Two Phase Flow Phase Change and Numerical Modeling Part 1 pot

Contents Preface IX Chapter 1 Modeling the Physical Phenomena Involved by Laser Beam – Substance Interaction 3 Marian Pearsica, Stefan Nedelcu, Cristian-George Constantinescu, Constan

TWO PHASE FLOW, PHASE CHANGE AND NUMERICAL MODELING

Edited by Amimul Ahsan

Two Phase Flow, Phase Change and Numerical Modeling

Edited by Amimul Ahsan

Published by InTech

Janeza Trdine 9, 51000 Rijeka, Croatia

Copyright © 2011 InTech

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Publishing Process Manager Ivana Lorković

Technical Editor Teodora Smiljanic

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Image Copyright alehnia, 2011 Used under license from Shutterstock.com

First published August, 2011

Printed in Croatia

A free online edition of this book is available at www.intechopen.com

Additional hard copies can be obtained from orders@intechweb.org

Two Phase Flow, Phase Change and Numerical Modeling, Edited by Amimul Ahsan

p cm

ISBN 978-953-307-584-6

Contents

Preface IX

Chapter 1 Modeling the Physical Phenomena Involved by

Laser Beam – Substance Interaction 3

Marian Pearsica, Stefan Nedelcu, Cristian-George Constantinescu, Constantin Strimbu, Marius Benta and Catalin Mihai

Chapter 2 Numerical Modeling and Experimentation on

Evaporator Coils for Refrigeration in Dry and Frosting Operational Conditions 27

Zine Aidoun, Mohamed Ouzzane and Adlane Bendaoud Chapter 3 Modeling and Simulation of the Heat Transfer Behaviour of

a Shell-and-Tube Condenser for a Moderately High-Temperature Heat Pump 61

Tzong-Shing Lee and Jhen-Wei Mai Chapter 4 Simulation of Rarefied Gas Between Coaxial Circular

Cylinders by DSMC Method 83

H Ghezel Sofloo Chapter 5 Theoretical and Experimental Analysis of Flows and

Heat Transfer Within Flat Mini Heat Pipe Including Grooved Capillary Structures 93

Zaghdoudi Mohamed Chaker, Maalej Samah and Mansouri Jed Chapter 6 Modeling Solidification Phenomena in the Continuous

Casting of Carbon Steels 121

Panagiotis Sismanis Chapter 7 Modelling of Profile Evolution by Transport Transitions in

Fusion Plasmas 149 Mikhail Tokar

VI Contents

Chapter 8 Numerical Simulation of the Heat Transfer from a Heated

Solid Wall to an Impinging Swirling Jet 173

Joaquín Ortega-Casanova Chapter 9 Recent Advances in Modeling Axisymmetric

Swirl and Applications for Enhanced Heat Transfer and Flow Mixing 193

Sal B Rodriguez and Mohamed S El-Genk Chapter 10 Thermal Approaches to Interpret

Laser Damage Experiments 217

S Reyné, L Lamaignčre, J-Y Natoli and G Duchateau Chapter 11 Ultrafast Heating Characteristics in Multi-Layer Metal Film

Assembly Under Femtosecond Laser Pulses Irradiation 239

Feng Chen, Guangqing Du, Qing Yang, Jinhai Si and Hun Hou

Chapter 12 On Density Wave Instability Phenomena – Modelling

and Experimental Investigation 257

Davide Papini, Antonio Cammi,

Marco Colombo and Marco E Ricotti

Chapter 13 Spray Cooling 285

Zhibin Yan, Rui Zhao, Fei Duan, Teck Neng Wong, Kok Chuan Toh,

Kok Fah Choo, Poh Keong Chan and Yong Sheng Chua

Chapter 14 Wettability Effects on Heat Transfer 311

Chiwoong Choi and Moohwan Kim

Chapter 15 Liquid Film Thickness in Micro-Scale Two-Phase Flow 341

Naoki Shikazono and Youngbae Han

Chapter 16 New Variants to Theoretical Investigations of

Thermosyphon Loop 365 Henryk Bieliński

Chapter 19 Nanofluids for Heat Transfer – Potential and

Engineering Strategies 435 Elena V Timofeeva

Chapter 20 Heat Transfer in Nanostructures Using the Fractal

Approximation of Motion 451

Maricel Agop, Irinel Casian Botez,

Luciu Razvan Silviu and Manuela Girtu

Chapter 21 Heat Transfer in Micro Direct Methanol Fuel Cell 485

Ghayour Reza

Chapter 22 Heat Transfer in Complex Fluids 497

Mehrdad Massoudi

Chapter 23 A Numerical Study on Time-Dependent Melting and

Deformation Processes of Phase Change Material (PCM) Induced by Localized Thermal Input 523

Yangkyun Kim, Akter Hossain, Sungcho Kim and Yuji Nakamura

Chapter 24 Thermal Energy Storage Tanks Using Phase Change Material

(PCM) in HVAC Systems 541 Motoi Yamaha and Nobuo Nakahara

Chapter 25 Heat Transfer and Phase Change in Deep CO 2 Injector for CO 2

Geological Storage 565

Kyuro Sasaki and Yuichi Sugai

Preface

The heat transfer and analysis on laser beam, evaporator coils, shell-and-tube condenser, two phase flow, nanofluids, and on phase change are significant issues in a design of wide range of industrial processes and devices This book introduces advanced processes and modeling of heat transfer, flat miniature heat pipe, gas-solid fluidization bed, solidification phenomena, thermal approaches to laser damage, and temperature and velocity distribution to the international community It includes 25 advanced and revised contributions, and it covers mainly (1) numerical modeling of heat transfer, (2) two phase flow, (3) nanofluids, and (4) phase change

The first section introduces numerical modeling of heat transfer on laser beam, evaporator coils, shell-and-tube condenser, rarefied gas, flat miniature heat pipe, particles in binary gas-solid fluidization bed, solidification phenomena, profile evolution, heated solid wall, axisymmetric swirl, thermal approaches to laser damage, ultrafast heating characteristics, and temperature and velocity distribution The second section covers density wave instability phenomena, gas and spray-water quenching, spray cooling, wettability effect, liquid film thickness, and thermosyphon loop

The third section includes nanofluids for heat transfer, nanofluids in minichannels, potential and engineering strategies on nanofluids, nanostructures using the fractal approximation, micro DMFC, and heat transfer at nanoscale and in complex fluids The forth section presents time-dependent melting and deformation processes of phase change material (PCM), thermal energy storage tanks using PCM, capillary rise

in a capillary loop, phase change in deep CO2 injector, and phase change thermal storage device of solar hot water system

The readers of this book will appreciate the current issues of modeling on laser beam, evaporator coils, rarefied gas, flat miniature heat pipe, two phase flow, nanofluids, complex fluids, and on phase change in different aspects The approaches would be applicable in various industrial purposes as well The advanced idea and information described here will be fruitful for the readers to find a sustainable solution in an industrialized society

The editor of this book would like to express sincere thanks to all authors for their high quality contributions and in particular to the reviewers for reviewing the chapters

X Preface

ACKNOWLEDGEMENTS

All praise be to Almighty Allah, the Creator and the Sustainer of the world, the Most Beneficent, Most Benevolent, Most Merciful, and Master of the Day of Judgment He is Omnipresent and Omnipotent He is the King of all kings of the world In His hand is all good Certainly, over all things Allah has power

The editor would like to express appreciation to all who have helped to prepare this book The editor expresses the gratefulness to Ms Ivana Lorkovic, Publishing Process Manager InTech Open Access Publisher, for her continued cooperation In addition, the editor appreciatively remembers the assistance of all authors and reviewers of this book

Gratitude is expressed to Mrs Ahsan, Ibrahim Bin Ahsan, Mother, Father, Law, Father-in-Law, and Brothers and Sisters for their endless inspirations, mental supports and also necessary help whenever any difficulty

Mother-in-Amimul Ahsan

Department of Civil Engineering,

Faculty of Engineering, University Putra Malaysia

Malaysia

Part 1

Numerical Modeling of Heat Transfer

1

Modeling the Physical Phenomena Involved by

Laser Beam – Substance Interaction

Marian Pearsica, Stefan Nedelcu, Cristian-George Constantinescu,

Constantin Strimbu, Marius Benta and Catalin Mihai

“Henri Coanda” Air Force Academy

Romania

1 Introduction

The mathematical model is based on the heat transfer equation, into a homogeneous material, laser beam heated Because transient phenomena are discussed, it is necessary to consider simultaneously the three phases in material (solid, liquid and vapor), these implying boundary conditions for unknown boundaries, resulting in this way analytical and numerical approach with high complexity

Because the technical literature (Belic, 1989; Hacia & Domke, 2007; Riyad & Abdelkader, 2006) does not provide a general applicable mathematical model of material-power laser beam assisted by an active gas interaction, it is considered that elaborating such model, taking into account the significant parameters of laser, assisting gas, processed material, which may be particularized to interest cases, may be an important technical progress in this branch The mathematical methods used (as well the algorithms developed in this purpose) may be applied to study phenomena in other scientific/technical branches too The majority

of works analyzing the numerical and analytical solutions of heat equation, the limits of applicability and validity of approximations in practical interest cases, is based on results achieved by Carslaw and Jaeger using several particular cases (Draganescu & Velculescu, 1986; Dowden, 2009, 2001; Mazumder, 1991; Mazumder & Steen, 1980)

The main hypothesis basing the mathematical model elaboration, derived from previous research team achievements (Pearsica et al., 2010, 2009; Pearsica & Nedelcu, 2005), are: laser processing is a consequence of photon energy transferred in the material and active gas jet, increasing the metal destruction process by favoring exothermic reactions; the processed material is approximated as a semi-infinite region, which is the space limited by the plane

z 0= , the irradiated domain being much smaller than substance volume; the power laser beam has a “Gaussian” type radial distribution of beam intensity (valid for TEM00 regime); laser beam absorption at z depth respects the Beer law; oxidations occurs only in laser irradiated zone, oxidant energy being “Gaussian” distributed; the attenuation of metal vapors flow respects an exponential law One of the mathematical hypothesis needing a deeper analysis is the shape of the boundaries between liquid and vaporization, respectively liquid and solid states, supposed as previously known, the parameters characterizing them being computed in the thermic regime prior to the calculus moment

The laser defocusing effect, while penetrating the processed metal is taken into consideration too, as well as energy losses by electromagnetic radiation and convection The

Two Phase Flow, Phase Change and Numerical Modeling

4

proposed method solves simultaneously the heat equation for the three phases (solid, liquid and vapor), computing the temperature distribution in material and the depth of penetration of the material for a given processing time, the vaporization speed of the material being measurable in this way

2 Analytical model equations

The invariant form of the heat equation for an isotropic medium is given by (1)

Because the print of the laser beam on the material surface is a circular one, thermic phenomena produced within the substantial, have a cylindrical symmetry Oz is considered

as symmetry axis of the laser beam, the object surface equation is z 0= and the positive sense of Oz axis is from the surface to the inside of the object The heat equation within cylindrical coordinates (θ,r,z) will be:

where: K[m /s] is the diffusivity of the material 2

Limit and initial conditions are attached to heat equation according to the particularly cases which are the discussed subject These conditions are time and space dependent In time, the medium submitted to the actions of the laser presents the solid, liquid and vapor state separated by previously unknown boundaries A simplifying model taking into consideration these boundaries, by considering them as having a cylindrical symmetry, was proposed By specifying the pattern D, the temperature initial conditions and the conditions on D pattern boundaries, one can have the solution of heat equation, T(x,y,z,t) for a certain substantial

2.1 Temperature source modeling

The destruction of the crystalline network of the material and its vaporization, along the pre-established curve, is completed by the energy of photons created inside the material, and by the jet of the assisting gas (O2) This gas intensifies the material destroying action due

to the exothermic reactions provided Dealing with a semi-infinite solid heated by a laser beam uniform absorbed in its volume, it is assumed that Beer law governs its absorption at z depth It is considered a radial “Gaussian” distribution of the laser beam intensity, which corresponds to the central part of the laser beam It is assumed that photons energy is totally transformed in heat So, the heat increasing rate, owing the photons energy, at z depth (under surface) is given by:

Modeling the Physical Phenomena Involved by Laser Beam – Substance Interaction 5 where: dV[m ] and dt[s] are the infinitesimal volume and time respectively, 3 σ[m /kg]2 – the absorption cross section, σ =1 / lρ ⋅ , I(r t) [W /m ] – photons distribution in material 2

volume, l[m] – the attenuation length of laser radiation, P [W] – the laser power; L πd [m ]2 2

– irradiated surface, r[m] – radial coordinate, and h [J]ν – the energy of one photon

The vaporized material diffuses in oxygen atmosphere and oxidizes exothermic, resulting in this way an oxidizing energy, which appears as an additional kinetic energy of the surface gas constituents, leading to an additional heating of the laser processed zone It is assumed

an exponential attenuation of the metal vapors flow and oxidizing is only inner laser irradiated zone, the oxidizing energy being “Gaussian” distributed The rate of oxidizing energy release on the material is given by (4):

2 ox 2

2

s s

2.2 Boundary and initial conditions for heat equation

Two Phase Flow, Phase Change and Numerical Modeling

- phase 1, for 0 t t≤ < top;

- phase 2, for ttop≤ <t tvap;

- phase 3, for t t≥ vap, where t and top tvap are the starting time moments of the melting, respectively vaporization of the material

The surfaces separating solid, liquid and vapor state are previously unknown and will be determined using the conditions of continuity of thermic flow on separation surfaces of two different substantial, knowing the temperature and the speed of separation surface (Mazumder & Steen, 1980; Shuja et al., 2008; Steen & Mazumder, 2010)

The isotropic domain D is assumed to be the semi-space z 0≥ , so its border, S, is characterized by the equation z 0= The laser beam acts on the normal direction, developing thermic effects described by (1) In the initial moment, t 0= , the domain temperature is the ambient one, Ta If the laser beam radius is d and axis origin is chosen on its symmetry axis, then the condition of type (7) (thermic flow imposed on the surface of the processed material) yields:

2 on p on

t

k t 2 t 1 4