Experimental and numerical analysis of Flat Plate ... · “Earth is the cradle of humanity, but one cannot remain in the cradle forever” Konstantin E. Tsiolkovsky Father of Rocketry

POLITECNICO DI MILANO

Scuola di Ingegneria Industriale e dell’Informazione

Dipartimento di Scienze e Tecnologie Aerospaziali

Corso di Laurea Magistrale in Ingegneria Aeronautica

Experimental and numerical analysis of Flat Plate Pulsating

Heat Pipes for space applications

Relatore: Prof. Manfredo Guilizzoni

Correlatore: Prof. Vincent Ayel

Tesi di laurea di:

Filippo Pagnoni Matr. 797028

Anno accademico 2014-2015

“Earth is the cradle of humanity, but one cannot

remain in the cradle forever”

Konstantin E. Tsiolkovsky

Father of Rocketry

Contents

List of figures........................................................................................................................................ i

List of tables......................................................................................................................................... v

List of Symbols ................................................................................................................................... vi

Abstract .............................................................................................................................................. vii

Estratto in lingua italiana ................................................................................................................ viii

Introduzione ................................................................................................................................................. viii

Materiali, metodi e risultati ........................................................................................................................... ix

Analisi sperimentale .................................................................................................................................. ix

Analisi numerica ......................................................................................................................................... x

Conclusioni ................................................................................................................................................... xii

Introduction and context of study....................................................................................................... 1

1. Two-phase heat exchangers ........................................................................................................ 3

1.1 Heat Pipe/ Thermosyphon ................................................................................................................. 3

1.2 The two-phase capillarity pumped loops ........................................................................................... 5

1.3 Pulsating Heat Pipes .......................................................................................................................... 6

2. Comparison between two-phase systems. .................................................................................... 9

3. Physics of Pulsating Heat Pipes ................................................................................................ 11

3.1 Capillarity and Wettability .................................................................................................................... 13

3.2 Classic studies on bubble motion inside channels ................................................................................. 15

4. PHP geometry ............................................................................................................................ 18

4.1 Internal channel diameter ...................................................................................................................... 18

4.2 Number of U-turns/ bends ..................................................................................................................... 20

4.3Typical lengths ....................................................................................................................................... 22

4.4 Internal PHP configuration: looped and un-looped ............................................................................... 23

4.5 Channels section type ............................................................................................................................ 23

5. Operating parameters ................................................................................................................ 25

5.1 Working fluid ........................................................................................................................................ 25

5.2 Filling ratio ............................................................................................................................................ 26

5.3 Heat power supplied .............................................................................................................................. 27

5.4 Gravity ................................................................................................................................................... 28

5.4.1 Ground tests .................................................................................................................................... 28

5.4.2 Parabolic Flight test ........................................................................................................................ 30

6. Experimental investigation ........................................................................................................ 34

6.1 Introduction ..................................................................................................................................... 34

6.2 Tested devices ................................................................................................................................. 35

6.2.1 PHP # 1 ........................................................................................................................................... 35

6.2.2 PHP # 2 ........................................................................................................................................... 36

6.2.3 PHP # 3 ........................................................................................................................................... 39

6.3 Test bench and experimental apparatus ................................................................................................. 40

6.4 System assembly and preparation.......................................................................................................... 42

6.5 Thermocouples fastening ....................................................................................................................... 42

6.6 Assembly of Evaporator and Condenser ............................................................................................... 43

6.7 Emptying and filling operations ............................................................................................................ 44

6.7.1 System emptying ............................................................................................................................ 45

6.7.2 Tank filling and non-condensable degassing .................................................................................. 46

6.7.3 PHP filling ...................................................................................................................................... 47

6.8 Thermal coating ..................................................................................................................................... 48

6.9 Experimental test procedure .................................................................................................................. 48

6.10 Post-processing .................................................................................................................................... 51

6.10.1 Evaluation of measurements uncertainties ................................................................................... 53

6.10.2 Repeatability of measurements ..................................................................................................... 54

6.11 Vacuum test ......................................................................................................................................... 54

7. Experimental results ..................................................................................................................... 57

7.1 Influence of PHP operative position ...................................................................................................... 57

7.2 Influence of primary working fluid ....................................................................................................... 61

7.3 Influence of the heat transport length .................................................................................................... 65

7.4 Influence of secondary fluid temperature .............................................................................................. 74

7.5 Influence of geometry ............................................................................................................................ 76

7.6 Influence of external separating grooves ............................................................................................... 79

7.7 Conclusions on the experimental campaign .......................................................................................... 83

8. Numerical modelling of a specific test case .............................................................................. 84

8.1 Introduction ........................................................................................................................................... 84

8.2 A simplified analysis of the annular flow. The analysed case and its experimental results .................. 84

8.3 The two-resistance model for PHP# 2 ................................................................................................... 88

8.4 Modelling of a liquid film in a rectangular channel .............................................................................. 89

8.5 PHP# 2: model settings and results ....................................................................................................... 90

9. A preliminary Matlab model of the Pulsating Heat Pipe ............................................................ 95

9.1 Introduction ........................................................................................................................................... 95

9.2 General overview of the earliest models ............................................................................................... 95

9.2.1 The mass- spring- damper model ................................................................................................... 96

9.2.2 Kinematic approach ........................................................................................................................ 97

9.2.3 Classic approach based on the conservation equations: Dobson’s model ...................................... 98

9.2.4 PHP modelling and flow patterns ................................................................................................. 102

9.3 Introduction to a PHP model for the semi-annular flow pattern.......................................................... 103

9.4 Model setting: PHP geometry and operating parameter ...................................................................... 106

9.5 Results of the model without the heat exchange ................................................................................. 109

9.6 Modelling of the heat and mass transfer .............................................................................................. 112

9.6.1 Evaporation through a liquid film................................................................................................. 114

9.6.2 Condensation through a liquid film .............................................................................................. 115

9.7 Model updating and closing equations ................................................................................................ 115

9.8 Conclusions on the numerical modelling ............................................................................................ 116

General Conclusions ....................................................................................................................... 117

Appendix I ....................................................................................................................................... 118

Thermophysical properties of the fluids ......................................................................................... 118

Appendix II ...................................................................................................................................... 120

Experimental apparatus .................................................................................................................. 120

Appendix III .................................................................................................................................... 123

Evaluation of thermal resistance contribution due to the presence of fluid, or “PHP effect”

(RPHP) ............................................................................................................................................... 123

Bibliography .................................................................................................................................... 124

List of Figures

i

List of figures

Figure 1.1 A classic thermosiphon. (Stony Brook University, Thermal Laser Lab.)........................... 4

Figure 1.2 A Capillarity Heat Pipe. (Aavid catalogue) ....................................................................... 5

Figure 1.3 Typical representation of a capillarity pumped two-phase loop. (Bensalem, [5]) ............ 6

Figure 1.4 a) A PHP obtained from a single tube ([ASME Journal of Heat Transfer]); b) A FPPHP

or Flat Plate Pulsating Heat Pipe. (Manno, [18]) .............................................................................. 7

Figure 1.5 An example of fluid distribution inside a PHP. (Bensalem, [5]) ....................................... 7

Figure 1.6 Typical FPPHP flow regimes; a) slug flow and b) annular. (Khandekar, [14]) ............... 8

Figure 3.1 Schematic representation of the main heat transfer mechanisms that take place in a PHP

channel in case of slug flow regime. (Bensalem, [5]) ........................................................................ 11

Figure 3.2 Generic P-h plot in which the points A, B and C represents some typical PHP working

conditions. (Manno, [18]) .................................................................................................................. 12

Figure 3.3 Droplet shape and contact angle due to a solid-liquid interaction. (Wikipedia)............. 14

Figure 3.4 Liquid droplet on a solid surface and 0< ϑ <π/2. (Bensalem, [5]) ................................. 14

Figure 3.5 Example of a slug flow regime inside a channel. ............................................................. 15

Figure 3.6 Bubble motion inside a channel filled with different fluids. (Khandekar, [13]) .............. 16

Figure 4.1 Initial flow arrangement in PHP channels. (Bensalem, [5]) ........................................... 18

Figure 4.2 Effects of U-turn; simple circuit tested by Khandekar, the lengths are in mm. ([15]) .... 20

Figure 4.3 Typical behaviour of a heated circuit made up with two interconnections. (Khandekar,

[15]) ................................................................................................................................................... 20

Figure 4.4 Effects of interconnections on the heat power exchanged for two different diameters.

(Charoensawan, [7]) .......................................................................................................................... 21

Figure 4.5 Influence of total PHP length on thermal resistance. (Charoensawan, [8]) ................... 22

Figure 4.6 Internal channels configuration: a) un-looped and b) looped. (Electronic Cooling) ...... 23

Figure 5.1 Influence of filling ratio on thermal resistance and on heat transfer rate.

(Charoensawan, [8]) .......................................................................................................................... 26

Figure 5.2 Possible vertical arrangements for a PHP a) vertical “favourable” position, or bottom

heated; b) vertical “un-favourable” position, or top heated. ............................................................ 28

Figure 5.3 Influence of PHP incidence inclination on a) evaporator mean temperature and b)

thermal resistance, as function of the heat power applied. (Mameli, [16]) ...................................... 28

Figure 5.4 A PHP placed on the edge position. (Manno, [18]) ........................................................ 29

Figure 5.5 Flow pattern visualisation on a PHP tested on the edge; effect of hydrostatic pressure on

flow behaviour. (Ayel, [3]) ................................................................................................................. 30

Figure 5.6 PHP setup for the parabolic flight campaign. (Ayel, [4]) ............................................... 31

Figure 5.7 FPPHP tested under a variable gravity field; a) parabolic flight test and b) ground test.

(Ayel, [4]) ........................................................................................................................................... 32

Figure 5.8 FPPHP tested in horizontal position under a variable gravity field; a) temperature

values and b) Pressure signal. (Ayel, [4]) ......................................................................................... 33

List of Figures

ii

Figure 6.1 Backside of a typical FPPHP and stainless steel pipes for the pressure captor and filling

valve. .................................................................................................................................................. 34

Figure 6.2 PHP # 1 with evaporator blocks and condenser. ............................................................. 35

Figure 6.3 PHP # 1; thermocouples arrangement. ........................................................................... 36

Figure 6.4 Front view of PHP # 2 and its external grooves. ............................................................. 37

Figure 6.5 Details of the electrical heater in the evaporator region. ................................................ 37

Figure 6.6 Thermocouples location for PHP# 2................................................................................ 38

Figure 6.7 Front view of PHP # 2 (left) and PHP # 3 (right) ........................................................... 39

Figure 6.8 Thermocouples arrangement for a) PHP# 2 and b) PHP# 3........................................... 40

Figure 6.9 Test bench and its degree of freedom. .............................................................................. 41

Figure 6.10 Condenser assembly on PHP# 3; the thermal gap filler on the left and fixing screws

and external clamps on the right........................................................................................................ 43

Figure 6.11 PHP# 1 condenser and evaporator ................................................................................ 44

Figure 6.12 PHP# 3 connected to tank and vacuum pump. .............................................................. 45

Figure 6.13 Degassing of the fluid inside the tank. ........................................................................... 46

Figure 6.14 PHP filling operations. .................................................................................................. 47

Figure 6.15 PHP # 3 inside its thermal insulating case. ................................................................... 48

Figure 6.16 PHP tested configurations; (a) Horizontal, (b) 45°inclination, (c) Vertical favourable

and (d) On the edge. ........................................................................................................................... 49

Figure 6.17 Additional tests for PHP # 2 and PHP # 3 with a different cold source placement; a)

configuration # 2 and b) configuration # 3. ....................................................................................... 51

Figure 6.18 Example of temperature versus time plot during a power rump up from 20 to 260 W

with a 30W step. (PHP# 2, FC 72, α = 45°, Tcryo= 40°C) ................................................................. 53

Figure 6.19 Schematic representation of temperature nodes and main thermal resistances. ........... 55

Figure 7. 1 PHPs global thermal resistances as function of the heat power supplied for all three

devices tested in four positions: horizontal (α=0°), α= 45°, vertical favourable (α= 90°) and on the

edge: a) PHP# 1; b) PHP# 2 and c) PHP# 3. (FC72, Tcryo= 5°C) .................................................... 59

Figure 7.2 PHP# 2 tested in horizontal position; a) temperatures signals, b) pressure signal.

(FC72, Tcryo=5°C) .............................................................................................................................. 60

Figure 7.3.a FC72 and Ethanol: a) saturation curve and b) dynamic viscosity. .............................. 61

Figure 7.3.b Critical values of hydraulic length for FC72 and Ethanol. .......................................... 62

Figure 7.4 Influence of primary working fluid on PHP# 1 tested in horizontal and vertical position.

............................................................................................................................................................ 62

Figure 7.5 Temperatures-Heat power versus time for PHP# 1 in vertical position and partially

filled with: above FC72, below Ethanol. (PHP# 1, Tcryo=40°C) ....................................................... 63

Figure 7.6 PHP# 3 temperatures curves registered in horizontal position and partially filled with:

FC72 above and Ethanol below. (PHP# 3, Tcryo=20°C) ................................................................... 64

Figure 7.7 PHP# 2 in horizontal position; a) temperatures signals, b) pressure signal. (Ethanol,

Tcryo=40°C) ........................................................................................................................................ 66

Figure 7.8 PHP# 2 tested on ground in horizontal position, by using a fans and fins cooling system:

temperatures signals above; pressure signal below. (FC72, τ=50%) (Ayel, [4]) ............................. 67

Figure 7.9 Typical lengths for PHP# 2: a) for parabolic flight campaign; b) for current ground

tests..................................................................................................................................................... 68

Figure 7.10 Influence of adiabatic length on PHP performance: a) Configuration # 1 (standard), b)

Configuration # 2 and c) Configuration # 3.. .................................................................................... 69

Figure 7.11 Influence of the adiabatic length in PHP# 2. (FC72, Tcryo=20°C) ................................ 70

Figure 7.12 Influence of the adiabatic length in PHP# 2. (Ethanol, Tcryo=20°C) ............................. 71

List of Figures

iii

Figure 7.13 Temperature trends over time and heat power supplied. (PHP# 2, Configuration # 1,

vertical position, Tcryo=20°C) ............................................................................................................ 71

Figure 7.14 Temperatures signals in horizontal position for all three configurations. (PHP# 2,

FC72, Tcryo=20°C) ............................................................................................................................. 73

Figura 7.15 Influence of Tcryo on PHP# 1 tested in different positions. (FC72) ................................ 75

Figure 7.16 Influence of Tcryo on PHP# 2 tested in different positions. (Ethanol) ............................. 75

Figure 7.17 PHP# 1 and PHP# 3 mean evaporator temperatures versus heat flux supplied for three

different positions. (FC72, Tcryo=20°C) ............................................................................................. 77

Figure 7.18 Evaporator contact area for PHP# 1 and PHP# 3. ....................................................... 77

Figure 7.19 Activation of PHP# 1 (a) and PHP# 3 (b) in vertical position: influence of geometry on

the input heat flux. (FC72, Tcryo=20°C) ............................................................................................. 78

Figure 7.20 Comparison of the thermal resistance associate to the presence of flow in PHP# 1 and

PHP# 3 placed on the edge. (FC72, Tcryo=20°C) .............................................................................. 79

Figure 7.21 Cross-sectional sketch of PHP# 2, evidencing the external groove to increase the

transverse thermal resistance. ........................................................................................................... 79

Figure 7.22 Comparison of thermal resistances values for PHP# 2 and PHP# 3 with: a) Ethanol,

Tcryo=20°C; b) FC72, Tcryo=5°C; c) FC72, Tcryo=40°C..................................................................... 81

Figure 7.23 PHP# 3 tested in different positions using ethanol as primary fluid and a Tcryo=20°C.82

Figure 8.1 PHP# 2, Ethanol, FR=50%, vertical, Tcryo=20°C; temperature, pressure curves and

thermocouples arrangement. ............................................................................................................. 86

Figure 8.2 Main thermal resistances associated to: a) a slug flow pattern; b) an annular flow

pattern. ............................................................................................................................................... 88

Figure 8.3 Two-resistance model of PHP# 2. .................................................................................... 88

Figure 8.4 Some possible distributions of the condensed phase in a channel cross section. ............ 89

Figure 8.5 Geometrical reconstruction of the liquid film on Star CCM+; sketch 2D and 3D channel

view. ................................................................................................................................................... 90

Figure 8.7 CAD model of PHP# 2 (left) and an example of visualisation of results (right). ............ 91

Figure 8.8 Two-resistance model in the case where hf tends to ∞. ................................................... 92

Figure 8.9 Thermal resistances values for PHP# 2 tested in vertical position: experimental and

numerical results. (Ethanol, Tcryo=20°C)........................................................................................... 93

Figure 8.10 Mean evaporator and condenser temperatures: experimental and numerical data.

(PHP# 2, Ethanol, Tcryo=20°C) .......................................................................................................... 93

Figure 9.1 Numerical solution of Zuo’s model: plot of oscillations vs time with three different

values of FR. (Zuo, [22]) ................................................................................................................... 96

Figure 9.2 Schematic representation of Wong’s model domain. (Wong, [19]) ................................. 97

Figure 9.3 Pressure oscillations vs time in second element. (Wong, [19]) ....................................... 98

Figure 9.4 Sketch of Dobson’s model for a single pipe and a two-phase fluid; the left end of the pipe

is open while the right end is closed. [9] ........................................................................................... 99

Figure 9.5 Dobson’s model results: trends of liquid position xp , vapour pressure Pv versus time.

(Dobson, [9]) ................................................................................................................................... 102

Figure 9.6 Flow visualisation in a flat plate CL-PHP placed on the edge and using ethanol as

primary working fluid. (Ayel, [3]) ................................................................................................... 104

Figure 9.7 Sequence of pictures taken in a time laps of 5 seconds: hydrostatic pressure contribution

to liquid menisci instabilisation. (Ayel , [3]) ................................................................................... 104

Figure 9.8 Evaporator temperatures vs heat power applied for PHP# 2 placed on the edge.

(ethanol, Tcond=20°C) ....................................................................................................................... 105

Figure 9.9 Representation of model domain with its geometrical features; all lengths are in mm. 106

List of Figures

iv

Figure 9.10 Example of liquid slug displacement............................................................................ 108

Figure 9.11 Displacements of the liquid slugs for the “cold” model. ............................................. 109

Figure 9.12 Liquid slugs speed. ....................................................................................................... 110

Figure 9.13 Forces acting on the external liquid slug. .................................................................... 110

Figure 9.14 Forces acting on the internal liquid slug. .................................................................... 111

Figure 9.15 Temperature of the vapour plugs. ................................................................................ 111

Figure 9.16 A schematic representation of the film released by the liquid meniscus. ..................... 113

Figure 9.17 Evaporation of liquid film. ........................................................................................... 114

Figure 9.18 Condensation on liquid film. ........................................................................................ 115

List of Tables

v

List of tables

Table 1 Heat transport lengths for three typical two-phase passive heat exchangers. (Bensalem,

[5]) ....................................................................................................................................................... 9

Table 2 Rth values for Heat Pipes, LHPs and PHPs. (Bensalem, [5]) ............................................... 10

Table 3. Geometrical features of all tested PHPs. ............................................................................. 35

Table 4. Resume of the tests done in the experimental campaign. ..................................................... 50

Table 5. General scheme of a vacuum test for a PHP. ...................................................................... 55

Table 6. Geometrical characteristics of PHP# 1 and PHP# 3. ......................................................... 76

Table 7. Thermal resistances of PHP# 2 tested in vertical position. (Ethanol, Tcryo=20°C)............. 87

Table 8. Conditions required for the two-resistance model............................................................... 91

Table 9. Comparison among the experimental and numerical data collected for PHP# 2 in vertical

position. (Ethanol, Tcryo=20°C) ......................................................................................................... 92

Table 10. Summary of all the conditions of the Dobson’s model. ................................................... 101

Table 11. Initial conditions for the Matlab model. .......................................................................... 108

Table 12. Thermophysical properties of Ethanol. ............................................................................ 118

Table 13. Thermophysical properties of FC72. ............................................................................... 119

Table 14. Datasheet of the Power Supply EA ELEKTRO-AUTOMATIK model PS 8360-10 T. ..... 120

Table 15. Datasheet of the thermoregulation HUBER CC240wl. ................................................... 120

Table 16. Data sheet of the vacuum pump Pascal 2010 C2. ........................................................... 121

Table 17 Datasheet of Leak Detector ASM Graph 142. .................................................................. 122

List of Symbols

vi

List of Symbols

α [deg] Incidence angle of PHP

δ [µm] Liquid film thickness

ρ [kg m-3] Density

λ [W m-1 K-1] Thermal conductivity

𝜎 [N m-1] Surface Tension

µ [Pa s] Dynamic viscosity

ϑ [rad] Wettability angle

CP-v [J kg-1 K-1] Specific Heat at constant pressure- volume

D [mm] Hydraulic diameter

hlv [kJ kg-1] Latent heat liquid-vapour phase

h [W m-2 K-1] Heat transfer coefficient

u [m s-1] Velocity

T [K] Temperature

P [Pa] Pressure

Q [W] Heat Power

Rth [K W-1] Thermal resistance

Eӧ [] Eӧtvos Number

Fr [] Froude Number

Mo [] Morton Number

Po [] Poiseuille Number

FR [] Filling Rati

Abstract

vii

Abstract

Il presente lavoro di tesi si contestualizza in un progetto di ricerca finanziato dall’ESA (Agenzia

Spaziale Europea) con l’obiettivo di valutare l’utilizzo dei Pulsating Heat Pipes come sistemi

passivi di controllo termico in applicazioni spaziali. L’obiettivo specifico di questa tesi è stato

quello di analizzare questi scambiatori sia da un punto di vista sperimentale che numerico, in modo

da fornire un quadro quanto più possibile completo per la loro caratterizzazione.

Il lavoro si divide dunque in due parti: un’analisi sperimentale ed una modellazione numerica. Per

quanto riguarda la prima parte, tre PHP aventi diverse caratteristiche geometriche sono stati testati

in diverse condizioni operative ed i risultati sono stati poi tra loro comparati. E’ stato dunque

possibile trarre alcune conclusioni generali in merito al comportamento di questi dispositivi,

individuando alcuni fattori critici per la loro progettazione ed evidenziandone gli aspetti peculiari in

termini di prestazioni termiche.

Per quanto riguarda la modellazione numerica, questa si compone di due parti; un primo studio si

interessa di replicare una prestazione termica ottenuta in via sperimentale basandosi su alcune

considerazioni in merito alla fluidodinamica interna al PHP. La seconda parte dello studio numerico

riguarda la scrittura di un modello Matlab basato sulle equazioni di conservazione per descrivere

una particolare condizione di funzionamento, per la quale la fluidodinamica e lo scambio termico

risultano particolarmente semplici.

Key words: Pulsating Heat Pipes, two-phase flow, heat transfer, evaporation, condensation.

The current thesis is part of a research project financed by the ESA (European Space Agency)

which investigates the use of the Pulsating Heat Pipes as passive thermal control systems for space

applications. The main goal of this work has been to analyse these heat exchangers both from an

experimental and a numerical point of view, in order to outline a general overview that can be

useful for their characterization.

The work is thus divided in two parts: an experimental and a numerical analysis. As for the first

part, three different PHPs having different geometrical features have been tested under various

operative conditions. The tests led to some general conclusions concerning the behaviour of these

devices, underlining some critical factors for their design and showing the peculiarities of the

thermal performances.

As for the numerical modelling, it is split in two parts; a first study concerns the reproduction of the

thermal performance measured during some of the tests, basing on some considerations about the

internal fluid dynamics of the PHP. The second part concerns the implementation of a Matlab

model based on the conservation equations in order to simulate a specific working condition of the

PHP, for which the fluid dynamics and the heat exchange are simplified.

Estratto in lingua italiana

viii


Introduzione

Le attività spaziali rappresentano da sempre una delle più grandi sfide per il genere umano; dietro

ogni missione si cela un’enorme complessità dovuta alla coesistenza di diversi fattori critici, tra

questi uno dei più importanti sicuramente rappresentato dal problema termico. Per questa ragione,

ogni sistema progettato per resistere nello spazio è dotato di un certo numero di dispositivi

predisposti al controllo termico, questi formano il TCS (Thermal Control System). Tra questi, i più

performanti sono quelli attivi che tuttavia necessitano di una sorgente di potenza per poter

funzionare. Vi è poi un secondo tipo di dispositivi, completamente passivi, con performance più

contenute ma un bassissimo margine di failure che li rende dunque molto attraenti. Tra i dispositivi

di questo secondo tipo rientrano i Pulsating Heat Pipes, degli scambiatori di calore brevettati da

Akachi intorno al 1990. Il Pulsating Heat Pipe, in breve PHP, deriva dai classici Heat Pipes e

consiste banalmente in una serpentina di canali interconnessi a formare un circuito chiuso. Questi

canali possono essere ricavati attraverso semplice piegatura di un tubo oppure attraverso fresatura di

una piastra (Flat Plate PHP) sulla quale ne verrà poi incollata una seconda in modo da realizzare i

canali interni. I materiali più comunemente utilizzati sono il rame e l’alluminio, per via della loro

elevata conduttività termica ed il loro costo contenuto. Dunque un vantaggio di questo dispositivo è

la semplicità di realizzazione unita al basso costo, analogamente ai classici Heat Pipes. A seguito di

un pompaggio iniziale in cui si genera una condizione di vuoto al suo interno, il PHP viene

parzialmente riempito con un fluido di lavoro, selezionato in base alle sue proprietà termofisiche; il

volume occupato dal fluido rispetto il volume totale interno dei canali è un parametro fondamentale

denominato Filling Ratio (FR). Nella porzione di volume non occupato dal liquido sarà presente il

suo vapore in condizioni di saturazione. La sezione interna dei canali è in genere circolare o

quadrata/rettangolare e la sua dimensione caratteristica è dell’ordine del millimetro. In questo

modo, il fluido all’interno dei canali assume una distribuzione costituita da sequenze di tappi di

liquido e bolle di vapore, nota come slug-flow. In questo modo si riducono gli effetti della gravità

aumentando quelli di capillarità. Il PHP è caratterizzato da tre lunghezze fondamentali che fanno

riferimento a tre regioni specifiche: la regione dell’evaporatore, in cui viene applicata la potenza

termica da rimuovere, la regione “adiabatica” rappresentativa della capacità del dispositivo di

trasportare il flusso termico e quella di condensazione, posta in corrispondenza della sorgente

fredda. Alla base del funzionamento di un PHP vi sono delle instabilità di pressione, generate tra la

regione di evaporazione e quella di condensazione; queste permettono alle bolle di vapore

surriscaldato di raggiungere la parte fredda del dispositivo, in cui si raffreddano e condensano. Si ha

cosi una riduzione della pressione nel canale che richiama del liquido all’evaporatore ed il ciclo si

ripete. In generale, funzionamento di un PHP è regolato dal comportamento del flusso bifase al suo

interno, per cui si tratta di un problema molto complesso, inoltre è sempre instazionario. Da


ix

precedenti campagne di visualizzazione del flusso, realizzate con dispositivi di tipo Flat Plate dotati

di parete trasparente, sono state osservate tre principali distribuzioni di flusso: il regime slug-flow

(sequenze di bolle di vapore e tappi di liquido) il regime anulare, in cui il flusso forma un sottile

film liquido a parete ed il vapore surriscaldato risale lungo l’asse centrale del canale ed il regime

semi-anulare, in cui c’è un solo menisco liquido che preme sul vapore surriscaldato rilasciando un

sottile film sulla parete interna dei canali. Le prestazioni in un PHP vengono quantificate

sperimentalmente attraverso il calcolo delle resistenze termiche, ottenute rapportando la differenza

del valore medio delle temperature di evaporatore e condensatore alla potenza termica trasferita

corretta delle perdite. In questo lavoro di tesi è stata fatta un’analisi sperimentale incentrata sulla

determinazione di queste resistenze termiche al variare di alcuni parametri operativi ed un’analisi

numerica con l’obiettivo di studiare alcuni casi di funzionamento specifico.

Materiali, metodi e risultati

Analisi sperimentale

La prima parte del lavoro riguarda un’analisi sperimentale in cui sono stati testati tre diversi Flat

Plate PHP, per semplicità PHP# 1, PHP# 2 e PHP# 3. Tutti e tre hanno le stesse lunghezze

caratteristiche delle regioni di evaporazione (1 cm) adiabatica (11 cm) e di condensazione (8 cm)

ma il PHP# 1 ha un numero di canali superiore (32) rispetto gli altri due (24) e dimensioni della

sezione differenti (PHP# 1: 1.1x1.1 mm2, PHP# 2-3: 1.6x1.7 mm2). L’unica differenza tra i PHP# 2

e 3 consiste nella presenza di scanalature esterne sulla superficie del PHP# 2, assenti nell’altro. I tre

PHP sono stati dotati di un blocco di evaporazione costituito da due cartucce resistive, connesse ad

un erogatore di potenza elettrica. Per quanto riguarda il condensatore, questo è costituito da una

scatola in alluminio, avente una serpentina interna di canali nei quali viene fatto circolare un fluido

di raffreddamento, mantenuto a temperatura costante tramite un termoregolatore. Le misure di

temperatura sono state effettuate fissando un numero adeguato di termocoppie di tipo T sulla

superficie esterna del PHP, mentre la misura di pressione avviene tramite un trasduttore fissato nella

regione di condensazione. Il PHP è stato montato su una piattaforma mobile e ricoperto con della

lana isolante ed un rivestimento riflettente. L’obiettivo dei test è quello di effettuare uno studio

parametrico in cui al variare di un certo parametro si valuta l’andamento delle resistenze termiche in

funzione della potenza applicata all’evaporatore. Inizialmente i tre PHP sono stati testati in quattro

diverse posizioni: orizzontale nel piano perpendicolare al vettore gravità, a 45°, verticale ed

orizzontale ma nel piano parallelo al vettore gravità (on the edge). Questi test hanno mostrato un

buon accordo con la letteratura, in particolare sono state individuate tre regioni operative

caratteristiche dei PHP: la regione di Start-Up, alle basse potenze termiche trasferite, in cui le

instabilità di pressione generate dal gradiente termico non sono sufficienti ad avviare le oscillazioni

nel fluido o a mantenerle con continuità, tutte le curve hanno un andamento decrescente e

l’influenza della gravità è minore. Dopo questa prima regione si trova la Normal Operating, in cui le

resistenze termiche raggiungono i valori minimi (massime performance) e l’influenza della gravità è


x

evidente, con un netto miglioramento passando dall’orizzontale al verticale. Infine la regione di

Medium-High inputs in cui si nota un brusco innalzamento delle resistenze termiche, si ha il dry out

all’evaporatore che non riceve più liquido ed il dispositivo smette di funzionare. Anche in questo

caso l’influenza della gravità si nota in quanto sembra ritardare la comparsa di questa crisi termica

dei PHP. Un secondo gruppo di tests ha riguardato il confronto di due diversi fluidi di lavoro: FC72

ed Etanolo. L’utilizzo dell’FC72 nel PHP# 1 ha portato ad un sensibile miglioramento delle

performance con attivazione avvenuta anche in posizione orizzontale. Questo è logico in quanto

l’FC72 ha una curva di saturazione a pendenza maggiore ed una viscosità dinamica più bassa

rispetto l’etanolo, entrambi aspetti fondamentali quando il PHP lavora in un regime slug flow.

Tuttavia, il PHP# 3 ha mostrato un comportamento opposto, non riuscendo a funzionare in modo

stabile con l’FC72 ma solamente con l’etanolo. Questo non ha spiegazioni evidenti e necessita di

ulteriori investigazioni. Dato che durante i test in orizzontale il PHP# 2 ha dato problemi di

attivazione, si è pensato di testarlo avvicinando progressivamente il condensatore all’evaporatore in

due posizioni aggiuntive, le configurazioni # 2 e 3 (la configurazione # 1 è quella standard con

condensatore posto all’estremità del PHP). In questi test si è dunque misurata l’influenza della

lunghezza adiabatica sul comportamento del PHP# 2; gli effetti sono un aumento significativo delle

prestazioni sia in orizzontale che in verticale e per entrambi i fluidi di lavoro passando dalla

configurazione # 1 alla #2 e 3. Inoltre, in quest’ultima, si nota anche un sensibile avvicinamento

delle curve di resistenza termica relative alla posizione orizzontale e verticale, dunque una riduzione

sensibile degli effetti di gravità. Un altro parametro analizzato è stata la temperatura del fluido del

circuito di raffreddamento, Tcryo; anche in questo caso gli effetti sono evidenti, si nota un

miglioramento progressivo delle prestazioni all’aumentare della Tcryo. Il risultato conferma quanto

riportato in letteratura ed è indice del fatto che l’innalzamento della Tcryo (temperatura minima nel

dispositivo) riducendo la viscosità dinamica del fluido ed il calore latente di evaporazione

contribuisca all’aumento delle prestazioni del PHP. Successivamente è stata analizzata l’influenza

combinata del numero di canali-dimensioni sezione, confrontando i PHP# 1 e 3 in una serie di test

identici. Dai risultati si evince come per la posizione verticale ad esempio, l’avere una sezione dei

canali più grande consenta di evacuare densità di flusso sensibilmente maggiori. Tuttavia, alle basse

densità di flusso, avere una sezione inferiore comporta un incremento delle prestazioni. Infine si

sono confrontati i PHP# 2 e 3 per valutare l’effetto della presenza delle scanalature esterne presenti

nel primo dispositivo sulle performance termiche. In questo caso si è osservato un aumento delle

oscillazioni di temperatura all’evaporatore nel PHP# 2, segno che un incremento dell’isolamento

termico tra i vari canali incentivi le instabilità tra gli stessi, tuttavia non sono stati rilevati

incrementi di performances e le curve sono risultate praticamente sovrapposte.

Analisi numerica

Il primo studio svolto nell’analisi numerica è dedicato al tentativo di replicare le prestazioni

termiche ottenute nel test del PHP# 2 posizionato in verticale con FC72 come fluido di lavoro e

temperatura del fluido secondario di 20°C. In questa condizione, osservando le curve di

temperatura, dopo una fase di assestamento iniziale il PHP sembra trovarsi ad operare con un flusso

anulare; l’obiettivo è dunque stato quello di ricreare una condizione simile e di valutare

numericamente le resistenze termiche in funzione delle potenze applicate. Per fare questo nel modo

più semplice possibile si è utilizzato il software Star CCM+; il primo passo è stato quello di


xi

realizzare un modello CAD del PHP, con una geometria molto prossima a quella reale, vista la

semplicità del sistema. Successivamente sono state fatte delle approssimazioni sul fluido all’interno

del PHP: volendo ricostruire un flusso anulare all’interno dei canali, l’effetto resistivo

preponderante nello scambio termico è dato dal film liquido depositato a parete. Si è considerato

uno spessore del film liquido costante lungo tutto il canale, per determinarne lo spessore medio da

considerare ci si è basati sui risultati delle precedenti campagne di visualizzazione in cui è emerso

che un canale che lavora in regime anulare presenta un rapporto 20% liquido-80% vapore

approssimativamente. In questo modo, facendo l’ulteriore ipotesi che il film liquido aderisca a tutte

le pareti del canale rettangolare e che lo spessore minimo sia di 50µm al centro di ogni lato, con

semplici considerazioni geometriche si è trovato uno spessore medio di 106 µm. A questo punto, è

stato possibile stimare il coefficiente di scambio termico globale tra il vapore e le pareti del PHP,

ottenuto semplicemente dividendo la conduttività termica del liquido per lo spessore medio trovato.

La temperatura di riferimento considerata per il vapore è quella della regione adiabatica, nota dai

dati sperimentali, cosi come i valori della potenza termica applicata. Con queste informazioni

quindi si hanno tutti i dati per poter effettuare un calcolo; è sufficiente applicare alle pareti interne

ai canali la condizione di scambio termico convettivo con il coefficiente trovato in precedenza e la

temperatura di riferimento del vapore. I risultati trovati con questo calcolo estremamente

semplificato si rivelano molto promettenti; infatti si sono ritrovate con buona approssimazione sia i

valori delle resistenze termiche che quelli delle temperature medie di evaporatore e condensatore.

Il secondo studio invece si propone di svolgere un’analisi più dettagliata del PHP quando questo

viene orientato “on the edge” ovvero orizzontalmente ma con i canali paralleli al piano in cui agisce

la gravità. In questa condizione di funzionamento si è visto che il PHP opera in regime semi-

anulare, per questo motivo la modellazione ne risulta semplificata. L’obiettivo è verificare che, in

queste condizioni specifiche, la presenza di un ΔP idrostatico svolga un ruolo attivo al

mantenimento delle instabilità all’interno del dispositivo. Per fare questo si è partiti da un modello

semplificato monodimensionale, per un PHP a 4 canali riempito con etanolo ad un FR attorno al

50%. Si sono scritte le equazioni di conservazione di massa, quantità di moto ed energia. In una

prima versione del modello lo scambio termico è stato trascurato, dunque in luogo dell’equazione

dell’energia si è utilizzata l’equazione di stato per gas perfetto per la fase vapore insieme

all’approssimazione adiabatica isentropica. Il fluido è assunto laminare, incomprimibile e si sono

trascurati gli effetti statici di capillarità. Non essendoci scambio termico la massa delle due fasi

resta costante, per cui la scrittura del bilancio risulta banale. Per quanto riguarda il bilancio di

quantità di moto, questo è stato scritto per il singolo menisco liquido e le forze considerate sono; la

forza di pressione intesa come differenza di pressione netta ai due estremi del menisco liquido, la

forza di attrito viscoso, la forza legata all’isteresi dell’angolo di contatto e la forza di gravità.

Esplicitando l’equazione di bilancio di quantità di moto e risolvendo in avanti si ottengono i valori

di posizione e velocità di spostamento dei menischi di liquido, determinando le condizioni iniziali

del nuovo punto di calcolo. I risultati ottenuti sono stati confrontati con una simulazione svolta con

il risolutore VOF bifase incluso nel software CFD OpenFOAM® e realizzata in condizioni

analoghe; le curve hanno mostrato un modesto scostamento intorno al 15%. Infine è stato

implementato lo scambio termico. Ancora una volta, le due fasi vengono considerate

completamente separate. Si considera che durante il suo moto di ritorno al condensatore, il menisco

liquido rilasci un film a parete, per una lunghezza pari a tutto il suo spostamento e per uno spessore

variabile solo nel condensatore. Una stima del suo spessore viene fornita da correlazioni empiriche

presenti in letteratura. Si considerano cosi delle equazioni di scambio termico attraverso il film

liquido, si determina il calore scambiato e se il vapore si trova in condizioni di saturazione, si valuta

lo scambio di massa dovuto alla transizione di fase, altrimenti si considera il solo effetto convettivo


xii

dello scambio termico. Le equazioni sono state implementate ma si sono riscontrati alcuni problemi

legati all’avviamento delle oscillazioni dei menischi di liquido, pertanto non sono stati trovati

risultati per questa parte ed il modello necessita di essere completato.

Conclusioni

La parte sperimentale ha fornito risultati interessanti; la maggior parte in buon accordo con la

letteratura mentre altri sono più controversi e difficili da interpretare. Ad ogni modo è evidente che

spesso è molto difficile risalire tramite considerazioni generali ad una giustificazione per un

risultato particolare, questo perché il funzionamento di questi dispositivi è estremamente

complesso. Per quanto riguarda la parte numerica, il primo studio ha portato a considerazioni

piuttosto interessanti, inerenti al fatto che le migliori performance in un PHP ricorrano in condizioni

di flusso anulare. Infine, l’ultima parte del lavoro inerente al modello Matlab ha fornito risultati

incoraggianti per la parte priva di scambio termico che sembrano confermare la validità delle ipotesi

di base adottate, tuttavia la parte di scambio termico non è ancora sufficientemente completa e

richiede degli ulteriori sviluppi.

1

Introduction and context of study

Space activities represent one of the hardest challenges for the human kind; the enormous

complexities behind each space mission and the low margin of failure, forces the adoption of the

best available technologies, often up to the current state of art. In addition, present technology

largely derives from space activities and frequently this research area expands our horizons and let

us to go beyond our limits.

Space, as well known, is a hostile and extreme environment where multiple critical factors act

simultaneously: high velocities, strong accelerations, electromagnetic fields and difficult thermal

conditions. The last ones might be particularly dangerous: for example an extremely low/high

environmental temperature (as happens in open space) or high temperature gradients. Satellites

orbiting around Earth are subjected to strong heating and cooling cycles because of their orbital

movement as well as their spin. In those conditions the integrity of the system could be

compromised by dangerous phenomena like the thermally induced vibrations of the flexible parts of

the structure and the electronic equipment failure due to overheating by Joule effect.

In order to manage thermal problems every space system is equipped with a number of dedicated

devices, which form the TCS (Thermal Control System). Those devices are divided into two

families:

- The Active Devices: that require an external power supply (generally electrical) in order to

function, indeed they have moving parts. Typical examples are: radiators, mono or two-

phase pressurized loops, heat pumps and refrigerators;

- The Passive devices: they do not require an external power supply. This group includes all

kind of coatings and conductive spreaders and two-phase systems like heat pipes, capillarity

pumped loops and pulsating heat pipes.

Devices of the first group are surely the best ones in terms of capacity to manage the thermal

problem, but on the other hand they have some limitations; for example the presence of moving part

makes the system heavier and less compact, furthermore the fact that they need to be powered from

an external source increases the possibility of failure. Devices of the second group overcome these

problems, with a less capability to adapt themselves into a dynamic situation. However aerospace

industries have shown a strong interest on these passive systems and a great number of researchers

are currently investigating their behaviour in the space environment. The present work belongs to

one of these research projects; the main purpose is to make an experimental and numerical

investigation on the Flat Plate Pulsating Heat Pipes, or shortly FPPHP; a passive, two-phase heat

exchanger. This rather recent technology appeared approximately forty years ago, it was conceived

by Smyrnov before 80’s and then Akachi in 1990 was the first to patent this heat exchanger. This

device belongs from Heat Pipes technology and it is an easy-building and relatively low cost

system. Unfortunately, there are still not enough criteria for its precise dimensioning because of its

Introduction and context of study

2

very complex functioning. Indeed its unsteady and chaotic nature as well the multiphase flow with a

pulsing motion make the numerical modelling very complex and still nowadays not enough precise.

Despite all, the PHPs has a good heat exchange capability, offered at a relatively low cost; thus

many researchers are studying its functioning, which leads to many physical questions still opened

in literature.

The study presented in this work takes part into a bigger research project financed by ESA (the

European Space Agency) in cooperation with different universities and research poles; Institute P’,

Ecole Nationale Supérieure de Méchanique et d’Aérotechnique, University of Pisa, University of

Bergamo, Politecnico Di Milano.

The aim is to evaluate the use of this technology for space applications through an experimental

investigation consisting of in ground tests (as for this work), in flight (as for the previous work

presented by Ayel [4]) and lastly in orbit around earth (future step). During the flight tests the

device was subjected to a variable gravity field and the results obtained have encouraged its use

under microgravity conditions. After the parabolic flight campaign a number of experimental

ground tests have been made, all data collected helped to better analyse the functioning of this

device and to compare it with others PHPs. Through experimental data a parametric study has been

performed and the influence of different parameters on its thermal performance has been

investigated. Some of those parameters are: PHP geometry, working fluid, position with respect to

gravity etc…

In addition to this experimental study, a numerical analysis has been developed. The latter could be

split in two parts:

- First part: by using Star CCM+ and adopting an extremely simplified thermal model based

on pure conductivity and the real device geometry, the aim is to reproduce the PHP thermal

performances which occurs in the best case;

- Second part: the formulation of a numerical model of the thermo-hydraulic behaviour to be

implemented in Matlab for a specific working condition. The purpose is to reproduce the

behaviour of the fluid flow observed within previous experimental campaigns.

Before getting into the details of the present work, a general and concise introduction on the

Pulsating Heat Pipes is provided in the further sections, trying to give an idea of the state of art of

this systems.

The next paragraph deal with a general introduction concerning the two-phase heat exchangers.

3

1. Two-phase heat exchangers

The modern era sees the establishment of the electronics in the everyday life among developed

countries. The number of electronic devices is constantly increasing, they are omnipresent in most

of the human activities: from telecommunications to data management, from control systems to

propulsion and so on. This tendency brings a series of challenges and critical problems to solve;

surely the most important one is the heat dissipation that affects all electronic devices. Thus thermal

science had a drastic improvement and many innovative solutions were proposed. Among all

possible heat exchange solutions, one of the most performing are those that involve a fluid change

of phase, in particular evaporation and condensation phenomena, because of the latent heat

exchanged during phase transition. Thus, two-phase systems have a higher potential with respect to

normal monophasic convective ones.

Among all existing two-phase heat exchangers, the most commons ones are:

- the Heat Pipe and classic thermosyphon;

- the Pulsating Heat Pipes;

- the Capillarity pumped loops.

1.1 Heat Pipe/ Thermosyphon

The thermosyphon (Figure 1.1) is surely the simplest one: it is made up with a copper, aluminium

or stainless steel tube with both extremities closed. It is partially filled with a working fluid such as

water, ammonia, ethanol or others, depending on applications and on the requested thermal

performance.


4

Figure 1.1 A classic thermosiphon. (Stony Brook University, Thermal Laser Lab.)

The thermosyphon works only if it is vertically positioned and in a favourable way; this means that

the bottom extremity is in contact with the heat source to be dissipated while the top one is

connected with the cold source. The working fluid, which is initially at the saturation state with the

liquid accumulated in the bottom extremity of the pipe, receives heat from the external source and

begins to evaporate: the pressure difference generated among the vapour phase moves it along the

pipe. Once the vapour reaches the upper part of the pipe, the cold source removes heat from vapour,

which condenses on tube internal surface. Then, due to gravity forces, the condensed phase moves

counter flow through the pipe and reaches the hot side at the bottom, where evaporation takes place

and an identical cycle begins.

The intermediate region among the two heat sources is ideally adiabatic and suggests the distance of

heat transport. It is clear that this device, as described, could work only in presence of gravity and if

it is properly aligned with it. Actually there are some similar devices that could work even in

horizontal position thanks to a porous internal coating which is able to trap the condensed phase that

comes back to the hot source thanks to capillarity effects (Figure 1.2). This kind of heat pipe can

operate in absence of gravity and sometimes even under unfavourable gravity field (top heated

mode). An intermediate solution between the capillarity porous and the classic one is represented by

the capillarity grooved heat pipes.

The heat pipes are widely used for satellites thermal control (they could represent up to 10% of their

total weight).


5

Figure 1.2 A Capillarity Heat Pipe. (Aavid catalogue)

The heat pipes are highly appealing solutions because of their simplicity and their reduced cost, in

addition, they are completely passive.

The heat exchange is based on absorption and dissipation of latent heat due to the change of phase;

thus the temperature difference between the two sources is always low. The device operates with

quite uniform temperature along all of its length that is well approximated by the one of the

adiabatic region.

1.2 The two-phase capillarity pumped loops

The two-phase capillarity pumped circuits appeared in 1960-1970 in the context of the space race

between Russia and United States of America. The most common ones are those of type LHP (Loop

Heat Pipe) developed in Russia and those of type CPL (Capillarity Pumped Loop) from US. The

aim was to exchange a huge quantity of heat and to transport it for long distances. Figure 1.3 shows

a typical scheme of a LHP.


6

Figure 1.3 Typical representation of a capillarity pumped two-phase loop. (Bensalem, [5])

Two heat sources are still present; the hot one and the cold one are at the opposite sides of the

circuit. A tube connects the sources in a closed cycle. The evaporator has an inlet region that

behaves as a liquid tank and it is in contact with a porous material; thanks to capillarity forces the

liquid is captured and moves until it reaches the evaporation region in a porous media situated in the

evaporator. Here the heat power vaporises the liquid phase pushing vapour along the tube, out from

condenser. Thus, vapour replaced liquid inside the condenser and on the other hand a portion of

liquid goes back into evaporator. The circulation inside the device is mono directional thanks to the

capillarity pumping action and the porous media, there are no thermal and viscous interactions due

to the opposite sense of motion among fluid and vapour phase, as happens for heat pipes. The

compensation chamber at evaporator inlet acts as a regulator; it controls autonomously the fluid

saturation temperature at evaporator as function of the heat power applied (simply by releasing or

storing a certain amount of liquid).

1.3 Pulsating Heat Pipes

The Pulsating Heat Pipes is the youngest system; this device consists in a number of parallels

channels connected together in a coil shape. Generally they are made from a single bended tube

(Figure 1.4 a) or from two flat plates (Figure 1.4b); in one plate channels are obtained by milling

one of its sides, then the other flat plate is brazed on it and acts as a lid. As for the materials used,

the most common ones are aluminium and copper.


7

(a) (b)

Figure 1.4 a) A PHP obtained from a single tube ([ASME Journal of Heat Transfer]); b) A

FPPHP or Flat Plate Pulsating Heat Pipe. (Manno, [18])

These devices are partially filled with a working fluid that is self-distributed by forming plugs and

bubbles because of the reduced channels diameter (Figure 1.5).

Figure 1.5 An example of fluid distribution inside a PHP. (Bensalem, [5])

The opposite sides of the PHP are connected with the hot and the cold source, respectively; the

effect of the heat flux supplied on one side and removed on the other combined with a number of

interconnected channels with a reduced internal diameter generate an unstable condition on the flow

which constitutes the main operative mechanism of a PHP.

The real behaviour of the fluid inside the PHP is still not clear but a number of experimental

campaign based on fluid flow visualisation on a FPPHP, have shown that three main two-phase

flow regimes could take place inside the device (Ayel, [3]):

- Slug flow regime: in which the fluid maintains a distribution of vapour bubbles and liquid

plugs; the heat flux at evaporator increases the size and the internal pressure of local bubbles

until they start to move. Thus the bubbles move towards the condenser region where they

implode and carry the motion on adjacent channels; as a consequence the local liquid


8

column increases. The pressure gradient needed to have a bubble motion depends on friction

forces, on liquid inertia and on surface tension at liquid-vapour interface (for further details

see section 4).

- Semi-annular regime: starting from a slug flow regime, if bubbles join each other during

their movement, they could form entire vapour columns that pushes on liquid menisci up to

condenser side. This regime is characterized by a rather sharp separation among the liquid

and vapour phase and if liquid is not able to reach the evaporator a dry out phenomena

occurs, with a strong increase of evaporator temperatures.

- Annular regime: the system behaves in a pretty similar way than a conventional

thermosyphon. Indeed the vapour phase moves along the center of the channel towards the

condenser and a liquid film on the internal surface moves in the opposite direction.

Figure 1.6 Typical FPPHP flow regimes; a) slug flow and b) annular. (Khandekar, [14])

Flow pattern visualisations brought several interesting considerations on PHP working principle. In

addition, the temperatures data collected during those experiments have permitted to associate the

fluid dynamic behaviour to the thermal one. Generally the heat transfer that occurs in a PHP

depends both on the latent heat and on the sensible one, thus in a perfect annular regime, similarly

to heat pipes, the latent heat dominates the whole heat transfer mechanism. Otherwise in a semi-

annular or slug flow regime the mass transfers due to variations of bubbles sizes and of the liquid

columns, as well as the pulsating motion, generate strong temperature fluctuations and the heat

exchange is also affected by sensible heat.

The Pulsating Heat Pipes works always under unsteady conditions with respect to time and space;

the instabilities that takes place in the fluid flow are the basis of its passive functioning. However

the complexity of these devices makes the thermo-hydraulic analysis particularly hard to treat.

9

2. Comparison between two-phase systems.

All the two-phase passive devices described are currently adopted for several applications and all of

them are potentially efficient solutions, but they have different features and they answer to different

needs. As for the heat transport distance for example, which is evaluable from the adiabatic length,

the best system is surely the LHP that reaches the longest distances, as shown in Table 1;

The Heat Pipe could reach, if vertical, a few metres transport length. On the other hand the PHP is

less capable to transport heat because of its variable flow regime (not always annular) and the

reduced channels diameter that increases drastically the pressure losses with a damping effect on

liquid and vapour oscillations. As for system arrangement, the most adaptable one is, once again,

the LHP circuit because it is not particularly affected by orientation and position with respect to

gravity field. The heat pipes, on the other hand, are the less adaptable ones because their

functioning largely depends on gravity forces. Finally, PHPs have a major adaptability of the heat

pipes and, as the micro gravity tests have shown, they could even work under microgravity

conditions.

In terms of thermal performances the parameter generally used to evaluate these heat exchangers is

the thermal resistance, defined as follows:

𝑅𝑡ℎ =�̅�𝑒𝑣−�̅�𝑐𝑜𝑛𝑑

𝑄 (1)

Where at the numerator there is the temperature difference among the space and time averaged

evaporator and condenser temperatures, while Q at denominator is the heat flux supplied at the

evaporator. In the form presented in equation (1), the thermal resistance includes conduction effects

and heat losses due to heat exchanges with external environment that are difficult to evaluate. Table

2 shows some typical thermal resistance values of these passive two-phase systems.

Reference author Length

Rosler Ltotal=0.4 cm, Le=3 cm and Lc=11.5 cm

Heat Pipe Faghri Ltotal=1.2 m, Le=20 cm and Lc=20 cm

Alario Ltotal=5.5 m, Le=91 cm and Lc=91 cm

Riehl Lvapour=80 cm, Lc=110 cm

LHP Maydanik Ltotal=5.2m

Maydanik Ltotal=21 m

Khandekar Le=La=Lc=50 mm

PHP Khandekar Le=La=Lc=150 mm

Kiseev Le+La+Lc=420 mm

Table 1 Heat transport lengths for three typical two-phase passive heat exchangers.

(Bensalem, [5])

2. Comparison among two-phase systems

10

Reference author Rth or Q

Scott Rth=0.2 KW-1

Tsai Rth=0.27 KW-1

Heat Pipes Rosler Q=1.82 Wcm-2

Faghri Q=6.45 Wcm-2

Holmes Q=15 Wcm-2

LHP Maydanik Rth,min=0.2 KW-1

North Qmax=78 Wcm-2

Akachi Rth=0.06 KW-1

PHP Akachi Rth=0.3 KW-1

Khandekar Qmax=3.5 Wcm-2

Khandekar Qmax=12 Wcm-2

Table 2 Rth values for Heat Pipes, LHPs and PHPs. Reported names refers to respective authors.

(Bensalem, [5])

As said, Q represents the heat flux supplied at evaporator and it is obtained by dividing the heat

power for the mean contact area among the heat source and the PHP surface. While in terms of

thermal resistance the PHP is the most performing device, followed by the heat pipes and LHP

circuit, as regards the heat power evacuated the situation is reversed and the PHP is the worst one.

As for the cost, heat pipes and PHPs are surely less expensive devices as compared to LHP. Indeed

their manufacturing is basically simple and do not requires complicate and expensive processing

techniques. The materials used, generally aluminium or copper, are quite cheap and commons. On

the contrary a LHP has a higher cost due to the particular porous structure of the evaporator that is

the fundamental component for the whole system. Thus, because of the higher costs as compared to

Heat Pipes, this technology is less frequently adopted.

As a conclusion, the brief comparison proposed in this paragraph evidences the main differences

among the three systems. Indeed, as emerged from the data collected from different authors, each

device performs well in a specific situation:

- The LHP circuit is suitable when a long heat transport distance is needed and when the heat

power (or heat flux density) to evacuate is high. Indeed in case of shorts transport lengths

and small heat powers the LHP has an unstable functioning and it could have start-up

problems;

- The PHP represents a suitable solution when the heat power to evacuate is relatively low

and the transport length is low too (less than 1m). The PHP maintains a temperature

difference among the two sources;

- The Heat Pipe represents an intermediate solution between the previous ones; its main

difference with the LHP circuit is the strong dependence on orientation and position with the

respect to gravity vector. As compared to PHP, the main difference is due to the different

heat transfer mechanism; in the Heat Pipe the heat exchange by latent enthalpy dominates,

11

thus there is a very small temperature difference among the two sources, the heat pipe tends

to maintain a uniform temperature.

3. Physics of Pulsating Heat Pipes

This section is focused on PHP physics; the main physical phenomena that affect its two-phase flow

will be described, by using the classical approach taken from literature.

As said in previous sections, this device is completely passive and only the external heat sources

can generate pressure instabilities on the internal flow. The heat transfer phenomena is due both to

latent heat associated to fluid change of phase and to the sensible one due to mass transfer, heat

convection and conduction in the axial and transversal directions (Figure 3.1).

Figure 3.1 Schematic representation of the main heat transfer mechanisms that take place in a

PHP channel in case of slug flow regime. (Bensalem, [5])

Referring to the picture above: Q1 involves a liquid film evaporation through conduction, Q2

involves the heat convection among the liquid and vapour phase and Q3 the liquid sensible heating.

Thermo-dynamically speaking, the working condition of a PHP is well visible in a pressure-

enthalpy diagram (Figure 3.2).


12

Figure 3.2 Generic P-h plot in which the points A, B and C represents some typical PHP

working conditions. (Manno, [18])

The point A represents an intermediate thermodynamic state for the system. Applying a heat flux

there is an increase of bubble sizes at evaporator; this brings a pressure increase that moves the

system towards point B. Then, bubbles implosions phenomena inside the condenser region causes a

reduction of temperature and pressure; the instabilities among this two points induces the fluid

motion and consequently a heat exchange. So the PHP uses, as happens for others passives devices,

the pressure gradient which occurs in vapour phase as driving force; thus, in order to provide

bubbles motion, this pressure gradient along the channel must be higher or at least equal, to the

pressure losses one.

∆𝑃𝑣𝑎𝑝𝑜𝑢𝑟 ≥ ∆𝑃𝑙𝑜𝑠𝑠𝑒𝑠 (2)

These pressure losses depend on many different factors such as: the viscous losses in the liquid and

vapour phases as well as the surface tension forces, the inertias and gravity ones. The precise

evaluation of this losses is complex because the contribution of each factor to the total loss depends

on the kind of two-phase flow inside the channels.

Another fundamental requirement for the continuous functioning of a PHP is the liquid return from

the condenser region to the evaporator one. If this return is not continuous a dry out of evaporator

region could occur with a progressive increase of temperatures. In a PHP this effect depends mainly

on capillarity and, for a minor part, on gravity. Furthermore, the numerous experimental campaigns

have shown the influence of such geometrical and operational parameter on PHP functioning, for

example:

- The hydraulic channels length;

- The shape of channels section;

- The lengths of each region (evaporator, condenser and adiabatic ones);


13

- The number of channels;

- The kind of working fluid;

- The filling ratio;

- The operating position.

And others…

The experimental investigation proposed in this work and discussed in section 7 analyse a good

number of these dependences, however it was not possible to test all parameters and configurations,

for which some results from other works will be recalled.

3.1 Capillarity and Wettability

Capillarity is one of the most important physical phenomenon which takes place in two-phase

passive heat transfers devices (except for thermosyphons). It interests the interfaces among the

liquid and vapour phase and it is the result of the cohesion, adhesion forces and the surface tension.

The cohesion forces have an electro static nature and they hold together particles of the same

substance against external perturbations; they could have different values that depend on the

molecular bond and so from the aggregation state of matter. The adhesion forces on the other hand,

regard the chemical-physical interactions among two materials of different nature which are in

contact. As the cohesion forces, even the adhesion ones have an electro static nature, indeed they

influence the molecular bond among two different materials. Lastly, the surface tension, measured

in N m-1 represents the surface density of bond energy at the interface of two different materials. In

other words a liquid drop has, everywhere inside of its volume, the resultant of the cohesion forces

applied in a single point equal to zero because all possible cohesion forces are of the same module

and acts in every space direction. This is not true for external surface because those forces are not

balanced in every direction; consequently molecules of the external surface tend to collapse towards

the internal volume, the external surface is thus minimized. Generally speaking, this corresponds to

the minimisation of the total energy of the system, where the gravitational contribution is neglected

for small volumes, as compared to the one of the surface tension.

The combination of these three capillarity effects are relied to the wettability concept, which

regards the interaction between solids and liquids (and solid/gas as well). A typical example is a

liquid droplet on a solid surface exposed to ambient air. As described above, the liquid will assume

a configuration which minimizes its external surface, nevertheless even molecules of the solid

surface generate adhesion and cohesion forces (even if their reciprocal immobility condition does

not allow them to move and warp their surface as happens for liquids). These last forces interact

with the liquid droplet, as a result, a solid-liquid interface is being created. If cohesion forces

prevails on adhesion ones because of the solid-liquid interaction, the liquid droplet takes a shape as

the one presented in Figure 3.3 (a), on the other hand if adhesion forces at solid-liquid interface

prevail on the liquid cohesion ones, the liquid drop assumes a shape of the second type (Figure 3.3

(b)).


14

(a) (b)

Figure 3.3 Droplet shape and contact angle due to a solid-liquid interaction; a) The cohesion

forces inside the drop prevail; b) The adhesive forces among the solid and liquid interface

prevail on the cohesion ones in the liquid drop. (Wikipedia)

Point P delimitates the border of the liquid-solid interface and ϑ, defined as the angle origins in P

between the tangent to the drop surface and the solid surface. The two limit cases are those in

which:

- ϑ=0; which implies a perfect wettability of the fluid that is totally extended on solid surface

and forms a single layer of molecular thickness;

- ϑ=π; which represents the total absence of wettability, the drop has a single contact point

with solid surface;

Assuming the case in which there is wettability and the drop forms an angle between 0 and π/2, on

the convex side of the external surface, pressure will be higher as compared to the concave one.

Young-Laplace equation gives an estimation of this ∆P as a function of the surface tension and the

sum of reciprocals of the local curvature radiuses (Figure 3.4), as expressed in equation (3);

∆𝑃𝑐𝑎𝑝𝑖𝑙𝑙𝑎𝑟𝑖𝑡𝑦 = 𝜎 (1

𝑅1+

1

𝑅2) (3)

Figure 3.4 Liquid droplet on a solid surface and 0< ϑ <π/2. (Bensalem, [5])

In a slug flow regime, the capillarity ∆P has two main effects: indeed if on one side it is important

because it maintains the separation of vapour bubbles and liquid plugs, on the on the other it has a

negative resistance effect on bubble motion, as established by Khandekar ([12]).

In order to point out this effect a tube of internal diameter ri inside of which a liquid plug separates

two bubbles is considered (Figure 3.5).

Liquid drop

Solid surface


15

Figure 3.5 Example of a slug flow regime inside a channel.

Figure 3.5 shows that liquid plug has a contact angle hysteresis for α; the situation illustrated is

dynamic and the liquid front is curved because of the vapour pressure inside the bubble. The

backside pressure generates a major inflexion of the liquid surface as compared to one in the front

side. This happens because the front surface of the liquid plug moves on a dry surface while the

back side moves on a wet one. The net capillarity force that acts in axial direction could be easily

evaluated by Laplace equation:

𝐹𝑐𝑎𝑝 = 2𝜋𝑟𝑖𝜎(cos α𝑓𝑟𝑜𝑛𝑡 − cos α𝑏𝑎𝑐𝑘)𝑑𝑦𝑛𝑎𝑚𝑖𝑐

(4)

Equation 4 states the resistance effect that the contact angle hysteresis has on fluid motion; indeed

the net capillarity force in axial direction is generated along the perimeter of the plug (p=2πri) and it

depends on the surface tension at liquid-vapour interface and from the contact angle. As a

consequence, the more are the liquid plugs inside a channel, the more this resistance effect becomes

important; the net resistance force is the sum of each contribution, it could happen that it causes the

completely break of bubbles motion and thus also of oscillations. So, if a high 𝜎

𝑟 is required in order

to maintain a slug flow regime, at the same time a higher resistance effect on bubbles motion will

occur, a compromise is needed.

3.2 Classic studies on bubble motion inside channels

This section recalls from literature some classic studies on bubble motion inside channels filled of

stagnant liquid, the aim is to transpose, if possible, some of the results proposed and to adapt them

to Pulsating Heat Pipes; it will be shown how, in some cases, from classical results was possible to

derive correlations for its dimensioning.

The first study proposed regards a channel aligned with gravitational axis and filled with a stagnant

liquid. A bubble, which contains vapour of the same liquid, moves along channel axis at a velocity

𝑢∞ . The forces that act on the bubble are:

- Floating force, due to the different densities among liquid and vapour phase;

- Viscous forces in liquid phase;

- Viscous forces in vapour phase;

- Surface tension forces at liquid-vapour interface;

- Inertiels forces.


16

Literature gives a series of non-dimensional parameters that relate these different effects:

- Froude number: it relates the inertial forces on gravitational one;

𝐹𝑟 =𝜌𝑙𝑖𝑞𝑢∞

2

𝐷𝑔(𝜌𝑙𝑖𝑞−𝜌𝑣𝑎𝑝)≈

𝑢∞2

𝐷𝑔 𝑖𝑓 𝜌𝑙𝑖𝑞 ≫ 𝜌𝑣𝑎𝑝 (5)

- Poiseuille number: it relates the viscous forces to gravity ones;

𝑃𝑜 =(𝑢∞𝜇𝑙𝑖𝑞)/𝐷

𝐷𝑔(𝜌𝑙𝑖𝑞−𝜌𝑣𝑎𝑝)≈

(𝑢∞𝜇𝑙𝑖𝑞)/𝐷

𝐷𝑔𝜌𝑙𝑖𝑞 𝑖𝑓 𝜌𝑙𝑖𝑞 ≫ 𝜌𝑣𝑎𝑝 (6)

- Eötvös number: relates the gravity forces to surface tension ones;

Eö =𝐷𝑔(𝜌𝑙𝑖𝑞−𝜌𝑣𝑎𝑝)

𝜎𝐷⁄

≈𝐷2𝑔𝜌𝑙𝑖𝑞

𝜎 𝑖𝑓 𝜌𝑙𝑖𝑞 ≫ 𝜌𝑣𝑎𝑝 (7)

Where D is a characteristic dimension of cross section.

As for the determination of bubble velocity 𝑢∞, if the floating force prevails on the other ones, the

Froude number permits to evaluate it directly. On the other hand if surface tension forces are

important, from Eötvös number there is no way to figure out bubble velocity, thus there is no way

to correlate together the surface tension effects on bubble velocity.

In order to overcome this problem Beardmore and White (1962) have done an experimental

campaign with the aim to find a critical value of Eötvös for which bubble doesn’t move. The results

are resumed in the following plot:

Figure 3.6 Bubble motion inside a channel filled with different fluids. (Khandekar, [13])

Each curve corresponds to a different fluid, the plot compares for different fluids the square root of

Froude number (which is proportional to bubble velocity) as function of the Eötvös one. To

consolidate all results the Morton number was introduced, that links the previous ones;

𝑀𝑜 =𝑔𝜇𝑙𝑖𝑞

4

𝜌𝑙𝑖𝑞𝜎3 =𝑃𝑜4𝐸ö

𝐹𝑟2 (8)

Each curve of the plot in Figure 3.6 refers to a fixed Morton number that increases in the sense

suggested by the Y line.


17

A common characteristic of all curves at constant Mo is the asymptotical trend at both low and

high values of Eö number. Generally speaking three main areas are identified:

- Eö ≤ 4: this value is defined as critical, below which the surface tensions are more

important than gravity and the bubble motion is completely broken;

- 4 < Eö < 100: (for such fluids like water and ethanol for example) intermediate zone where

velocity varies with the Eö; if it decreases also bubble velocity decreases;

- Eö > 100: (for such fluids like water and ethanol for example) area in which √𝐹𝑟 ≈ 0.35;

bubble velocity remains fixed at a constant value different from zero. The viscous forces and

surface tension could be neglected.

The Eö number is currently adopted in order to dimension internal diameter of PHPs channel

sections (see 4.1).

18

4. PHP geometry

In this part some experimental results concerning the influence of the main geometrical parameters

on PHP behaviour and performances will be recalled from literature.

4.1 Internal channel diameter

The diameter of internal channels is the most critical element for the PHP dimensioning. As already

stated in previous paragraphs, the PHP working principle is based on bubbles movement under a

pressure gradient that develops across the device; thus a slug flow regime is requested inside

channels. In order to achieve this flow arrangement a correct value of channels diameter must be

chosen. Indeed, once the PHP is partially filled with a working fluid, the flow distributes

spontaneously in a vapour bubbles and liquid plugs arrangement, as shown in Figure 4.1.

Figure 4.1 Initial flow arrangement in PHP channels; a series of bubbles and liquid plugs

distribution is spontaneously formed. (Bensalem, [5])

This distribution could be achieved if the influence of gravity is reduced as compared to surface

tension forces, thus a motionless condition of bubbles is needed even if the channel is placed

vertically. The experimental analysis of Beardmore and White has shown that there is a critical,

threshold value for Eö number (around 4 for common fluids) below which the surface tension

forces dominates on gravity ones; it is possible to estimate a limit value for diameter associated to

critic Eö number.

Eö𝑐𝑟𝑖𝑡 ≈𝐷𝑐𝑟𝑖𝑡

2 𝑔(𝜌𝑙𝑖𝑞−𝜌𝑣𝑎𝑝)

𝜎≈ 4 (9)

4. PHP Geometry

19

𝐷𝑐𝑟𝑖𝑡 ≈ 2√𝜎

𝑔(𝜌𝑙𝑖𝑞−𝜌𝑣𝑎𝑝) (10)

The critical diameter depends on the surface tension and on the densities of the liquid and vapour

phase, so it is a function of temperature as well. Also gravity influences the critical diameter, indeed

on microgravity conditions it tends to infinite.

The Eö critical number criterion is commonly used in order to dimension PHP internal diameter,

however, different studies have proposed alternative approaches. An interesting result for example

comes from Gu. et al [11] who referred on typical behaviours of two-phase flows under

microgravity conditions. They observed that the most common fluid flow regimes inside channels

are slug flow and annular flow. The transition from first to second one is mainly due to instabilities

at liquid-vapour interface and driving factors are flow velocity and surface tension; Gu compared

the two energies associated to these parameters, the kinetic energy of liquid and the surface tension

one:

𝐸𝑐𝑖𝑛,𝑙𝑖𝑞 =1

2𝜌𝑙𝑖𝑞𝑣𝑙𝑖𝑞

2 (11)

𝐸𝑠 =𝜎

𝑅 (12)

The condition requested is to have a slug flow regime inside the channel, so energy associated to

surface tension must be higher or at least equal to kinetic energy of flow multiplied by a constant

value k, which is unknown, as well as for 𝑣𝑙𝑖𝑞.

𝑅 =2𝜎

1

2𝑘𝜌𝑣𝑙𝑖𝑞

2 (13)

Starting from some experimental data concerning the behaviour of two-phase flows inside channels

under microgravity condition, Gu evaluated both unknowns and thus he found some critical

diameters different from those evaluated through Eö critical number. He concluded that for space

applications the range of adoptable diameters is higher, with respect to what Eö number suggests.

He is not the only author that have criticized the use of Eö critical number for the PHP internal

diameter; indeed, in other works it is outlined that for such common fluids as water and ethanol, the

critical diameter is being overestimated. The Eö number is not strictly related to PHP working

principle, but only to the existence condition of bubbles inside a channel filled with stagnant fluid,

therefore many authors consider as inappropriate the use of this number as dimensioning criterion

of PHPs. The theoretical question on internal diameter estimation is still open, but Eö critical

number is still the adopted criterion. The experimental investigation shows that the heat power

transferred increases with internal channel diameter, this tendency is more pronounced in such fluid

as water, ethanol or R-123. Indeed, as discussed in previous section, a reduced hydraulic diameter

increases the pressure losses, if they are not compensated the heat transfer capacity will be reduced.

4. PHP Geometry

20

4.2 Number of U-turns/ bends

In a PHP channels are connected together in a coil shape, thus, each channel communicates with

two adjacent channels thanks to U-turns placed at each extremity. These connection elements

generates pressure losses due to their curvature and at the same time they provide an additional heat

exchange surface. In order to point out if there is a real need to interconnect a number of channels,

Khandekar [15] has investigated the behaviour of a simple apparatus made up with a single circuit

of two pipes and two U-turns (Figure 4.2).

Figure 4.2 Effects of U-turn; simple circuit tested by Khandekar, the lengths are in mm. ([15])

The circuit has been partially filled with ethanol and different filling ratios under 50% (see section

6) were tested. A circular section has been chosen with an internal diameter estimated through Eö

number. With this simple configuration Khandekar reported for all tested configurations an

identical behaviour: from an initial arrangement of bubbles and liquid plugs, as the heating supply

started, a net separation among the vapour and the liquid phases occurred (dry out), followed by an

abruptly interruption of oscillations and a progressive temperature increase (Figure 4.3).

Figure 4.3 Typical behaviour of a heated circuit made up with two interconnections.

(Khandekar, [15])

4. PHP Geometry

21

There is no criterion available that could suggest the optimum number of interconnections, however

some tests were made in order to compare devices with a different number of interconnections. An

interesting study from Charoensawan et al. [7] analyses devices having different internal channels

diameters (1 and 2 mm) and both tested with different fluids (ethanol and R123). The number of U-

turns was varied from 5 to 23. The following plots report the heat power exchanged as function of

the inclination angle with respect to vertical direction.

Figure 4.4 Effects of interconnections on the heat power exchanged for two different

diameters. (Charoensawan, [7])

As shown in the plot of Figure 4.4 a minimum value on interconnections, around 16 for both

diameters, allows to PHP to work in all positions without any problem, otherwise, a lower number

of interconnections causes the progressive reduction of performances for inclinations close to the

horizontal one. Thus for the limit case of 5 interconnections the PHP has not functioned

horizontally. Moreover from these results emerges that a good number of interconnections could

also reduce the influence of gravity on PHP functioning.

4. PHP Geometry

22

4.3Typical lengths

The PHP has three main lengths that refer to its three main regions:

- evaporator region length: it is implicitly known from the thermal problem that the device is

asked to solve, thus it’s usually imposed;

- adiabatic region length: it is the distance between the two sources, it represents the heat

transport capability and it couldn’t be too high because of the pressure losses generated.

- condenser region length: it depends on the kind of cold source that is being adopted or

available (as air, liquids, conductive systems or others) and on the heat flux to be evacuated.

Of course, the sum of these three lengths represents the total device length. Even in this case, there

aren’t specific criterions that indicate the optimum lengths of each region. Moreover the

experimental investigation on this parameter is quite expensive, so only few data are available.

Nevertheless an interesting study was proposed by Charoensawan and Terdtoon [8]; they have

tested two different evaporator lengths (Le1 and Le2) for a total device length of three times the

evaporator one (Ltot1= 3Le1 and Ltot2= 3Le2). For each length, two different internal channels

diameters were used (1 and 2 mm). The following plot outlines the thermal resistances offered

(Equation (1)) as function of the evaporator length for each tested device.

Figure 4.5 Influence of total PHP length on thermal resistance. (Charoensawan, [8])

It is clear from the figure, that high values of PHP length decrease the thermal performance because

of the higher pressure losses.

4. PHP Geometry

23

4.4 Internal PHP configuration: looped and un-looped

A PHP consists in a number of channels arranged in a coil shape; the two external channels could

be then linked together, as often happens in Flat Plate Pulsating Heat Pipes, or they could stay

separated. In the first case the device has a “looped” configuration, while in the second case it has

an “un-looped” configuration (Figure 4.6).

Figure 4.6 Internal channels configuration: a) un-looped and b) looped. (Electronic Cooling)

An experimental analysis has been made in order to investigate the effect of channels configuration

on the thermal performance (Bonnenfant, [6]). From collected data emerged that at low heat power

applied the looped configuration had lower values of thermal resistance as compared to the un-

looped one, as the power increases no differences were found and both systems perform in the same

way. It was also noted that a high number of interconnections, together with a small tube diameter,

limit the difference among the two configurations.

4.5 Channels section type

Channel section shape is an important parameter for PHPs; the most commonly adopted shapes are

the circular and the squared ones. Indeed the first is preferred in those PHP obtained from a single

bended tube, while the second is a typical section shape for a FPPHP because they are simpler to

4. PHP Geometry

24

obtain from milling. In some specific applications even other shapes are used as the triangular and

trapezoidal ones. Literature suggests to adopt circular sections because of the lower pressure losses

generated as compared to squared ones. However, in such particular flow regimes as the annular

one, the presence of corners could help liquid returns towards the evaporator region thanks to

capillarity. Moreover, a squared shape could easily break up a liquid menisci and promote an

annular flow regime even at low heat powers applied (see paragraph 5.3).

25

5. Operating parameters

In this section the influence of some operating parameters on PHP performances will be discussed.

5.1 Working fluid

The choice of the working fluid is strictly related with the PHP application; it must be chosen the

one which has the most suitable thermo-physical properties, which is chemically inert to PHP

material and, if possible, cheap and easy to find, not dangerous for operators in filling/emptying

operations. For conventional Heat Pipes and Capillarity pumped loops there are some parameters

that could help to find the best fluid; they are based on the combinations of different thermo-

physical quantities ((14), (15)).

𝑀𝑏𝑓 =𝜎(ℎ𝑙𝑣)1.75𝜌𝑣𝑎𝑝

(𝜇𝑣𝑎𝑝)0.25 (14)

𝑀𝑐𝑐 =𝜎ℎ𝑙𝑣𝜌𝑙𝑖𝑞

𝜇𝑙𝑖𝑞 (15)

These numbers compare those quantities that promote the driving forces over viscosity, which

works against them by generating pressure losses. Unfortunately for PHPs there are not similar

parameters, however fluids with low liquid dynamic viscosity and high values of 𝑑𝑃

𝑑𝑇 on the liquid-

vapour coexistence region could offer the best performances.

Furthermore, Khandekar [12] suggests the use of fluids with a low latent heat of evaporation and a

reduced hysteresis of dynamic contact angles for the solid-liquid combination adopted.

Indeed the growth rate of bubbles at evaporator is linked to latent heat; if this latter is low, bubble

growth will be fast and pressure fluctuations develop fast as well. Moreover Khandekar explains

that an excessive low value of latent heat could cause a quick evaporation of the entire liquid phase

in the evaporator region, thus dry out phenomena occurs. As for the hysteresis contact angle, the

negative effect that capillarity has in a slug flow regime have been already discussed in section 3.1;

from some visualisations Khandekar has observed that in the same aluminium device the contact

angle hysteresis phenomena is pronounced for water while for ethanol it is almost non-existent.

5. Operating Parameters

26

These considerations are limited to those situations in which PHP has a slug flow pattern, otherwise

they could be completely wrong.

5.2 Filling ratio

Filling ratio (FR) is defined as the rate between the liquid volume (evaluated at ambient

temperature) injected in the PHP and its total internal volume (16).

𝐹𝑅 =𝑉𝑙𝑖𝑞

𝑉𝑃𝐻𝑃 (16)

So a filling ratio of 100% implies that all internal volume is occupied by liquid, on the other hand a

filling ratio of 0% implies a vacuum condition. The influence of filling ratio on PHP thermal

performance has been investigated, for example, by Charoensawan [8] (Figure 5.1).

Figure 5.1 Influence of filling ratio on thermal resistance and on heat transfer rate.

(Charoensawan, [8])

The results outlined in figure 5.1 show that filling ratio affects thermal resistance and heat power

exchanged in a opposite way: indeed while a low filling ratio provides lower resistances, for heat

power the situation is reversed, thus in order to transfer more heat power a high filling ratio is

requested (the maximum occurs at around 60%). Generally in most applications a filling ratio of

50% is being adopted; it represents a good compromise in terms of thermal resistance and heat

power transferred.

This parameter establishes the equilibrium among the saturated liquid and vapour phase inside the

device; it is observed that for high filling ratios, around 70%, the huge quantity of liquid reduces

bubbles presence, which have not enough space to develop. As a consequence the hydraulic

behaviour will be similar to a classic mono phase thermo-syphon. On the other hand for low filling

ratios (under 30%) the vapour presence will be dominant and dry outs phenomena occur.


27

5.3 Heat power supplied

The external heat power supplied is the only source needed to activate and maintain flow

instabilities inside all two-phase passives systems. Thus the heat power applied and PHP behaviour

are strongly correlated; tests show that there is a minimum heat power to supply in order to start and

keep continuous oscillations, below this minimal value the PHP behaves in an unstable way, with

cycles of activation and deactivations or, in the worst case, in pure conductive mode, reaching high

temperatures. In a flow pattern visualisation campaign made by Khandekar [15], it was observed

that once oscillations start, the first flow regime is the slug flow characterised by weak and non-

continuous oscillations, with low thermal performances. As the power heat flux is increased (up to 1

W cm-2) oscillations became more stable, their amplitude increases with power density; in this

phase performances are significantly higher and evaporator temperatures lowered. If the heat power

is further increased, the fluid flow regime passed from a slug flow to quasi-annular and finally

annular; this last condition brings the higher performances, no more oscillations are present and the

temperature differences among evaporator and condenser regions are lower. PHP works in a pretty

similar way to classic Heat Pipe thermosyphon where heat exchange is realised through a thin liquid

film (more efficient because of the low thermal resistance offered). As Khandekar states, the ideal

working condition for a PHP is characterised by no oscillations, thus the adjective “pulsating”

becomes misnomer. Finally, for a further increase of heat power density a strong reduction of PHP

performance is observed with a dry out of evaporator.

It must be underlined that this behaviour observed by Khandekar, even if it has been verified by

other authors, cannot be assumed as identical for all PHPs and the sequence of flow regimes that

take place inside these devices as function of heat power applied, could be pretty different. In

addition, it is important to remind that the flow pattern in a PHP depends even on some geometrical

features as its lengths, U-turns number, channels section shape and so on.


28

5.4 Gravity

5.4.1 Ground tests

Many experimental campaigns have shown the PHP sensitivity to gravity; ground tests have

underlined a strong difference in its behaviour when position changes. For example a PHP

vertically positioned in a “favourable” way, that means with evaporator under condenser (Figure 5.2

a), represents the best operative conditions with the highest performance; on the other hand a

vertical “unfavourable” condition, with evaporator above condenser (Figure 5.2 b), represents the

worst one.

Figure 5.2 Possible vertical arrangements for a PHP a) vertical “favourable” position, or

bottom heated; b) vertical “un-favourable” position, or top heated.

In a study proposed by Khandekar et al. [12], a PHP (6 interconnections, circular channels with

internal diameter 2 mm, water) was tested for different inclinations, from horizontal to vertical with

an incidence angle step of 5°. From 0° < α < 15° no flow oscillations were observed; as α was

slightly increased from 15°, first oscillations started and the PHP started to work.

Another interesting study on this subject comes from Mameli and Marengo [16], for a PHP (copper,

31 U-turns, fluid FC72, FR=0.5) tested in the same range of inclinations 0° < α < 90°; their results

are reported in Figure 5.3.

(a) (b)

Figure 5.3 Influence of PHP incidence inclination on a) evaporator mean temperature and b)

thermal resistance, as function of the heat power applied. (Mameli, [16])


29

In Figure 5.3 (b) three main regions are outlined:

- the start-up region for the low heat powers applied;

- the normal operation region in which the best performances occur;

- the medium high inputs region where the device has a thermal crisis with a strong reduction

of performances.

It is clear that in the range of heat power between 30 and 60 W in which the best thermal

performances occur, gravity has an influence on them; indeed the highest values of resistance are

those of horizontal and α=15° positions, with values around 0.7 K W-1, while all other inclinations

(15°< α ≤ 90°) report values around 0.4 K W-1. Thus, when the flow begins to oscillate, little value

of α could provide the best performances, indeed all curves for 30°≤ α ≤ 90° are superimposed in

the normal operation region. In those cases where gravity does not assist fluid motion (α=0°:15°)

the heating time needed to have an increase of bubble size and pressure that pushes on the adjacent

liquid plug is higher. Indeed, as shown in Figure 5.3 (a) temperature fluctuations in these cases are

bigger as compared to the other ones.

All these considerations are wrong in the start-up region, where more or less all curves have the

same trend, while in the higher inputs region all inclinations ranged between 30°< α < 90° have a

strong increase of resistance, this does not affect the curves α=0°:15° which stay constants.

Another possible configuration for PHP is to place it “on the edge” that means with gravity acting

on the same plane of the PHP and perpendicularly to channel axis, as shown in Figure 5.4.

Figure 5.4 A PHP placed on the edge position. (Manno, [18])

In this position a hydrostatic pressure gradient affects the liquid menisci stored in the condenser

region; this transversal ∆P among two adjacent channels (Figure 5.5) could affect the entire

behaviour of the flow inside the PHP. In a visualisation campaign made by Ayel et al. [3], it was

observed that when the heat power supplied to evaporator was high enough, vapour pushed on the

liquid menisci that began to oscillate. Then, thanks to the hydrostatic pressure gradient the external

liquid menisci was first destabilized and consequently all the others channels began to oscillate as

well. A pressure wave which propagates rapidly from the top to the bottom of the device affected all

the liquid menisci.

�̅�


30

Figure 5.5 Flow pattern visualisation on a PHP tested on the edge; effect of hydrostatic

pressure on flow behaviour. (Ayel, [3])

It was observed that when a liquid menisci is destabilised, it slips along the channel and reaches the

evaporator region, then it quickly returns into condenser region. A liquid film is deposed on the

evaporator region that is wet again, so temperatures decrease and the process starts again.

From temperature analysis it has been noticed that the PHP works pretty well in this position, with

interesting performance, however the heat transfer coefficient is completely unsteady and difficult

to estimate.

5.4.2 Parabolic Flight test

As for tests under a variable gravity field, it will be recalled the experimental results of the last

parabolic flight campaign (Ayel, [4]) which concerns one of the devices presented and tested in this

work.

A parabolic flight consists in six series of five consecutive parabolas in which the plane passes from

a normal to hyper gravity condition (nominal gravity ~ 1.8m s-2) because of the high flight

incidence accelerations during the ascending phase, to a microgravity one during the descending

phase (nominal gravity ~ 0.1m s-2), of about 22s. Then a second hyper gravity phase follows

(nominal gravity ~ 1.6m s-2) and cycle restarts. The device tested is a FPPHP (copper, 24 squared

channels 1.6x1.7 mm2, FC-72, FR=0.5) with an evaporator region of 1x12 cm2 and a condenser

region of 16.5x12 cm2; the heat sink consists in an aluminium plate with a number of fins cooled by

ambient air thanks to forced convection provided by two fans (Figure 5.6).


31

Figure 5.6 PHP setup for the parabolic flight campaign. (Ayel, [4])

At each parabola a fixed value for the heat power is kept, a range of powers from 30W to 180W

were tested with a 30W step. In order to compare the transient behaviour of PHP during a parabola,

a similar condition was reproduced on ground, tilting the device from vertical to horizontal position

for 22s and then turning it vertically again. Figure 5.7 reports the temperature values registered for a

heat power supplied of 90W and 150W during two flights parabolas (a) and PHP in vertical

position, and during ground test (b). The red-violet curves (namely Te) refer to evaporator

temperatures whilst the blue ones (namely Tc) are those measured in the condenser region. The

black signal tracks the gravity acceleration measured by the accelerometer placed on the PHP case

(minor fluctuations of the signal are caused by vibrations).


32

(a) (b)

Figure 5.7 FPPHP tested under a variable gravity field; a) parabolic flight test and b) ground

test. (Ayel, [4])

It is clear that transition from normal/hyper to micro gravity cause an increase of evaporator

temperatures (Te curves) because flow is no more assisted by gravity. Then, the return to a hyper

gravity condition from micro gravity quickly restores the initial situation. Hyper gravity seems to

have no influence on evaporator temperatures, on ground test a similar situation is observed.

Figure 5.8 reports the temperature (a) and pressure (b) signals registered during two consecutives

parabolas with the PHP horizontally positioned for heat powers of 30W and 180W.


33

(a) (b)

Figure 5.8 FPPHP tested in horizontal position under a variable gravity field; a) temperature

values and b) Pressure signal. (Ayel, [4])

When the heat power supplied is low temperature and pressure oscillations occur, this effect does

not depend on the variable gravity field but on the excessively low heat power applied: indeed, as

shown in Figure 5.8 (upper), oscillations occurs even during the normal 1g gravity phase.

Furthermore at higher heat power supplied (Figure 5.8, bottom pictures) no significant variations

occur under variable gravity field. It could be assumed that the FPPHP can operate similarly under

microgravity than on ground when it is tilted horizontally. This result encourages the use of

pulsating heat pipes for space applications.

Starting from this last study, the main purpose of this work is to analyse the behaviour of the same

PHP used for parabolic flight campaign on ground, investigating the influence of different

parameters on its thermal performance.

34

6. Experimental investigation

6.1 Introduction

The first part of this work concerns an experimental investigation where three different devices of

the same type (Flat Plate Pulsating Heat Pipe, or FPPHP) were tested. The aim is to perform a

parametric analysis and to find a correspondence with the results illustrated and discussed in

previous section.

A simple FPPHP consists in two copper plate brazed together; channels are formed by milling one

of these two plates while the other acts as a lid for the back side creating the internal coil.

Furthermore the backside has two holes that communicates with the internal channels as shown in

Figure 6.1; the top hole is linked with the pressure sensor while the bottom one with the filling

valve. Connections are made with stainless steel tube welded to the copper plate.

Figure 6.1 Backside of a typical FPPHP and stainless steel pipes for the pressure captor and

filling valve.

6. Experimental Investigation

35

6.2 Tested devices

The following table reports the main geometric features of the three tested devices:

PHP# 1 PHP# 2 PHP# 3

Dimensions (length x width x

thickness) mm3

200 x 80 x 3 200 x 120 x 3 200 x 120 x 3

U-turns # (channels) 16 (32) 12 (24) 12 (24)

Channel section type 1.1x1.1 mm2

squared

1.6x1.7 mm2

rectangular

1.6x1.7 mm2

rectangular

Evaporator length (mm) 10 10 10

Condenser length (mm) 80 80 80

Table 3. Geometrical features of all tested PHPs.

6.2.1 PHP # 1

Figure 6.2 shows a frontal view of this first device.

Figure 6.2 PHP # 1 with evaporator blocks and condenser.

As for the evaporator region the heat flux is provided by two cartridge heaters (VULSTAR 10164)

connected to an electrical power supply. They are inserted into two aluminum supports connected

together; the PHP is sandwiched between them.


36

The cold source is made up with an aluminium box clamped on the PHP external surface. Inside

this box, there are channels in which water flows. Thanks to an external thermoregulation system

the water is continuously recirculated inside the condenser and kept at a constant temperature; in

this way it is possible to control the average temperature of the cooled surface during the tests.

As regards the sensors, a number of thermocouples of T type are fixed on plate surface (Figure 6.3);

- 3 thermocouples in the evaporator area (T0; T1; T3);

- 2 thermocouples in the adiabatic area (T4; T10);

- 3 thermocouples in the condenser area (T5; T6; T7).

Figure 6.3 PHP # 1; thermocouples arrangement.

The pressure sensor (point P) used is a GE PTX5076-TA-A3-CA-H0-PS, 5 bars absolute.

6.2.2 PHP # 2

The second device that has been tested comes from the parabolic flight campaign sponsored by

ESA (European Space Agency) for the tests under a variable gravity field. Figure 6.4 shows its front

view and a particular characteristic of this FPPHP; the presence of external grooves (1 x 1.6 mm2

cross section). The role of these grooves is to increase the thermal resistance between adjacent

channels thus to reduce the transversal heat flux and consequently the heat homogenisation that

could reduce flow instabilities ([12]).


37

Figure 6.4 Front view of PHP # 2 and its external grooves.

In the evaporator region, heat is provided by an electrical wire (Thermocoax Type ZEZAc10, 1 mm

external diameter, electrical resistance R = 3.81 ) embedded in a copper plate of 10 x 120 mm²

dimensions and 2 mm thick, thanks to a serpentine groove machined on the front side of the plate,

as shown in Figure 6.5 The latter is connected to an electrical power supply.

Figure 6.5 Details of the electrical heater in the evaporator region.

The cold source is of the same kind of the one used for PHP # 1 but with a different geometry (see

the length of condenser region in Table 3).

Thirteen T-type thermocouples of have been glued on the front surface of PHP as represented in

Figure 6.6;

- 5 thermocouples in the evaporator region (Tevap_A, E, G, I, K);

- 3 thermocouples in the adiabatic region (Tadia_1, 2, 3);

- 5 thermocouples in the condenser region (Tcond_M, U, P, T, X).


38

Figure 6.6 Thermocouples location for PHP# 2.

In order to provide a good contact between the heat/cold source and PHP surface, those

thermocouples who are placed in evaporator/condenser region are fixed inside the grooves while

those of the adiabatic region are placed on top of the channels.

The pressure captor used is, even in this case, a GE PTX5076-TA-A3-CA-H0-PS, 5 bars absolute.


39

6.2.3 PHP # 3

The third device that has been tested is identical to PHP # 2 but without the external grooves

(Figure 6.7 right). It uses the same evaporator and condenser devices. This PHP has been built in

order to investigate the effects of thermal insulation between channels as discussed above.

Therefore it is mandatory to have the same operating conditions and an identical arrangement of the

temperature and pressure sensors as far as possible. To achieve this goal some shorts grooves were

made in the front surface of PHP, in the evaporator and low condenser region.

Figure 6.7 Front view of PHP # 2 (left) and PHP # 3 (right). The only difference consists on the

external grooves.

Further practical details on this subject could be founded in the next section, concerning the

experimental apparatus and system assembling. As a result the PHP# 3 has the same sensors

arrangement except for the condenser region where three captors are located in different positions.

Referring to Figure 6.8: C1 and C2, fixed on the condenser of PHP# 3 (Figure 6.8 (b)), replace P

and X of PHP# 2 (Figure 6.8 (a)) and instead of T (situated in the upper part of PHP# 2 condenser)

there is Q (placed in the bottom area of PHP# 3 condenser).


40

(a) (b)

Figure 6.8 Thermocouples arrangement for a) PHP# 2 and b) PHP# 3.

The pressure sensor is the same one used for the other devices.

6.3 Test bench and experimental apparatus

This paragraph describes briefly the experimental apparatus and the acquisition system used for the

tests, further details on its components could be found in Appendix II.

All tested devices were mounted on the same test bench, which consists in an assembly of a number

of aluminium rods fixed together. This parallelepiped structure has two angular degrees of freedom

in the longitudinal and transverse axis (Figure 6.9) and it allows to test easily the device in different

orientations with respect to gravity.


41

Figure 6.9 Test bench and its degree of freedom.

As for the evaporators the heat power in both systems comes from a power supply (EA ELEKTRO-

AUTOMATIK model PS 8360-10 T) that can deliver an electrical power up to 1000 W.

On the other hand a thermoregulation system (HUBER CC240wl) provides the heat absorption in

the condenser region using water as coolant.

The acquisition system used of this bench is a CompactRIO (model NI cRIO-9074). Both the

pressure transducer and the thermocouples are connected to the data acquisition system.

As for the acquisition frequency of signals; for thermocouples was chosen 1 Hz while for the

pressure sensor 100 Hz. Indeed pressure fluctuations are considerably quicker than temperature

ones, especially when a modification of flow pattern occurs (see section 8 for further details).

Previous experiences confirmed that these settings are proficient in terms of quality of the result

curves obtained.

Two modules are employed inside this acquisition system:

- Module for Analog Input (NI 9215);

- Module for thermocouple (NI 9213).

The first module is needed to elaborate the pressure signal, the second one to monitor all

temperature signals from each thermocouple. The latter module has 16 inlets, therefore no more

sensors could be installed; PHP# 1 has only 12 thermocouples, while PHP# 2 and 3 use all module

capacity. Furthermore, in addition to those sensor placed directly on PHP surface there are three

more thermocouples:

- one sensor measures the ambient temperature during the test;

- two sensors measure the inlet/outlet temperature of cooling flow just outside the condenser.

The first measure helps to estimate the heat losses due to the heat exchange with the environment,

while the seconds suggests the amount of heat removed in the condenser region, moreover they can

help operator to control fluid temperature during the test. Actually, an additional sensor controls

evaporator temperature and prevent the system to exceed a maximum temperature of 120°C; this

thermocouple of K –type is not connected to the data logger module but to a security device, that

immediately turns off the power heating system if the upper limit temperature is exceeded.


42

A USB connection permits acquisition system to send all data to a PC, where Labview software

converts all measurements data in terms of pressure and temperatures units and stores them in .xls

files. The Labview interface provides a real time plots of temperature, pressure versus time.

6.4 System assembly and preparation

This section describes the procedure adopted in order to prepare the PHP to the test. Normally there

is a series of operations to do, as resumed in the following list:

- to fix all thermocouples on PHP;

- to assemble evaporator and condenser in their specifics regions;

- to fill partially the PHP with a working fluid;

- to provide a thermal insulation around the system from external environment.

All these operations are very important because the quality of the tests as well as the functioning of

the device depend on them.

6.5 Thermocouples fastening

This operation is very important for the test phase, it is obvious that from the temperature data it is

possible to evaluate PHP thermal performances and to compare different devices. The

thermocouples used for these applications are of T- type, with a sensitivity of 48.2 µV/K; a number

of them are located in all the three regions of the PHP but the most important data come from

temperatures taken in the evaporator and condenser regions. These sensors are usually fixed on PHP

surface by using an epoxy glue or in some cases, where there is a free surface (as in adiabatic

region), an adhesive thermal resistant tape could be enough. The choosing of the right arrangement

of these sensors is not obvious and it depends on what is the final target of the test. Anyway, for an

overall evaluation of the system thermal performances it could be useful to map the whole

temperatures of the device, especially those of the regions where the heat transfer takes place.


43

6.6 Assembly of Evaporator and Condenser

The assembly of the evaporator and condenser is a simple operation; the aim is to provide a good

contact between their surface and the PHP one. First, all surfaces are cleaned with acetone or other

common solvent, then a thin layer of a silicon paste (Heat Sink Compound, λ= 2.9 W m-1 K-1) or a

thermal gap filler (Tflex Series Lard technologies, thickness δ= 0.5 mm, λ~6 W m-1 K-1) are applied

on the evaporator/condenser surfaces, in this way the local effects of roughness are reduced. Then,

once the evaporator/ condenser are positioned on the PHP surface, they are screwed up to this latter

because of the possible local deformations (Figure 6.10).

Figure 6.10 Condenser assembly on PHP# 3; the thermal gap filler on the left and fixing

screws and external clamps on the right.

Because of the higher width of PHP# 2-3 as compared to PHP# 1, four holes are present along their

centerlines, they are additional tightening points for evaporator and condenser. In those case where

the PHP has no grooves on its external surface that could be used for sensors placement, the

thermocouples thickness has a non negligible effect on thermal contact resistance between

evaporator/condenser and the PHP plate (as in the case of PHP # 1 and for the condenser of PHP #

3). Therefore, some grooves are created on evaporator/condenser as for the PHP # 1 (Figure 6.11).


44

Figure 6.11 PHP# 1 condenser and evaporator, the black blots are due to the glue used in order

to fix thermocouples.

6.7 Emptying and filling operations

Once the device is mounted on the test bench, the next step is to ensure that the PHP is totally

empty and then to partially fill it with a working fluid. In the present study two fluids are used:

ethanol and FC72, their thermophysical properties are listed in Appendix I. The filling ratio at

ambient temperature is FR=50%; indeed this value represents a good compromise between the

transferred heat power and low thermal resistance (section 5.2).


45

6.7.1 System emptying

The first thing to do is to empty the PHP; to do this, the device is first connected with a fluid tank

and vacuum pump through a series of independent connections made up with hydraulics elements

and valves Swagelok SS-41S2 (Figure 6.12).

Figure 6.12 PHP# 3 connected to tank and vacuum pump.

Once connecting nuts are well tightened and all valves open, the vacuum pump is turned on and the

pumping goes on for at least one day. Actually, if the PHP has been already filled with a fluid,

before starting with the pumping action, a cycle of heating with the filling valve opened could be

done. Thus when the fluid saturation temperature generates a pressure that exceeds the ambient one

the vapour is self-pumped outside the device and consequently the pump action will be more

effective. The pump used is an oil seal rotary vane pump (Pascal 2010 C2) that permits to achieve a

minimum of 0.75 Torr (1 mbar), in addition it has a gas ballast enabling the pumping of

condensable vapours, and of a neutral gas purge used to degas oil and dilute pumped gases. Further

details on this pump are listed Appendix II.

After this first emptying operation all valves are closed and another pump is connected; the Leak

Detector (ASM Graph 142) which is a powerful rotary vane pump (see Appendix II). This device

permits to reach a reduced pressure level at the inlet and in addition it has a Helium Leak Detection

system that could verify the presence of leakage in all hydraulics connections simply releasing a

small quantity of helium directly on them with a small gun. Because of its higher cost, this device is

used for few hours just after the first pumping cycle (made with a less expensive pump).

Once the Leak Detection has proved that there is no evidence of leaks, all valves are opened again

for the last pumping cycle (max 30’). Now all valves are closed and the system is ready for a

preliminary test under vacuum condition in order to evaluate the pure conductive performance (in

this case all connections are removed and the system is insulated as explained in section 6.8) or, if

not needed, the filling procedure could start.


46

6.7.2 Tank filling and non-condensable degassing

After the emptying phase all valves are closed and the tank is unfastened; it is now ready to be filled

with the working fluid. The procedure adopted is resumed in the following list of operations:

1- An electronic balance evaluates the initial weight of the empty tank;

2- The tank is then filled with a higher quantity of working fluid than the needed one;

3- The tank weight is evaluated again and its value is noted;

4- With a heat gun the bottom part of the tank is heated (Figure 6.13); when it is sufficiently hot the

valve is opened for few seconds and then closed again. This operation permits to evacuate the non-

condensable gases accumulated in the vapour phase inside of the tank (and trapped by the fluid

during the filling procedure) thanks to the pressure generated by heating which exceeds the outside

one (ambient);

5- The hot tank is cooled in water and weighted again and then its value is being noted, in order to

control the mass ejected during degassing.

Figure 6.13 Degassing of the fluid inside the tank.

The process is repeated from point 4 to 5 until the mass of fluid inside the tank reaches a value as

close as possible to the target one. A minimum number of cycles (>4) should be done in order to

reduce significantly the quantity of non-condensable gases. Before continuing with the filling

operations a final check based on a qualitative criterion permits to evaluate if there is still a

remarkable quantity of non-condensable gases or not. Indeed, because of the shape of the tank

which ends with a short pipe on the top before the upper valve (well visible in Figure 6.13), the

non-condensable gases tend to accumulate there when the tank is in vertical position. If the tank is

bottom heated and heat quickly reaches the pipe (with a fast augmentation of its temperature) this

means that there is no evidence of non-condensable gases. On the other hand, if the heat spreads

slowly in the pipe it is because of the insulating effect due to low thermal conductivity of non-

condensable gases (preventing condensation of generated vapour). In this case further

heating/ejecting cycles must be done.


47

6.7.3 PHP filling

When the tank reaches acceptable values of fluid mass and there is no evidence of non-condensable

gases, it is mounted again on the system. Now the Leak Detector pump (still turned on to keep the

system empty) could pump the air accumulated in the hydraulics connections and once the pressure

reaches vacuum condition, the bottom valve that connects the pump to hydraulics elements is closed

and the PHP is ready to be filled. The procedure is resumed in the following points (see as reference

Figure 6.14);

1- First the thermoregulation system is turned on; the cooling water inside the condenser reaches a

temperature of about 10°C (below the ambient one, in order to promote fluid condensation in this

cold spot of the PHP);

2- Then both tank and hydraulics connections must be strongly heated (all valves are still closed);

the whole fluid mass inside the tank should vaporize and the hydraulics connections must be at the

same temperature (more or less) in order to avoid condensation phenomena inside of them;

3- After an intense heating the PHP valve first and the tank one after could be opened;

4- With the heat gun a continuous heating is provided for a little while and then the tank and PHP

valves are closed; the vapour should cross all connections and reaches finally the condensation area,

where the low temperature quickly condenses and stores it inside the PHP;

5- The last thing to do in order to check the injected mass is to fasten off the tank and to weight it

again. By the mass difference between the two values before and after the filling procedure one can

verify if the filling ratio is in the range of the requested one or not.

Figure 6.14 PHP filling operations.

Usually the most crucial step is the second one; indeed if the fluid inside the tank is not well

vaporized or hydraulic connections are not enough hot, not all vapour reaches the PHP filling valve,


48

therefore the filling ratio should be under the expected one and the procedure must be started again

(from vacuum operations).

6.8 Thermal coating

During a test it is fundamental to reduce as much as possible all heat losses due to heat exchange

with external environment because of the difficulty to evaluate them in performance analysis. In

order to do that a thick coating of rockwool ( λ=0.04 W m-1K-1 ) is mounted all around the PHP,

then the whole system is covered by an aluminium adhesive tape with high reflectivity; in this way

even radiation heat losses are decreased. Figure 6.15 shows the system ready to be tested.

Figure 6.15 PHP # 3 inside its thermal insulating case.

6.9 Experimental test procedure

The test procedure adopted is the same for all tested devices and consists in a ramp up of power

dissipated at the evaporator starting from 20W up to 260W maximum (if the device temperature

stays under the upper limit of 120°C) with 10:30W steps. The duration of each power step is not

fixed but it depends on the time needed for the PHP to reach a stable working condition. This means


49

that PHPs do not operate under pure steady state conditions, but there are fluctuations rather

periodical and stable around a mean value that do not affect substantially the mean temperature of

each region (the hot, cold and adiabatic ones). All the three devices were filled with two different

fluids: FC72 and ethanol. For each of this working fluids, three temperatures of the secondary fluid

(the coolant) were tested thanks to the thermoregulation device; Tcryo = 5, 20 and 40°C (the name

Tcryo derives from the Cryostat thermoregulation system used to set the coolant temperature).

Finally for each coolant temperature, different positions with the respect to an incidence angle α

were performed (see Figure 6.16):

- Horizontal inclination, α=0° (a);

- α=45° (b);

- Vertical favourable inclination (bottom heated), α=90° (c);

- “On the edge” inclination (d) vertical with horizontal channels.

Figure 6.16 PHP tested configurations; (a) Horizontal, (b) 45°inclination, (c) Vertical

favourable and (d) On the edge. The red and blue markers represents the evaporator and

condenser respectively.


50

Table 4 resumes all the main tests performed for each device.

Tcryo= 5°C horizontal, vertical, on the edge

PHP # 1 Tcryo= 20°C horizontal, vertical, on the edge


Tcryo= 5°C horizontal, α=45°, vertical, on the edge

FC72 PHP # 2 Tcryo= 20°C horizontal, α=45°, vertical, on the edge



PHP # 3 Tcryo= 20°C horizontal, α=45°, vertical, on the edge


Tcryo= 5°C Horizontal, vertical, on the edge

PHP # 1 Tcryo= 20°C horizontal, vertical, on the edge



Ethanol PHP # 2 Tcryo= 20°C horizontal, α=45°, vertical, on the edge



PHP # 3 Tcryo= 20°C horizontal, α=45°, vertical, on the edge


Table 4. Resume of the tests done in the experimental campaign.

In addition to tests presented in Table 4, for PHP # 2 and 3 with FC72 as working fluid and

Tcryo= 20°C further tests were made by moving the condenser box along the PHP length, so two

additional positions were performed, as shown in Figure 6.17.


51

(a) (b)

PHP # 2 Tcryo= 20°C Condenser configuration # 2 horizontal, vertical favourable

FC 72 Tcryo= 20°C Condenser configuration # 3 horizontal, vertical favourable

PHP # 3 Tcryo= 20°C Condenser configuration # 2 horizontal, vertical favourable

Tcryo= 20°C Condenser configuration # 3 horizontal, vertical favourable

Figure 6.17 Additional tests for PHP # 2 and PHP # 3 with a different cold source placement;

a) configuration # 2 and b) configuration # 3.

At each condenser position, the PHPs were tested in horizontal and vertical favourable inclinations.

It will be called “Configuration # 1” the position for which the condenser is located at the upper

extremity of the FPPHP, as shown in Figure 6.8.

6.10 Post-processing

All measurements taken from each test were automatically stored in different .xls files; one for the

temperatures data, one for the pressure signal and one for the voltage and electrical current intensity


52

from the heat power supply. The post processing of experimental data is based on the evaluation of

a performance parameter, the thermal resistance, at each power step where a temperature

fluctuations stability is observed. Recalling thermal resistance definition (from equation (1));

𝑅𝑡ℎ =�̅�𝑒𝑣−�̅�𝑐𝑜𝑛𝑑

𝑄−𝑄𝑑𝑖𝑠𝑠 (17)

The numerator is the difference between the spatial and temporal averaged evaporator and

condenser temperatures while at denominator there is the difference between the heat power

provided at the evaporator and the heat losses with external environment. In this form, equation (17)

does not allow to evaluate the thermal resistance because there is no way to measure the heat power

dissipated, however it could be approximated as follows:

𝑄𝑑𝑖𝑠𝑠 = 𝐺𝑙𝑜𝑠𝑠𝑒𝑠(�̅�𝑒𝑣 − �̅�𝑎𝑚𝑏) (18)

Where Glosses represents the thermal conductance of the heat losses and Tamb the average ambient

temperature. Finally, by substituting (18) in (17) thermal resistance becomes;

𝑅𝑡ℎ =�̅̅�𝑒𝑣−�̅̅�𝑐𝑜𝑛𝑑

𝑄−𝐺𝑙𝑜𝑠𝑠𝑒𝑠(�̅�𝑒𝑣−�̅�𝑎𝑚𝑏) (19)

Instead of the heat dissipated there is a temperature difference that could be easily determined, the

only unknown term is Glosses, that is supposed to be constant (actually it depends on the external

natural convection, thus on ambient temperature) and it is experimentally evaluated during the

vacuum test of a PHP (see section 6.11).

The post- processing phase can be summarized as follows:

- To obtain a plot of temperatures-heat power/ time as the one reported in Figure 6.18 below;

the red blended curves represent the evaporator temperatures, the green curves the adiabatic

and the blue ones those of the condenser region;

- To find a stability regime at each power step (if there is) by looking at the evaporator curves

(where fluctuations are always more pronounced); for example the numbered areas in Figure

6.18. If temperatures are particularly stable, as it happens in pure conduction mode or

annular flow regime, a minimum of 15 up to 50 samples along the temperature profiles are

enough. On the other hand, if the temperatures fluctuations are more intense (typical in slug

flow or semi annular flow regime at high powers) the number of samples must increase

(150:500). In this case, the important thing is to include an entire period of oscillation, in

order to have a good estimation of the region mean temperature;

- Considering the same time intervals, to evaluate also the condenser and the ambient mean

temperatures;

- Using equation (19) a value of thermal resistance at each power step can be computed now.


53

Figure 6.18 Example of temperature versus time plot during a power rump up from 20 to 260

W with a 30W step. (PHP# 2, FC 72, α = 45°, Tcryo= 40°C)

6.10.1 Evaluation of measurements uncertainties

All the collected data are affected by a systematic uncertainty, which depends mainly on the quality

of the measurement devices and on the test procedures adopted.

The results of the experimental analysis are always linked with the data of temperature and of the

heat power applied at the evaporator. These two parameters are needed to estimate the thermal

resistance of the PHP, thus their uncertainties affect the thermal performance as well.

The systematic uncertainty is evaluated from the data given by the manufacturer; for the

thermocouple of T-type that is ±1°C in the range of temperature 0:130°C.

As for the supplied power, from data sheet of EA ELEKTRO-AUTOMATIK model PS 8360-10 T

it is possible to estimate the uncertainties on both outputs: voltage (accuracy 0.2% and stability of

0.05% on full scale) and current (accuracy 0.2% and stability of 0.15% on full scale). Once the

accuracy and stability errors are expressed in absolute terms, the overall uncertainties can be

estimated as follows:

𝑒𝑣𝑜𝑙𝑡𝑎𝑔𝑒/𝑐𝑢𝑟𝑟𝑒𝑛𝑡 = ±√𝑒𝑎𝑐𝑐𝑢𝑟𝑎𝑐𝑦2 + 𝑒𝑠𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦

2 (20)

The supplied power is derived from the previous quantities through a non linear relation. However,

by assuming the linearity of the relation for small perturbations within the confidence interval of the

input quantities, the propagation of the uncertainties can be computed as shown:

𝑒𝑄 = ±√(𝜕𝑄

𝜕𝐼)

2

𝑒𝐼2 + (

𝜕𝑄

𝜕𝑉)

2

𝑒𝑉2 = ±√𝑉2𝑒𝐼

2 + 𝐼2𝑒𝑉2 (21)

In which I is the current intensity (Ampere) and V the voltage (Volt).


54

The evaluation of the uncertainties for the thermal resistance follows the same procedure described

for the supplied power, in this case, referring to (17) equation (21) becomes:

𝑒𝑅𝑡ℎ= ±√(

𝜕𝑅𝑡ℎ

𝜕𝑄)

2

𝑒𝑄2 + (

𝜕𝑅𝑡ℎ

𝜕𝑇)

2

𝑒𝑇2 (22)

Actually, at denominator of (15) the heat power is corrected by the losses with the external

environment, which are also affected by uncertainty. However, since they are significantly smaller

than the total heat power supplied (<2%) their contribution to the thermal resistance error is

neglected.

Within the range of temperatures and powers supplied, the overall absolute uncertainties have been

always estimated below ±0.04K/W.

6.10.2 Repeatability of measurements

Some repeatability tests done in previous works have shown that after 12 weeks from the first

filling the FPPHPs performances are affected by a remarkable degradation which occurs only at the

low heat power densities; the thermal performance is decreased of about 10%. The reason of this

fact is probably the different thermal dilatation of the plate because of the bondage and the resulting

formation of non condensable gases. Indeed, the pressure captor revealed a corresponding increase

of the internal pressure of about 5%.

6.11 Vacuum test

Generally, this is the first test done for a new PHP; the aim is to estimate its thermal performance in

absence of primary working fluid, which means to evaluate only the pure conductive thermal

performance. The key parameter is always the thermal resistance Rcond (K W-1) or thermal

conductance Gcond = Rcond -1 (W K-1). This represent the basic capability of the device to transfer

heat and they are used as reference values for performance analysis. Indeed, the presence of

working fluid will increase the heat transfer rate, the resulting thermal performance will be then

compared to the pure conductive one.

As shown in Figure 6.19, the PHP global thermal resistance value depends on two terms: the

thermal resistance associate to pure conduction mode, Rcond, and the thermal resistance due to the

presence of working fluid, RPHP. These two resistances refer to the same potentials, so according to

Ohm low and electrical analogy, the global value Rth could be seen as follows:

𝑅𝑡ℎ = (1

𝑅𝑐𝑜𝑛𝑑+

1

𝑅𝑃𝐻𝑃)

−1

(23)


55

Figure 6.19 Schematic representation of temperature nodes and main thermal resistances.

Thus the global thermal resistance has an upper limit (less performing PHP), which corresponds to

the pure conductive mode, the lower limit (most performing PHP) tends to zero, it means that no

thermal resistance is given; this condition will be objected to further discussions (see section 8).

A typical vacuum test consists in collecting a number of pure conductive steady state samples at

different heat powers and coolant temperatures. Table 5 shows the combinations of Tcryo and Q

applied and the mean temperatures evaluated at each of them, in the grey shaded area on the left there

are input parameters while on the right side the evaluated temperatures.

At each combination of Tcryo_i and Qj the knots temperatures Tev ij and Tcond ij relatives to a steady

state regime at evaporator and condenser are noted as well as the correspondent time averaged

ambient temperature. The heat power supplied could be seen as the sum of two contributions; the

heat power transferred by conduction and the heat losses, as shown in equation (24):

𝑄𝑗 = 𝑄𝑐𝑜𝑛𝑑 𝑗 + 𝑄𝑑𝑖𝑠𝑠 𝑗 (24)

From classical thermal analysis, the previous equation could be expressed in terms of thermal

conductance;

For Tcryo_i 𝑄𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑑 𝑗 = 𝐺𝑐𝑜𝑛𝑑(�̅�𝑒𝑣 𝑖𝑗 − �̅�𝑐𝑜𝑛𝑑 𝑖𝑗) + 𝐺𝑙𝑜𝑠𝑠𝑒𝑠(�̅�𝑒𝑣 𝑖𝑗 − �̅�𝑎𝑚𝑏 𝑖𝑗) (25)

Q1 =5W �̅�𝑒𝑣11 �̅�𝑐𝑜𝑛𝑑11 �̅�𝑎𝑚𝑏11

Tcryo_1 = 5°C Q2 =10W �̅�𝑒𝑣12 �̅�𝑐𝑜𝑛𝑑12 �̅�𝑎𝑚𝑏12

Q3 =20W �̅�𝑒𝑣13 �̅�𝑐𝑜𝑛𝑑13 �̅�𝑎𝑚𝑏13

Q1 =5W �̅�𝑒𝑣21 �̅�𝑐𝑜𝑛𝑑21 �̅�𝑎𝑚𝑏21


Q3 =20W �̅�𝑒𝑣23 �̅�𝑐𝑜𝑛𝑑23 �̅�𝑎𝑚𝑏23

Q1 =5W �̅�𝑒𝑣31 �̅�𝑐𝑜𝑛𝑑31 �̅�𝑎𝑚𝑏31


Q3 =20W �̅�𝑒𝑣33 �̅�𝑐𝑜𝑛𝑑33 �̅�𝑎𝑚𝑏33

Table 5. General scheme of a vacuum test for a PHP.


56

Now, in order to find out the two unknowns Gcond and Glosses, supposed as constant, an iterative

procedure could be started.

The main steps are:

- To give an initial value to Gcond and Glosses, the order of magnitude is around 1 and 0.01 (W K-1)

respectively;

- To evaluate with equation (25) all heat powers Qj by using the corresponding temperatures;

- To evaluate all squared differences between the measured heat flow and the calculated one as

follows:

휀𝑗 = (𝑄𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑗 − 𝑄𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑗)2 (26)

- To sum all 𝜺𝒋 terms and minimize it as a function of Gcond and Glosses.

This simple iterative calculation could be performed by using Microsoft Excel or any other platform

for calculus.

57

7. Experimental results

This section reports a multi-parametric investigation on the three devices introduced in section 6.2;

as already discussed, all PHPs were tested with two different fluids (ethanol and FC72) with the

same filling ratio of 50%. The aim is to analyse the influence of a number of parameters on PHPs

thermal performances and behaviour.

The investigated parameters are:

- PHP operative position;

- Primary working fluid;

- Heat transport lengths;

- Secondary fluid temperature (Tcryo);

- Geometry;

- Transversal thermal resistance between channels.

All tests presented in following sections refer to condensers located in Configuration # 1 (Figure 6.8

section 6.2.3) which means that condensers are fixed at the upper extremity of the PHPs. The only

exception is in section 7.3 where the influence of the heat transport length is investigated and the

condenser is moved according to Configuration # 2 and # 3 (Figure 6.17).

The following results provide an overall idea of the PHPs behaviours and of their thermal

performances. Due to the vast amount of collected data only the most remarkable results are here

reported and discussed.

7.1 Influence of PHP operative position

This kind of test is very common because it is cheap and easy to do; in literature there are several

publications that analyse this parameter for different PHPs and from different authors. Figure 7.1

reports the thermal resistances obtained for all the three PHPs as a function of the heat power

applied in different positions; these results refer to FC 72 as working fluid and a secondary working

fluid temperature (Tcryo) of 5°C.

7. Experimental Results

58

(a)

(b)


59

(c)

Figure 7. 1 PHPs global thermal resistances as function of the heat power supplied for all

three devices tested in four positions: horizontal (α=0°), α= 45°, vertical favourable (α= 90°)

and on the edge: a) PHP# 1; b) PHP# 2 and c) PHP# 3. (FC72, Tcryo= 5°C)

The empty curve corresponds to the experimental value of R measured with empty PHP.

According to Mameli and Marengo [16], three main regions could be easily identified in all cases:

- The start-up region;

- The normal operation region;

- The medium-high thermal inputs.

PHP# 1 (Figure 7.1 (a)) has already relatively low values of thermal resistances starting from 20W;

the light concavity of curves that reaches their lower value for all position in the range of 30:40W

suggests that it is the “normal operating” region. In this area, the effects of gravity are well

observable, indeed, as compared to empty system, a reduction of thermal resistance of around 70%

is registered for α=45°, α=90° and around 40% for α=0° and on the edge. Indeed where gravity does

not assist the fluid, the higher time needed for bubbles growth reduces thermal instabilities [16].

Then for higher heat power inputs, for α=45° and α=90° there is a significant increase of thermal

resistance while horizontal and edge position seem to be less affected by this fact and remain rather

stable. The relative new thing in this analysis is the interesting result obtained when the PHP is on

the edge; indeed it has a trend which is pretty similar to that of α=0° curve but with lower values of

thermal resistances. This fact is due to hydrostatic pressure contribution, which affects the fluid

menisci in the condenser region and helps to generate pressure instabilities. From the figure it is


60

clear that this contribution (discussed in section 5.4.1) has a net positive effect on thermal

performances. Finally it could be noticed that, for higher heat inputs, all curves tend to converge

each other towards a unique value of thermal resistance; gravity doesn’t influence the device

anymore.

PHP# 2 and PHP # 3 (Figure 7.1 (b) and (c)), as said in previous section, have an identical

geometry, the only difference is the presence of external grooves on PHP# 2 that increase its

transverse thermal resistance. The first important thing to observe is the really low performances in

horizontal position for both devices. Actually, PHP# 3 has an activation point at 50W but it is

insignificant because this result is not reproducible (as confirmed in other tests made). By looking

the temperatures trend of PHP# 2 in horizontal position (Figure 7.2), it is clear that no continuous

oscillations take place in the flow and the device behaves as a pure conductive system (except

within the circled regions).

(a) (b)

Figure 7.2 PHP# 2 tested in horizontal position; a) temperatures signals, b) pressure signal.

(FC72, Tcryo=5°C)

From Figure 7.2 one can observe that at low heat powers applied a pure conduction mode occurs

because energy transferred is not enough to generate pressure instabilities, thus there are no

oscillations. As the power increases to 50W some oscillations appear, but quickly the system

switches again to a pure conduction mode. Finally at 80W after a heating period the system has an

abrupt activation; few seconds of temperature and pressure oscillations and then again the PHP

restarts a heating cycle.

Figure 7.1 (b) and (c) show that PHP# 2 and PHP# 3 have a pretty good performances when they

are positioned on the edge (it is worth to say that the result has a high repeatability); as compared to

empty device, the PHP has a reduction of its thermal resistance up to 60% in this position. This fact

may seem strange because the horizontal performances are too low, however PHP#2 and 3 have a

minor number of U-turn as compared to PHP# 1 but they are wider, thus the hydrostatic pressure

gradient becomes more important (up to 40% higher) and could promote flow instabilities.

Furthermore, the channel dimensions are also bigger, this leads to smaller viscous pressure losses as

compared to PHP# 1.

In these two devices it could be observed that curves related to α=45° and α=90° are superimposed

in “normal operating” region, then a crisis for α=45° occurs prematurely once the input heat power

exceeds 110W, while curves for α=90° remain below them. Indeed there is a little increase of

thermal resistance for PHP# 2 while for PHP# 3 it remains constant; this suggests that there is a


61

further range of heat inputs available for vertical position, anyway this trend was not exploited.

Once again this behaviour agrees with that described by Mameli.

7.2 Influence of primary working fluid

The aim of this section is to point out some differences that emerge in PHP behaviour when a

different working fluid is used. As discussed in section 5.1, a suitable fluid for a PHP should have:

- high 𝑑𝑃

𝑑𝑇 in the saturation region;

- low dynamic viscosity;

- a high specific heat CpL value;

- low latent heat value;

- chemically inert with the PHP materials.

While the first three points and the last one are indisputable, the fourth one, proposed by Khandekar

is not always desirable, indeed even if a high latent heat is not suitable (for a slug flow pattern) a

latent heat which is too low could easily bring to a dry out of the evaporator.

As said, two fluids were tested, FC72 and Ethanol; their tables with all the thermo-physical

properties can be found in Appendix I, in this section some of their main ones will be reported.

A first comparison among FC72 and Ethanol concerns the saturation curve and the liquid dynamic

viscosity one (Figure 7.3.a).

(a) (b)

Figure 7.3.a FC72 and Ethanol: a) saturation curve and b) dynamic viscosity.

As compared to ethanol, in the temperature range of the experiments, FC72 has a higher slope of

the saturation curve and a lower dynamic viscosity.


62

Another important requirement for a primary working fluid concerns the Eö number analysis; for a

given hydraulic length of channels section and a critical value of Eö equal to 4 for both fluids, there

is a range of temperatures in which the effects of gravity are less important than surface tension

ones. The following diagram shows the limit values of hydraulic length for both fluid in the range

of the exploited temperatures. It is worth to observe the large gap between two fluids, mainly due to

the different densities in the liquid phase and lower surface tension of FC72. It is clear that,

following the Eö criterion, all PHPs are less affected by gravity if filled with ethanol, while with

FC72 they have a temperature limitation:

- PHP# 1 satisfies the Eö criterion up to 90°C;

- PHP# 2-3 exceeds the critical diameter from 30°C.

The following figure reports some thermal resistances obtained for PHP# 1 tested in horizontal and

vertical position at Tcryo=40°C for both fluids.

Figure 7.4 Influence of primary working fluid on PHP# 1 tested in horizontal and vertical

position.

Figure 7.3.b Critical values of hydraulic length for FC72 and Ethanol.


63

Figure 7.5 suggests that FC72 works better in PHP# 1; according to thermo-physical properties, as

compared to Ethanol, it has a larger (𝑑𝑃

𝑑𝑇)

𝑠𝑎𝑡 and a lower dynamic viscosity which are able to

activate the device even in horizontal position. No remarkable differences emerge in the vertical

position; even if in this device gravity plays a minor role as compared to surface tension effects, for

all the exploited temperatures only a very small reduction of thermal resistance is registered. This

fact could depend on channel section type; as seen in previous section, the presence of edges could

break the liquid menisci among two bubbles and promote an annular flow pattern instead of a slug

flow one. In this case the high (𝑑𝑃

𝑑𝑇)

𝑠𝑎𝑡 is no more useful because the device behaves as a two-phase

thermosyphon and liquid returns to evaporator along the edges thanks to capillarity and gravity

forces.

As reported in Figure 7.6, the stability of the system at each power step, combined with the reduced

amplitude of temperature oscillations observed in both vertical cases support this idea.

Figure 7.5 Temperatures-Heat power versus time for PHP# 1 in vertical position and partially

filled with: above FC72, below Ethanol. (PHP# 1, Tcryo=40°C)


64

In this case it could be observed that the weak reduction of thermal resistance obtained with FC72

in vertical position is probably due to its lower dynamic viscosity as compared to ethanol (which

represents an important requirement because it is responsible of the pressure losses).

Actually, if results obtained for PHP# 1 seem to agree with the analysis based on thermo-physical

properties, for PHP# 3 all considerations made could be in contrast with the experimental results.

Indeed, while for the vertical position the trend of thermal resistances is more or less the same as

the one of PHP# 1, for horizontal position an interesting result has been observed (Figure 7.7).

Figure 7.6 PHP# 3 temperatures curves registered in horizontal position and partially filled

with: FC72 above and Ethanol below. (PHP# 3, Tcryo=20°C)

The comparison of thermal resistance is useless because it is clearly visible from Figure 7.7 that

PHP# 3 has a net improvement of its performances when partially filled with ethanol, on the other

hand it has activation problems and unstable working with FC72. This objective result has no

obvious justification and it is apparently against all considerations done before. Nevertheless it


65

could be the result of a complex combination of factors that affect two-phase flow inside PHP

channels; thus a visualisation campaign could help to figure out this fact.

This behaviour has been observed at each temperature Tcryo investigated, thus it is a highly

repeatable result.

7.3 Influence of the heat transport length

Differently from what observed in PHP# 1 and 3, PHP# 2 shown from the beginning activation

problems when placed horizontally; this behaviour was confirmed for all for all temperatures Tcryo

and for both fluids. The problem concerns the incapacity of the device to maintain a continuous

oscillations regime, indeed after a short period of instabilities it switches to a pure conduction

mode, as the curves of Figure 7.7 suggest.


66

(a)

(b)

Figure 7.7 PHP# 2 in horizontal position; a) temperatures signals, b) pressure signal.

(Ethanol, Tcryo=40°C)

PHP# 2 comes from the parabolic flight campaign; a number of ground tests were made before

those under a variable gravity field, Figure 7.8 shows the curves of temperatures and pressure

registered in horizontal position.


67

Figure 7.8 PHP# 2 tested on ground in horizontal position, by using a fans and fins cooling

system: temperatures signals above; pressure signal below. (FC72, τ=50%) (Ayel, [4])

So, in the tests made before the parabolic flight, PHP# 2 behaved in a completely different way;

oscillations of pressure and temperatures occur continuously in the whole range from 40W up to

150W (and even more than 180W for other tests) with a lower amplitude for temperatures starting

from 90W that means a more stable functioning.

As introduced in section 5.4.2, for the parabolic flight campaign PHP# 2 was equipped with a

different cooling system consisting in an aluminium plate with fins and two fans in the front (Figure

5.6, section 5.4.2). The condenser area in this case extends for 16.5 cm, this implies an adiabatic

length of about 2.3 cm (Figure 1.9 (a)); a high length of the cooling region is needed in order to

reduce heat losses effects, indeed the PHP is not insulated as in the tests which concern this work.

On the other hand the condenser adopted for the current campaign consists in an aluminium box in

which water flows (kept at a given temperature Tcryo) and where an internal channel coil ensures a

rather homogeneous cooling (section 6.2). This second condenser has a shorter length, more or less


68

half of the previous one (Figure 1.9 (b)); in this case the adiabatic length becomes 10.8 cm, more

than four times the previous one.

(a) (b)

Figure 7.9 Typical lengths for PHP# 2: a) for parabolic flight campaign; b) for current

ground tests.

Thus it was thought that the problem could derive from the excessive extension of the adiabatic

length.

As established in section 4.3, the adiabatic length is representative of the heat transport distance and

in a PHP and it could not be too high because of the reduced diameters adopted which increases the

pressure losses along the channels.

The choice of this kind of condenser for ground tests is mainly based on the possibility to test the

device inside an insulated coating and thus to reduce drastically the heat losses effects on thermal

performances. For obvious reason this kind of cooling needs a thermoregulation system, which is

heavy and not easy to transport, so it was not admissible for parabolic flight, where a

conduction/convection system based on fins and fans represents, on the other hand, a compact and

efficient solution.

So it has been decided to move the condenser along the PHP approaching the evaporator; two new

different condenser locations were tested in horizontal and vertical position with Tcryo=20°C, as

shown in Figure 7.10.


69

(a) (b) (c)

Figure 7.10 Influence of adiabatic length on PHP performance: a) Configuration # 1

(standard), b) Configuration # 2 and c) Configuration # 3. The dark blue frames indicate the

new top adiabatic region formed.

Actually, if the condenser is being moved along the PHP length one additional adiabatic region

appears; this region extends on the gap between the top side of the condenser and the top side of the

PHP (Figure 7.10 (b) and (c), dark blue rectangles). This region could not be seen as a heat

transport length because it is not ranged between two heat sources, anyway it represents a region in

which no further (relevant) heat exchanges occurs and in which the flow is influenced by the

presence of condenser. For this reasons the thermal resistance expression takes into account, as for

the time and space average temperature at the condenser, even these values of the top adiabatic

region; they are considered as condenser temperatures as well as those placed effectively under the

condenser itself (27):

�̅�𝑐𝑜𝑛𝑑 =∑ {

∑ 𝑇𝑐𝑜𝑛𝑑 𝑖𝑛𝑖=1 +∑ 𝑇𝑡𝑜𝑝−𝑎𝑑𝑖𝑎 𝑗

𝑚𝑗=1

𝑛+𝑚}𝑡=𝑡+∆𝑡

𝑡=𝑡0

∆𝑡 (27)

Where n is the number of thermocouples located in condenser region while m is the number of

those placed in the top adiabatic one.

Figure 7.11 reports the result found and compares all the three configurations:


70

Figure 7.11 Influence of the adiabatic length in PHP# 2. (FC72, Tcryo=20°C)

The reduction of adiabatic length among evaporator and condenser has a clear effect on PHP

behaviour: thermal resistances are lowered when condenser passes from first to third configuration.

Furthermore it can be noticed that the gap between the horizontal and vertical curves at each

condenser configuration decreases passing from the first to the third configuration; this fact is also

confirmed from the same tests using ethanol as primary working fluid (Figure 7.12). Indeed in this

case the curves for α=0° and α=90° are superimposed in Configuration # 3. This could be explicated

recalling the results discussed in the previous section; as seen for ethanol, the reduced hydraulic

length of the channels as compared to the critical one permits to decrease the gravity influence as

well. On the other hand, with FC72, gravitational effects are more important, thus the horizontal and

vertical curves are always separated, with an exception in the “start-up” region.


71

Figure 7.12 Influence of the adiabatic length in PHP# 2. (Ethanol, Tcryo=20°C)

One interesting aspect that emerges from the temperature plots presented in 7.11 – 7.12 is the

unexpected peak of the thermal resistance for the curves α=90°, clearly visible at low heat powers.

Indeed, whilst in horizontal position all curves have a monotonic decreasing trend in the transition

from the start up to the normal operation region, in the vertical position there is an anomalous,

isolated, peak of R, followed by a drastic decrease which then brings the thermal resistances at the

lowest values registered. This peak is present in all the three configuration, but it is surely more

pronounced in the first configuration.

Figure 7.13 show the temperature trends of PHP# 2 tested in vertical position and first configuration:

Figura 7.13 Temperature trends over time and heat power supplied. (PHP# 2, Configuration

# 1, vertical position, Tcryo=20°C)


72

At the first power step, 20W, the PHP has an initial heating as a pure conductive system; this is

suggested by the fact that the evaporator curves (Tev) are smooth, without any evidence of oscillation.

When the evaporator temperatures reach approximately 36°C, a drop of the curves is observed, this

means that something has changed inside the fluid flow and the PHP begins to work. Once the system

looks stable, the first value of thermal resistance can be computed and the heat power can be further

increased. At 50W, the system has an initial behaviour which corresponds to the previous one, but

this time, temperatures grow up considerably up to 74°C for evaporator. There is no evidence of

activation after 25 minutes, thus the heat power is further increased at 80W: the system now has an

abrupt activation, which occurs few instants after the heat power is increased. From now on, the PHP

temperatures increase regularly with the heat power and fluctuations are well visible. This behaviour

could be explained by considering that, in the “ramp up” of heat powers, at 20W the PHP works with

an annular flow pattern after activation; all temperatures of the device are ranged from 20°C to 30°C

and the absence of oscillations suggest that the main heat transfer mechanism consists in the

evaporation of a thin liquid film. At 50W the temperature increase is probably provoked by the dry

out of the evaporator; indeed if the vapour relegates the liquid into the condenser, pressure instabilities

could be not enough powerful to recall the liquid in the evaporator, thus the system approaches its

asymptotical equilibrium temperature. However, when the heat power is further increased, the heating

produces some pressure instabilities which activate and allow the PHP to work properly.

The following figures represent the evolution of temperature during a ramp up of heat power in all

three configuration with FC72 in horizontal position.


73

Figure 7.14 Temperatures signals in horizontal position for all three configurations. (PHP# 2,

FC72, Tcryo=20°C)

Configuration I

Configuration II

Configuration III


74

As shown in Figure 7.14, in the third configuration there are no sensors located in the adiabatic region

among evaporator and condenser, indeed the green curves visible in Configuration # 1 and 2 disappear

because the condenser is now above them. Nevertheless, a new adiabatic region appears (T top adia)

and the measured temperatures are in the same range of the ones under the condenser. The orange

line represents the ambient temperature while the brown ones the secondary fluid temperature (around

20°C). This series of figures of 7.14 is significant because it gives an idea on the influence of the heat

transport length: from a pure conduction mode at the highest adiabatic length, the device switches to

what seems to be a slug flow in Configuration # 2, with a significant decrease of oscillations

amplitudes passing from second to third configuration. Furthermore there is an increase in the heat

transfer capability of the PHP and it works with a higher stability and regularity. By looking at

temperatures curves in Configuration II, one could observe that if a low heat power is supplied (20W)

the PHP has still difficulties to operate continuously and many cycles of activation/deactivation occur

because pressure fluctuations are still weak. Once the heat power is increased, pressure fluctuations

becomes more intense and exceeds the pressure losses along the channels, thus it starts to work

continuously being stable.

7.4 Influence of secondary fluid temperature

One of the advantages in the use of a condenser based on liquid forced convection with a

thermoregulation system consists in the possibility to manage and control the coolant temperature

inside the condenser; this represents the lowest temperature of the PHP. This effect has an obvious

correlation with the kind of primary working fluid used because it influences its thermo-physical

properties. Differently from what it has been observed for primary working fluid where results are

contradictories, the influence of secondary working fluid temperature (Tcryo) has only one clear

effect on a PHP, as shown in following plot:


75

Figura 7.15 Influence of Tcryo on PHP# 1 tested in different positions. (FC72)

Figura 7.16 Influence of Tcryo on PHP# 2 tested in different positions. (Ethanol)

Figures 7.15 and 7.16 are significant because they both show a univocal influence of Tcryo on

thermal performance: for each position tested and both working fluids, the thermal resistance values

decrease if Tcryo increases. For example, the curve that refers to vertical position at Tcryo=5°C is


76

above the one for Tcryo=20°C which is above the one for Tcryo=40°C; this is verified at each position

and for all PHPs. The only exceptions come from the start-up region and in those cases where the

PHP works in a pure conduction mode (as for α= 0° and on the edge in PHP# 2). If the minimum

temperature of the system is increased, liquid dynamic viscosity decreases in both fluids (especially

ethanol, as shown in Figure 7.3 (b)) the liquid specific heat value CpL increases and latent heat has a

slight reduction (see Appendix I). Liquid dynamic viscosity, as already discussed, is responsible for

viscous pressure losses; thus its reduction brings a net improvement of system performances. Liquid

specific heat at constant pressure, or CpL, becomes important in the slug flow pattern or in semi-

annular one; indeed in those situations where vapour pushes a liquid plug or a liquid menisci in the

condenser region, the heat exchange among the liquid and vapour phase (as well as the heat

exchange through channel walls and liquid menisci) mainly depends on this term.

7.5 Influence of geometry

This analysis concerns PHP# 1 and PHP# 3 because they have the same characteristic lengths of

adiabatic, evaporator and condenser region. In addition, they are equipped with the same condenser

type and they have been tested under the same external conditions. The geometrical differences

between these two devices consist in the number of channels and on their internal dimensions, it

could be interesting to see how the combined effect of these two geometrical parameters affects the

PHP performances.

Table 6 summarizes the main geometrical features of both devices (further details are available in

section 6.2).

PHP# 1 PHP# 3

Evaporator region (length x width) 1 x 8 cm2 (x2) 1 x 12 cm2

Condenser region (length x width) 8 x 8 cm2 8 x 12 cm2

Adiabatic region (length x width) 11 x 8 cm2 11 x 12cm2

Channel section type (dimensions) Squared (1.1 x 1.1 mm2) Rectangular (1.6 x 1.7 mm2)

Number of channels 32 24

Table 6. Geometrical characteristics of PHP# 1 and PHP# 3.

Figure 7.17 shows the trends of mean evaporator temperatures as functions of the heat flux density

applied at evaporator wall for both PHPs partially filled with FC72 (FR=50%) for three different

positions.


77

Figure 7.17 PHP# 1 and PHP# 3 mean evaporator temperatures versus heat flux supplied for

three different positions. (FC72, Tcryo=20°C)

The heat flux is simply evaluated by dividing the heat power supplied for the evaporator area. As

shown in section 6.2, PHP# 3 is heated only on one side while PHP# 1 has a different heating

system which is in contact with both external sides of the plate. However, since transversals

discontinuities are supposed to be negligible compared to the longitudinal ones, the evaporator

surface for PHP# 1 is considered as the contact area among evaporator and PHP only on one side, in

the same way of PHP# 3 (Figure 7.18). In other words, the reference surface of PHP# 1 is taken

only on one side of the evaporator, as for PHP# 3; nevertheless, this surface modification does not

change the actual heat flux density received by channels.

Figure 7.18 Evaporator contact area for PHP# 1 and PHP# 3.

From Figure 7.17 it could be observed that PHP# 3 has a significantly higher heat transport

capability, this is verified for all positions and becomes more visible in the vertical one; this fact is

relied to the combined effect of the difference between thermal conductance of the empty PHPs

(GPHP# 1 = 0.46GPHP# 2) and to channels inner dimension. Indeed PHP# 3, when positioned vertically,

works mostly as a two-phase gravity assisted thermosyphon because of the higher hydraulic length

of channels cross section (as compared to the critical one) and of its rectangular shape which

promotes an annular flow regime. Even if PHP# 1 has a similar functioning (as temperatures and

pressure curves suggest) its lower hydraulic length implies an increase of pressure losses along the

channels and a premature dry out of the evaporator region. It is interesting to see that in the range of


78

low heat fluxes that goes approximately from 2 to 5 W cm-2, the PHP# 1 performs better in vertical

position as compared to PHP# 3; this could depend on flow inertias that requires a minimal energy

in order to start their motion and then to switch to an annular flow pattern (Figure 7.19).

(a) (b)

Figure 7.19 Activation of PHP# 1 (a) and PHP# 3 (b) in vertical position: influence of

geometry on the input heat flux. (FC72, Tcryo=20°C)

As shown in Figure 7.19, a minor heat flux density is needed in order to activate PHP# 1, as

compared to PHP# 3.

As for horizontal position, in both PHPs no oscillations occur, indeed mean evaporator temperatures

curves are quite similar; the temperature difference between the two curves is mainly due to the

lower conduction resistance (in the empty configuration) that PHP# 3 has, compared to PHP# 1.

The higher number of channels of PHP# 1 has no influence on its activation in horizontal position.

Another interesting result comes from the case where the devices are placed on the edge; indeed

even here there is a net improvement of performances switching from PHP# 1 to PHP#3. This fact

could be linked to the higher width of the latter device that increases the hydrostatic pressure

gradients among channels together with the lower viscous pressure losses caused by their higher

cross section that permit to PHP to perform better. Figure 7.20 reports the net specific thermal

resistance due to the pure PHP effect (see Appendix III). In PHP# 3 is one order of magnitude lower

than that of PHP# 1 with the only exception at the low heat fluxes because of the higher energy

needed from PHP# 3 to start oscillations.


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Figure 7.20 Comparison of the thermal resistance associate to the presence of flow in PHP# 1

and PHP# 3 placed on the edge. (FC72, Tcryo=20°C)

7.6 Influence of external separating grooves

The effect of the inter-channels heat balance plays a negative role in PHP operation because it

reduces the instabilities among adjacent channels; thus pressure oscillations and consequently

performances are reduced as well. This problem affects the PHP of kind Flat Plate, because of their

compact structure where two adjacent channels are separated by a thin layer of highly conductive

material that quickly homogenize their temperatures [12].

PHP# 2 and PHP# 3 have an identical geometry and the only difference is the presence of external

grooves on PHP# 2 (Figure 7.21). In order to investigate the effect of the transversal thermal

resistance, they have been tested under the same conditions.

Figure 7.21 Cross-sectional sketch of PHP# 2, evidencing the external groove to increase the

transverse thermal resistance.


80

𝑅𝑃𝐻𝑃# 3 𝑡𝑟𝑎𝑛𝑠𝑣~3𝑠

𝜆𝑐𝑜𝑝𝑝𝑒𝑟ℎ= 2.56𝑥10−3 𝑚𝐾

𝑊; (28)

𝑅𝑃𝐻𝑃# 2 𝑡𝑟𝑎𝑛𝑠𝑣~𝑠

𝜆𝑐𝑜𝑝𝑝𝑒𝑟ℎ+ (

𝜆𝑎𝑖𝑟ℎ1

𝑠+

𝜆𝑐𝑜𝑝𝑝𝑒𝑟ℎ2

𝑠)

−1

+𝑠

𝜆𝑐𝑜𝑝𝑝𝑒𝑟ℎ= 4.27𝑥10−3

𝑚𝐾

𝑊;

In a rough approximation, the increase of the transversal thermal resistance can be estimated by

using the electrical analogy from the Ohm law. As reported in (28) the augmentation of thermal

resistance is around 65% in PHP# 2 compared to PHP# 3.

The tests have been made by comparing the two PHPs performances obtained with both fluids,

different Tcryo and inclinations, as reported in Figure 7.22.

(a)


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(b)

(c)

Figure 7.22 Comparison of thermal resistances values for PHP# 2 and PHP# 3 with: a)

Ethanol, Tcryo=20°C; b) FC72, Tcryo=5°C; c) FC72, Tcryo=40°C.

When PHPs are placed at α=45°, α=90° and on the edge, for all Tcryos and both fluids, the curves are

well superimposed, except in the start-up region. PHP# 3 filled with ethanol works well also in

horizontal position, improving its performances passing from Tcryo=5°C to Tcryo=40°C (according to


82

the decrease of the flow dynamic viscosity). On the other hand with FC72 both PHPs have

activation problems and PHP# 2 has the same even with ethanol. As for temperature oscillation

amplitudes at the evaporator, in all tests a slight increase of ΔTmax = (Tev MAX -Tev MIN) is observed in

PHP#2 as compared to PHP# 3.

The behaviour of PHP# 3 with ethanol is not anomalous; indeed in this case the critical diameter

based on Eö criterion is well higher than its channel hydraulic length, thus gravity forces have a

minor role on surface tension ones and the thermal resistance gap between the horizontal and

vertical position is being reduced (Figure 7.23). On the other hand, the behaviour of PHP# 2 is

unexpected; indeed, even if temperature oscillations are increased as compared to PHP# 3, the fact

that in horizontal position it does not work at all is not well understandable. Furthermore, the

increase of temperature and pressure fluctuations, does not correspond to an increase of the thermal

performances, this is in contrast with the results found by Khandekar [12].

Actually no obvious answer can be found from the available data; further investigations could be

helpful to better understand this result.

Figure 7.23 PHP# 3 tested in different positions using ethanol as primary fluid and a Tcryo=20°C.


83

7.7 Conclusions on the experimental campaign

Within the experimental campaign a large number of parameters have been investigated and

interesting results were found. Most of them show a good agreement with those of literature;

influence of PHP inclination with respect to gravity field, influence of the temperature of the cold

source and choice of the primary working fluid. An exception occur for the latter, for which the

PHP# 3 tested in horizontal position have not worked with FC72 while with Ethanol it had no

problems at all. This is apparently in contrast with what the thermophysical properties of the fluids

suggest, but it means that a combination of multiple factors occur and that sometimes it is not

enough to isolate the effect of a single parameter in order to predict the PHP performances.

Another interesting result has been found within the investigation of the heat transport length; this

analysis comes from the evidence that PHP# 2 has activation problems in horizontal position. The

choice of the condenser was done in order to have the same characteristic lengths (evaporator,

adiabatic and condenser region) in all the three PHPs. However, it was clear from the beginning that

the adiabatic length was too high for PHP# 2, thus the tests made with the shifted condenser

outlined the importance of viscous and pressure losses have on PHP performances. Indeed, by

reducing the adiabatic length, the PHP have shown a higher stability, lower performances and a

significant reduction of gravity effects.

The tests on PHP internal channel length have underlined that a smaller channel section brings more

viscous losses and thus it reduces the heat transfer performances. Nevertheless, from the

comparison among PHP# 1 and PHP# 3 it has been seen that, at low heat flux densities, a smaller

channel allows the PHP to work in a more stable way and with better performances.

Finally, the presence of external grooves has increased the temperature and pressure oscillations of

PHP# 2 but they have not brought an increase of the thermal performance. Furthermore, PHP# 2 did

not work at all in horizontal position and with both working fluids. On the other hand PHP# 3

worked pretty well in horizontal position but only with ethanol. This result do not agree with

literature and it deserve further investigations. However, even in this case, the result is affected by a

combination of factors which are not easy to account.

Due to the complex nature of the flow inside these devices, the experimental campaigns are not

thorough to understand the behaviour of the PHPs and to predict their thermal performances, indeed

only general considerations can be done through the recording of the temperatures and pressure

values during the tests. So, the development of numerical models of the fluid flow inside these

devices is mandatory to obtain a more in-depth knowledge about this technology and make it more

reliably understood.

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8. Numerical modelling of a specific test case

8.1 Introduction

The second part of the work concerns a numerical study of the PHPs and it consists in two different

analyses. One is presented is this chapter whilst the second analysis could be found in chapter 9.

The aim of the analysis presented in this chapter is to reproduce the thermal performance observed

in a vertical test of PHP# 2 when it is supposed to work with an annular flow regime and to support

this consideration with a simplified model based on pure conduction. In order to reach this goal, the

multi-physics platform Star CCM+ has been used.

8.2 A simplified analysis of the annular flow. The analysed case and its

experimental results

The analysed case concerns PHP# 2 partially filled with ethanol, placed on vertical position and

with Tcryo= 20°C; Figure 8.1 shows the temperatures and pressure curves from the experimental test.

8. Numerical Modelling of a specific Test Case

85


86

Figure 8.1 PHP# 2, Ethanol, FR=50%, vertical, Tcryo=20°C; temperature, pressure curves and

thermocouples arrangement.

As emerges from experimental data, the device has activation problems when the heat power

supplied is below 80W; indeed at 20W, from an initial activation it turns off quickly to a pure

conduction mode, as the smooth and asymptotic curves suggest. At 50W another activation occurs

after a shorter heating cycle up to ~78°C at the evaporator, this fact is clearly visible from pressure

curve, in which the pretty stable trend during heating cycle is followed by an abrupt pressure

variation (ΔP~13kPa) that then returns stable.

Even in this case the PHP is not working in a stable way because curves show long period

oscillations. With an additional increase of heat power the system switches again to a heating cycle

that seems to be asymptotically stable at ~95°C at the evaporator, no activation occurs. As said in

previous sections this initial behaviour is typical of the start-up region, where the input heat power

is not enough to start and hold pressure instabilities in the vapour phase, thus oscillations are not

continuous and the PHP has low thermal performances.

As the input heat power is furthered increased, a strong activation occurs and brings temperatures at

~40°C and oscillations start (ΔPactivation~22kPa) as clearly visible in Figure 8.1. From now on,

temperatures and pressure fluctuations occur regularly and continuously at all heat power steps,

both with an increasing amplitude.


87

Once the maximum input heat power (260W) has been reached, two lower steps were tested again,

the first 170W and then 80W; the PHP behaviour does not change, indeed at 170W it goes in the

same range of temperatures with an identical amplitude of oscillations, while at 80W it is still

unstable, as observed during the ramp up phase.

Starting from 110W of input heat power, the flow regime is supposed to be annular because of the

high regularity of temperatures and pressure curves as well as the high level of performance

reached, as suggested from thermal resistance values found (Table 7).

P (W) R (K/W)

20.47 1.12

50.60 0.16

80.33 0.89

110.32 0.14

140.30 0.13

170.82 0.18

201.34 0.20

230.58 0.20

260.66 0.21

Table 7. Thermal resistances of PHP# 2 tested in vertical position. (Ethanol, Tcryo=20°C)

Considering a vertical favourable position for a PHP (bottom heated) when an annular flow takes

place, condensed phase forms a thin layer (liquid film) on internal channel surfaces; thanks to

gravity and capillarity, the liquid moves towards the evaporator, where the heat source generates

vapour which flows in the opposite direction along the internal region of the channel (see chapter

2). This kind of flow pattern is really efficient in terms of heat transfer because of the lower thermal

resistance offered by the fluid; indeed the only significant resistance is the one of the liquid film,

which is generally low because of its reduced thickness (Figure 8.2).


88

Figure 8.2 Main thermal resistances associated to: a) a slug flow pattern; b) an annular flow

pattern.

8.3 The two-resistance model for PHP# 2

In order to reproduce the annular flow condition inside PHP# 2, a two-resistance model has been

set; evaporator and condenser are associated to single resistances linked to a node which represents

saturated fluid temperature, approximated by the mean adiabatic region one (Figure 8.3).

Figure 8.3 Two-resistance model of PHP# 2.

Rchannel-liquid

Rvapour-liquid

Rliquid-film

Rliquid-film


89

Each thermal resistance has two contributions: one is relied to a pure conduction effect due to

copper plate geometry and the other to the presence of flow. While the first one depends mainly on

the quality of the CAD and mesh model (in terms of geometry) the second one is more complex to

estimate because of the complex behaviour of the two-phase flow inside the device.

8.4 Modelling of a liquid film in a rectangular channel

In a flow pattern visualisation campaign it was observed that in case of annular flow, only a number

of channels work effectively in an annular mode whilst the others are completely filled with liquid

and do not participate to heat transfer. Thus, the post-processing of the images allowed to estimate

the average quantity of condensed flow in each channel as compared to their total internal volume, a

value which is around 20% (Ayel, [3]).

Basing on this experimental evidence it was first approximated that all PHP channels work in an

annular mode, thus the resistance effect due to the presence of flow depends only on the liquid film

thickness and on its thermal conductivity (the contribution of the vapour phase and the evaporation

resistance at the interface are neglected). Because of the rectangular shape of channels, the

evaluation of a mean liquid film thickness is not easy; indeed the liquid distribution along the axial

and radial direction of the channel could be different and not directly measurable or evaluable, in

addition, transition phase phenomena that occur in evaporator and condenser deeply modify its

thickness and its thermal resistance as well. However it was approximated an identical distribution

of the flow along the axial direction, while as for the radial one, it was supposed that the film

extends to all sides of the section, with a minimum thickness reached in the centre of each edge and

with the maximum value at the corners (Figure 8.4 left).

Figure 8.4 Some possible distributions of the condensed phase in a channel cross section.

As said, the condensed phase occupies only 20% of the total internal volume, thus in order to

recreate the geometrical shape of the liquid film in channel cross section, a minimum value of film

thickness is required; it was chosen 50µm.

The shape of the liquid film is shown in Figure 8.5; a constant thickness of 50µm is chosen in the

central region of each side, connected at the corners with a circular arc boundary. All dimensions

are evaluated through simple geometrical considerations, based on the 80% of total surface for

vapour and 20% of total surface for liquid.


90

Figure 8.5 Geometrical reconstruction of the liquid film on Star CCM+; sketch 2D and 3D

channel view.

8.5 PHP# 2: model settings and results

In order to further simplify the model setting, for the whole PHP modelling, asymmetrical effects in

channel cross section due to the variable thickness of liquid film are neglected, thus there is no need

to add and extend the liquid film to all channels (as shown in Figure 8.5 right part). So, the presence

of a liquid film is replaced by a convective boundary condition imposed to all internal channels

surfaces of the PHP. The needed quantity is the mean heat transfer coefficient among the vapour

phase and the internal channel surfaces, which could be evaluated as follows:

ℎ𝑓 ~𝜆𝑙𝑖𝑞(𝑇)

�̅� [

𝑊

𝑚2𝐾] (28)

Where at numerator there is the thermal conductivity of the liquid phase (which is a function of

temperature) and at denominator the mean thickness of the liquid film. The latter could be easily

evaluated once liquid film geometry has been reproduced (29):

𝛿̅ =∫ 𝛿0𝜕𝑥+∫ (

𝑟+𝛿0cos 𝛼

−𝑟)(𝑟+𝛿0)1

cos2 𝛼𝜕𝛼

𝜋 4⁄

0𝑥1

0

𝑥1+𝑥2 (29)

By using 𝛿0 = 50µ𝑚 a mean thickness value 𝛿̅ = 106µ𝑚 was

found.

At each power step in which an annular flow was experimentally observed, the adiabatic mean

temperature of the PHP has been evaluated and used as reference value for the mean flow/vapour

temperature inside channels as well as for the evaluation of thermal conductivity of ethanol.


91

Thus a number of conditions were found: the following table resumes the estimated heat transfer

coefficient at each power step.

# Heat power (W) Tf (K) hf (W m-2K-1)

1 110.32 302 1670

2 140.30 304 1655

3 170.82 308 1640

4 201.34 311 1625

5 230.58 313 1610

6 260.66 316 1595

Table 8. Conditions required for the two-resistance model: the heat power applied, a

reference temperature of vapour inside the channels and a mean heat transfer coefficient that

takes into account the resistance effect due to the liquid film.

The following Figure shows the CAD model which represent the half PHP# 2 (the right hand side).

Some temperatures probes replaced the thermocouples of PHP# 2 (not shown). Evaporator and

condenser are represented by a thin plate (thickness of 1mm) in which the input heat power is

applied and removed respectively.

Figura 8.7 CAD model of PHP# 2 (left) and an example of visualisation of results (right).

The set parameters of this model in Star CCM+ are:

- Steady state;

- Three dimensional;

- Material model: Solid (Cu);

- Equation of state: Constant density;

- Segregated solid energy.

As for the mesh model, a hexahedral mesh of 2 mm base size has been adopted because it provides

a good convergence in a rather short time.


92

Table 9 reports the results of simulations done at each step from 110W up to 260W.

Experimental Numerical

# Q (W) Tev (K) Tcond (K) R (K/W) Q (W) Tev (K) Tcond (K) R (K/W)

1 110.32 313.95 298.43 0.14 55.16 317.48 297.17 0.18

2 140.30 317.46 299.52 0.13 70.15 323.8 297.80 0.19

3 170.82 330.68 300.87 0.18 85.41 332.26 300.4 0.19

4 201.34 341.49 302.15 0.20 100.67 339.76 301.96 0.19

5 230.58 349.23 303.72 0.20 115.29 346.13 302.56 0.19

6 260.66 359.22 304.96 0.21 130.33 353.68 304.27 0.19

Table 9. Comparison among the experimental and numerical data collected for PHP# 2 in

vertical position. (Ethanol, Tcryo=20°C)

In the numerical analysis the heat losses are not taken into account because it has been observed

from experimental data that they do not affect substantially the thermal resistance values, in

addition, their effect is difficult to model. Moreover, the approximation made for flow distribution

(20% of volume occupied by liquid phase and 80% by vapour one) does not agree with the real

filling ration of this device which is around 50%.

From table 9 emerges that the pure annular flow condition permits to obtain rather reasonable

values for thermal resistance, this fact supports the idea that this is the kind of flow pattern which

takes place in those range of heat input powers.

This analysis have shown that in vertical inclination with annular flow, the global thermal resistance

of a PHP is mainly due to a conduction resistance, which depends on flat plate geometry as well as

the material used (its thermal conductivity) and on the flow contribution to thermal resistance. As

for the latter contribution, if the flow is annular the main effect is due to the presence of the liquid

film; from experimental tests it has been observed that this kind of flow regime represents the best

operative condition in terms of thermal performance because of the lower resistance values

measured. It could be interesting to simulate the best case, for which the fluid does not offer any

resistance contribution; in order to do that, the two-resistances model was modified as shown in

Figure 8.8.

Figure 8.8 Two-resistance model in the case where hf tends to ∞.

In this situation, the input parameters to set are the heat flow at evaporator and condenser and an

average flow temperature; both are arbitrary parameters because the purpose of this analysis is to

find a lower limit for thermal resistance of PHP# 2, the resulting temperatures obtained at


93

evaporator and condenser are not useful because there is no experimental case to compare with. The

result found is Rh_f →∞ = 3x10-3 K W-1.

Figure 8.9 resumes all the results for thermal resistances found from experimental and numerical

analysis, while Figure 8.10 compares the mean temperatures of evaporator and condenser from

experimental test and numerical analysis.

Figure 8.9 Thermal resistances values for PHP# 2 tested in vertical position: experimental and

numerical results. (Ethanol, Tcryo=20°C)

Figure 8.10 Mean evaporator and condenser temperatures: experimental and numerical data.

(PHP# 2, Ethanol, Tcryo=20°C)


94

The numerical simplified model based on a pure annular flow with a constant thermal resistance

effect gives interesting results, with a good agreement on the thermal performance of the system. A

further step for this analysis could be to refine the filling ratio of the PHP by including the effects of

those channels completely filled of liquid, that do not take part on the heat transfer.

95

9. A preliminary Matlab model of the Pulsating Heat Pipe

9.1 Introduction

The second analysis concerns the implementation of a numerical model of the PHP when tilted on

the edge. Indeed, as widely discuss further, in this specific working condition the fluid and vapour

phase are well separated, thus the modelling becomes easier to set, as compared with the typical

slug flow pattern condition. Before getting into the details of the current work, the next paragraph

introduce some of the previous models which have been proposed in literature.

9.2 General overview of the earliest models

The working fluid in a Pulsating Heat Pipe, as largely discussed in previous chapters, is

characterized by a complex fluid dynamics, which concerns heat and mass transfer of a two-phase

oscillating fluid. These features make the numerical modelling of a PHP extremely complex.

Moreover, the relatively low costs of manufacture and of the ground tests, make the experimental

investigation the easiest way to study these devices. Obviously, this approach relates some known

features of the device (geometry, working fluid etc) with the measured thermal performance, but the

behaviour inside the PHP cannot be fully understood. Thus, the visualisation campaigns of the flow

regime inside a PHP made by Kandekhar, Ayel et al. [3] are surely helpful but not exhaustive. This

is one of the reasons that curb the use of Pulsating Heat Pipes among industrial applications.

Since when Akachi patented the PHP in the ‘90s, a number of researchers tried to develop

analytical and numerical models of these heat exchangers through different approaches.

9. A preliminary Matlab Model of the Pulsating Heat Pipe

96

9.2.1 The mass- spring- damper model

One of the earliest model proposed by Zuo et al. [22] is concerned with the hydraulic behaviour of

the liquid meniscus inside the device: this is reduced to a damped system driven by a pressure

gradient, generated by the heat and mass exchange at the ends of the plug itself. Thus, the plug

motion represents the displacement of its mass centre. Furthermore, no vapour bubbles take place

inside the plug and the separation among liquid and vapour phase occurs in a single contact surface.

The main hypotheses of this model are:

- vapour phase considered as a perfect gas;

- the average mass of liquid and vapour inside each channel is constant;

- the redistribution of mass in the liquid and vapour phases depends on the volume variation

due to the liquid displacement, due to the pressure gradient between two consecutives

branches;

- the fluid motion is supposed to be fully laminar.

Under these hypotheses, a governing equation for the oscillating phenomena can be written:

𝜕2𝑥

𝜕𝑡2 + 𝑐𝜕𝑥

𝜕𝑡+ 𝑘𝑥 = 0 (30)

Which is the general differential equation of free one d.o.f. oscillating systems, where x is the

displacement coordinate of the meniscus as a function of time t, the other parameters are:

- The coefficient c, damping term, refers to the friction parameter due to viscous effect;

- The coefficient k, stiffness term, refers to the pressure gradient among the liquid plug.

The previous equation has been implemented in MathCad and numerically solved, no information

about the thermal boundary has been provided.

The following plot resumes the displacements curves of the liquid plug for three different values of

filling ratios ϕ0 :

Figure 9.1 Numerical solution of Zuo’s model: plot of oscillations vs time with three different

values of FR. (Zuo, [22])


97

The solution of Figure 9.1 correlates the oscillating trend with the FR of the PHP: the higher is the

liquid plug mass, the higher will be the dumping effect due to drag forces, thus a strongly reduction

of oscillation amplitude is obtained. On the other hand, with the lowest value of filling ratio the

oscillations increase their amplitude, while for a filling ratio of 0.73 the oscillations are rather

stable, moreover all the three cases have the same frequency.

The model presented by Zuo is extremely simplified and it neglects different factors:

- the surface tension effects of the liquid;

- the presence of vapour bubbles inside the liquid meniscus;

- the number of channels.

Therefore, this model cannot be used in order to predict PHP performances.

9.2.2 Kinematic approach

The PHP fluid, due to the reduced diameters of its channels, has a random distribution of liquid

plugs and vapour bubbles; this configuration is generally assumed as the reference working

conditions and characteristic of this device. Starting from this consideration, Wong et al. [19]

proposed a model of an OLPHP (Open Loop) made up by 20 sub- regions of mono phase flow

(Figure 9.2).

Figure 9.2 Schematic representation of Wong’s model domain. (Wong, [19])

In this model, the fluid motion is driven by a pressure impulse that acts on the vapour phase element

located in the evaporator area (the 20th in Figure 9.2); the thermal condition is replaced by a

pressure impulse. The whole system is considered as adiabatic, the vapour phase treated as a perfect

gas and each element is perfectly mono-phase. In addition, the system is considered in the

horizontal position, thus gravity is neglected, as well as for the additional friction effects due to the

U-turns. The resulting system of non-linear first order Lagrangian equations for quantity of motion

and one additional equation of state is solved using the implicit Runge-Kutta method, setting the

following features:

- length of each element 0.06 m;

- 6 channels;

- total length 0.3 m;

- temperature of 25°C;


98

- initial pressure of P=101330 Pa;

- pressure Impulse 1.1 P.

Figure 9.3 plot the pressure trend inside the second element:

Figure 9.3 Pressure oscillations vs time in second element. (Wong, [19])

The pressure wave crosses the entire serpentine reaching the second element. Hence, it increases the

pressure consequently, the dumping effect due to friction rapidly reduces the fluctuations and

pressure asymptotically tends to a slightly higher value.

In this case too, the model cannot be used in order to predict PHP performance because the

behaviour of a PHP is widely different from what it has been found in this model. The pressure

gradient, which acts on each element, must be related to the heat and mass transfer phenomena and

the two problems cannot be uncoupled. Furthermore, the motion of a liquid plug inside a channel

depends even on the hysteresis of dynamic contact angle, which is completely neglected here.

9.2.3 Classic approach based on the conservation equations: Dobson’s model

In order to reproduce the real behaviour of a Pulsating Heat Pipes (or at least what it is supposed to

be) further models were proposed; the common approach is based on the resolution of conservation

equation of mass, momentum and energy. The equation of state is the perfect gas law and the

thermal problem is treated with a boundary heat flux or constant wall temperature condition.

This paragraph concerns the model proposed by Dobson [9] that is relevant because it has been used

as a starting point for the one presented in the current work.

Dobson work concerns only one pipe with an open end and the opposite one closed, inside of which

there is a two-phase flow, represented by a vapour bubble and a liquid plug, as shown in Figure 9.4.


99

Figure 9.4 Sketch of Dobson’s model for a single pipe and a two-phase fluid; the left end of the

pipe is open while the right end is closed. [9]

Referring to figure 9.4, the main lengths are:

- Lh heated region;

- La adiabatic region;

- Lc cooled region;

- Llf liquid film;

- Llvc condensation region.

In this model, when the pressure gradient pushes liquid plug out of the heated region, a liquid film

on the pipe surface is deposed; this layer has a constant thickness and it mediates the heat exchange

on the heated side. The liquid plug movement is driven by a pressure difference between the vapour

side and the external side (value Pe), which is a boundary condition. The fundamental equations are

listed below:

Mass conservation equation for the vapour bubble:

𝑑𝑚𝑣𝑎𝑝

𝑑𝑡= �̇�𝑣𝑎𝑝,𝑖𝑛 − �̇�𝑣𝑎𝑝,𝑜𝑢𝑡 − �̇�𝑣𝑎𝑝,𝑐𝑜𝑚𝑝 (31)

where each term on the right side is computed as follows:

�̇�𝑣𝑎𝑝 =𝑈𝜋𝑑𝐿𝛥𝑇

ℎ𝑙𝑣 (32)

U is the global heat exchange coefficient (W/m2K), d is the internal diameter, L an axial length, hlv

is the latent heat of evaporation and ΔT the temperature difference.

- �̇�𝑣𝑎𝑝,𝑖𝑛 is the vapour mass produced by liquid film evaporation. Thus in (32), U is referred

to the heat exchange among the internal wall of the pipe (fixed temperature condition) and

the liquid film, L is the length of the film itself and ΔT is the temperature difference between

the wall and the vapour;

- �̇�𝑣𝑎𝑝,𝑜𝑢𝑡 is the liquid mass produced during condensation. The condensation involves the

vapour confined in the cooled region, in Figure 9.4 the condensation is confined into the

length Llvc;


100

- �̇�𝑣𝑎𝑝,𝑐𝑜𝑚𝑝 is the mass of vapour which eventually condenses into the heated region if the

vapour temperature is higher than the wall one. This case can occur if the liquid plug

compresses the vapour.

Momentum conservation equation for the liquid plug:

𝑚𝑙𝑖𝑞𝑑𝑣𝑙𝑖𝑞

𝑑𝑡= 𝐹𝑃 − 𝐹𝜏 − 𝐹𝜎 ± 𝐹𝑔 (33)

This conservation equation expresses the equilibrium among the inertial forces on the liquid plug

and an algebraic sum of forces, which are supposed to be important in liquid motion.

- FP is the resulting pressure force acting on the liquid plug, computed as follow:

𝐹𝑃 =𝜋𝑑2

4(𝑃𝑣 − 𝑃𝑒) (34)

where Pv is the vapour pressure subjected to variation due to the heat exchange and to the phase

transition phenomena.

- 𝐹𝜏 is the drag force due to viscosity effect:

𝐹𝜏 = 𝑓𝜌𝑙𝑖𝑞𝜋𝑑𝐿𝑝

𝑣𝑙𝑖𝑞2

2 (35)

𝑓 =16

𝑅𝑒 if Re ≤ 1180

𝑓 = 0.078𝑅𝑒−0.25 if Re > 1180

where f is the friction coefficient, computed as function of the fluid motion regime inside the

pipe (Reynolds).

- 𝐹𝜎 is the resulting force due to surface tension of the liquid and the contact angle of the plug

surface, this latter is supposed to be constant:

𝐹𝜎 = 𝜎𝜋𝑑 cos 𝜃 (36)

- 𝐹𝑔 is the gravity force, its contribution can be either negative or positive, if the pipe is top or

bottom heated respectively, the angle 𝛽 accounts the inclination of the pipe as compared to

horizontal reference:

𝐹𝑔 = 𝜌𝑙𝑖𝑞𝐿𝑝𝑔𝜋𝑑2

4sin 𝛽 (37)

Internal energy conservation equation for the vapour phase written in the adiabatic region:

𝑚𝑣𝑎𝑝𝑐𝑣,𝑣𝑎𝑝𝑑𝑇𝑣𝑎𝑝

𝑑𝑡= (�̇�𝑣𝑎𝑝,𝑖𝑛 − �̇�𝑣𝑎𝑝,𝑜𝑢𝑡)(ℎ𝑙𝑣 + 𝑐𝑝,𝑣𝑎𝑝𝑇𝑣) − 𝑃𝑣𝐴

𝑑𝑥𝑝

𝑑𝑡 (38)


101

The last derivative term represents the liquid plug speed: 𝑣𝑙𝑖𝑞 =𝑑𝑥𝑝

𝑑𝑡 .

Equation of state for the perfect gas:

𝑃𝑣 =𝑚𝑣𝑎𝑝𝑅(𝑇𝑣+273.15)

𝜋𝑑2𝑥𝑝

4

(39)

Dobson chose water as working fluid, thus the properties used in the equations presented, they all

refer to liquid water and its vapour phase. As for the liquid film thickness, some experimental

results have been chosen, for liquid water moving in a glass tube of 4 mm internal diameter at a

20 °C. The following table summarizes all the conditions set for the model:

Boundary conditions Values

Evaporator wall temperature Th 125 °C

Condenser wall temperature Tc 25°C

External pressure Pe 100981 Pa

Global heat exchange coefficient evaporator 1000 Wm-2K-1

G. H. E. coefficient condensation 600 Wm-2K-1

G. H. E. coefficient condensation into heated region 1000 Wm-2K-1

Initial Conditions

Initial position of liquid vapour xp0 0.2 m

Initial speed of liquid plug vliq,0 0 m/s

Initial vapour temperature Tv,0 25°C

Initial vapour pressure Pv,0 105 Pa

Numerical data

Internal diameter d 3.34 mm

Evaporator length Lh 0.2 m

Adiabatic length La 0.02 m

Condenser length Lc 0.28 m

Contact angle θ 60°

Liquid film thickness 30 µm

Table 10. Summary of all the conditions of the Dobson’s model.

The results are shown in Figure 9.5 in which it is well visible that both the liquid plug and the

vapour pressure have continuous cycles of dumped oscillations.


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Figure 9.5 Dobson’s model results: trends of liquid position xp , vapour pressure Pv versus

time. (Dobson, [9])

At the end of each cycle the liquid plug is in the condenser region and suddenly a pressure drop

pushes it into the evaporator one.

The Dobson’s model is remarkable because it introduces the effects of the liquid film released by

the plug and it includes the surface tension effects and gravity into dynamic equilibrium.

The limitations of this model are mainly the following:

- all global heat exchanges coefficients are constants;

- the liquid film thickness is constant;

- the domain consists of a single pipe open at one side and close on the other;

- the vapour phase is treated as a perfect gas.

However, this model represents the starting point of the further results mentioned in the literature

and of the one presented in the current work.

9.2.4 PHP modelling and flow patterns

As discussed in previous sections (Chapter 1, paragraph 1.3) the PHP has three main possible flow

regimes:

- annular;

- semi-annular;

- slug flow pattern.

The first one has been treated in the previous section; it has been remarked that this flow pattern

occurs only when the PHP is positioned vertically and bottom heated. Thus the working mechanism

is close to the thermosyphons one and it brings the highest thermal performances. On the other

hand, the third one, represents the normal operating condition; the slug flow requires a proper

internal tubes diameter and it allows the PHP to work in all external conditions (position, variable

gravity field).


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The semi-annular flow is a transient condition between the slug flow and the annular one; the

vapour bubbles join each others and form one big agglomeration of vapour on the evaporator side,

while on the condenser one the liquid forms a column. However, this flow regime has been

observed as stable when the PHP is placed on the edge and on horizontal position at low heat

powers. Thus, the semi-annular flow can be assumed as specific working condition of the PHP

when it is placed on the edge.

Coming back to the numerical analysis, researchers proposed and implemented some models based

on conservation equations for the slug-flow pattern. One of the most exhaustive and complete

model ever developed is the one of Holley and Faghri [10] , later improved by Mameli et al. [17] .

It concerns a 1D analysis of a closed loop PHP with water: the approach used is Lagrangian, for the

single vapour plug and liquid slug, or Eulerian, for the pipe walls. Therefore, the implementation of

the conservation equations on each unsteady element makes this model really complex; vapour

bubbles can collapse, expand or mix together.

On the other hand, the aim of this work is to implement a simplified model, written in Matlab, for

the semi-annular flow. Differently from the slug-flow, which requires a control volume for each

liquid slug and vapour plug, the semi-annular flow can be well approximated as a single vapour

bubble and liquid meniscus, reducing the complexity of the model.

9.3 Introduction to a PHP model for the semi-annular flow pattern

The model proposed in this work refers to semi-annular flow pattern: this condition seems to occur

frequently when the PHP is tilted on the edge and it is stable for different heat powers applied.

Hence the liquid meniscus and the vapour plugs are assumed as completely separated by one

contact surface, the liquid is accumulated in the cooled part of the device while the vapour on the

heated one. Figure 9.6 comes from one of the visualisation campaigns for a flat plate CL-PHP

(closed-loop PHP) with 20 channels with a 2 mm squared cross section: the lighter lines on the right

part (condenser region) are the liquid menisci which pushes the vapour column on the left part.

Instead of a planar contact surface, the separation between the two phases seems to occur through a

vapour bubble that moves with the liquid meniscus.


104

Figure 9.6 Flow visualisation in a flat plate CL-PHP placed on the edge and using ethanol as

primary working fluid. (Ayel, [3])

Figure 9.7 Sequence of pictures taken in a time laps of 5 seconds: hydrostatic pressure

contribution to liquid menisci instabilisation. (Ayel , [3])

i ii iii

iV V Vi


105

Figure 9.7 introduce the sequence of the same device tested under a heat power of 100 W. The

bottom, channel is moving towards the evaporator region pushed by the hydrostatic pressure

gradient, while the others continue to oscillate with a rather small amplitude through the condenser

and adiabatic region (possible dry out of the evaporator). In sequence iV the liquid meniscus is

nearly out of the adiabatic region and close to evaporator one. The vapour plug of the bottom

channel is compressed. When the liquid reaches the evaporator, assuming that the vapour attends

the saturation conditions, the phase transition causes a further increase of the vapour mass inside the

plug. On the other hand, the first channel (upper part of the PHP) is nearly empty of the liquid and

the vapour phase is expanded through it. This pressure difference that affects the liquid plug induces

a huge destabilisation of fluid meniscus, which is consequently pushed backwards to condenser

region in the bottom channel (forward to evaporator region for the upper channel). This quick

oscillation is enough to destabilise all the channels; a pressure wave crosses the device. Thanks to

this mechanism, each liquid slug is pushed for a while up to the evaporator region, where it deposes

a thin liquid film. Due to this fact, the temperatures of the evaporator region have a strong

reduction. As shown in the following plot, taken from a test of PHP# 2 (Figure 9.8) the evaporator

temperatures have intense fluctuations at high frequency that increase with the heat power applied.

Compared to a pure annular flow, the oscillations have a higher amplitude; this fact leads to think

that a slug-flow or semi annular one are dominants.

Figure 9.8 Evaporator temperatures vs heat power applied for PHP# 2 placed on the edge.

(ethanol, Tcond=20°C)


106

9.4 Model setting: PHP geometry and operating parameter

The initial geometry considered consists of four channels serpentine, with squared section of 2mm

side length. Figure 9.9 shows the geometrical features with the corresponding lengths of the domain

considered.

Figure 9.9 Representation of model domain with its geometrical features; all lengths are in

mm.

The working fluid considered is ethanol, one of the most common fluid for these applications, with

a filling ratio around 50%. Actually, the fluid is supposed to fill all the internal channels volume

from x=0 on (referring to Figure 9.9). The PHP is not symmetric as compared to the x=0 axis,

hence the filling ratio is not exactly 50%, but a slightly higher value. The exact value of FR can be

computed but it is not relevant for the purpose of the work.

Initially the PHP has all the liquid stored on the right side and its vapour phase at saturation

condition on the left one (Figure 9.9). Even if this separation among the fluid and vapour phases

does not agree with the real flow pattern (which is initially a slug flow); it represents the effective

working condition to reproduce. Indeed it has been observed that from an initially slug flow regime

the PHP quickly switches to a semi-annular flow when it is tilted on the edge, thus with the liquid

and vapour phases completely separated and stored at the opposite extremities of the PHP.

Hence, the first step of the model implementation concerns the conservation equations of mass and

momentum for the “cold system”, which means with no heat power supplied; the system,

considered as adiabatic, is left free to evolve from the initial configuration.

The approximation of the model for the cold part are:

- vapour phase considered as a perfect gas;

- mono-dimensional;

- uncompressible fluid;

- static contact angle of liquid-vapour interface 90°;

- fully laminar flow;


107

- the U-turns on the condenser and evaporator region are always filled with liquid and vapour

respectively.

Mass conservation equation for both liquid and vapour phases:

𝑑𝑚𝑣𝑎𝑝

𝑑𝑡= 0 (40)

𝑑𝑚𝑙𝑖𝑞

𝑑𝑡= 0

As long as no heat power is applied, no mass transfers occur, thus the initial masses of liquid and

vapour are preserved.

As for the conservation of momentum, Dobson’s model equation is recalled (33), for the generic

liquid plug at instant t :

𝑚𝑙𝑖𝑞

𝑑𝑣𝑙𝑖𝑞

𝑑𝑡= 𝐹𝑝 − 𝐹𝜏 − 𝐹𝜎 + 𝐹𝑔

where the terms at second member are:

- 𝐹𝑝: the resultant pressure force:

𝐹𝑝 = (𝑃𝑣,1 − 𝑃𝑣,2)𝑎2 (41)

where 𝑃𝑣,1−2 refer to the vapour pressure at the slug ends, a is the length of the section side;

- 𝐹𝜏: the viscous drag force, friction coefficient f comes from smooth pipes correlation:

𝐹𝜏 =1

2𝜌𝑙𝑖𝑞4𝑎𝐿𝑙𝑖𝑞𝑓(𝑅𝑒)𝑣𝑙𝑖𝑞

2 (42)

𝑓 =16

𝑅𝑒

- 𝐹𝜎: the tension surface force resultant:

𝐹𝜎 = 4𝑎𝜎𝑙𝑖𝑞 cos(𝜗𝑙𝑖𝑞,𝑓𝑟𝑜𝑛𝑡 − 𝜗𝑙𝑖𝑞,𝑏𝑎𝑐𝑘) (43)

The static contact surface angle is supposed to be 90°, thus there is no static capillarity contribution.

The 𝜗 angles refer to the dynamic hysteresis between the two meniscus ends (front/back).

- 𝐹𝑔: the gravity force:

𝐹𝑔 = 𝜌𝑙𝑖𝑞𝑔ℎ𝑔𝑎2 (44)

where ℎ𝑔 is the geodetic displacement.

The perfect state gas equation replaces the energy one:

𝑃𝑣𝑎𝑝 =𝑚𝑣𝑎𝑝𝑅0𝑇𝑣𝑎𝑝

𝑉𝑣𝑎𝑝 (45)

𝑅0 =𝑅

𝑚𝑚𝑣𝑎𝑝= 180.5

𝐽

𝑘𝑔 𝐾


108

Furthermore, accounting that:

- the liquid phase temperature is constant and fixed at the condenser value;

- for the vapour phase, the adiabatic and isentropic approximation is adopted, pressures and

temperatures are relied by the equation below:

𝑃2

𝑃1= (

𝑇2

𝑇1)

𝛾

𝛾−1 (46)

- the mass transfer is neglected.

The resulting equation of conservation of momentum can be written in the explicit form (forward

Eulerian) with respect to time instants ti and ti-1 and solved for the n-th liquid menisci, a proper time

step it must be selected:

𝑚𝑙𝑖𝑞,𝑛𝑣𝑙𝑖𝑞(𝑖)−𝑣𝑙𝑖𝑞(𝑖−1)

Δt= (𝑃𝑣,𝑛1

− 𝑃𝑣,𝑛2)𝑎2 −

1

2𝜌𝑙𝑖𝑞4𝑎𝐿𝑙𝑖𝑞𝑓(𝑅𝑒(𝑖 − 1))𝑣𝑙𝑖𝑞

2 (𝑖 − 1) −

4𝑎𝜎𝑙𝑖𝑞 cos(𝜗𝑙𝑖𝑞,𝑓𝑟𝑜𝑛𝑡 − 𝜗𝑙𝑖𝑞,𝑏𝑎𝑐𝑘) + 𝜌𝑙𝑖𝑞𝑔ℎ𝑔,𝑛𝑎2 (47)

Thus, at each time t, a value of liquid slug speed is evaluated. The integration of speed in the time

gives the displacement of the liquid meniscus. For the hypothesis mentioned above, it has the same

module but with opposite sign at its two ends (Figure 9.10).

Figure 9.10 Example of liquid slug displacement: if the meniscus is uncompressible, pure

mono-phase, its two ends must have the same displacement.

The code has been written in Matlab with the following initial conditions:

Working fluid Ethanol

Initial Vapour temperature 293 K

Liquid temperature 293 K

Filling Ratio 50%

Universal gas constant (vapour phase) 180.5 J/kg K

Vapour density 0.1 kg/m3

Liquid density 790 kg/m3

Gravity acceleration 9.8 m2/s

Liquid viscosity 0.0012 Pa s

Surface Tension 0.0288 N/m

Adiabatic Isentropic transformation

Coefficient (vapour phase)

1.13

Dynamic contact angle hysteresis 10°

Table 11. Initial conditions for the Matlab model.


109

A reasonable time step that matches the accuracy of the solution with the solving time is 10-3s.

The initial pressure value of the vapour phase is the saturation one, thus Pvap,0(Tvap,0) = 5.8 103 Pa.

9.5 Results of the model without the heat exchange

The following plots show the curves of the liquid slug displacement, its speed and the forces acting

on it as a function of time and the temperature trend in the vapour phase.

The curves refer to the position of the upper ends of the channels, by looking at Figure 9.9: the first

and the second channel starting from the top are the outer and inner respectively.

Figure 9.11 Displacements of the liquid slugs for the “cold” model.


110

Figure 9.12 Liquid slugs speed.

Figure 9.13 Forces acting on the external liquid slug.


111

Figure 9.14 Forces acting on the internal liquid slug.

Figure 9.15 Temperature of the vapour plugs.


112

From Figure 9.11 it can be noticed that both slugs have an initial positive displacement, as

confirmed from the velocity plot of Figure 9.12. They both move downwards for the first 0.1

seconds, thus, they compress the bottom vapour plug (Figure 9.15 blue curve).

At ̴0.08 s, the inner plug speed changes sign; the pressure force overcome the gravity one and the

inner liquid slug is moved upwards. Due to the initial pressure oscillation in the vapour phase, the

speed curves are not monotone but rather damped oscillating; they reach an asymptotical value

after ̴1 second. It is important to remark that under these conditions, gravity is the only

perturbative effect acting on the system. Hence the liquid slugs are pushed continuously

downwards, the effect of the external meniscus is dominant. As a result, after an initial oscillating

transient phase, both slugs moves with a constant speed, which verifies the dynamic equilibrium.

After ̴9.8 s the slugs exit the boundaries of the domain considered (Figure 9.11 shaded lines) with

a pretty linear trend. Figures 9.13 and 9.14 show the trends of the forces accounted in the

momentum conservation equation for both liquid plugs, outer and inner respectively. It can be seen

that pressure and drag forces have an oscillating trend, indeed they both derive from the speed

values, while the gravity one depends only on the hydrostatic pressure gradient, thus it is fixed

within the considered domain. As for the surface tension forces, only the hysteresis of the dynamic

contact angle is accounted, so if this angle difference is fixed, the force will depend only from the

surface tension, which depends on the fluid temperature.

This result is not representative of the real behaviour of a PHP; when no heat power is applied, the

flow distribution attends a slug flow pattern that leads to a completely different behaviour. Anyway,

this is a good starting condition for the operative PHP when it is tilted on the edge and it works with

steady boundary conditions.

9.6 Modelling of the heat and mass transfer

The basic assumption made for this model is that the liquid slugs and the vapour plugs are

completely separated and stored in condenser and evaporation region respectively. Then, thanks to

pressure and gravity perturbation, the liquid menisci begin to oscillate, reaching the evaporator area.

Thus, once they are called back to condenser region, a thin liquid film is released. Figure 9.16

represents this situation; the liquid film is released only if the condition ΔX> 0 occurs.


113

Figure 9.16 A schematic representation of the film released by the liquid meniscus.

The liquid film is supposed to be homogeneous across the whole channel perimeter and with a

constant thickness. The latter is surely a strong assumption; anyway, it can be a good starting

condition and eventually object of further investigations.

The average liquid film thickness is evaluated by using the Han and Shikazono [21] empirical

correlation:

𝛿0

𝐷𝑖=

0.61𝐶𝑎23

1+3.13𝐶𝑎23+0.504𝐶𝑎0.672𝑅𝑒0.589−0.352𝑊𝑒0.629

𝑖𝑓 𝑅𝑒 < 2000 (48)

𝛿0

𝐷𝑖=

106(𝜇𝑙

2

𝜌𝑙𝜎𝐷𝑖)

23

1+497(𝜇𝑙

2


23

+7303(𝜇𝑙

2


0.672

𝑅𝑒0.589−5000(𝜇𝑙

2


0.629 𝑖𝑓 𝑅𝑒 > 2000 (49)

Where 𝐷𝑖 is the internal hydraulic diameter, 𝐶𝑎 =𝜇𝑙𝑖𝑞𝑈𝑚𝑒𝑛

𝜎 is the capillarity number,

𝑅𝑒 =𝜌𝑙𝑖𝑞𝑈𝑚𝑒𝑛𝐷𝑖

𝜇𝑙 is the Reynolds number and 𝑊𝑒 =

𝜌𝑙𝑖𝑞𝑈𝑚𝑒𝑛2𝐷𝑖

𝜎 is the Weber one. It can be noticed

that the liquid speed affect the film thickness only when Re< 2000.

The thermal equations implemented refer to a constant internal wall temperature boundary

condition (Dirichlet), so:

- the evaporator region is characterized by the constant temperature TP ;

- the condenser region is characterized by the constant temperature Tcond ;

Now, if the vapour plug reaches saturation a mass transfer occurs (condensation or evaporation).

The amount of heat exchanged during time ti-ti-1 across the liquid film is computed by as in (50):

𝑄𝑓𝑖𝑙𝑚(𝑖) =𝜆𝑙𝑖𝑞

𝛿0(𝑖−1)4(𝑎 − 𝛿0)𝐿𝑓𝑖𝑙𝑚(𝑖 − 1) 𝑎𝑏𝑠|𝑇𝑃 − 𝑇𝑣𝑎𝑝(𝑖 − 1)| (50)

where 𝑇𝑃 is one of the boundary conditions defined above.


114

The quantity of mass transferred is then computed as:

�̇�𝑡𝑟𝑎𝑛𝑠𝑓(𝑖) =𝑄𝑓𝑖𝑙𝑚(𝑖)

ℎ𝑙𝑣 (51)

where ℎ𝑙𝑣 is the latent heat of the liquid.

If the vapour plug does not arrive at saturation conditions, the heat exchange is reduced to a

convective heat transfer among the liquid and the vapour phase:

𝑄𝑓𝑖𝑙𝑚,𝑐𝑜𝑛𝑣 = ℎ𝑣𝑎𝑝4(𝑎 − 2𝛿0)𝐿𝑓𝑖𝑙𝑚(𝑖 − 1) 𝑎𝑏𝑠|𝑇𝑃 − 𝑇𝑣𝑎𝑝(𝑖 − 1)| (52)

where ℎ𝑣𝑎𝑝 is the convective heat transfer coefficient, evaluated from Nusselt number correlation,

assuming a fully developed thermal and flow boundary layer.

𝑁𝑢 =ℎ𝑣𝑎𝑝𝐷𝑖

𝐿 (53)

where Nu=3.66 for a constant wall temperature boundary condition.

9.6.1 Evaporation through a liquid film

Until now, the procedure described is valid in both region; either the evaporator or the condenser

ones.

However, the mass transfer affects the liquid film in a different way between these two regions.

In the evaporator region the liquid film thickness is considered constant. Thus, the vaporised mass

does not affect its thickness but only the length, as shown in Figure 9.17.

Figure 9.17 Evaporation of liquid film.

This assumption affects drastically the heat transfer properties: actually the liquid film thickness is

not constant, thus the thermal resistance changes during the evaporation phenomena, recalling (50):


115

𝑄𝑓𝑖𝑙𝑚(𝑖) =𝜆𝑙𝑖𝑞

𝛿0(𝑖 − 1)4(𝑎 − 𝛿0)𝐿𝑓𝑖𝑙𝑚(𝑖 − 1) 𝑎𝑏𝑠|𝑇𝑃 − 𝑇𝑣𝑎𝑝(𝑖 − 1)|

𝑅𝑡ℎ𝑙𝑖𝑞 𝑓𝑖𝑙𝑚=

𝜆𝑙𝑖𝑞

𝛿0

However, as a first approach, this assumption allows getting the right order of magnitude of the heat

exchange rate and makes the code easier to write. So, in (50) the term 𝛿0 is considered constant in

time.

It is worth to notice that the film thickness involved in the heat transfer is the one confined into the

evaporator region.

9.6.2 Condensation through a liquid film

In the condenser region the liquefied vapour mass is considered as homogeneously distributed along

the whole liquid film, increasing its average thickness value.

Figure 9.18 Condensation on liquid film.

So in (50) 𝛿0is updated during the time. As represented in Figure 9.18, the portion of the liquid film

involved in the heat and mass transfer is the one that extends from x≥0.

9.7 Model updating and closing equations

The main iterative cycle of the code updates, at each time step, the total vapour mass inside the n-th

plug:

𝑚𝑣𝑎𝑝(𝑖) = 𝑚𝑣𝑎𝑝(𝑖 − 1) − 𝑚𝑐𝑜𝑛𝑑(𝑖 − 1) + 𝑚𝑒𝑣(𝑖 − 1) (54)


116

The equation above is the mass conservation for the vapour plug. The liquid slug mass conservation

equation is not considered in the first approach.

Then, momentum conservation equation is solved, the liquid displacement and the volumes of the

vapour plugs are evaluated.

The vapour pressure is computed by using the perfect gas state equation:

𝑃𝑣𝑎𝑝(𝑖) =𝑚𝑣𝑎𝑝(𝑖)𝑅𝑣𝑇𝑣𝑎𝑝(𝑖−1)

𝑉𝑣𝑎𝑝(𝑖) (55)

Finally, comparing the vapour pressure conditions with the saturation ones, the proper heat transfer

equation is chosen and temperature computed. Then the cycle restarts.

9.8 Conclusions on the numerical modelling

Starting from the work by Dobson, the model here reported represents a development for a simple

four channels PHP. The hypothesis of an annular flow leads to many simplification and the flow

pattern becomes easier to model. As for the results concerning the “cold” part (without the heat and

mass transfer) a simulation done with the two-phase Volume-Of-Fluid solver included in the

OpenFOAM® CFD Software, under the same conditions, confirmed the trend observed for speed

and displacement curves with a difference of about 15% in the computed values.

On the other hand, the addition of the heat and mass transfer brought several complications and the

model has to be completed yet. Indeed, the main problem concerns the generation of the first

oscillation of the outer liquid meniscus that then it is supposed to activate the PHP by generating a

pressure wave across all channels. The adoption of a real gas model for the vapour phase represents

a better approximation which can bring better results. Furthermore, the heat exchange modelled

through a liquid film kept at a constant thickness is surely a rough assumption; indeed it has been

observed that during the evaporation and condensation, even small changes in the liquid film

thickness deeply affect the heat transfer. Thus even the shape and the supposed distribution of the

liquid film can be not proper to describe exactly what happens inside these devices. However, for

the purpose of the model, the approximations adopted represents a good starting condition, when a

more refined version of the model will be implemented.

117

General Conclusions

This work has been devoted to an experimental and numerical analysis of a FPPHP. The Pulsating

Heat Pipes are always drawing the attention of both researchers and industries. Indeed for

researchers they represent a challenge that concerns many open questions in literature, while for

industries they are highly appealing because of their reduced cost, the simplicity and the good

performances offered.

The experimental analysis has been performed by following the methods and the procedures

commonly described in literature in order to get comparable data. However, from the analysis of the

results it is clear that the behaviour of these devices is still far from being well known. Thus, the use

of this technology for industrial applications needs first a deep improvement in the knowledge of its

internal fluid dynamics, in order to outline some specific criteria for the PHP design.

As for the numerical analysis, the aim has been to show how, adopting some of the consideration

from the experimental tests, it is possible to get interesting results with simplified models. Adopting

this way of procedure, the modelling of the fluid flow inside the PHP becomes simpler enough to be

described through classic approaches like those proposed in this work. Once the main physics has

been modelled, the dimensioning of the PHP could be carried out and further improved through the

comparison with experimental tests, thus the role of the experiments is still fundamental, as they are

the starting point to tune some important parameters in the models and the reference for their

validation

Finally, a simplified model would see also an additional point of interest in the fact that the space

environment - for which FPPHP seems a very promising technology -is characterised by the

extreme thermal conditions which have not been tested yet.

118

Appendix I

Thermophysical properties of the fluids

i) Ethanol

Table 12. Thermophysical properties of Ethanol.

Appendix I

119

ii) FC72

Table 13. Thermophysical properties of FC72.

120

Appendix II

Experimental apparatus

Power supply: EA ELEKTRO-AUTOMATIK model PS 8360-10 T.

Input data

Input voltage 90 ÷ 264 𝑉

Frequency 45 ÷ 65 𝐻𝑧

Power factor > 0.99

Inrush current < 25 𝐴

Output voltage

Nominal voltage 360 𝑉

Stability at 10…..90% load 0.05 %

Accuracy = 0.2 %

Output current

Nominal current 0 ÷ 10 𝐴

Stability at 10…..100% load < 0.15 %

Accuracy = 0.2 %

Output power and others

Nominal power 1000 𝑊

Dimensions (WxHxD) 90𝑥240𝑥393 𝑚𝑚

Weight 9 𝑘𝑔

Table 14. Datasheet of the Power Supply EA ELEKTRO-AUTOMATIK model PS 8360-10 T.

Thermoregulation system: HUBER CC240wl.

Operating temperature range −40 ÷ 200 ℃

Temperature stability at – 𝟏𝟎℃ 0.02 𝐾

Temperature adjustment digital

Temperature indication digital

Resolution 0.1 𝐾

Internal temperature sensor Pt 100

Cooling capacity

at 𝟏𝟎𝟎℃ 1.2 𝑘𝑊

at 𝟎℃ 1 𝑘𝑊

at −𝟐𝟎℃ 0.6 𝑘𝑊

Refrigerant 𝑅507

Pressure of pump max 0.5 𝑏𝑎𝑟

Table 15. Datasheet of the thermoregulation HUBER CC240wl.

Appendix II

121

Acquisition system:

The main features of this module are:

- Integrated CompactRIO systems with a reconfigurable FPGA chassis and embedded real-time

controller;

- Low-cost systems for high-volume OEM applications;

- Up to 400 𝑀𝐻𝑧 real-time processor;

- Up to 256 𝑀𝐵 DRAM memory, 512 𝑀𝐵 of nonvolatile storage;

- Up to two 10/100BASE-TX Ethernet ports with built-in FTP/HTTP servers;

- LabVIEW remote panel Web server;

- RS232 serial port and available USB port for peripherical devices.

Module for thermocouple (NI 9213) monitor all temperature signals from each thermocouple.

Vacuum pumps:

1) Oil seal rotary vane pump Pascal 2010 C2.

Frequency 50 𝐻𝑧

Number of stages 2

Rotation Speed 9.7 𝑚3/ℎ

Max pumping speed 8.5 𝑚3/ℎ

Max Gas throughput 3263 𝑚𝑏𝑎𝑟 𝑙/𝑠

Partial ultimate pressure 5 ∙ 10−4 𝑚𝑏𝑎𝑟

Ultimate pressure with

gas

ballast closed

3 ∙ 10−3 𝑚𝑏𝑎𝑟

Maximum pressure at

inlet

in continuous operation

without oil recovery

with oil recovery

10 𝑚𝑏𝑎𝑟

100 𝑚𝑏𝑎𝑟

Maximum exhaust

relative overpressure 0.50 𝑏𝑎𝑟

Oil capacity 0.95 𝑙 Weight (pump+motor) 26 𝑘𝑔

Inlet and exhaust end

fittings DN 25 150-KF

Table 16. Data sheet of the vacuum pump Pascal 2010 C2.

Appendix II

122

2) Leak Detector ASM Graph 142 rotary vane pump.

Backing pump with oil sealed backing pump

Backing pump capacity 10 𝑚3/ℎ

Detectable gases 𝐻𝑒4

Maximum inlet test pressure 10 ℎ𝑃𝑎

Minimum detectable leak rate

for helium (sniffing leak

detection)

1 10−8𝑃𝑎 𝑚3/𝑠

Minimum detectable leak rate

for helium (vacuum leak

detection)

5 10−13𝑃𝑎 𝑚3/𝑠

Operating temperature 0 ÷ 45 ℃

Pumping speed for He 1.3 𝑙/𝑠

Start-up temperature 10 ÷ 45 ℃

Supply 200 − 240 𝑉, 50/60 𝐻𝑧

Test method Vacuum and sniffing leak detection

Weight 56 𝑘𝑔

Table 17 Datasheet of Leak Detector ASM Graph 142.

123

Appendix III

Evaluation of thermal resistance contribution due to the presence of fluid,

or “PHP effect” (RPHP)

Recalling the scheme of Figure 6.19 (Chapter 6):

𝑄 =(�̅�𝑒𝑣−�̅�𝑐𝑜𝑛𝑑)

𝑅𝑡ℎ+

(�̅�𝑒𝑣−�̅�𝑎𝑚𝑏)

𝑅𝑙𝑜𝑠𝑠𝑒𝑠 (I)

Where Rth can be split in two contributions;

𝑅𝑡ℎ = (1

𝑅𝑐𝑜𝑛𝑑+

1

𝑅𝑃𝐻𝑃)

−1 (II)

Then by substituting (II) in (I) RPHP can be easily figured out;

𝑅𝑃𝐻𝑃 =𝑅𝑐𝑜𝑛𝑑[

�̅�𝑒𝑣−�̅�𝑐𝑜𝑛𝑑𝑄−𝐺𝑙𝑜𝑠𝑠𝑒𝑠(�̅�𝑒𝑣−�̅�𝑎𝑚𝑏)

]

𝑅𝑐𝑜𝑛𝑑−(�̅�𝑒𝑣−�̅�𝑐𝑜𝑛𝑑)

𝑄−𝐺𝑙𝑜𝑠𝑠𝑒𝑠(�̅�𝑒𝑣−�̅�𝑎𝑚𝑏)

(III)

124

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126

Ringraziamenti

Ringrazio la mia famiglia e tutte le persone che mi hanno sostenuto in questo lungo

percorso.

Ringrazio i prof. Vincent Ayel e Manfredo Guilizzoni che mi hanno assistito e guidato

in questo lavoro di tesi.

Dedicato a mio nonno Corrado.

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