(3.47-3.54)

The cooling power per pipe will be checked by calculating the maximum coolingcapacity of a heat pipe in the specific situation, based on a correlation that matchesbest with the performed experiments. So far, the correlation of Tien [20] is adapted inthe program, see code and chapter 2, which predicts the operating limit temperaturedependent within 100 W in vertical orientation of the heat pipe heat exchanger pipes.The Eq’s (2.9-2.14) to predict operating limits can be implemented in a later stage.Since the assumption that every pipe will deliver the same cooling capacity will notbe valid, a heat transport capacity check for the hottest and coldest row of pipes isnecessary. The inner pressure and temperature will be different, changing theoperating limit. Also the temperature difference over the first and last row will bedifferent. Therefore, the mean heat transport per pipe is corrected with a factor = (Thi- Tcu)/LMTD for the hottest row and = (Tho - Tci)/LMTD for the coldest row. Carehas to be taken that the inner temperature of the hottest row does not exceed thecritical temperature, resulting in erroneous calculations and a physical stop of properoperation of the heat exchanger.In the present code, average condensation heat transfer coefficient is calculated with amodel of Butterworth, where for evaporation, a model of Cooper is applied. Thisresults in heat transfer resistances for condensation and evaporation. These models aredescribed in chapter 1 and 2. Heat transfer for condensation, especially at lowsaturation temperatures (20˚C), will be overpredicted up to a factor 2 for powerthroughput below 200 W per pipe. At higher saturation temperatures (75˚C),condensation heat transfer coefficients are predicted fairly well (within 20%)compared to measurements outlined in chapter 2. The model of Cooper predicts theevaporation heat transfer coefficient very well for low saturation temperatures (20˚C),but overpredicts up to 30% for high power throughput at high saturation temperatures(75˚C). So, care has to be taken with the predicted heat transfer coefficients calculatedin the design program. From analysis of the results obtained in chapter 2, the next stepis to enhance the program HPHE.m with an adjusted model of Cooper for evaporationand an enhanced model of Nusselt for condensation heat transfer predictions.

69

By summing the heat resistances of condensation, evaporation, pipe walls and air tofin heat transfer, a total heat transfer resistance of the design can be compared withthe maximum allowable heat transfer resistance following from the heat balance.Now, one can see if the design is correct and an overcapacity will be achieved. As ahelp for the design process, the percentage in heat transfer resistance of the severalparts of the heat pipe heat exchanger are displayed. The designer can now change thecold air volume flow and/or the geometry until the design matches the desireddemands.

An example of a possible output is shown in figure 3.5.

Figure 3.5: Screen output of design program

70

Chapter 4: Steady-state numerical model of the single pipethermosyphon

Nomenclature

Cf friction coefficient [-]Hp liquid pool height [m]L length of the thermosyphon [m]Mff total amount of working fluid [kg]M molar mass of working fluid [kg/kmol]Pr Prandtl number [-]R thermosyphon inner radius [m]Re Reynolds number [-], 4�/�Ro typical surface roughness [�m]T temperature [K]V vapor condensation velocity [m/s]cp liquid specific heatdx grid size [m]g gravitational acceleration [m/s2]hfg latent heat of vaporization [J/kg]mc mass flow rate of condenser cooling water [kg/s]p pressure [Pa]q” wall heat flux [W/m2]r vapour core radius [m]u velocity [m/s]x axial distance from top end of condenser [m]

Greek:Γ liquid mass flow per unit tube perimeter [kg/ms]α heat transfer coefficient [W/m2K]δ liquid film thickness [m]λ liquid thermal conductivity [W/mK]µ dynamic viscosity [Ns/m2]ν kinematic viscosity [m2/s]ρ mass density [kg/m3]σ liquid surface tension [N/m]τ shear stress [N/m2]ϕ phase change correction factor [-]

Subscripts:a adiabatic regionatm atmosphericc condenser regione evaporator regioni phase interfacein condenser cooling inlet

71

l liquidp pool surfacer reducedsat saturationw wallv vapor

4.1. Introduction

Several researchers [38, 49-51] numerically modelled a two-phase thermosyphon. Thegoal is to enhance these models to predict liquid film thickness, liquid pool height andoperating limits dependent on temperature, geometry and working fluid inventory. Apredictive model is observed as a way to gain more understanding of the flowoccurring in a thermosyphon, additional to the experiments described in chapter 2.

This text is a first initiative for numerical simulation of the internal flow in athermosyphon and not the core of the investigation as a whole. No results are obtainedyet. The thermosyphon is shown schematically in figure 4.1. The constructed model isbased on the investigations of [38, 49-51].

Figure 4.3: A gravity assisted two phase closed thermosyphon

72

4.2. Model of a single closed two phase thermosyphon

The model uses the following assumptions:- fluid flow is one dimensional, steady state Newtonian flow- fluid is incompressible- fluid is at saturation temperature and pressure- no pressure drop in the liquid film- axial conduction and viscous dissipation are neglected- heat flux is uniform

For the liquid film along the wall, the following equations hold:

Continuity:( )[ ]

RVdx

urRd l 222

=−(4.1)

Momentum:

( )[ ] ( ) ( ) 0223

4 2222222

=++−−��

�

� −−−

iwll

ll

l rRgrRdx

durR

dx

d

dx

urRd ττρµρ

(4.2)

Energy:

( )lfg

wsat

lfg h

TT

h

qV

ρα

ρ−

== "(4.3)

In the momentum equation (4.2) the terms account for: total momentum change, axialnormal stress, gravity, wall shear stress and interfacial shear stress, respectively. Theenergy equation (4.3) only considers heat transfer due to latent heat from phasechange. Conductive and convective heat transfer is neglected at the two phaseinterface.Expressions for both wall shear stress and interfacial shear stress in (4.2) arenecessary. We write:

( ) fivlvi

fwllw

Cuu

Cu

2

2

21

21

+=

=

ρτ

ρτ(4.4)

In first instant we assume laminar flow in both the liquid film as well as the vapourcore. For turbulent flow, the friction coefficients can be adjusted.

lfwC

Re

16= (4.5)

1Re

16

−= ϕ

ϕe

Cv

fi (4.6)

73

with � a correction factor accounting for two-phase flow with phase change:

v

lVR

µρϕ4

−= (4.7)

An expression for the film heat transfer coefficient α in eq.(4.3), assuming laminarflow in first approximation again, results in:

δλα = (4.8)

For the vapour core, the continuity equation is written as:

( )RV

dx

urdl

vv 2

2

ρρ = (4.9)

Substituting (4.1) in (4.9) yields a relationship for total mass flow continuity duringsteady state operation:

( )[ ] ( )dx

urd

dx

urRd vv

ll

222

ρρ =−

(4.10)

Integration and rearranging leads to an expression for the vapour core velocity:

lv

lv u

r

rRu

2

22 −=ρρ

(4.11)

Eq. (4.11) can be substituted in (4.4) to eliminate uv from the interfacial shearexpression.

To close the system of equations, two equations for the liquid pool remain:

Continuity: ( ) vppvlppl ururR 222 ρρ =− (4.12)

Energy: fgvppvpe hurRHq 22" ρ= (4.13)

Eq. (4.12) and (4.13) imply a steady state pool height. Mass from the liquid film intothe pool equals the vapour mass flow out of the pool and energy input at theevaporator wall results in the same energy output at the pool surface to the vapour.

The two variables that have to be solved from the system of equations are ul (x), theaxial liquid film velocity also resulting in uv (x) and r (x), resulting in the local filmthickness R-r.

The following boundary conditions are applied:- at the top of the thermosyphon (x = 0):

74

o ul = 0o r = R

- at the liquid pool interface (x = xp) we combine (4.12) and (4.13):

o ( ) lpplfg

pe urRh

RHq 222"

−= ρ

We will prescribe the pool height Hp by defining xp, resulting in the total fluid mass inthe system (mass balance for the total thermosyphon):

( )[ ]� −++=px

lvlpff dxrRrHRM0

2222 ρπρπρπ (4.14)

Furthermore, assuming steady state, the energy balance for the thermosyphon systemreads:

( ) ( ) ( )��� −+−=−e

p

p

a

c x

x

satwep

x

x

satwe

x

wcsat dxTTdxTTdxTT ααα0

(4.15)

where we assume film condensation and evaporation with a heat transfer coefficientobtained from (4.8). The model of Cooper [5] (4.16) is applied to calculate α p, thepool boiling heat transfer coefficient.

( ) ( )( ) 0.550.12 0.4343ln

0.5 0.67

55 0.4343lnpR

r rp P

M q

α −−

−

= − ×(4.16)

The wall temperatures at the evaporator and the condenser will be prescribed asboundary conditions, as well as the evaporator heat flux. All fluid properties areevaluated at Tsat, where Twc<Tsat<Twe has to be satisfied at any time for operation ofthe thermosyphon.

75

5. Conclusions and recommendations

The goal of this study was to develop an operational model for the thermal design ofan air-to-air heat exchanger equipped with heat pipes. From measurements at aprototype as described in chapter 1, it resulted that this type of heat exchanger canserve as an alternative for present air-to-air heat exchangers without loss ofperformance where air heat exchangers become too large / expensive and air-waterheat exchangers are not applicable. Electricity generator cooling with ambient air,even in warmer countries should be possible with the present configuration. Overallheat transfer coefficients at the evaporator side of 10-40 W/m2K and 20-50 W/m2K atthe condenser side have been measured. Experiments with filling ratios of 19% and59% were carried out. The temperature distribution over the heat pipe showed to beindicative for the operating limit. A model to predict the heat transfer and to calculatethe performance of an air-heat pipe-air heat exchanger based on correlation fromliterature has been presented.

After the proven applicability of heat pipe equipped heat exchangers for generatorcooling in a first prototype test rig, more knowledge of the processes occurring insidethe single heat pipes needed to be gained in order of appropriate scaling to sizesinteresting for commercial use of heat pipes in heat pipe equipped heat exchangers.Therefore, chapter 2 presented a further study on a single heat pipe of 3 m lengthfilled with R-134a, which is relevant for further commercial use. Relations betweenheat flux, operating limits, filling ratios and inclination angles were assessed. Furtherrefinement of the models presented in chapter 1 was proposed. Evaporation heattransfer increased from 1000 to over 3000 W/m2K with an increase of the heat flowrate. Heat transfer coefficients for condensation resulted to be around 1500 W/m2K. Amodel of Cooper predicts the evaporation heat transfer well after a small amendment.A model of Nusselt predicts the condensation heat transfer well at low heat flow rates,but underpredicts at high heat transfer rates. Nusselt does not take turbulentcondensate film heat transfer into account, which is likely to occur at high heattransfer rates. A slight enhancement of the Nusselt model, as proposed by [47] isnecessary to obtain a better agreement with the present measurements.The operating limit decreased with increased saturation temperature and increasedwith increased inclination angle to the vertical. The entrainment limit showed to bethe limiting factor in heat transport capability of the heat pipe. A fair agreement withcorrelations to predict the heat transfer limit depending on saturation temperaturefrom literature and the present measurements was found. To take the inclination angleinto account, a new correlation to predict the operating limit is proposed for theexperimental range.Remarkable is the proven normal operation up to the operating limit at inclinationangles up to 87˚ from vertical. No optimal angle for heat transfer could be detected.The filling ratio resulted not to affect the heat transfer of the heat pipe as long asenough fluid is present to avoid dry-out in all process conditions. Three filling ratioswere tested: 25%, 62% and 100%. 25% filling ratio resulted in dry-out.

Chapter 3 was a manual for the computer program HPHE developed for the thermaldesign of air-to-air heat pipe equipped heat exchangers, based on the experimentalresults of chapter 1 and 2. This chapter is for internal use at VDL Klima bv.

76

Chapter 4 describes a first initiative to model the flow in a thermosyphon to obtain anumerical model to get more insight in the entrainment limit as observed in theexperiments. This has not led to results yet.

As a next step in the development, a new prototype designed with the aid of thedeveloped computer program, will be tested. If these experiments are successful andthe design program is validated (possibly with some small amendments of the modelsas suggested in chapter 2), first tests in the field can be carried out.Depending on the air temperature range of the application it will be useful to continuein the search for alternative working fluids for the heat pipe.If the evaporation and condensation heat transfer needs to be enhanced, an option is toapply a grooved inner surface in the heat pipe, but when applying this pipe in a heatpipe equipped heat exchanger, the air to fin heat transfer will usually be the limitingfactor in heat transfer, which makes an improvement like a grooved inner pipe wallpossibly useless and only expensive.

77

References

[1] Dunn, P.D and Reay, D.A., 1994, Heat Pipes, fourth edition, Pergamon

[2] Wadowski, T., Akbarzadeh, A. and Johnson, P, Characteristics of a gravityassisted heat pipe based heat exchanger, Heat Recovery Systems CHP, (1991) Vol. 11,pp. 69-77.

[3] Morgan M.J. and Shapiro, H.N., Fundamentals of Engineering Thermo-dynamics,2nd ed., John Wiley & Sons, Inc., 1992

[4] NIST Standard Reference Database 69, June 2005 Release: NIST ChemistryWebBook.

[5] Unk J, Ein Beitrag zur Theorie des geschlossenen Zweiphasen-Thermosiphons,Dissertation Technische Universität Berlin., 1988

[6] Fröba, A.P., Penedo Pellegrino, L. and Leipertz, A, Viscosity and Surface Tensionof Saturated n-Pentane, Int J Thermophysics, (2004) Vol. 25, pp. 1323-1337.

[7] Fröba, A. P., Will, S. and Leipertz, A., Saturated liquid viscosity and surfacetension of alternative refrigerants, 14th Symposium on Thermophysical Properties,Boulder, Colorado, U.S.A., 2000

[8] Reay, D.A., Heat exchanger selection part 4: Heat pipe heat exchangers, Int.Research & Development Co. Ltd., 1984

[9] Lee, H.S., Yoon J.I., Kim, J.D. and Pradeep Bansal, Evaporating heat transfer andpressure drop of hydrocarbon refrigerants in 9.52 and 12.70 mm smooth tube, Int. J.Heat Mass Transfer, (2005) Vol. 48, pp. 2351-2359.

[10] Kline, S.J., McKlintock, F.A., Describing uncertainties in single-sampleexperiments, Mech. Eng, (1953) Vol. 75, pp. 3-8.

[11] VDI-Wärmeatlas: Berechnungsblaetter fuer den Waermeuebergang, 6. erw.Auflage, VDI Verlag GmbH, 1991

[12] Rohsenow, W. M., Hartnett, J. P.and Cho, Y. I., Handbook of Heat Transfer, 3rd

ed., McGraw-Hill, 1998

[13] R.L.Webb, Principles of Enhanced Heat Transfer, 1994

[14] Baehr, H.D. and Stephan, K., Heat and Mass Transfer, Springer, 1998

[15] Collier. J.G. and Thome, J.R., Convective boiling and condensation, ClarendonPress, 1994

[16] I. Golobic, B. Gaspersic, Corresponding states correlations for maximum heatflux in two-phase closed thermosyphon, Int. J. Refrig., vol. 20, 402-410, 1997

78

[17] R. K. Sakhuja, Flooding constraint in wickless heat pipes, ASME Publ. 73-WA/HT-7, (1973)

[18] Z. Nejat, Effects of density ratio on critical heat flux in closed and vertical tubes,lnt. J. Multiphase Flow, (1981) 7 321-327

[19] Y. Katto, Generalized correlation for critical heat flux of the natural convectionboiling in confned channels, Trans. Japan. Soc. Mech. Engrs, (1978) 44 3908-3911

[20] C. L. Tien and K. S. Chung, Entrainment limits in heat pipes, AIAA J. (1979) 17643-646

[21] Z. R. Gorbis and G. A. Savchenkov, Low temperature two-phase closedthermosyphon investigation, 2nd Int. Heat Pipe Conf. Bologna, Italy (1976) 37-45

[22] M. K. Bezrodnyi, Isledovanie krizisa teplomassoperenosa v nizkotemperaturnihbesfiteljinyih teplovih trubah, Teplofizika visokih temperatur (1977) 15 371-376

[23] T. Fukano, K. Kadoguchi and C. L. Tien, Experimental study on the critical heatflux at the operating limit of a closed two-phase thermosyphon, Heat Transfer -Japanese Research (1988) 17 43-60

[24] H. Imura, K. Sasaguchi and H. Kozai, Critical heat flux in a closed two-phasethermosyphon, Int. J. Heat Mass Transfer (1983) 26 1181-1188

[25] Y. J. Park, H. K. Kang, C. J. Kim, Heat transfer characteristics of a two-phaseclosed thermosyphon to the fill ratio, Int. J. of Heat and Mass Transfer 45 (2002),4655-4661

[26] M. S. El-Genk, H. H. Saber, Determination of operation envelopes for closed,two-phase thermosyphons, Int. J. of Heat and Mass Transfer 42 (1999), 889-903

[27] H. P. v. Kemenade, The design of a combustion heated thermionic ernergyconvertor, TUE, 1995

[28] U. Gross, Reflux condensation heat transfer inside a closed thermosyphon, Int. J.of Heat and Mass Transfer 35 (1992), 279-294

[29] J. W. Palen, Heat Exchanger Sourcebook, Hemisphere Publ. Corp., 1986

[30] H. Z. Abou-Ziyan, A. Helali, M. Fatouh, M .M. Abo El-Nasr, Performance ofstationary and vibrated thermosyphon working with water and R 134a, AppliedThermal Eng. 21 (2001), 813-830

[31] J. C. Y.Wang, Yiwei Ma, Condensation Heat Transfer Inside Vertical andInclined Thermosyphons, J. Heat Transfer 113 (1991), 777-780

[32] J. C. Chato, Laminar Condensation Inside Horizontal and Inclined Tubes,ASHREA Journal, Vol. 4, No. 2 (1962), p. 52

79

[33] E. Hahne, U. Gross, The influence of the inclination Angle on the performance ofa Closed Two-Phase Thermosyphon, Heat Recovery Systems, Vol. 1, 267-274, (1981)

[34] Y. P. Wen, S. Guo, Experimental Heat Transfer Performance of Two-PhaseThermosyphons, Proc. 5th Int. Heat Pipe Conf. Tsukuba, Japan (1984)

[35] K. Negishi, T. Sawards, Heat Transfer Performance of an Inclined Two-PhaseClosed Thermosyphon, Int. J. of Heat and Mass Transfer 26 (1983), No. 8

[36] R. S. Larkin, A heat pipe for control of heat sink temperature, Proc. 7th Int. HeatTransfer Conf., Munchen, Germany, p.319-324, (1982)

[37] G. S. H. Lock, J. D. Kirchner, Some characteristics of the inclined, closed tubethermosyphon under low Rayleigh number conditions, Int. J. Heat Transfer 35(1992), No. 1, p. 165-173

[38] Z. J. Zuo and F. S. Gunnerson, Heat Transfer Analysis of an Inclined Two-PhaseClosed Thermosyphon, J. Heat Transfer 117 (1995), p. 1073-1075

[39] M. Shiraishi, P. Terdtoon, M. Murakami, Visual Study on Flow Behavior in anInclined Two-Phase Closed Thermosyphon, Heat Transfer Eng. 16 (1995), No. 1, p.53-59

[40] M. Shiraishi, P. Terdtoon, M. Chailungkar, S. Ritthidej, Effects of Bond numberson internal flow patterns of an inclined, closed, two-phase thermosyphon at normaloperating conditions, Exp. Heat Transfer 10 (1997), p. 233-251

[41] M. Shiraishi, P. Terdtoon, M. Chailungkar, Effects of Aspect Ratios on InternalFlow Patterns of an Inclined Closed Two-Phase Thermosyphon at Normal OperatingCondition, Heat Transfer Eng. 19 (1998), Vol. 4, p. 75-85

[42] P. Terdtoon, N. Waowaew, P. Tantakom, Internal Flow Patterns of an Inclined,Closed Two-Phase Thermosyphon at Critical State: Case Study I, Effect of AspectRatio, Exp. Heat Transfer 12 (1999), p. 347-358

[43] P. Terdtoon, N. Waowaew, P. Tantakom, Internal Flow Patterns of an Inclined,Closed Two-Phase Thermosyphon at Critical State: Case Study II, Effect of BondNumber, Exp. Heat Transfer 12 (1999), p. 359-373

[44] T. Payakaruk, P. Terdtoon, S. Ritthidech, Correlations to predict heat transfercharacteristics of an inclined closed two-phase thermosyphon at normal operatingconditions, Applied Thermal Eng. 20 (2000), p. 781-790

[45] E. Hahne, U. Gross, G. Barthau, Optische Erscheinungen im thermodynamischkritischen Gebiet, Beobachtung und Deutung der Vorgänge in einem Thermosyphon,Wärme und Stoffübertragung 21 (1987), p. 155-162 (in German)

[46] G. R. Kudritskii, Operation of thermosyphons at small angles of inclination to thehorizontal, Journal of Engineering Physics and Thermophysics 67 (1994), No. 3-4,

80

translated from Inzehrno Fizicheskii Zhurnal 67 (1994) , No. 3-4, p. 258-260 (inRussian)

[47] S. Thumm, Ch. Phillipp, U. Gross, Film condensation of water in a vertical tubewith countercurrent vapour flow, Int. J. of Heat and Mass Transfer 44 (2001), p.4245-4256

[48] R. K. Shah, E. C. Subbaroa, R. A. Mashelkar, Heat Transfer Equipment Design,Hemisphere Publ. 1988

[49] Z. J. Zuo, F. S. Gunnerson, Numerical modeling of the steady-state two-phaseclosed thermosyphon, Int. J. Heat Mass Transfer 37 (17) (1994) 2715-2722

[50] J. G. Reed, C. L. Tien, Modeling of the Two-Phase Closed Thermosyphon,Transactions of the ASME 109 (1987), 722-730

[51] C. Harley, A. Faghri, Complete Transient Two-Dimensional Analysis of Two-Phase Closed Thermosyphons Including the Falling Condensate Film, Transactions ofthe ASME 116 (1994), 418-426

[52] G.F., Hewitt, Heat Exchanger Design Handbook, Begell House, 1998.

[53] Stephan, K., Wärmeübertragung und Druckabfall bei nicht ausgebildeterLaminarströmung in Rohren und in ebenen Spalten, Chem-Ing Techn, (1959) Vol. 31,pp. 773-778.

[54] Kayansayan, N., Plate fin-tube heat exchangers, Int. J. of Refrigeration, 1994 vol17 No 1, 51-57

[55] Gray and Webb, Proc. 8th Int. Conf. Heat Transfer, 1986, vol 6, 2745-2750

[56] HTFS Handbook, Convective heat transfer of air through tube in plate heatexchangers, 1979

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81

Appendix A

Start up behaviour

Normal situation, cold start

Figure A.1: Startup

82

Start up with preheated cooling water, hotstart

Figure A.2: Startup if Tevap < Tcond

The distance between the thermocouples is 190 mm. The temperature response ofeach thermocouple to switching on the uniform electric heating is about 30 s. Wettingof the wall takes place with about 6 mm/s

83

No working up side down

If the condenser is positioned below the evaporator, no natural cycle exists based ongravity. In a heat pipe (with wick), this would not be true due to capillary working ofa wick. Now, the evaporator wall is heated, without any heat transport fromevaporator to condenser.

Figure A.3: Condenser below evaporator

84

Control of the filling procedure

To fill the pipe with working fluid, the pipe has to be vacuum. This is achieved with avacuum pump which evacuates all air up to a pressure of less than 50 �m Hg (6.65Pa). Then the container with R-134a is put on to a weighing machine, accurate up toone milligram. After connecting the container with a nipple to the pipe, R-134a willflow into the pipe. The mass flow can be controlled with a valve, where the totalfilling mass is monitored by the decrease of the container mass. The pressure ismonitored and at room temperature, saturation will be reached at an overpressure of 5bar.

Figure A.4: Pressure relative to environment during filling procedure

85

Offset between Pt-100’s to calculate Qcond.

When performing an isothermal run at several cooling water temperatures, the Pt-100’s at the water inlet and water outlet should show similar values and the calculatedQcond should be zero. During measurements, Qcond was structurally too low. This wasdue to an offset in the Pt-100’s. The Pt-100 at the water outlet gave lowertemperatures then the Pt-100 at the water inlet at equal water temperatures. Acorrection in the calculation of Qcond is therefore applied depending on the averagewater temperature.

Figure A.4: Offset between Pt-100’s at water inlet and outlet during isothermalruns

86

Calculation of filling ratio

The following geometrical properties have to be entered in the specific fields:• inner diameter• length of the evaporator• total pipe length• number of pipes per row that are interconnected for one filling session

The following fluid properties have to be filled out (default on R-134a):• liquid density at temperatures from 20 – 90 ˚C• vapour density at temperatures from 20 – 90 ˚C

By choosing the liquid volume to the total evaporator volume at 20˚C (=Fe) if thethermosyphon is at rest (no fluid in the cycle), the total fluid mass is calculated withthe filling ratios of liquid to the evaporator volume at all temperatures in the range.

Figure A.5: Calculation sheet for determination of the filling ratio

87

Operation at too low filling ratio of 25%

At high saturation temperatures with a filling ratio of 25%, no liquid is present and thethermosyphon cannot operate.

Figure A.6: Temperature history at lack of fluid

88

Slow cooling of the thermosyphon. Above about 55 °C no operation of the system canbe detected. When the saturation temperature drops, enough liquid is present dueequilibrium and the natural heat transport cycle starts again.

Figure A.7: Restart at low filling ratio due to temperature drop

89

Calibration of the RB-16 manometer

The full range is 0-100 bar, the application requires maximum 40.6 bar. Thecalibration is done with 3 different Econosto class 0.6% control pressure sensors, allsensitive in another range: RA-01 0-25 bar, AR-02 0-40 bar, AR-03 0-100 barNitrogen is applied to bring the thermosyphon on pressure. The calibration curve forthe RB-16 manometer fits within 2% from the control pressure sensors in theirspecific range. After calibration, the thermosyphon stays on pressure for a few days tocheck forleaks.

Figure A.8: Calibration of RB-16 WIKA manometer

Manometer:

WIKA type RB ECORange: 0 – 100 barAccuracy: 0.5 bar, after calibration 1 % of full rangeOutput signal: 4 – 20 mA DCHorizontal connectionsInput: 24 V DC

90

Calibration of Pt-100’s

The Pt-100 temperature sensors are all calibrated with a thermal bath. The thermalbath is equipped with a digital thermometer, accurate at 0.1 ºC and 3 heaters with acontrol system and a mixer. To improve accuracy, a mercury thermometer is inserted.The control temperature is the average over 3 Pt-100 sensors, coupled to the samesignal convertor and datalogger as applied in the experiments. The controltemperature is monitored with the resistance of each sensor. The results of thecalibration for example of sensor ‘SD-TU’, which is mounted in the thermosyphon, isseen in figure A.10.

Figure A.9: Calibration of the Pt-100 sensors in a thermal bath

Pt-100:Resistance thermometerIC Istec ME 1009Range: -260 – 650 ºCAccording DIN / IEC 7513-wireAccuracy after calibration: better than 0.1 ºC in range of 0 – 100 ºC

91

Measurement of inclination angle

Mitutoyo Digital Protractor 360Accuracy 0.2º, resolution 0.1ºThe inclination to the vertical is measured at several positions over the 3 mthermosyphon. Over the length, a maximum variation of 1.0º was measured, due tomounting in the construction.

Type K thermocouples:

IC Istec Chromel / AlumelNiChr / Ni, type KRange: -40 – 1200 ºCAccording DIN / IEC 584, class 2Tolerance of manufacturer (without own calibration): 2.5 ºC or 0.0075*tDiameter: 3.0 mmIsolated measurement tipConnection to cable: 6 x 40 mm RVSConnection cables: Teflon FEP isolated wires and jacket, wire diameter 2 x 0.50 mm2,IEC class 3After own calibrations accuracy within 0.75 ºC on 0 – 200 ºC

Signal Conditioning unit for thermocouples:

IOTech DBK4816-slot, isolated, with linearized thermocouple modules, range: -100 – 1350 ºC

Datalogger: IOTech DBK 1516 channels

Heat Flux Sensor:TNOSensitivity: 49.5 W/m2mV +/- 2%, mounted on insulation with D=90 mm. Totalevaporator area at this position is 0.41 m2, so 20,3 W/mV measured losses with aHewlett Packard 3468 multimeter, resolution in µV.

92

Appendix B

Correlations to predict the maximum heat flux in thermosyphons

Some correlations will be shown here. For others see [16-24], [1] ,[8], [27]

In general:

( ) 21

��

�

�

��

�

� −=

f

gfgdBoσ

ρρ

( )( ) 25.05.0gffgfg ghKuq ρρσρ −∆⋅=

evapAqQ ⋅=max

Katto [19]:

( ) 3.0491.01

1.0−+

=BodL

Kuevap

Sakhuja [17]:

24

1

212

1

4

725.0

��

�

�

�

��

�

�

��

�

�+

=

f

g

evapLdBoKu

ρρ

Nejat [18]:

( )2

41

9.0

21

1

09.0

��

�

�

�

��

�

�

��

�

�+

=

f

g

evapLdBoKu

ρρ

93

Tien & Chung [20]:

( )2

41

22

1

1

5.0tanh4

2.3

��

�

�

�

��

�

�

��

�

�+

��

�� �

���

��=

f

g

evapLdBoKu

ρρ

Golobic and Gaspersic [16] correlation 1

Tc = 374.06 Critical temperature [K]pc = 4.07e6 Critical pressure [Pa]M = 102.032 Molecular weight [kg/kmol]Tr= (T+273.15)/Tc Reduced temperature [-]� = 1-Tr Temperature function

( )2

41

41

1211

31

137.13530.2exp16.0 ττ −⋅

⋅=

ML

gpTdq

evap

cc

Golobic and Gaspersic [16] correlation 2

� = 0.325 Pitzer acentric factor

( )tohML

gpTdq

evap

cc ..096.17387.1233.8530.2exp16.0 2

41

41

1211

31

+++−⋅⋅

= τωττ

94

Appendix C

Air side heat transfer: correlations

Several prediction methods from literature are known to calculate the heat transferfrom the air to the fins on the staggered tube bank with flat continuous fins. This isusually based on a Nusselt number for heat transfer and a Reynolds number for the airflow. This appendix gives a short overview of some correlations. An example of theresults obtained for the geometry of the 4-row test coil with fin distance 1.6 mm atevaluation temperature of 60 ˚C are seen in figure App. C1. The line ‘Klima’ is ameasured value of an air-water heat exchanger with equal geometry.

In general:

λα hfin D

Nu =

νhvD

=Re

SDh 2=

ανµ

==f

p

k

cPr

Hewitt [52]:

33.065.014.018.02.0

PrRe19.0−

��

���

���

���

���

���

�=d

h

d

S

b

aNu

with h the local fin length.

Stefan [53], based on laminar flow between flat plates:

64.0

81.0

14.1

RePr0358.01

RePr024.0

55.7

��

���

�+

��

�

�

��

�

���

���

�

+=

L

D

L

D

Nuh

h

Kayansayan [54]:

���

����

�−⋅��

�

����

���

���

�−=H

N

a

d finfinδσ 11

with H the channel height in [m]

95

σπε

211

41

���

����

� ⋅

⋅��

���

� −⋅��

���

� −⋅⋅+=H

Nd

a

d

d

b

d

a

fin

362.028.0Re15.0 −−= εj

31

PrRejNu =

Valid for:5.232.11 ≤≤ ε

30000Re500 ≤≤9.36.2 ≤≤ hD mm

The following correlations are not based on the hydraulic diameter, but on the tubediameter d.

νdv ⋅=Re

31

PrRejNu =

McQuiston [29]:

15.04.0Re2618.00014.0

−−

��

���

�

⋅⋅⋅+=

HdRnN

Aj

π

with Rn the number of rows and N the maximum number of tubes in a row

Valid for:3.1396.9 ≤≤ d mm

49.269.1 ≤≤d

a

58.295.1 ≤≤d

b

findensities from 115 - 811 /m and fin thickness of 0.15 - 0.40 mm

Gray and Webb [55]:

031.0502.0328.0Re14.0 �

�

���

���

���

�=−

−

d

S

b

aj

Valid for more than 4 rows and:

96

51.1996.9 ≤≤ d mm

60.282.1 ≤≤d

a

79.270.1 ≤≤d

b

24700Re500 ≤≤

64.008.0 ≤≤d

S

024.0011.0 ≤≤dfinδ

HTFS Handbook [56]:

33.0Re13.0 −=j

A typical example:

Figure App C1: Air side heat transfer coefficients of flow in tube-in-plate heatexchangers, example at 60˚, distance between fins 2.6 mm

97

Appendix D

For all calculations at the working fluid R-134a at saturation, data from NIST [4] areobtained. In this appendix, the data are shown graphically.

Name: Ethane, 1,1,1,2-tetrafluoro-Formula: C2H2F4

Molecular weight: 102.03Other names: Norflurane; 1,1,1,2-Tetrafluoroethane; Norfluran; R 134a; 1,2,2,2-Tetrafluoroethane; CF3CH2F; HFA-134a

98

99

100

101

102

103

104

Appendix E

105

106

107

108

109

110

111

112

113

114

115

116

117

Summary

Stand-alone electricity generators are usually cooled with ambient air. Standardpractice is air-to-air heat transfer or using a tube-in-plate heat exchanger with water asan intermediate. In some situations water is not available, ambient temperatures aretoo low to use water or ambient temperatures are too high to use ambient air intraditional air-to-air heat exchangers. In those cases heat pipes may provide analternative for cooling powers in excess of 100 kW. Multiple heat pipes then connecttwo plate heat exchangers to transfer heat between two air streams at high heatrecovery effectiveness.

The goal of this study is to gain knowledge about heat pipes in general and to developan operational model for the optimization and design recommendations of heat pipeequipped heat exchangers.The study in chapter 1 presents measurements and predictions of a small scale heatpipe-equipped heat exchanger with two filling ratios of R134a, 19% and 59%. Thelengths of the heat pipes, or rather thermosyphons, are long (1.5 m) as compared tothe diameter (16 mm). The airflow rate varied from 0.4 to 2.0 kg/s. The temperaturesat the evaporator side of the heat pipe varied from 40 to 70°C and at the condenserpart from 20 to 50°C. The measured performance of the heat pipe has been comparedwith predictions of two pool boiling models and two filmwise condensation models.The study demonstrates that a heat pipe equipped heat exchanger is a good alternativefor generator cooling in process conditions when air-water cooling or traditional air-air cooling is impossible, typically in warmer countries.

With the proven applicability of heat pipe equipped heat exchangers for generatorcooling as an alternative for air-air exchangers, more research is carried out to find theoperating limits, optimum filling ratio and limitations with regard to the inclinationangle of a heat pipe when the heat pipes are scaled to future commercially attractivesize of 3 m length. Measurements and further refinements of the predictive models ofa full-scale 3 m single pipe thermosyphon are presented in chapter 2. Filling ratios of25%, 62% and 100% of R-134a are assessed. Saturation temperatures varied from 20to 75°C and inclination angles with the vertical varied from 0 to 87°. A newcorrelation is suggested to predict the operating limit of thermosyphons at varioussaturation temperatures and inclination angles.

With the knowledge obtained in the studies presented in chapter 1 and 2, a computerprogram is developed to optimize the design of a heat pipe equipped heat exchanger.Chapter 3 explains the structure of the design methodology in the computer programand serves as a manual for the designers at VDL Klima bv.

Finally a few words are added to model the flow in a single closed two phasethermosyphon to numerically predict operating limits, liquid film thickness and liquidpool height dependent on temperature, geometry and filling ratio. This work is inprogress and at present a literature survey has been carried out.

118

Samenvatting

Industriële generatoren voor elektriciteitsopwekking worden meestal gekoeld metomgevingslucht. Dit gebeurt dan met lucht-lucht warmteoverdracht of met een lucht-water koeler. Er zijn echter situaties waarbij deze koelmethoden niet geschikt zijn: insommige situaties is er geen water beschikbaar, of is de omgevingstemperatuurdusdanig laag dat water zou bevriezen. De temperatuur kan ook te hoog zijn,waardoor eenvoudige lucht-lucht koeling met omgevingslucht ongeschikt is. In zulkegevallen zou een ‘heat pipe’ een alternatief kunnen zijn bij vereiste koelvermogensgroter dan 100 kW. Meerdere ‘heat pipes’ verbinden dan tweeplatenwarmtewisselaars om efficiënt warmte over te dragen tussen twee luchtstromen,zelfs bij kleine temperatuurverschillen tussen de luchtstromen.

Het doel van deze studie is om kennis te verzamelen over ‘heat pipes’ in het algemeenen om een operationeel model te ontwikkelen om te komen tot optimalisatie enontwerpadviezen ten aanzien van met ‘heat pipes’ uitgeruste warmtewisselaars in hetbijzonder.De studie in hoofdstuk 1 presenteert metingen en voorspellingen aan een kleinschaligprototype van een met ‘heat pipes’ uitgeruste lucht-lucht warmtewisselaar. De ‘heatpipes’ zijn gevuld met R-134a, waarbij de vullingsgraden 19% en 59% bedragen. Delengte van de ‘heat pipes’, of beter gezegd thermosyphons, is groot (1.5 m) tenopzichte van de diameter (16 mm). De massastroom lucht varieerde van 0.4 tot 2.0kg/s. De temperatuur aan de verdamperzijde van de ‘heat pipe’ varieerde van 40 tot70°C en aan de condenseerzijde van 20 tot 50°C. De gemeten prestaties van de ‘heatpipe’ wordt vergeleken met voorspellingen van twee kookmodellen en tweefilmcondensatiemodellen uit de literatuur. Deze studie toont aan dat een met ‘heatpipes’ uitgeruste warmtewisselaar een goed alternatief biedt voor lucht-lucht koelersin het geval van generatorkoeling bij procescondities die lucht-water koeling of lucht-lucht koeling ongeschikt maken. Denk hierbij aan toepassingen op industriëlecomplexen in gebieden met een woestijnklimaat.

Na de bewezen geschiktheid van een ‘heat pipe’ warmtewisselaar als alternatief voorlucht-lucht koelers voor de koeling van generatoren is een volgende stap in deontwikkeling genomen. Opschaling naar een geschikte afmeting (3 m lengte) voortoekomstige commerciële toepassing van de ‘heat pipe’ vereist meer kennis van dewarmtetransportlimiet, de geschikte vullingsgraad en de limieten die het onder eenbepaalde hoek zetten van de ‘heat pipe’ met zich meebrengt. Experimenten en eenverfijning van voorspellende modellen met betrekking op een enkele ‘heat pipe’ opware grootte zijn weergegeven in hoofdstuk 2. De vulling was R-134a metvullingsgraden van 25%, 62% en 100%. De verzadigingstemperatuur varieerde van 20tot 75°C. De hoek varieerde van 0 tot 87° uit het lood. Er wordt een nieuwe correlatievoorgesteld om de warmtetransportlimiet van een ‘heat pipe’ te voorspellen bijverschillende verzadigingstemperaturen en hoeken ten opzichte van de verticale stand.

Met de opgedane kennis uit de studies zoals die beschreven staan in hoofdstuk 1 en 2,is een computerprogramma ontwikkeld om het ontwerp van een met ‘heat pipes’uitgeruste warmtewisselaar te optimaliseren. Hoofdstuk 3 dient dan ook als een uitlegvan de gevolgde ontwerpmethodes zoals toegepast in het computerprogramma en kangebruikt worden als een handleiding voor de ontwerpers van VDL Klima bv.

119

Aan het einde zijn enkele woorden toegevoegd over het modelleren van de stromingbinnen in een gesloten twee-fase thermosyphon. Dit is een eerste stap op weg naarnumerieke simulaties om op deze wijze de warmtetransportlimiet, de dikte van devloeistoffilm en de vloeistofhoogte te voorspellen afhankelijk van de temperatuur,geometrie en vullingsgraad. Momenteel bevindt dit deel van het onderzoek zich in defase van literatuurstudie.

Errata

p 3. Nomenclature: β should be inserted as the inclination angle to the vertical, ˚

Bond number σρ 2gdBo f=

p. 6 Footnote should read: ‘Based on this chapter, a paper is submitted forpublication as: Air heat exchangers with long heat pipes: experiments andpredictions, H. Hagens, F. L. A. Ganzevles, C. W. M. van der Geld, M. H. M.Grooten, Appl. Thermal Engng. 1 (1), 1-40 (2007)’

p. 8 Line above Eq. (1.1), the volume should read evapi Lr 2πFe is determined within 0.1

p. 13 Eq (1.11) it should be added thatww

w AR

α1=

p. 31 The Bond number should be defined as σρ 2gdBo f=

p. 34 Fig. 2.4, α must be replaced by β

p. 36 Eq. (2.3) m must read m�

p. 44 and 45 The heat transfer coefficients are measured within 10% accuracy.Errors are mainly due to uncertainties in temperature measurements

p. 44 line 1: ‘Heat transfer coefficients for condensation are around 1500 W/m2Kand not very sensitive for heat transfer rate and saturation temperature.’This statement is wrong after further analysis of the influence of saturationtemperature and heat transfer rate on condensation heat transfer coefficients atthe single 3 m thermosyphon.

p. 54 Subscript of Fig. 2.25 should read: ‘Operating limits of a thermosyphon withR-134a, length 3 m, diameter 16 mm, correlations of Tien [20] and Nejat [18]compared with the present datafit.’

p. 55 Fig 2.26, The lines of the Butterworth model in this figure are approximately afactor 2 too high, due to an erroneous calculation of Ref, applied in this model.After correction, the Butterworth model agrees fairly with the measurementsat low heat transfer rates, but predicts too low heat transfer coefficients forcondensation at high heat transfer rates. This is the same trend as observedwith the Nusselt model. Clearly, Both models do not (Nusselt) or not enough(Butterworth) account for wavy and turbulent flow of the condensate filmalong the thermosyphon inner wall. Also, both models show an opposite trendwith respect to the effects of saturation temperature on condensation heattransfer coefficients as observed in measurements. Further analysis andliterature study result in a model of Thumm [47] for heat transfer in filmcondensation of water in a vertical tube with countercurrent vapour flow. This

model corrects the Nusselt model at high Ref for turbulent condensate filmflow. At first sight, this model seems to agree with the present measurements.After further analysis, the correlation turns out to be poor (in [47] all data‘agree’ with the proposed models on a logarithmic Ref – Nu scale).The work of Chun and Kim [M. H. Chun, K. T. Kim, A natural convectionheat transfer correlation for laminar and turbulent film condensation on avertical surface, ASME / JSME Thermal Engineering Proceedings Vol. 2,1991, pp 459-464] presents a more robust correlation for film-wisecondensation heat transfer on vertical surfaces:

294.089.0631

1022.8PrRe1056.9Re33.1 −−− ⋅+⋅+= ffNu (Err. 1.1)

This correlation does not take countercurrent vapour flow into account, whichphysically effects the waves or turbulence of the condensate film and thus theheat transfer. The Ref number where a transition from laminar to turbulentfilm flow occurs is seen as static or dependent on Pr only. From the presentmeasurements, sensitivity for this transition point on the saturationtemperature (and thus pressure) is observed. Taking this sensitivity intoaccount and applying a data-fit to the present measurements, the followingcorrelation results, based on (Err. 1.1):

( ) 94.001.088.007.004.163104.059.0 PrRe108.09.6Re2.02.4 ⋅⋅⋅⋅±+⋅⋅±= ±±−−−±

freducedfreduced ppNu

(Err. 1.2)

with:

ifgcond dh

Qm

π∆=� (Err. 1.3)

f

condf

m

µ�4

Re = (Err. 1.4)

creduced p

pp = (Err. 1.5)

31

2

���

����

�=

gL

ν(Err. 1.6)

f

LNu

λα= (Err. 1.7)

valid for:

5000Re200 ≤≤ f

5811.01411.0 ≤≤ reducedp

All uncertainties on a 95% confidence interval.

Fig. Err.1 shows a comparison of measured and predicted heat transfercoefficients with the present datafit (Err. 1.2), condenser side at varioussaturation temperatures, vertical at Fe = 62%

Figure Err. 1

Still, further study will be necessary.

p. 59 Chapter 3: the latest results as described in chapter 2 and discussed aboveshould be implemented in a new version of the computer program HPHE.m.Therefore, chapter 3, which is a manual for the program, must be updated.

p. 84 Line 2: m Hg should be µ m Hg

p. 93 Temperature function: rT−= 1τPitzer acentric factor: 325.0=ω

p. 94αν

λµ

== pcPr