Experimental and numerical analysis of Flat Plate ... · “Earth is the cradle of humanity, but...
Transcript of Experimental and numerical analysis of Flat Plate ... · “Earth is the cradle of humanity, but...
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
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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
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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
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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
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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
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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
Estratto in lingua italiana
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
Estratto in lingua italiana
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
Estratto in lingua italiana
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
Estratto in lingua italiana
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
Estratto in lingua italiana
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.
1. Two-phase heat exchangers
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).
1. Two-phase heat exchangers
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.
1. Two-phase heat exchangers
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.
1. Two-phase heat exchangers
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
1. Two-phase heat exchangers
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).
3. Physics of Pulsating Heat Pipes
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);
3. Physics of Pulsating Heat Pipes
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)).
3. Physics of Pulsating Heat Pipes
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
3. Physics of Pulsating Heat Pipes
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.
3. Physics of Pulsating Heat Pipes
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.
3. Physics of Pulsating Heat Pipes
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.
5. Operating Parameters
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.
5. Operating Parameters
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])
5. Operating Parameters
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.
�̅�
5. Operating Parameters
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).
5. Operating Parameters
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).
5. Operating Parameters
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.
5. Operating Parameters
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.
6. Experimental Investigation
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]).
6. Experimental Investigation
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).
6. Experimental Investigation
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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.
6. Experimental Investigation
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).
6. Experimental Investigation
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.
6. Experimental Investigation
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.
6. Experimental Investigation
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.
6. Experimental Investigation
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).
6. Experimental Investigation
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).
6. Experimental Investigation
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.
6. Experimental Investigation
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.
6. Experimental Investigation
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,
6. Experimental Investigation
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
6. Experimental Investigation
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.
6. Experimental Investigation
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= 40°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
Tcryo= 40°C horizontal, α=45°, vertical, on the edge
Tcryo= 5°C horizontal, α=45°, vertical, on the edge
PHP # 3 Tcryo= 20°C horizontal, α=45°, vertical, on the edge
Tcryo= 40°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
Tcryo= 40°C horizontal, vertical, on the edge
Tcryo= 5°C horizontal, α=45°, vertical, on the edge
Ethanol PHP # 2 Tcryo= 20°C horizontal, α=45°, vertical, on the edge
Tcryo= 40°C horizontal, α=45°, vertical, on the edge
Tcryo= 5°C horizontal, α=45°, vertical, on the edge
PHP # 3 Tcryo= 20°C horizontal, α=45°, vertical, on the edge
Tcryo= 40°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.
6. Experimental Investigation
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
6. Experimental Investigation
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.
6. Experimental Investigation
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).
6. Experimental Investigation
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)
6. Experimental Investigation
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
Tcryo_2 = 10°C Q2 =10W �̅�𝑒𝑣22 �̅�𝑐𝑜𝑛𝑑22 �̅�𝑎𝑚𝑏22
Q3 =20W �̅�𝑒𝑣23 �̅�𝑐𝑜𝑛𝑑23 �̅�𝑎𝑚𝑏23
Q1 =5W �̅�𝑒𝑣31 �̅�𝑐𝑜𝑛𝑑31 �̅�𝑎𝑚𝑏31
Tcryo_3 = 20°C Q2 =10W �̅�𝑒𝑣32 �̅�𝑐𝑜𝑛𝑑32 �̅�𝑎𝑚𝑏32
Q3 =20W �̅�𝑒𝑣33 �̅�𝑐𝑜𝑛𝑑33 �̅�𝑎𝑚𝑏33
Table 5. General scheme of a vacuum test for a PHP.
6. Experimental Investigation
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)
7. Experimental Results
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
7. Experimental Results
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
7. Experimental Results
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.
7. Experimental Results
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.
7. Experimental Results
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)
7. Experimental Results
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
7. Experimental Results
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.
7. Experimental Results
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.
7. Experimental Results
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
7. Experimental Results
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.
7. Experimental Results
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:
7. Experimental Results
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.
7. Experimental Results
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)
7. Experimental Results
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.
7. Experimental Results
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
7. Experimental Results
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:
7. Experimental Results
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
7. Experimental Results
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.
7. Experimental Results
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
7. Experimental Results
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.
7. Experimental Results
79
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.
7. Experimental Results
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)
7. Experimental Results
81
(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
7. Experimental Results
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.
7. Experimental Results
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.
84
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
8. Numerical Modelling of a specific Test Case
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.
8. Numerical Modelling of a specific Test Case
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).
8. Numerical Modelling of a specific Test Case
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
8. Numerical Modelling of a specific Test Case
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.
8. Numerical Modelling of a specific Test Case
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.
8. Numerical Modelling of a specific Test Case
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.
8. Numerical Modelling of a specific Test Case
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
8. Numerical Modelling of a specific Test Case
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)
8. Numerical Modelling of a specific Test Case
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.
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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])
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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;
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- 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.
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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;
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- �̇�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)
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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.
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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
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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)
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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;
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- 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
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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.
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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.
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Figure 9.12 Liquid slugs speed.
Figure 9.13 Forces acting on the external liquid slug.
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Figure 9.14 Forces acting on the internal liquid slug.
Figure 9.15 Temperature of the vapour plugs.
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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.
9. A preliminary Matlab Model of the Pulsating Heat Pipe
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
𝜌𝑙𝜎𝐷𝑖)
23
+7303(𝜇𝑙
2
𝜌𝑙𝜎𝐷𝑖)
0.672
𝑅𝑒0.589−5000(𝜇𝑙
2
𝜌𝑙𝜎𝐷𝑖)
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.
9. A preliminary Matlab Model of the Pulsating Heat Pipe
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):
9. A preliminary Matlab Model of the Pulsating Heat Pipe
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)
9. A preliminary Matlab Model of the Pulsating Heat Pipe
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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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.