Advances in heat transfer

VOLUME FORTY SIX

ADVANCES IN

HEAT TRANSFER

VOLUME FORTY SIX

ADVANCES IN

HEAT TRANSFER

Series Editors

EPHRAIM M. SPARROW

Department of Mechanical Engineering,

University of Minnesota, MN, USA

YOUNG I. CHO

Mechanical Engineering, Drexel University, PA, USA

JOHN P. ABRAHAM

School of Engineering, University of St. Thomas,

St. Paul, MN, USA

JOHN M. GORMAN

University of MinnesotaMinneapolis, USA

Founding Editors

THOMAS F. IRVINE, JR.

State University of New York at Stony Brook, Stony Brook, NY

JAMES P. HARTNETT

University of Illinois at Chicago, Chicago, IL

Amsterdam • Boston • Heidelberg • London

New York • Oxford • Paris • San Diego

San Francisco • Singapore • Sydney • Tokyo

Academic Press is an imprint of Elsevier

CONTENTS

List of Contributors vii

Preface ix

1. On the Computational Modelling of Flow and Heat Transfer

in In-Line Tube Banks 1

Alastair West, Brian E. Launder, Hector Iacovides

1. Introduction 4

2. Computational and Modelling Schemes 7

3. Fully Developed Flow through In-Line Tube Banks 13

4. Modelling the Complete Experimental Assembly of Aiba et al. [13] 29

5. Thermal Streak Dispersion in a Quasi-Industrial Tube Bank 34

6. Concluding Remarks 43

Acknowledgments 44

References 45

2. Developments in Radiation Heat Transfer: A Historical Perspective 47

Raymond Viskanta

1. Introduction 49

2. Early Concepts of Light (Radiation) 50

3. The Nineteenth Century 51

4. Quantum Theory and Planck’s Radiation Law 52

5. Radiant Heat Exchange between the Surfaces of Solids 56

6. Radiative Transfer in a Participating Medium 66

7. Interaction of Radiation with Conduction and Advection in

Participating Media 73

8. Future Challenges 79

Acknowledgments 80

References 80

3. Convective Heat Transfer Enhancement: Mechanisms,

Techniques, and Performance Evaluation 87

Ya-Ling He and Wen-Quan Tao

1. Introduction 90

2. Verifications of FSP 114

v j

3. Contributions of FSP to the Development of Convective

Heat Transfer Theory 123

4. Performance Evaluation of Enhanced Structures 160

5. Conclusions 177

Acknowledgments 180

References 180

4. Recent Analytical and Numerical Studies on Phase-Change

Heat Transfer 187

Ping Cheng, Xiaojun Quan, Shuai Gong, Xiuliang Liu, Luhang Yang

1. Introduction 188

2. Surface Characteristics 190

3. Onset of Bubble Nucleation 193

4. Thermodynamic Analyses for Onset of Dropwise Condensation 208

5. Level-Set and VOF Simulations of Boiling and Condensation Heat Transfer 213

6. Lattice Boltzmann Simulations of Boiling Heat Transfer 220

7. Lattice Boltzmann Simulations of Condensation Heat Transfer 232

8. CHF Models in Pool Boiling 238

9. Concluding Remarks 244

Acknowledgments 244

References 245

Author Index 249

Subject Index 253

vi Contents

LIST OF CONTRIBUTORS

Ping Cheng

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, P. R. China

Shuai Gong

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, P. R. China

Ya-Ling He

Key Laboratory of Thermo-Fluid Science & Engineering of Ministry of Education, School

of Energy & Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, China

Hector Iacovides

School of Mechanical, Aeronautical & Civil Engineering, University of Manchester,

Manchester, UK

Brian E. Launder

School of Mechanical, Aeronautical & Civil Engineering, University of Manchester,

Manchester, UK

Xiuliang Liu

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, P. R. China

Xiaojun Quan

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, P. R. China

Wen-Quan Tao

Key Laboratory of Thermo-Fluid Science & Engineering of Ministry of Education, School

of Energy & Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, China

Raymond Viskanta

School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA

Alastair West

School of Mechanical, Aeronautical & Civil Engineering, University of Manchester,

Manchester, UK

Luhang Yang

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, P. R. China

viij

PREFACE

This volume of Advances in Heat Transfer contains four distinct and significant

contributions to the thermal-science literature. One contribution, by Brian

Launder and his colleagues, is a detailed investigation of the flow and heat

transfer associated with in-line tube-bank geometries. The authors explore

the sensitivity of results to the geometric configuration of the tube bank,

the number of tubes, and to the numerical modeling methodology.

A second chapter, by Raymond Viskanta, is a treatise on the develop￾ments of radiation heat transfer. This comprehensive discussion not only

documents the historical development of our understanding of radiation

heat transfer (from the nineteenth century through quantum mechanics,

to the present)dbut it also identifies current unsolved problems in this living

field of study.

A contribution by Wen-Quan Tao and Yao-Ling He proposes a means

of enhancing single-phase convective heat transfer. That method, termed

the field synergy principle, reduces the intersection angle between the fluid

velocity and temperature gradients. Clear guidelines are proposed to accom￾plish the optimization in practical problems.

Finally, Ping Cheng and colleagues write about recent advancements to

our understanding of phase-change heat transfer (boiling and condensation).

They document both analytical and numerical approaches to solving phase￾change problems while clarifying and providing perspective on the literature

of experimentation in this field.

This diverse collection by leading researchers in the field is a valuable

resource for professional practitioners and academicians. These authoritative

voices have brought much clarity and completion to complex subjects.

EPHRAIM M. SPARROW

YOUNG I. CHO

JOHN P. ABRAHAM

JOHN M. GORMAN

ix j

CHAPTER ONE

On the Computational Modelling

of Flow and Heat Transfer in

In-Line Tube Banks

Alastair West*, Brian E. Launder1

, Hector Iacovides

School of Mechanical, Aeronautical & Civil Engineering, University of Manchester, Manchester, UK

1

Corresponding author: E-mail: [email protected]

Contents

1. Introduction 4

2. Computational and Modelling Schemes 7

2.1 Discretization practices and boundary conditions 7

2.2 Turbulence modelling 10

3. Fully Developed Flow through In-Line Tube Banks 13

3.1 Domain-dependence and mesh-density issues for the LES treatment 13

3.2 Effects of pitch:diameter ratio 17

3.3 Effects of Reynolds number 20

3.4 Performance of URANS models for a square array for P/D ¼ 1.6 22

4. Modelling the Complete Experimental Assembly of Aiba et al. [13] 29

4.1 Scope of the study 29

4.2 Computed behaviour for the Test Section of Aiba et al. [13] 29

5. Thermal Streak Dispersion in a Quasi-Industrial Tube Bank 34

5.1 Rationale and scope 34

5.2 Streamwise fully developed flow 35

5.3 Computations of the complete industrial tube bank with thermal spike 37

6. Concluding Remarks 43

Acknowledgments 44

References 45

Abstract

This chapter reexamines the problem of computationally modelling the flow over

moderately close-packed, in-line tube banks that are a frequently adopted configura￾tion for large heat exchangers. While an actual heat exchanger may comprise thou￾sands of tubes, applied computational research aimed at modelling the heat￾exchanger performance will typically adopt, at most, a few tens of tubes. The present

contribution explores the sensitivity of the computed results to the pitch:diameter ratio

* Present address: CD-adapco, 200 Shepherds Bush Road, London W6 7NL.

Advances in Heat Transfer, Volume 46

ISSN: 0065-2717

http://dx.doi.org/10.1016/bs.aiht.2014.08.003

© 2014 Elsevier Inc.

All rights reserved. 1 j

of the tube, to the number of tubes in the domain, and to the particular modelling

practices adopted. Regarding the last aspect, both large-eddy simulation (LES) and

URANS (unsteady Reynolds-averaged Navier–Stokes modelling) approaches have

been tested using periodic boundary conditions. The results show that URANS results

adopting a second-moment closure are in closer accord with the LES data than those

based on linear eddy-viscosity models. Moreover, the treatment of the near-wall region

is shown to exert a critical influence not just on wall parameters like the Nusselt number

but also on such fundamental issues as the flow path adopted through the tube bank.

Comparison is also made with experiments in two small, confined, tube-bank clusters

such as are typically used to provide data for performance estimation of a complete

industrial tube bank. It is shown that such small clusters generate very substantial sec￾ondary flows that may not be typical of those found in a full-sized heat exchanger.

Nomenclature

aij Dimensionless anisotropic part of the Reynolds stress, ðuiuj 2dijk=3Þ=k

A2 Second invariant of the Reynolds stress, aijaji

A3 Third invariant of the Reynolds stress, aijajkaki

CCFL Courant number

Cl Lift coefficient, Fy=1=2rU2

gap

Cp Pressure coefficient, ðp p0Þ=1=2rU2

gap

D Cylinder diameter

Eu Euler number for tube bank, 2DP=ðrU2

gapÞ

Fy Force per unit area on cylinder in y direction (including pressure and shear forces)

f Shedding frequency

f Parameter in f f model of turbulence, [24]

k Turbulent kinetic energy

La Dimension of computational domain in direction a (a ¼ x, y, or z)

Nu Local Nusselt number, q_

wD=DTl

Nu Circumferentially averaged Nusselt number

Ntot Total number of grid nodes used in the simulation

Nz Number of nodes in z direction

n Radial coordinate

nþ Radial distance from cylinder surface, in wall units, n ffiffiffiffiffiffiffiffiffiffiffiffiffi

ðsw=rÞ p =n

Dnþ Height of wall-adjacent control volume, in wall units

P Pitch, i.e., distance between adjacent tube centres

p Static pressure on cylinder at given value of q

p0 Static pressure at q ¼ 0

DP Pressure difference across a single column of tubes

Pk Production rate of turbulent kinetic energy by mean shear, Eqn (1)

q_

w Local heat flux at the cylinder surface

Re Reynolds number of tube bank, UgapD/n

Ret Turbulent Reynolds number, k2

/nε

s Circumferential coordinate

S Scalar strain rate, [2Sij Sji]

½

St Strouhal number, fD/Ugap

Sij Strain rate tensor, ½(vUi/vxjþvUj/vxi)

Ds

þ Circumferential dimension of wall-adjacent control volume in wall units,

s ffiffiffiffiffiffiffiffiffiffiffiffiffi

ðsw=rÞ p =n

T, t Temperature, resolved and turbulent contributions

Tn Normalized temperature, (TTref)/(TinTref)

2 Alastair West et al.

Tin Inlet temperature to tube bank

Tref A reference temperature (chosen as 15 C)

DT Local difference between the temperature at a point on the surface and the bulk

fluid temperature just ahead of the cylinder

t (Fig. 8 only) time

U Mean velocity in x direction

Ugap Mean velocity through the narrowest cross-section of the tube bank

Ui Mean velocity in direction xi

ui Turbulent velocity in direction xi

uiuj Turbulent kinematic Reynolds stress

uit Turbulent kinematic heat flux in direction xi

V Local mean velocity in y direction

xi Cartesian coordinate, tensor notation

x Streamwise Cartesian coordinate

y Cartesian coordinate normal to stream and tube axes

z Cartesian coordinate along the tube axis

Dzþ Axial dimension of control volume in wall units, z ffiffiffiffiffiffiffiffiffiffiffiffiffi

ðsw=rÞ p =n

Greek Symbols

ε Kinematic dissipation rate of turbulence energy

q Angular position around tube

l Thermal conductivity of fluid

n Kinematic viscosity

nt Turbulent kinematic viscosity

r Fluid density

s Fluid Prandtl number

st Turbulent Prandtl number (set to 1.0, a constant)

sw Local wall shear stress on cylinder surface

f Notional wall-normal mean-square velocity fluctuations normalized by k. A variable in

f f model of turbulence [24]

F Elliptic-blending parameter in the EB-RSM found from solving an elliptic pde

u Turbulence scale-determining variable in k-u SST EVM [23]

Acronyms

2D Two-dimensional computation

3D Three-dimensional computation

AGR Advanced Gas-Cooled Reactor

CERL Central Electricity Research Laboratories (UK) (operating from the early 1950s

until 1992)

CFD Computational Fluid Dynamics

EB-RSM Elliptic-blending Reynolds stress model of turbulence [26]

EDF Electricité de France

EVM Eddy-Viscosity Model (of turbulence)

HECToR High-End Computing Terra-scale Resource (the UK’s national high-intensity

computational provision)

LES Large-Eddy Simulation (of turbulence)

RANS Reynolds Averaged Navier Stokes (treatment of the pde equations of motion)

RSM Reynolds stress model (a type of turbulence model which prescribes transport

equations for the Reynolds stresses, i.e., a second-moment closure)

sgs Sub-grid-scale (model of turbulence for LES simulations)

On the Computational Modelling of Flow and Heat Transfer in In-Line Tube Banks 3

SIMPLEC Semi-implicit method for pressure-linked equationsdcorrected, [20]

SSG Second-moment closure devised by Speziale, Sarkar, and Gatski [25]

SST Shear-stress transport (descriptive label applied to the EVM model of [23])

URANS Unsteady RANS treatment

1. INTRODUCTION

The present contribution examines, principally by considering

computational fluid dynamics (CFD) explorations, various aspects of flow

and heat-transfer characteristics for the flow normal to arrays of circular

tubes arranged in in-line formation. This configuration provides an impor￾tant element in heat-exchanger designs used in fossil-fuel and nuclear power

plants and, indeed, over many other sectors of thermal and process engineer￾ing. Numerous purely thermal performance studies of cross-flow tube-bank

arrays have been carried out in the past (see, for example, the detailed early

review by Zukauskas [1]). Such studies, almost exclusively experimental,

have for the most part examined the dependence of mean Nusselt number

for a tube on the geometric configuration of the tube cluster and, of course,

on the flow Reynolds and Prandtl numbers. From the mid-1980s onward

the increasing availability of laser Doppler anemometry (LDA) and other €

laser-based systems has meant that the detailed flow dynamics of particular

tube-bank configurations have been examined (e.g., Simonin & Barcouda

[2], Balabani & Yianneskis [3], Meyer [4]).

More recently, partly stimulated by the availability of these flow-field

experiments and by an ever-increasing computational resource, several nu￾merical studies have also been undertaken. The great majority of the pub￾lished computational researches on tube banks have been of staggered

tube arrangements (Rollet-Miet et al. [5], Benhamadouche & Laurence

[6], Moulinec et al. [7], Liang & Papadakis [8], Ridluan & Tokuhiro [9],

Johnson [10]). This reflects partly the fact that staggered tube banks are

employed more widely in industry than in-line arrangements and, quite

possibly, that the availability of the LDA studies such as those noted above

has provided a direct means of assessing the accuracy of the computations.

In-line tube banks are, however, far from being without industrial

importance. The heat exchangers in the UK’s current advanced gas￾cooled (nuclear) reactors (AGRs) employ such in-line configurations as do

many industrial applications where the greater accessibility offered by such

arrangements outweigh possibly small advantages in overall mean heat trans￾fer coefficients with a staggered tube bank. Early flow-field experiments on

widely spaced, in-line tube banks, motivated by vibrational problems, have

4 Alastair West et al.

been reported by Ishigai et al. [11]. The overall heat-exchanger costs with

tightly packed tube bundles are lower, however; yet it is here that experi￾mental data are scanty. Exceptions are the works of Iwaki et al. [12] who

have used particle-image velocimetry (PIV) to examine the dynamics of a

square array and Meyer [4] who has reported both local heat-transfer coef￾ficients for a single heated tube and limited flow-field data in a rectangular

array with a longitudinal and transverse pitch of 1.5  1.8. Unfortunately,

the latter thesis came to our attention too late to be the subject of direct

computational comparisons. Fortunately, the earlier work by Aiba et al.

[13] has reported local heat-transfer coefficients for square arrays with a

range of tube spacings along with a limited amount of flow-field data.

There has in fact been a significant computational study of flow over in-line

tube banks by Afgan [14]. Unfortunately (for the heat-transfer community)

that was a wide-ranging exploration of several configurations (including, inter

alia, computations around an automobile wing mirror) but which did not

include solution of the thermal energy equation. Thus, no heat transfer

data were obtained. Nevertheless, that thesis brought out, with greater clarity

than earlier experiments, the great sensitivity of the flow structure to small

changes in the pitch:diameter ratio of the tube bankdor even to none at

all. Figure 1 shows, for example, Afgan’s time-averaged streamlines for two

separate runs for a pitch:diameter ratio of 1.5:1 at the same Reynolds

numbers. The left-hand figure exhibits what is known as alternating asym￾metric behaviour where only one recirculating eddy remains behind each

Figure 1 Mean streamlines for separate realizations of fully developed flow through an

in-line tube bank for P:D of 1.5:1. From the large-eddy simulation (LES) predictions of

Afgan [14].

On the Computational Modelling of Flow and Heat Transfer in In-Line Tube Banks 5

cylinder but where, in successive rows, the eddy is alternately shed from the

upper and lower surfaces with a corresponding variation in sign of the shed

vorticity. The right-hand figure, however, shows a purely asymmetric pattern

with the flow as a whole displaying an upward tilt even though at the start of

the computation the flow was purely from left to right. Evidence of the actual

existence of such asymmetry may be found in a number of experimental

studies. Figure 2, for example, taken from the work of Jones et al. [15] in a

20x12 bank, documents the progressive displacement of a temperature spike

as the flow passes over successive rows in the tube bank. Their measurements

of the corresponding behaviour in a staggered tube bank (not shown) exhibited

no such displacement. Aiba et al. [13] in their most closely packed array also

noted that “it is very clear that the flow through the tube bank deflects as a

whole.”

Of course, a vital question with respect to the computational studies of

limited arrays cited above is to what extent they can be taken as representa￾tive of the flow in an actual heat exchanger. In a large-scale industrial plant,

the heat exchanger will consist of many hundreds, perhaps thousands, of

tubes whereas computational tests such as those noted above will consider

a small array of from two to, at most, a few tens of tubes. The implicit

hope is that, by imposing fully developed or repeating boundary conditions

Figure 2 Measurement of the development of a hot spike temperature through an in￾line tube bank. From Jones et al. [15].

6 Alastair West et al.

around the edges of the computed flow domain, one will simulate condi￾tions representative of what will exist in the interior of the complete heat

exchanger, excluding entry, edge, and exit regions. The same hope also rests

with detailed experimental studies of limited tube-bank arrays. Indeed, then

there is, in addition, the problem that such flows must be confined by side￾and endwalls which will be substantially more intrusive on the interior flow

structure than the bounding surfaces in a full-scale heat exchanger.

The present contribution to the body of information on flow through

in-line tube banks attempts to throw light on the above issues. It provides

a reexamination of the sensitivity of the flow pattern to the pitch:diameter

of the bank and also to the size of the domain chosen as a representative

of the tube bank as a whole. We also provide some insight into the last of

the matters noted in the previous paragraph by examining the complete

experimental configurations measured by Aiba et al. [13] and Jones et al.

[15]. These complete enclosed-cluster simulations bring out for the first

time the presence of large secondary motions that make a major contribu￾tion to the mixing of the fluid. Section 2 of the chapter outlines the compu￾tational strategies adopted along with alternative approaches to accounting

for the effects of turbulence. Section 3 is concerned with the modelling

of fully developed flow through the tube bank, examining by way of

both large-eddy simulations (LES) and unsteady RANS closures, the effects

of pitch:diameter ratios, Reynolds number, and the size of the flow domain

considered. Attempts to mimic the flow and thermal behaviour of a com￾plete tube-bank array with both the above approaches are presented in

Section 4 while thermal dispersion in a larger industrial array using, in this

case, principally an unsteady RANS (URANS) approach is examined in

Section 5. Finally, Section 6 provides a summary of the principal results

from the foregoing explorations. Further detailed coverage may be found

in the Eng.D. thesis of Alastair West [16], available online.

2. COMPUTATIONAL AND MODELLING SCHEMES

2.1 Discretization practices and boundary conditions

The explorations reported herein have been made with the freely

available and versatile industrial software, Code_Saturne developed by

Electricité de France (EDF) (Archambeau et al. [17]) that is becoming widely

used within the European heat-transfer community. While it does not

currently offer some of the more advanced modelling practices incorporated

in our in-house code, STREAM (Lien & Leschziner [18]; Craft et al. [19])

On the Computational Modelling of Flow and Heat Transfer in In-Line Tube Banks 7

the study has attempted to draw generic conclusions, more widely than for

this particular software, related to the types of flow modelling and boundary

conditions that are employed. A few computations were also made with

STREAM (West [16]) which broadly confirmed the conclusions reached

with the former code.

Code_Saturne incorporates a finite-volume discretization of the unsteady

equations of motion suitable for resolving incompressible laminar or turbulent

flows. In the latter case, the alternative strategies of LES or solution of the un￾steady form of the Reynolds-averaged Navier–Stokes equations (URANS) are

available. Both approaches are explored in the present study, some detail of the

models examined being provided below. The velocity–pressure coupling is

achieved by a predictor/corrector method using the SIMPLEC algorithm,

Van Doormal & Raithby [20], where the momentum equations are solved

sequentially. The Poisson-like pressure-correction equation is solved using a

conjugate-gradient method and a standard pressure-gradient interpolation to

avoid oscillations. A collocated grid is employed. As spatial and temporal dis￾cretizations are second order (central-difference and Crank-Nicolson interpo￾lations, respectively), the time step was kept sufficiently small to ensure the

maximum Courant number, CCFL, was below unity. Body-fitted, block￾structured grids are adopted. These gave greater control of the number of cells

and a more precise resolution of the near-wall regions than alternatives. As

flow periodicity is used for the test cases examined in Section 3, a constant

mass flow rate is imposed to obtain the desired bulk velocity by specifying

an explicit, self-correcting mean pressure gradient at every time step.

Previous periodic calculations of square in-line tube banks (Afgan [11],

Benhamadouche et al. [21]) have found a 2  2 tube domain to be sufficient

Figure 3 Base line 2  2 flow domain for study. (a) Definitions of dimensions; (b) coarse

grid layout in x-y plane for Case 1.

8 Alastair West et al.