Numerical Modelling of Subcooled Nucleate Boiling for Thermal Management Solutions Using OpenFOAM

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Thermal Management Solutions

Using OpenFOAM

ISBN 978-91-7485-497-8 ISSN 1651-9256

Address: P.O. Box 883, SE-721 23 Västerås. Sweden Address: P.O. Box 325, SE-631 05 Eskilstuna. Sweden E-mail: info@mdh.se Web: www.mdh.se

Achref Rabhi is a doctoral candidate at the Future Energy Center of

Mälardalen University (MDH), Sweden. He holds a National

Engineer-ing Diploma in scientific computEngineer-ing from the National EngineerEngineer-ing

School of Tunis (ENIT), and a Master of Science in fluid dynamics,

energy and heat transfer from the National Polytechnic Institute of

Toulouse (INPT), France. His research interests are multiphase flows and

heat transfer modelling, with a special focus on two-phase cooling,

phase-change processes and boiling flows.

Achref Rabhi ER IC A L M O D EL LIN G O F S U B C O O LE D N U C LE A TE B O IL IN G F O R T H ER M A L M A N A G EM EN T S O LU TIO N S U SIN G O P EN FO A M 202 1

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Mälardalen University Press Licentiate Theses No. 304

NUMERICAL MODELLING OF SUBCOOLED NUCLEATE BOILING

FOR THERMAL MANAGEMENT SOLUTIONS USING OPENFOAM

Achref Rabhi 2021

School of Business, Society and Engineering

Mälardalen University Press Licentiate Theses No. 304

NUMERICAL MODELLING OF SUBCOOLED NUCLEATE BOILING

FOR THERMAL MANAGEMENT SOLUTIONS USING OPENFOAM

Achref Rabhi 2021

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ISSN 1651-9256

Printed by E-Print AB, Stockholm, Sweden

ISSN 1651-9256

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Abstract

Two-phase cooling solutions employing subcooled nucleate boiling flows e.g. thermosyphons, have gained a special interest during the last few decades. This interest stems from their enhanced ability to remove ex-tremely high heat fluxes, while keeping a uniform surface temperature. Consequently, modelling and predicting boiling flows is very important, in order to optimise the two-phase cooling operation and to increase the involved heat transfer coefficients.

In this work, a subcooled boiling model is implemented in the open-source code OpenFOAM to improve and extend its existing solver react-ingTwoPhaseEulerFoam dedicated to model boiling flows. These flows are modelled using Computational Fluid Dynamics (CFD) following the Eulerian two-fluid approach. The simulations are used to evaluate and analyse the existing Active Nucleation Site Density (ANSD) models in the literature. Based on this evaluation, the accuracy of the CFD simulations using existing boiling sub-models is determined, and features leading to improve this accuracy are highlighted. In addition, the CFD simulations are used to perform a sensitivity analysis of the interfacial forces acting on bubbles during boiling flows. Finally, CFD simulation data is employed to study the Onset of Nucleate Boiling (ONB) and to propose a new model for this boiling sub-model, with an improved prediction accuracy and ex-tended validity range.

It is shown in this work that predictions associated with existing boil-ing sub-models are not accurate, and such sub-models need to take into account several convective boiling quantities to improve their accuracy. These quantities are the thermophysical properties of the involved mate-rials, liquid and vapour thermodynamic properties and the heated surface micro-structure properties. Regarding the interfacial momentum transfer, it is shown that all the interfacial forces have considerable effects on boil-ing, except the lift force, which can be neglected without influencing the simulations’ output. The new proposed ONB model takes into account convective boiling features, and it able to predict the ONB with a very good accuracy with a standard deviation of 2.7% or 0.1 K. This new ONB model is valid for a wide range of inlet Reynolds numbers, covering both regimes, laminar and turbulent, and a wide range of inlet subcoolings and applied heat fluxes.

Abstract

Two-phase cooling solutions employing subcooled nucleate boiling flows e.g. thermosyphons, have gained a special interest during the last few decades. This interest stems from their enhanced ability to remove ex-tremely high heat fluxes, while keeping a uniform surface temperature. Consequently, modelling and predicting boiling flows is very important, in order to optimise the two-phase cooling operation and to increase the involved heat transfer coefficients.

In this work, a subcooled boiling model is implemented in the open-source code OpenFOAM to improve and extend its existing solver react-ingTwoPhaseEulerFoam dedicated to model boiling flows. These flows are modelled using Computational Fluid Dynamics (CFD) following the Eulerian two-fluid approach. The simulations are used to evaluate and analyse the existing Active Nucleation Site Density (ANSD) models in the literature. Based on this evaluation, the accuracy of the CFD simulations using existing boiling sub-models is determined, and features leading to improve this accuracy are highlighted. In addition, the CFD simulations are used to perform a sensitivity analysis of the interfacial forces acting on bubbles during boiling flows. Finally, CFD simulation data is employed to study the Onset of Nucleate Boiling (ONB) and to propose a new model for this boiling sub-model, with an improved prediction accuracy and ex-tended validity range.

It is shown in this work that predictions associated with existing boil-ing sub-models are not accurate, and such sub-models need to take into account several convective boiling quantities to improve their accuracy. These quantities are the thermophysical properties of the involved mate-rials, liquid and vapour thermodynamic properties and the heated surface micro-structure properties. Regarding the interfacial momentum transfer, it is shown that all the interfacial forces have considerable effects on boil-ing, except the lift force, which can be neglected without influencing the simulations’ output. The new proposed ONB model takes into account convective boiling features, and it able to predict the ONB with a very good accuracy with a standard deviation of 2.7% or 0.1 K. This new ONB model is valid for a wide range of inlet Reynolds numbers, covering both regimes, laminar and turbulent, and a wide range of inlet subcoolings and applied heat fluxes.

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Acknowledgements

The research in this licentiate thesis was conducted at the Future Energy Center (FEC), Mälardalen University, Västerås, Sweden, with the finan-cial support from the Swedish Knowledge Foundation (KKS), ABB AB, Hitachi ABB Powergrids and Westinghouse Electric Sweden AB.

My first and foremost thanks go to my main supervisor Prof. Rebei Bel Fdhila for his continuous and invaluable guidance, support, sugges-tions and inspiration throughout this thesis work.

I would like to acknowledge my co-supervisors Prof. Konstantinos Kyprianidis and Dr. Ioanna Aslanidou for their guidance and support dur-ing my thesis work.

My special thanks go to my colleagues and friends at my department for many fruitful discussions.

Finally, I would like to show my deepest gratitude to all my family members. Without their support, this thesis would have been impossi-ble. I would like to thank my father, Hedi Rabhi and my mother, Toffaha Harrabi, for supporting me through my journey in this life. Special ac-knowledgements go to my beloved wife Awatef Issaoui, who is sharing with me my ups and downs, my joy and sadness and my success and fail-ure.

Achref Rabhi

Västerås, Sweden, January 2021

Acknowledgements

The research in this licentiate thesis was conducted at the Future Energy Center (FEC), Mälardalen University, Västerås, Sweden, with the finan-cial support from the Swedish Knowledge Foundation (KKS), ABB AB, Hitachi ABB Powergrids and Westinghouse Electric Sweden AB.

My first and foremost thanks go to my main supervisor Prof. Rebei Bel Fdhila for his continuous and invaluable guidance, support, sugges-tions and inspiration throughout this thesis work.

I would like to acknowledge my co-supervisors Prof. Konstantinos Kyprianidis and Dr. Ioanna Aslanidou for their guidance and support dur-ing my thesis work.

My special thanks go to my colleagues and friends at my department for many fruitful discussions.

Finally, I would like to show my deepest gratitude to all my family members. Without their support, this thesis would have been impossi-ble. I would like to thank my father, Hedi Rabhi and my mother, Toffaha Harrabi, for supporting me through my journey in this life. Special ac-knowledgements go to my beloved wife Awatef Issaoui, who is sharing with me my ups and downs, my joy and sadness and my success and fail-ure.

Achref Rabhi

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Summary

The advancement of engineering equipment and industrial processes is usually limited by the ability to dissipate the released heat. Consequently, optimal heat removal will enable the next generation of these equipment and processes. Despite the fact that they were extensively used for cool-ing, single phase cooling means and methods hit their maximum perfor-mance at around 100 W/cm2_{, which can be far below current released heat}

fluxes. Then a novel heat removal method allowing to dissipate extreme heat fluxes is required, while operating at a lower cost. Two-phase cooling and boiling flows allowing heat removal by phase-change are a promising solution to dissipate high heat fluxes, while keeping the surface temper-ature uniform, a few degrees above the saturation point. Such flows can operate at a lower pressure drop, and several orders of magnitude higher heat transfer coefficient can be achieved when operating in their subcooled nucleate boiling heat transfer regime.

This thesis is focused on the Computational Fluid Dynamics (CFD) modelling of the low and moderate pressure subcooled boiling flows in minichannels using the open-source tool OpenFOAM. High fidelity multi-dimensional CFD simulations are carried out to model upward water flow boiling in a narrow rectangular channel (3 mm x 100 mm x 400 mm) heated from one side by a constant heat flux. Several existing boiling sub-models are evaluated and analysed to determine their prediction capabili-ties. It is shown in this thesis that predictions associated with the available boiling sub-models are not accurate. Convective boiling key parameters as the thermophysical properties of the involved materials (density, spe-cific heat capacity and thermal conductivity of the working fluid and the heated surface), liquid-vapour thermodynamic properties (surface tension, contact angle and pressure) and the heated surface micro-properties (av-erage surface roughness and total number of the present micro-cavities) have to be taken into account in a boiling sub-model, in order to improve the prediction’s accuracy.

A sensitivity analysis for the interfacial moment transfer is carried out using CFD simulations of refrigerant boiling flows up narrow annular pipes. This configuration is often met in industrial applications related to power generation. The results show that all the interfacial forces acting on bubbles have significant effects on the boiling field, except the lift force which has a minor effect and can be neglected in the simulations. Within

Summary

The advancement of engineering equipment and industrial processes is usually limited by the ability to dissipate the released heat. Consequently, optimal heat removal will enable the next generation of these equipment and processes. Despite the fact that they were extensively used for cool-ing, single phase cooling means and methods hit their maximum perfor-mance at around 100 W/cm2_{, which can be far below current released heat}

fluxes. Then a novel heat removal method allowing to dissipate extreme heat fluxes is required, while operating at a lower cost. Two-phase cooling and boiling flows allowing heat removal by phase-change are a promising solution to dissipate high heat fluxes, while keeping the surface temper-ature uniform, a few degrees above the saturation point. Such flows can operate at a lower pressure drop, and several orders of magnitude higher heat transfer coefficient can be achieved when operating in their subcooled nucleate boiling heat transfer regime.

This thesis is focused on the Computational Fluid Dynamics (CFD) modelling of the low and moderate pressure subcooled boiling flows in minichannels using the open-source tool OpenFOAM. High fidelity multi-dimensional CFD simulations are carried out to model upward water flow boiling in a narrow rectangular channel (3 mm x 100 mm x 400 mm) heated from one side by a constant heat flux. Several existing boiling sub-models are evaluated and analysed to determine their prediction capabili-ties. It is shown in this thesis that predictions associated with the available boiling sub-models are not accurate. Convective boiling key parameters as the thermophysical properties of the involved materials (density, spe-cific heat capacity and thermal conductivity of the working fluid and the heated surface), liquid-vapour thermodynamic properties (surface tension, contact angle and pressure) and the heated surface micro-properties (av-erage surface roughness and total number of the present micro-cavities) have to be taken into account in a boiling sub-model, in order to improve the prediction’s accuracy.

A sensitivity analysis for the interfacial moment transfer is carried out using CFD simulations of refrigerant boiling flows up narrow annular pipes. This configuration is often met in industrial applications related to power generation. The results show that all the interfacial forces acting on bubbles have significant effects on the boiling field, except the lift force which has a minor effect and can be neglected in the simulations. Within

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this work, the available models of interfacial forces in the literature are implemented and evaluated.

The most accurate models are highlighted and proposed as recommen-dations for future simulations. Using the improved CFD predictions data of subcooled nucleate boiling of water at atmospheric pressure flowing up a narrow rectangular channel heated from one side, a boiling sub-model (the Onset of Nucleate Boiling) is studied and evaluated. The Onset of Nu-cleate Boiling (ONB) marks the transition between the single phase forced convection heat transfer regime to the two-phase subcooled nucleate boil-ing heat transfer regime. The convective dependencies of the ONB are determined and taken into account to develop a new mathematical model for this boiling parameter. The new developed model for the ONB takes into account the inlet Reynolds number, the flow regime, the inlet sub-cooling, the applied heat flux and to the thermophysical properties of the involved materials. This model is characterised by a wide validity range, acquired from the extended range of operating conditions used in the CFD simulations. The new ONB model predictions fall within an accuracy of 2.7% instead of 30% of the majority of the models from the literature.

The work proposed in this thesis consists of a knowledge foundation for the high fidelity CFD simulations of boiling flows. Propositions of boiling sub-models leading to better CFD simulation accuracy are pro-vided. A methodology of building highly accurate boiling sub-models based on CFD simulation data is presented. The work presented here can be used further to develop a hybrid 1D-3D simulation tool, allowing for the optimisation of two-phase cooling operation and schemes, and to ad-dress the thermal management of complex industrial and energy systems.

this work, the available models of interfacial forces in the literature are implemented and evaluated.

The most accurate models are highlighted and proposed as recommen-dations for future simulations. Using the improved CFD predictions data of subcooled nucleate boiling of water at atmospheric pressure flowing up a narrow rectangular channel heated from one side, a boiling sub-model (the Onset of Nucleate Boiling) is studied and evaluated. The Onset of Nu-cleate Boiling (ONB) marks the transition between the single phase forced convection heat transfer regime to the two-phase subcooled nucleate boil-ing heat transfer regime. The convective dependencies of the ONB are determined and taken into account to develop a new mathematical model for this boiling parameter. The new developed model for the ONB takes into account the inlet Reynolds number, the flow regime, the inlet sub-cooling, the applied heat flux and to the thermophysical properties of the involved materials. This model is characterised by a wide validity range, acquired from the extended range of operating conditions used in the CFD simulations. The new ONB model predictions fall within an accuracy of 2.7% instead of 30% of the majority of the models from the literature.

The work proposed in this thesis consists of a knowledge foundation for the high fidelity CFD simulations of boiling flows. Propositions of boiling sub-models leading to better CFD simulation accuracy are pro-vided. A methodology of building highly accurate boiling sub-models based on CFD simulation data is presented. The work presented here can be used further to develop a hybrid 1D-3D simulation tool, allowing for the optimisation of two-phase cooling operation and schemes, and to ad-dress the thermal management of complex industrial and energy systems.

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Sammanfattning

Utveckling och framåtskridande av ingenjörsmässig utrustning och indus-triella processer är ofta begränsat av möjligheten att föra bort den utveck-lade värmen. Därför möjliggör ett optimalt sätt att bortföra värme en nästa generation av utrustning och processer. Trots en omfattande användning av utrustning för kylning så når metoder för enfaskylning sin maximala prestanda vid c:a 100 W/cm2_{, vilket kan vara betydligt lägre än nuvarande}

överförda värmeflöden. Därför krävs en exklusivare/effektivare metod för att bortföra extrema värmeflöden, samtidigt som driftkostnaderna hålls låga. Tvåfaskylning och kokande flöden som genomgår en fasändring är en lovande metod att bortföra höga värmeflöden, samtidigt som yttemper-aturen hålls likformig några grader över mättnadstemperyttemper-aturen. Sådana flöden kan arbeta med låga tryckfall och ett flera gånger större värmeöver-föringstal kan uppnås om mekanismen för värmeöverföring sker i området för underkyld kärnkokning.

Detta arbete fokuserar på CFD modellering av underkylda kokande flöden vid låga och måttliga tryck i mikrokanaler genom att använda det öppna verktyget OpenFOAM. Flerdimensionella CFD simuleringar med trovärdig återkoppling är utförda för att modellera uppåtströmmande kokande vatten i en smal rektangulär kanal (3 mm x 100 mm x 400 mm) vilken värms på ena sidan av ett konstant värmeflöde. Ett flertal befintliga mod-eller för underkyld kokning är utvärderade och analyserade för att fast-ställa deras kapacitet för utfall/resultat. Det visas i detta arbete att ut-fall associerade med befintliga modeller för underkyld kokning inte är noggranna/precisa. Nyckelparametrar vid konvektiv kokning såsom ter-mofysikaliska egenskaper för de inblandade ämnena (densitet, specifikt värme, termisk konduktivitet för arbetsmediet och den uppvärmda ytan), vätske-/ångfas termodynamiska egenskaper (ytspänning, kontaktvinkel och tryck) och den uppvärmda ytans mikroegenskaper (medelvärde på ytråhet och totala antalet mikrokaviteter) måste beaktas i en modell för underkyld kokning för att förbättra utfallets noggrannhet.

En känslighetsanalys för transport av rörelsemängd mellan två ytor vid kokande köldmedium, som strömmar uppåt i smala cirkulära rör, är utfört med hjälp av CFD simuleringar. Denna konfiguration ses ofta i in-dustriella applikationer relaterade till kraftproduktion. Resultaten visar att alla krafter som verkar på bubblor mellan två ytor har signifikant påverkan

Sammanfattning

Utveckling och framåtskridande av ingenjörsmässig utrustning och indus-triella processer är ofta begränsat av möjligheten att föra bort den utveck-lade värmen. Därför möjliggör ett optimalt sätt att bortföra värme en nästa generation av utrustning och processer. Trots en omfattande användning av utrustning för kylning så når metoder för enfaskylning sin maximala prestanda vid c:a 100 W/cm2_{, vilket kan vara betydligt lägre än nuvarande}

överförda värmeflöden. Därför krävs en exklusivare/effektivare metod för att bortföra extrema värmeflöden, samtidigt som driftkostnaderna hålls låga. Tvåfaskylning och kokande flöden som genomgår en fasändring är en lovande metod att bortföra höga värmeflöden, samtidigt som yttemper-aturen hålls likformig några grader över mättnadstemperyttemper-aturen. Sådana flöden kan arbeta med låga tryckfall och ett flera gånger större värmeöver-föringstal kan uppnås om mekanismen för värmeöverföring sker i området för underkyld kärnkokning.

Detta arbete fokuserar på CFD modellering av underkylda kokande flöden vid låga och måttliga tryck i mikrokanaler genom att använda det öppna verktyget OpenFOAM. Flerdimensionella CFD simuleringar med trovärdig återkoppling är utförda för att modellera uppåtströmmande kokande vatten i en smal rektangulär kanal (3 mm x 100 mm x 400 mm) vilken värms på ena sidan av ett konstant värmeflöde. Ett flertal befintliga mod-eller för underkyld kokning är utvärderade och analyserade för att fast-ställa deras kapacitet för utfall/resultat. Det visas i detta arbete att ut-fall associerade med befintliga modeller för underkyld kokning inte är noggranna/precisa. Nyckelparametrar vid konvektiv kokning såsom ter-mofysikaliska egenskaper för de inblandade ämnena (densitet, specifikt värme, termisk konduktivitet för arbetsmediet och den uppvärmda ytan), vätske-/ångfas termodynamiska egenskaper (ytspänning, kontaktvinkel och tryck) och den uppvärmda ytans mikroegenskaper (medelvärde på ytråhet och totala antalet mikrokaviteter) måste beaktas i en modell för underkyld kokning för att förbättra utfallets noggrannhet.

En känslighetsanalys för transport av rörelsemängd mellan två ytor vid kokande köldmedium, som strömmar uppåt i smala cirkulära rör, är utfört med hjälp av CFD simuleringar. Denna konfiguration ses ofta i in-dustriella applikationer relaterade till kraftproduktion. Resultaten visar att alla krafter som verkar på bubblor mellan två ytor har signifikant påverkan

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på kokområdet, med undantag av lyftkraften som har en minimal påverkan och kan försummas vid simuleringarna.

I detta arbete har tillgängliga modeller, som finns i litteraturen, för krafter mellan två ytor implementerats och utvärderats. De mest nog-granna/exakta modellerna är framhävda här och föreslagna som rekom-mendationer för framtida simuleringar. Genom att använda förbättrade CFD data för underkyld kärnkokning av vatten vid atmosfärstryck som flödar uppåt i smala rektangulära kanaler, värmda från ena sidan, så kan en modell för underkyld kokning (ONB) studeras och utvärderas. Då kärnkokning startar (ONB) sker ett omslag från enfas påtvingad konvek-tiv värmeöverföring till värmeöverföring vid tvåfas underkyld kärnkokn-ing. De konvektiva beroendena som påverkar vid kärnkokning fastställs och tas i beaktelse för att utveckla en ny matematisk modell för denna kokparameter. Den nya utvecklade modellen för kärnkokning involverar Reynolds tal vid inloppet, flödesområdet, underkylning vid inloppet, det pålagda värmeflödet samt termofysikaliska data för de inblandade mate-rialen. Denna modell kännetecknas av ett stort giltighetsintervall, erhål-let från den utökade vidden av driftvillkor som använts vid CFD simu-leringarna. Den nya modellen för kärnkokning ger utfall med en nog-grannhet på 2.7% istället för 30% som de flesta modeller i litteraturen. Det föreslagna arbetet här består av en kunskapsbas för trovärdiga CFD simuleringar av kokande flöden. Modeller för underkyld kärnkokning som skall leda till noggrannare/bättre CFD modelleringar är presenterade. En metodik för att bygga noggranna modeller för underkyld kärnkokning baserade på CFD simuleringar är presenterad. Arbetet som presenteras här kan användas vidare för att utveckla ett hybrid 1D-3D simuleringsverktyg som kan användas för optimering av drift och system med tvåfas kylning samt att termiskt förvalta komplexa industriella energisystem.

på kokområdet, med undantag av lyftkraften som har en minimal påverkan och kan försummas vid simuleringarna.

I detta arbete har tillgängliga modeller, som finns i litteraturen, för krafter mellan två ytor implementerats och utvärderats. De mest nog-granna/exakta modellerna är framhävda här och föreslagna som rekom-mendationer för framtida simuleringar. Genom att använda förbättrade CFD data för underkyld kärnkokning av vatten vid atmosfärstryck som flödar uppåt i smala rektangulära kanaler, värmda från ena sidan, så kan en modell för underkyld kokning (ONB) studeras och utvärderas. Då kärnkokning startar (ONB) sker ett omslag från enfas påtvingad konvek-tiv värmeöverföring till värmeöverföring vid tvåfas underkyld kärnkokn-ing. De konvektiva beroendena som påverkar vid kärnkokning fastställs och tas i beaktelse för att utveckla en ny matematisk modell för denna kokparameter. Den nya utvecklade modellen för kärnkokning involverar Reynolds tal vid inloppet, flödesområdet, underkylning vid inloppet, det pålagda värmeflödet samt termofysikaliska data för de inblandade mate-rialen. Denna modell kännetecknas av ett stort giltighetsintervall, erhål-let från den utökade vidden av driftvillkor som använts vid CFD simu-leringarna. Den nya modellen för kärnkokning ger utfall med en nog-grannhet på 2.7% istället för 30% som de flesta modeller i litteraturen. Det föreslagna arbetet här består av en kunskapsbas för trovärdiga CFD simuleringar av kokande flöden. Modeller för underkyld kärnkokning som skall leda till noggrannare/bättre CFD modelleringar är presenterade. En metodik för att bygga noggranna modeller för underkyld kärnkokning baserade på CFD simuleringar är presenterad. Arbetet som presenteras här kan användas vidare för att utveckla ett hybrid 1D-3D simuleringsverktyg som kan användas för optimering av drift och system med tvåfas kylning samt att termiskt förvalta komplexa industriella energisystem.

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List of papers

Publications included in the thesis

This thesis is based on the following papers, which are referred to in the text by their roman numerals:

I. Rabhi, A. and Bel Fdhila, R. (2019). Numerical Evaluation and Analysis of Active Nucleation Site Density Models in Boiling. In Proc. of The Second Pacific Rim Thermal Engineering Conference, PRTEC-24140, December 13-19, 2019, Maui, Hawaii, USA. II. Rabhi, A., Aslanidou, I., Kyprianidis, K. and Bel Fdhila, R. (2020).

CFD Investigations of Subcooled Nucleate Boiling Flows and Act-ing Interfacial Forces in Concentric Pipes. In Proc. of the 61st

Inter-national Conference of Scandinavian Simulation Society, SIMS-36, September 22-24, 2020, Oulu, Finland.

III. Rabhi, A., Aslanidou, I., Kyprianidis, K. and Bel Fdhila, R. (2021). Onset of Nucleate Boiling for Rectangular Upward Narrow Chan-nel: CFD Based Approach. International Journal of Heat and Mass Transfer, Volume 165, Part B:120715.

Reprints were made with permission from the publishers.

The author’s contribution to the included publications

In all the appended papers (Paper I, II and III), the author (Achref Rabhi) conceptualised, performed the numerical simulations, analysed the nu-merical results and wrote the drafts and the final versions of the papers.

Publications not included in the thesis

• Soibam, J., Rabhi, A., Aslanidou, I., Kyprianidis, K. and Bel Fd-hila, R. (2020). Derivation and Uncertainty Quantification of a Data-Driven Subcooled Boiling Model. Energies 13(22):5987.

List of papers

Publications included in the thesis

This thesis is based on the following papers, which are referred to in the text by their roman numerals:

I. Rabhi, A. and Bel Fdhila, R. (2019). Numerical Evaluation and Analysis of Active Nucleation Site Density Models in Boiling. In Proc. of The Second Pacific Rim Thermal Engineering Conference, PRTEC-24140, December 13-19, 2019, Maui, Hawaii, USA. II. Rabhi, A., Aslanidou, I., Kyprianidis, K. and Bel Fdhila, R. (2020).

CFD Investigations of Subcooled Nucleate Boiling Flows and Act-ing Interfacial Forces in Concentric Pipes. In Proc. of the 61st

Inter-national Conference of Scandinavian Simulation Society, SIMS-36, September 22-24, 2020, Oulu, Finland.

III. Rabhi, A., Aslanidou, I., Kyprianidis, K. and Bel Fdhila, R. (2021). Onset of Nucleate Boiling for Rectangular Upward Narrow Chan-nel: CFD Based Approach. International Journal of Heat and Mass Transfer, Volume 165, Part B:120715.

Reprints were made with permission from the publishers.

The author’s contribution to the included publications

In all the appended papers (Paper I, II and III), the author (Achref Rabhi) conceptualised, performed the numerical simulations, analysed the nu-merical results and wrote the drafts and the final versions of the papers.

Publications not included in the thesis

• Soibam, J., Rabhi, A., Aslanidou, I., Kyprianidis, K. and Bel Fd-hila, R. (2020). Derivation and Uncertainty Quantification of a Data-Driven Subcooled Boiling Model. Energies 13(22):5987.

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List of figures

1.1 Pumping power requirements for a squared channelled heat

sinks of 1 mm dimension (adapted from Green et al. (2009)). . 2

1.2 Range of channel sizes employed in various applications (adapted from Kandlikar and Steinke (2003)). . . 3

1.3 Schematic view of the research methodology followed in this thesis (adapted from Leedy and Ormrod (2015)). . . 9

1.4 Schematic view of the relationship between the research top-ics and the appended papers with the formulated research ques-tions. . . 10

2.1 Phenomenology of boiling flows (adapted from Sphaier et al. (2017)). . . 13

2.2 Flow regimes in a vertical evaporator tube (adapted from Col-lier and Thome (1994)). . . 15

2.3 Boiling curve (adapted from Stephan (1992)). . . 16

3.1 Eulerian two-fluid framework to model boiling flows. . . 29

3.2 Schematic view of the experimental test body of Al-Maeeni (2015) and Kromer et al. (2016). . . 32

3.3 Computational domain and mesh adopted in the simulations of CS1. . . 33

3.5 Heat flux variation with the wall superheat near the ONB (adapted from Carey (2018)). . . 40

4.1 Graphical abstract for Paper I. . . 43

4.2 Graphical abstract for Paper II. . . 44

4.3 Graphical abstract for Paper III. . . 45

5.1 CFD predictions of the heated surface temperature associated with each tested ANSD model compared with the experimen-tal data of Al-Maeeni (2015) and Kromer et al. (2016). . . 47

5.2 Radial boiling fields predictions by the CFD with different interfacial forces vs. experimental data of Roy et al. (2002): a. Void fraction, b. Liquid temperature, c. Liquid velocity, d. Vapour velocity. . . 50

List of figures

1.1 Pumping power requirements for a squared channelled heat sinks of 1 mm dimension (adapted from Green et al. (2009)). . 2

1.2 Range of channel sizes employed in various applications (adapted from Kandlikar and Steinke (2003)). . . 3

1.3 Schematic view of the research methodology followed in this thesis (adapted from Leedy and Ormrod (2015)). . . 9

1.4 Schematic view of the relationship between the research top-ics and the appended papers with the formulated research ques-tions. . . 10

2.1 Phenomenology of boiling flows (adapted from Sphaier et al. (2017)). . . 13

2.2 Flow regimes in a vertical evaporator tube (adapted from Col-lier and Thome (1994)). . . 15

2.3 Boiling curve (adapted from Stephan (1992)). . . 16

3.1 Eulerian two-fluid framework to model boiling flows. . . 29

3.2 Schematic view of the experimental test body of Al-Maeeni (2015) and Kromer et al. (2016). . . 32

3.5 Heat flux variation with the wall superheat near the ONB (adapted from Carey (2018)). . . 40

4.1 Graphical abstract for Paper I. . . 43

4.2 Graphical abstract for Paper II. . . 44

4.3 Graphical abstract for Paper III. . . 45

5.1 CFD predictions of the heated surface temperature associated with each tested ANSD model compared with the experimen-tal data of Al-Maeeni (2015) and Kromer et al. (2016). . . 47

5.2 Radial boiling fields predictions by the CFD with different interfacial forces vs. experimental data of Roy et al. (2002): a. Void fraction, b. Liquid temperature, c. Liquid velocity, d. Vapour velocity. . . 50

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5.3 Radial boiling fields predictions by the CFD with different lift coefficients models vs. experimental data of Roy et al. (2002): a. Void fraction, b. Liquid temperature, c. Liquid velocity, d. Vapour velocity. . . 51 5.4 CFD prediction of the void fraction near the heated surface at

an inlet subcooling of 5 K: a. Fixed inlet Reynolds number of 1878 with variable heat flux, b. Fixed inlet Reynolds number of 3756 with variable heat flux, c. Variable inlet Reynolds number with fixed heat flux of 50 kW/m2_{. . . 53}

5.5 The new ONB model predictions comparison with current ONB data and predictions of correlations from the literature at∆Tsub,in = 5 K: a. Rein = 939, b. Rein = 1409, c. Rein =

1878, d. Rein = 2348, e. Rein = 2818, f. Rein= 3757. . . 55

5.6 The new ONB model predictions compared with ONB current data: a. Different inlet Reynolds numbers, b. Different inlet subcoolings. . . 56 5.7 Comparison between the predicted ONB superheats by the

new model and the current ONB superheat data. . . 57 A.1 Heat flux decomposition according to the RPI model. . . 84

5.3 Radial boiling fields predictions by the CFD with different lift coefficients models vs. experimental data of Roy et al. (2002): a. Void fraction, b. Liquid temperature, c. Liquid velocity, d. Vapour velocity. . . 51 5.4 CFD prediction of the void fraction near the heated surface at

an inlet subcooling of 5 K: a. Fixed inlet Reynolds number of 1878 with variable heat flux, b. Fixed inlet Reynolds number of 3756 with variable heat flux, c. Variable inlet Reynolds number with fixed heat flux of 50 kW/m2_{. . . 53}

5.5 The new ONB model predictions comparison with current ONB data and predictions of correlations from the literature at∆Tsub,in = 5 K: a. Rein = 939, b. Rein = 1409, c. Rein =

1878, d. Rein= 2348, e. Rein= 2818, f. Rein = 3757. . . 55

5.6 The new ONB model predictions compared with ONB current data: a. Different inlet Reynolds numbers, b. Different inlet subcoolings. . . 56 5.7 Comparison between the predicted ONB superheats by the

new model and the current ONB superheat data. . . 57 A.1 Heat flux decomposition according to the RPI model. . . 84

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List of tables

1.1 Channel classification scheme adopted in this thesis following Kandlikar and Grande (2003). . . 4 1.2 Relationship between the research questions and the appended

papers. . . 10 2.1 Existing ANSD models in the literature. . . 23 3.1 Heated surface temperature measurements by Al-Maeeni (2015)

and Kromer et al. (2016). . . 32 3.2 Test matrix for Roy et al. (2002) experiment. . . 35 3.3 Used interfacial forces in the simulations of CS2. . . 37 3.4 Operating conditions for the simulations performed in CS3. . . 39 5.1 Wall superheat for different inlet subcoolings. . . 54 A.1 The standard k − ε turbulence model constants (Launder and

Spalding, 1972). . . 83

List of tables

1.1 Channel classification scheme adopted in this thesis following Kandlikar and Grande (2003). . . 4 1.2 Relationship between the research questions and the appended

papers. . . 10 2.1 Existing ANSD models in the literature. . . 23 3.1 Heated surface temperature measurements by Al-Maeeni (2015)

and Kromer et al. (2016). . . 32 3.2 Test matrix for Roy et al. (2002) experiment. . . 35 3.3 Used interfacial forces in the simulations of CS2. . . 37 3.4 Operating conditions for the simulations performed in CS3. . . 39 5.1 Wall superheat for different inlet subcoolings. . . 54 A.1 The standard k − ε turbulence model constants (Launder and

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Nomenclature

Abbreviations

ANSD Active Nucleation Site Density

BDD Bubble Departure Diameter

BDF Bubble Departure Frequency

CFD Computational Fluid Dynamics

CHF Critical Heat Flux

CS Case Study

ONB Onset of Nucleate Boiling

OSV Onset of Significant Void

RANS Reynolds Averaged Navier-Stokes

RDT Rapid Distortion Theory

RPI Rensselaer Polytechnic Institute

RQ Research Question

VoF Volume of Fluid

Special characters

α Phase fraction

Γ Mass transfer rate per unit volume

γ Coefficient in the ONB model or evaporation mass flux per

unit area

κv Interfacial curvature

λ Thermal conductivity

µ Dynamic viscosity

ν Kinematic viscosity

Ψ Correction factor in the ONB model

ρ Density

Nomenclature

Abbreviations

ANSD Active Nucleation Site Density

BDD Bubble Departure Diameter

BDF Bubble Departure Frequency

CFD Computational Fluid Dynamics

CHF Critical Heat Flux

CS Case Study

ONB Onset of Nucleate Boiling

OSV Onset of Significant Void

RANS Reynolds Averaged Navier-Stokes

RDT Rapid Distortion Theory

RPI Rensselaer Polytechnic Institute

RQ Research Question

VoF Volume of Fluid

Special characters

α Phase fraction

Γ Mass transfer rate per unit volume

γ Coefficient in the ONB model or evaporation mass flux per

unit area

κv Interfacial curvature

λ Thermal conductivity

µ Dynamic viscosity

ν Kinematic viscosity

Ψ Correction factor in the ONB model

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σ Surface tension

θ Contact angle

ε Dissipation rate of the turbulent kinetic energy

Subscripts

b Bubble

c Cavity, Convective or Critical

D Drag e Evaporation f c Forced convection H Hydraulic k Phase indicator L Lift

l Liquid phase indicator

out Outlet q Quenching re f Reference sat Saturation T D Turbulent dispersion th Thermal

v Vapour phase indicator

V M Virtual mass

w Wall

W L Wall lubrication

ONB Quantity at the ONB

Superscripts ∗ Modified or non-dimensional e f f Effective T Transpose σ Surface tension θ Contact angle

ε Dissipation rate of the turbulent kinetic energy

Subscripts

b Bubble

c Cavity, Convective or Critical

D Drag e Evaporation f c Forced convection H Hydraulic k Phase indicator L Lift

l Liquid phase indicator

out Outlet q Quenching re f Reference sat Saturation T D Turbulent dispersion th Thermal

v Vapour phase indicator

V M Virtual mass

w Wall

W L Wall lubrication

ONB Quantity at the ONB

Superscripts

∗ Modified or non-dimensional

e f f Effective

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t Turbulent Symbols

∆Tsub Subcooling (Tsat− T )

∆Tsup Superheat (T − Tsat)

n Normal unit vector

Ur Relative velocity (Uv-Ul)

AB Surface area fraction affected by boiling

ai Interfacial area concentration

ANB Surface area fraction not affected by boiling

C Force coefficient

Cp Specific heat capacity

C(µ,1,2,3) k − ε turbulence model coefficients

Cw,(1,2,c,d) Empirical coefficients D Diameter d Diameter ddep BDD Dth Thermal diffusivity f Function fdep BDF

Gprod Production of the turbulent kinetic energy

h Specific enthalpy or Heat transfer coefficient

hlv Enthalpy of vaporisation

k Kinematic turbulent energy

Lc Characteristic length

m Coefficient in the ONB model

Na ANSD p Pressure Q Heat q” _{Heat flux} t Turbulent Symbols

∆Tsub Subcooling (Tsat− T )

∆Tsup Superheat (T − Tsat)

n Normal unit vector

Ur Relative velocity (Uv-Ul)

AB Surface area fraction affected by boiling

ai Interfacial area concentration

ANB Surface area fraction not affected by boiling

C Force coefficient

Cp Specific heat capacity

C(µ,1,2,3) k − ε turbulence model coefficients

Cw,(1,2,c,d) Empirical coefficients D Diameter d Diameter ddep BDD Dth Thermal diffusivity f Function fdep BDF

Gprod Production of the turbulent kinetic energy

h Specific enthalpy or Heat transfer coefficient

hlv Enthalpy of vaporisation

k Kinematic turbulent energy

Lc Characteristic length

m Coefficient in the ONB model

Na ANSD

p Pressure

Q Heat

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r Radius

S Suppression factor

Sε Turbulence coupling term

tw Bubble waiting time

x Mass quality

Y Corrected wall thermal function

y Distance from the wall

y+ _{Wall function}

F Force per unit volume

g Gravitational acceleration I Identity tensor M Momentum transfer R Stress tensor U Velocity vector Bo Boiling number (q” w/(˙mhlv)) Eo Eötvös number (∆ρgLc/σ) Ja Jakob number (Cp∆T/hlv) Nu Nusselt number (hLc/λ) Pr Prandtl number (µCp/λ)

Re Reynolds number (ULc/ν)

r Radius

S Suppression factor

Sε Turbulence coupling term

tw Bubble waiting time

x Mass quality

Y Corrected wall thermal function

y Distance from the wall

y+ _{Wall function}

F Force per unit volume

g Gravitational acceleration I Identity tensor M Momentum transfer R Stress tensor U Velocity vector Bo Boiling number (q” w/(˙mhlv)) Eo Eötvös number (∆ρgLc/σ) Ja Jakob number (Cp∆T/hlv) Nu Nusselt number (hLc/λ) Pr Prandtl number (µCp/λ)

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Preface

This thesis is submitted in partial fulfilment of the requirement for a licen-tiate degree in Energy and Environmental Engineering at Mälardalen University.

The licentiate degree, customary to many Swedish Universities, is an intermediate degree that Ph.D. candidates are encouraged to fulfil. The notion is unfamiliar in most other countries, and hence it is difficult to relate. However, the licentiate degree is acknowledged as a degree in Sweden, but for many Ph.D. candidates the licentiate thesis is merely a "midterm-report".

Preface

This thesis is submitted in partial fulfilment of the requirement for a licen-tiate degree in Energy and Environmental Engineering at Mälardalen University.

The licentiate degree, customary to many Swedish Universities, is an intermediate degree that Ph.D. candidates are encouraged to fulfil. The notion is unfamiliar in most other countries, and hence it is difficult to relate. However, the licentiate degree is acknowledged as a degree in Sweden, but for many Ph.D. candidates the licentiate thesis is merely a "midterm-report".

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1 Introduction

This chapter presents the research background, motivations behind this work and the formulated research questions based on identified literature gaps. The research methodology and framework are presented next, with the relationship between the research topics and the appended papers. At the end of this chapter, the thesis outline is presented.

1.1 Background

World population and economic growth have significantly increased in the past few years. These have led to higher and continuously growing de-mands for food, energy and power supply, faster communications, faster data transfer and storage, efficient transportation and shipping and ad-vanced wellness and health care. Consequently, many engineering fields and industrial processes have been competitively advanced. Among these fields and processes, one can cite nuclear engineering, power-electronics and computer data centres, transportation means, military applications, food production and conservation industry. Nevertheless, the main lim-iting factor for the development of advanced technologies is often the large heat release. An optimal, efficient and safe operation requires an in-evitably systematic heat removal. However, the recent advances in these engineering fields and industrial processes have led to an alarming heat release that has pushed the traditional air or liquid single-phase cooling means to hit their performance ceiling at 100 W/cm2_{(Anderson and}

Mu-dawar, 1989; Saenen, 2013).

Generally, heat generation varies significantly with the considered tech-nology. Densely packed integrated circuits and laser mirrors generate heat fluxes in the order of 102 W/cm2_{(Phillips, 1988; Pop and Goodson, 2006;}

Ali, 2010). Heat fluxes in the order of 103 W/cm2_{are encountered in}

avi-ation and space applicavi-ations (Lee and Mudawar, 2008), while defence applications can release heat fluxes in the order of 104 W/cm2 _{(Lee and}

Mudawar, 2009; Kandlikar, 2005). Even so, extreme heat fluxes of 300 W/cm2 _{can be released by computer chips (Saha and Celata, 2015). All}

these heat releases for different technologies by far exceed the heat re-moval ability of the most complicated air or liquid single-phase cooling schemes, and a new efficient heat removal method is needed with high pri-ority. Two-phase cooling means and boiling flows allowing phase-change

1 Introduction

This chapter presents the research background, motivations behind this work and the formulated research questions based on identified literature gaps. The research methodology and framework are presented next, with the relationship between the research topics and the appended papers. At the end of this chapter, the thesis outline is presented.

1.1 Background

World population and economic growth have significantly increased in the past few years. These have led to higher and continuously growing de-mands for food, energy and power supply, faster communications, faster data transfer and storage, efficient transportation and shipping and ad-vanced wellness and health care. Consequently, many engineering fields and industrial processes have been competitively advanced. Among these fields and processes, one can cite nuclear engineering, power-electronics and computer data centres, transportation means, military applications, food production and conservation industry. Nevertheless, the main lim-iting factor for the development of advanced technologies is often the large heat release. An optimal, efficient and safe operation requires an in-evitably systematic heat removal. However, the recent advances in these engineering fields and industrial processes have led to an alarming heat release that has pushed the traditional air or liquid single-phase cooling means to hit their performance ceiling at 100 W/cm2_{(Anderson and}

Mu-dawar, 1989; Saenen, 2013).

Generally, heat generation varies significantly with the considered tech-nology. Densely packed integrated circuits and laser mirrors generate heat fluxes in the order of 102 W/cm2_{(Phillips, 1988; Pop and Goodson, 2006;}

Ali, 2010). Heat fluxes in the order of 103 W/cm2_{are encountered in}

avi-ation and space applicavi-ations (Lee and Mudawar, 2008), while defence applications can release heat fluxes in the order of 104 W/cm2 _{(Lee and}

Mudawar, 2009; Kandlikar, 2005). Even so, extreme heat fluxes of 300 W/cm2 _{can be released by computer chips (Saha and Celata, 2015). All}

these heat releases for different technologies by far exceed the heat re-moval ability of the most complicated air or liquid single-phase cooling schemes, and a new efficient heat removal method is needed with high pri-ority. Two-phase cooling means and boiling flows allowing phase-change

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Solutions Using OpenFOAM

Figure 1.1: Pumping power requirements for a squared channelled heat sinks of 1 mm dimension (adapted from Green et al. (2009)).

heat removal showed their ability to overcome such extreme heats, and these flows are the main focus of this thesis.

1.1.1 Two-phase cooling

Two-phase cooling is obtained for systems where phase-change is allowed for the coolant. The resulted flows are referred to as boiling flows, and they are the main subject of this thesis following the motivations and at-tributes that will be presented next.

Two-phase cooling methods and technologies are a promising solution to dissipate extremely high heat fluxes, while keeping a low and uniform surface temperature. They are much more preferred to traditional liquid or air single-phase cooling solutions from two main considerations. First, two-phase cooling allowing phase-change to capitalise the latent heat of vaporisation of the coolant in addition to its sensible heat, instead of the coolant’s sensible heat alone as for single-phase cooling. This allows the achievement of extremely high heat transfer coefficients. For example, with laminar flow of water in a 200 µm square channel, a heat transfer coefficient of 104_W/(m2_{·K) can be achieved, whereas if phase-change and}

convective boiling are allowed, a heat transfer coefficient of 105_W/(m2_·K)

can be reached (Steinke and Kandlikar, 2004). Second, two-phase cooling provides higher heat removal ability for the same given mass flow rate of the coolant, compared to single-phase cooling. The required pumping power to dissipate a given heat amount obtained for a square channelled heat sink of 1 mm dimension is given in Figure 1.1. This figure shows that water phase-change cooling at an outlet quality of xout∼ 1 outperforms the

Figure 1.1: Pumping power requirements for a squared channelled heat sinks of 1 mm dimension (adapted from Green et al. (2009)).

heat removal showed their ability to overcome such extreme heats, and these flows are the main focus of this thesis.

1.1.1 Two-phase cooling

Two-phase cooling is obtained for systems where phase-change is allowed for the coolant. The resulted flows are referred to as boiling flows, and they are the main subject of this thesis following the motivations and at-tributes that will be presented next.

Two-phase cooling methods and technologies are a promising solution to dissipate extremely high heat fluxes, while keeping a low and uniform surface temperature. They are much more preferred to traditional liquid or air single-phase cooling solutions from two main considerations. First, two-phase cooling allowing phase-change to capitalise the latent heat of vaporisation of the coolant in addition to its sensible heat, instead of the coolant’s sensible heat alone as for single-phase cooling. This allows the achievement of extremely high heat transfer coefficients. For example, with laminar flow of water in a 200 µm square channel, a heat transfer coefficient of 104_W/(m2_{·K) can be achieved, whereas if phase-change and}

convective boiling are allowed, a heat transfer coefficient of 105_W/(m2_·K)

can be reached (Steinke and Kandlikar, 2004). Second, two-phase cooling provides higher heat removal ability for the same given mass flow rate of the coolant, compared to single-phase cooling. The required pumping power to dissipate a given heat amount obtained for a square channelled heat sink of 1 mm dimension is given in Figure 1.1. This figure shows that water phase-change cooling at an outlet quality of xout∼ 1 outperforms the

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Figure 1.2: Range of channel sizes employed in various applications (adapted from Kandlikar and Steinke (2003)).

single-phase liquid and air cooling in terms of minimising pumping power for the same heat or power dissipation. From single-phase air cooling to two-phase water cooling, 7 less orders of magnitude in pumping power are required by the phase-change cooling to dissipate the same amount of heat. Consequently, from an economic point of view, two-phase cooling means are much more efficient than single-phase cooling means.

Being encouraged by these attributes, two-phase cooling methods ob-served exponential growth in all engineering disciplines. Boiling flows are now integral parts in power generation, thermal management, chem-ical, space, cryogenics, and other industries (Ozawa et al., 2001; Bergles et al., 2003).

1.1.2 Mini- and microchannel flows

Fluid flow inside a channel and the associated heat and mass transfer across its walls exist extensively in several natural and industrial systems. They are widely presented in biological systems such as in lungs, kidneys, intestines and blood vessels, as well as in industrial and engineering pro-cesses, such as heat exchangers, nuclear systems, cooling schemes, etc. In these internal flows, the cross-section of channels serves as conduit to transport the bulk fluid to and away from the channel’s walls, while across the walls heat and mass transport processes occur.

The range of channel sizes employed in various applications is pre-sented in Figure 1.2. It is clear that from an engineering perspective, there has been a steady shift from larger diameters in the order of 20 mm to smaller size channels in the range of millimetres and hundreds of

mi-Figure 1.2: Range of channel sizes employed in various applications (adapted from Kandlikar and Steinke (2003)).

single-phase liquid and air cooling in terms of minimising pumping power for the same heat or power dissipation. From single-phase air cooling to two-phase water cooling, 7 less orders of magnitude in pumping power are required by the phase-change cooling to dissipate the same amount of heat. Consequently, from an economic point of view, two-phase cooling means are much more efficient than single-phase cooling means.

Being encouraged by these attributes, two-phase cooling methods ob-served exponential growth in all engineering disciplines. Boiling flows are now integral parts in power generation, thermal management, chem-ical, space, cryogenics, and other industries (Ozawa et al., 2001; Bergles et al., 2003).

1.1.2 Mini- and microchannel flows

Fluid flow inside a channel and the associated heat and mass transfer across its walls exist extensively in several natural and industrial systems. They are widely presented in biological systems such as in lungs, kidneys, intestines and blood vessels, as well as in industrial and engineering pro-cesses, such as heat exchangers, nuclear systems, cooling schemes, etc. In these internal flows, the cross-section of channels serves as conduit to transport the bulk fluid to and away from the channel’s walls, while across the walls heat and mass transport processes occur.

The range of channel sizes employed in various applications is pre-sented in Figure 1.2. It is clear that from an engineering perspective, there has been a steady shift from larger diameters in the order of 20 mm to smaller size channels in the range of millimetres and hundreds of

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mi-Solutions Using OpenFOAM

Table 1.1: Channel classification scheme adopted in this thesis following Kandlikar and Grande (2003).

Channel type Diameter

Conventional channels 3 mm ≤ D

Minichannels 200µm ≤ D ≤ 3 mm

Microchannels D ≤ 200 µm

crometres. This shift is encountered especially in heat and mass trans-fer equipment, mainly for efficiency purposes. In fact, the rate of the heat and mass transfer, and of the transport processes generally, depends on the available surface area to transfer, which varies with the channel hydraulic diameter, while the flow rate depends on the square of this hy-draulic diameter. Thus, the ratio of the surface area to the volume varies as the inverse of the hydraulic diameter. Consequently, as this diameter decreases, more surface area to volume ratio is obtained (Kandlikar et al., 2005). Small-sized channels are then characterised with an improved ther-mal hydraulic performance, that allows larger heat transfer area per unit flow volume. Accordingly, when phase-change is allowed, higher overall heat transfer coefficients are achieved compared with phase-change heat removal in bigger sized channels (Thome and Ribatski, 2005). Following these attributes, minichannel boiling flows are considered in this thesis.

Consequently, channel classification should be made, since the chan-nel’s size reduction has different effects on different processes (Kandlikar et al., 2005). Several classifications can be found in the literature based on simple dimensional classification or on physical parameters that govern transitions from regular to microscale phenomena (Mehendale et al., 2000; Kandlikar and Grande, 2003). In the scope of this work, the physically based channel classification proposed by Kandlikar and Grande (2003) and presented in Table 1.1 is adopted. This classification proposes diame-ters higher than 3 mm for conventionally sized channels, diamediame-ters within 3 mm and 200µm for minichannels and diameters less than 200 µm for microchannels.

1.2 Motivations and research challenges

Cooling in the aforementioned industrial applications is of great impor-tance. It allows dissipation of the released heats, and will ensure opti-mal and safe operation, as well as technology advancement and the next generations of engineering devices. However, the most advanced cooling schemes evolving single-phase flows fail to dissipate such large heat dis-sipation, as discussed previously in §1.1. An alternative approach and a

Table 1.1: Channel classification scheme adopted in this thesis following Kandlikar and Grande (2003).

Channel type Diameter

Conventional channels 3 mm ≤ D

Minichannels 200µm ≤ D ≤ 3 mm

Microchannels D ≤ 200 µm

crometres. This shift is encountered especially in heat and mass trans-fer equipment, mainly for efficiency purposes. In fact, the rate of the heat and mass transfer, and of the transport processes generally, depends on the available surface area to transfer, which varies with the channel hydraulic diameter, while the flow rate depends on the square of this hy-draulic diameter. Thus, the ratio of the surface area to the volume varies as the inverse of the hydraulic diameter. Consequently, as this diameter decreases, more surface area to volume ratio is obtained (Kandlikar et al., 2005). Small-sized channels are then characterised with an improved ther-mal hydraulic performance, that allows larger heat transfer area per unit flow volume. Accordingly, when phase-change is allowed, higher overall heat transfer coefficients are achieved compared with phase-change heat removal in bigger sized channels (Thome and Ribatski, 2005). Following these attributes, minichannel boiling flows are considered in this thesis.

Consequently, channel classification should be made, since the chan-nel’s size reduction has different effects on different processes (Kandlikar et al., 2005). Several classifications can be found in the literature based on simple dimensional classification or on physical parameters that govern transitions from regular to microscale phenomena (Mehendale et al., 2000; Kandlikar and Grande, 2003). In the scope of this work, the physically based channel classification proposed by Kandlikar and Grande (2003) and presented in Table 1.1 is adopted. This classification proposes diame-ters higher than 3 mm for conventionally sized channels, diamediame-ters within 3 mm and 200µm for minichannels and diameters less than 200 µm for microchannels.

1.2 Motivations and research challenges

Cooling in the aforementioned industrial applications is of great impor-tance. It allows dissipation of the released heats, and will ensure opti-mal and safe operation, as well as technology advancement and the next generations of engineering devices. However, the most advanced cooling schemes evolving single-phase flows fail to dissipate such large heat dis-sipation, as discussed previously in §1.1. An alternative approach and a

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promising heat removal solution consists of employing two-phase cooling means involving phase-change heat removal. Several orders of magnitude of the heat transfer coefficients are achieved when employing two-phase cooling and boiling flow means, since these flows combine the latent and the sensible heats of the coolant, rather than the sensible heat alone when phase-change is excluded.

The largest heat transfer coefficients are achieved when operating in the subcooled nucleate boiling heat transfer regimes, that is anterior to the single-phase forced convection heat transfer regime and posterior to the saturated boiling heat transfer regime as presented in the literature review of Chap. 2. Consequently, two-phase cooling means need to be employed in this regime, allowing the system to operate at high heat fluxes and en-suring a uniform and low surface temperature. However, two-phase cool-ing means need to operate outside the critical boilcool-ing conditions as well, reached when the Critical Heat Flux (CHF) occurs. In such conditions, the liquid near the heated surface is subject to an aggressive evaporation, leading the surface to dry out. This will result in decreased heat transfer coefficients, leading to sharp increases in the heated surface temperature within a fraction of seconds, which can reach the melting temperature of the material, in turn leading to a burnout phenomenon (Stephan, 1992; Collier and Thome, 1994). Consequently, it is extremely important to maintain a safety margin.

Despite its efficiency as a heat removal method, two-phase cooling means and boiling flows need to be carefully and extensively studied. This makes it possible to propose more efficient cooling schemes and to en-sure that these flows are operating within their safety margin, far from the critical boiling conditions and the CHF. Two-phase cooling thermal man-agement needs to be addressed and optimised in order to achieve optimal operation in terms of ability to dissipate heat, energy saving, cost reduc-tion and safe operareduc-tion. For this purpose, several boiling parameters need to be quantified, determined and estimated. These parameters include the Onset of Nucleate Boiling (ONB), which marks the boiling incipience and the start location of the two-phase flow region and the subcooled nucle-ate boiling heat transfer regime, and the Onset of Significant Void (OSV) marking the start location of the saturated boiling heat transfer regime, the CHF as presented previously, among others. In addition, optimal operat-ing conditions and optimal thermal management system design leadoperat-ing to higher heat removal rates at low costs need to be determined.

Experiments can be used successfully to fulfil this task. However, they are still very expensive and time-consuming to perform. In addition, de-spite the fact that its outcomes are robust and cannot violate the laws of physics, they are characterised by non-universality, having reduced

valid-promising heat removal solution consists of employing two-phase cooling means involving phase-change heat removal. Several orders of magnitude of the heat transfer coefficients are achieved when employing two-phase cooling and boiling flow means, since these flows combine the latent and the sensible heats of the coolant, rather than the sensible heat alone when phase-change is excluded.

The largest heat transfer coefficients are achieved when operating in the subcooled nucleate boiling heat transfer regimes, that is anterior to the single-phase forced convection heat transfer regime and posterior to the saturated boiling heat transfer regime as presented in the literature review of Chap. 2. Consequently, two-phase cooling means need to be employed in this regime, allowing the system to operate at high heat fluxes and en-suring a uniform and low surface temperature. However, two-phase cool-ing means need to operate outside the critical boilcool-ing conditions as well, reached when the Critical Heat Flux (CHF) occurs. In such conditions, the liquid near the heated surface is subject to an aggressive evaporation, leading the surface to dry out. This will result in decreased heat transfer coefficients, leading to sharp increases in the heated surface temperature within a fraction of seconds, which can reach the melting temperature of the material, in turn leading to a burnout phenomenon (Stephan, 1992; Collier and Thome, 1994). Consequently, it is extremely important to maintain a safety margin.

Despite its efficiency as a heat removal method, two-phase cooling means and boiling flows need to be carefully and extensively studied. This makes it possible to propose more efficient cooling schemes and to en-sure that these flows are operating within their safety margin, far from the critical boiling conditions and the CHF. Two-phase cooling thermal man-agement needs to be addressed and optimised in order to achieve optimal operation in terms of ability to dissipate heat, energy saving, cost reduc-tion and safe operareduc-tion. For this purpose, several boiling parameters need to be quantified, determined and estimated. These parameters include the Onset of Nucleate Boiling (ONB), which marks the boiling incipience and the start location of the two-phase flow region and the subcooled nucle-ate boiling heat transfer regime, and the Onset of Significant Void (OSV) marking the start location of the saturated boiling heat transfer regime, the CHF as presented previously, among others. In addition, optimal operat-ing conditions and optimal thermal management system design leadoperat-ing to higher heat removal rates at low costs need to be determined.

Experiments can be used successfully to fulfil this task. However, they are still very expensive and time-consuming to perform. In addition, de-spite the fact that its outcomes are robust and cannot violate the laws of physics, they are characterised by non-universality, having reduced