thermal-hydraulic analysis of gas- cooled reactor core flows

382 Pages·2010·15.08 MB·English

THERMAL-HYDRAULIC
ANALYSIS OF GAS-
COOLED REACTOR
CORE FLOWS

AMIR KESHMIRI
JULY 2010

A Thesis Submitted to the University of Manchester for the
Degree of Doctor of Philosophy in the Faculty of
Engineering and Physical Sciences

School of Mechanical, Aerospace and Civil Engineering (MACE), The University of
Manchester, Manchester, M60 1QD, United Kingdom.
2
Dedicated to the Loving Memory of My Sister, Arezoo ...
LIST OF CONTENTS
LIST OF CONTENTS __________________________________________________ 4
LIST OF FIGURES ____________________________________________________ 7
LIST OF TABLES ____________________________________________________ 18
ABSTRACT _________________________________________________________ 20
DECLARATION _____________________________________________________ 22
COPYRIGHT STATEMENT____________________________________________ 23
THE AUTHOR_______________________________________________________ 24
ACKNOWLEDGEMENTS _____________________________________________ 25
NOMENCLATURE ___________________________________________________ 27
1 INTRODUCTION ________________________________________________ 32
1.1 COMPUTATIONAL FLUID DYNAMICS _______________________________ 32
1.2 TURBULENCE MODELLING SCHEMES_______________________________ 33
1.3 ADVANCED GAS-COOLED NUCLEAR REACTORS ______________________ 36
1.3.1 Mixed Convection under Post-Trip Conditions ____________________ 37
1.3.2 Thermal-Hydraulics of the Fuel Elements ________________________ 38
1.4 OBJECTIVES OF THE PRESENT STUDY_______________________________ 41
1.5 OUTLINE OF THE THESIS_________________________________________ 43
2 LITERATURE REVIEW___________________________________________ 47
2.1 PRELIMINARY REMARKS ________________________________________ 47
2.2 MIXED CONVECTION HEAT TRANSFER IN VERTICAL FLOWS_____________ 48
2.2.1 Introduction________________________________________________ 48
2.2.2 Experimental Works_________________________________________ 49
2.2.3 Numerical Works ___________________________________________ 51
2.3 RIB-ROUGHENED SURFACES _____________________________________ 59
2.3.1 Introduction________________________________________________ 59
2.3.2 Experimental Works_________________________________________ 60
2.3.3 Numerical Works ___________________________________________ 64
2.4 AGR FUEL ELEMENTS__________________________________________ 72
2.4.1 Introduction________________________________________________ 72
2.4.2 Experimental Works_________________________________________ 73
3 MATHEMATICAL MODELLING OF TURBULENCE __________________ 80
3.1 PRELIMINARY REMARKS ________________________________________ 80
3.2 NAVIER-STOKES EQUATIONS_____________________________________ 81
3.3 REYNOLDS-AVERAGED NAVIER-STOKES (RANS) EQUATIONS___________ 82
3.4 EDDY VISCOSITY MODELS (EVMS)________________________________ 84
3.4.1 Introduction________________________________________________ 84
3.4.2 Zero-Equation Models _______________________________________ 86
3.4.3 One-Equation Models________________________________________ 87
3.4.4 Two-Equation Models________________________________________ 88
3.5 NEAR-WALL TREATMENTS ______________________________________ 91
3.5.1 Introduction________________________________________________ 91
4
List of Contents 5
3.5.2 Low-Reynolds-Number Models ________________________________ 94
3.5.3 Wall Functions _____________________________________________ 99
3.6 MODEL FORMULATIONS________________________________________ 103
3.6.1 Launder-Sharma k-ε Model (CONVERT) _______________________ 103
3.6.2 Lien-Chen-Leschziner k-ε Model (STAR-CD) ___________________ 104
3.6.3 Wilcox k-ω Model__________________________________________ 106
3.6.4 Standard k-ω-SST Model (STAR-CD & Code_Saturne)____________ 107
3.6.5 The v2-f Model (STAR-CD)__________________________________ 110
3.6.6 Manchester v2-f Model (Code_Saturne)_________________________ 112
3.6.7 Cotton-Ismael k-ε-S Model (CONVERT) _______________________ 114
3.6.8 Suga Non-Linear k-ε Model (CONVERT & STAR-CD)____________ 116
4 THEORETICAL FORMULATION__________________________________ 121
4.1 PRELIMINARY REMARKS _______________________________________ 121
4.2 DISCRETIZATION _____________________________________________ 121
4.2.1 Introduction_______________________________________________ 121
4.2.2 Finite Volume Method ______________________________________ 122
4.3 BOUNDARY LAYER APPROXIMATIONS_____________________________ 124
4.4 BOUSSINESQ APPROXIMATION___________________________________ 125
4.5 BUOYANCY PRODUCTION TERM _________________________________ 126
4.6 TURBULENT HEAT FLUX MODELLING _____________________________ 127
4.7 DESCRIPTION OF THE CODES USED _______________________________ 129
4.7.1 In-house Code: CONVERT __________________________________ 129
4.7.2 Commercial Code: STAR-CD ________________________________ 132
4.7.3 Industrial Code: Code_Saturne________________________________ 138
5 VERTICAL HEATED PIPE________________________________________ 143
5.1 PRELIMINARY REMARKS _______________________________________ 143
5.2 CASE DESCRIPTION ___________________________________________ 145
5.2.1 Introduction_______________________________________________ 145
5.2.2 Mesh and Numerical Details__________________________________ 146
5.3 RESULTS OF LOCAL NUSSELT NUMBER AND FRICTION COEFFICIENT _____ 150
5.3.1 Forced Convection _________________________________________ 151
5.3.2 CONVERT; Ascending and Descending Flow____________________ 153
5.3.3 Cross-Code Comparison; Ascending Flow_______________________ 156
5.4 MEAN FLOW AND TURBULENCE PROFILES__________________________ 158
5.4.1 Results of the Launder-Sharma Model (CONVERT)_______________ 159
5.4.2 Results of the Cotton-Ismael Model (CONVERT)_________________ 167
5.4.3 Results of the Suga Model (CONVERT and STAR-CD)____________ 172
5.4.4 Results of the Lien-Chen-Leschziner k-ε Model (STAR-CD)________ 177
5.4.5 Results of the v2-f Model (STAR-CD)__________________________ 178
5.4.6 Results of the k-ω-SST Model (STAR-CD and Code_Saturne)_______ 179
5.5 NUSSELT NUMBER DEVELOPMENT _______________________________ 181
5.5.1 Streamwise Development of Nu and c for Case (C) _______________ 181
f
5.5.2 The Experiments of Polyakov and Shindin_______________________ 183
5.6 EFFECTS OF THE REYNOLDS NUMBER _____________________________ 184
5.7 SUMMARY __________________________________________________ 186
6 2-DIMENSIONAL RIB-ROUGHENED SURFACES ___________________ 222
6.1 PRELIMINARY REMARKS _______________________________________ 222
6.2 CASE DESCRIPTION ___________________________________________ 224
List of Contents 6
6.2.1 Two-Dimensional Channel Approximation ______________________ 224
6.2.2 Numerical Procedures_______________________________________ 225
6.2.3 Geometry and Grids ________________________________________ 225
6.3 PRELIMINARY RESULTS ________________________________________ 227
6.3.1 Preliminary Remarks________________________________________ 227
6.3.2 Sensitivity Tests ___________________________________________ 229
6.4 RESULTS FOR DISCRETE EFFECTS ________________________________ 235
6.4.1 Effects of Turbulence Models_________________________________ 235
6.4.2 Effects of Rib Profile _______________________________________ 242
6.4.3 Effects of Near-Wall Treatment _______________________________ 246
6.4.4 Effects of Mesh Type _______________________________________ 249
6.5 RESULTS FOR CONTINUOUS EFFECTS______________________________ 252
6.5.1 Effects of Pitch-to-Rib Height Ratio (P/k) _______________________ 252
6.5.2 Effects of Rib Height (k/H)___________________________________ 256
6.5.3 Effects of Rib Width (b/k)____________________________________ 260
6.5.4 Effects of Reynolds Number__________________________________ 262
6.6 SUMMARY __________________________________________________ 265
7 3-DIMENSIONAL AGR FUEL ELEMENTS__________________________ 322
7.1 PRELIMINARY REMARKS _______________________________________ 322
7.2 CASE DESCRIPTION ___________________________________________ 324
7.3 RESULTS ___________________________________________________ 327
7.4 SUMMARY __________________________________________________ 335
8 CONCLUSIONS AND FUTURE WORK_____________________________ 352
8.1 PRELIMINARY REMARKS _______________________________________ 352
8.2 CONCLUSIONS _______________________________________________ 353
8.2.1 Mixed Convection Heat Transfer ______________________________ 353
8.2.2 2D Rib-Roughened Channels _________________________________ 356
8.2.3 3D AGR Fuel Element ______________________________________ 359
8.3 FUTURE WORK_______________________________________________ 360
8.3.1 Mixed Convection Heat Transfer ______________________________ 360
8.3.2 2D Rib-Roughened Channels _________________________________ 361
8.3.3 3D AGR Fuel Element ______________________________________ 362
BIBLIOGRAPHY____________________________________________________ 364
APPENDIX A_______________________________________________________ 376
APPENDIX B_______________________________________________________ 378
APPENDIX C_______________________________________________________ 381

Total word count: 73,000
LIST OF FIGURES
Figure 1.1 – Schematic of an AGR. (Adapted from http://www.ecology.at.) _______ 44
Figure 1.2 – Schematic of an AGR fuel element. (Adapted from CORE, 1999.)_____ 44
Figure 1.3 – Trends of Nusselt number impairment and enhancement for ascending and
descending mixed convection flows. ______________________________________ 45
Figure 1.4 – An early design of AGR fuel pins with transverse ribs.______________ 45
Figure 1.5 – Regimes of the mean flow over rod roughness (a) Skimming flow (d-type)
(b) Un-reattached flow (k-type) (c) Reattached flow (k-type).___________________ 46
Figure 1.6 – A 2-dimensional representation of AGR fuel elements.______________ 46
Figure 2.1 – Schematic diagram of ascending mixed convection flow.____________ 77
Figure 2.2 – Range of Buoyancy influence encompassed by mixed convection data._ 78
Figure 2.3 – Range of heat loading parameter encompassed by mixed convection data.
____________________________________________________________________ 78
Figure 2.4 – Schematic diagram of a rib-roughened surface.____________________ 79
Figure 2.5 – Schematics of transverse-ribbed, multi-start ribbed and longitudinally
finned fuel pins (from Wilkie, 1983b) _____________________________________ 79
Figure 3.1 – Variation of the mixing length with distance from the wall. __________ 87
Figure 3.2 – Schematic of various wall regions and layers in a boundary layer (adapted
from Iacovides, 2006). _________________________________________________ 93
Figure 3.3 – Near-wall treatment approaches; (a) Low-Reynolds number approach (b)
Wall Function approach._______________________________________________ 100
Figure 4.1 – A typical cell centred with node P and neighbour cell centred with node N.
___________________________________________________________________ 141
Figure 4.2 – CONVERT solution sequence.________________________________ 141
Figure 4.3 – Definition of ‘Symmetry’ and ‘Cyclic’ boundary conditions. ________ 141
Figure 4.4 – Node labelling convention for flux discretization._________________ 142
Figure 4.5 – Definition of the standard wall function in STAR-CD. _____________ 142
Figure 5.1 – Schematic diagram of an ascending mixed convection flow._________ 188
Figure 5.2 – CONVERT solution sequence.________________________________ 188
Figure 5.3 – Schematic of the mesh used in STAR-CD and Code_Saturne. _______ 189
Figure 5.4 – Results for fully-developed forced convection. (The computations using
Manchester v2-f model and LES were carried out by F. Billard and Y. Addad,
7
List of Figures 8
respectively, and are also reported in Billard et al., 2008, Addad and Laurence, 2008
and Keshmiri et al., 2008a; b). __________________________________________ 189
Figure 5.5 – Heat transfer impairment and enhancement in ascending and descending
mixed convection flows using CONVERT. ________________________________ 190
Figure 5.6 – Friction coefficient impairment and enhancement in ascending and
descending mixed convection flows using CONVERT._______________________ 191
Figure 5.7 – Cross-code comparison of heat transfer impairment and enhancement in
ascending mixed convection flows. ______________________________________ 192
Figure 5.8 – Cross-code comparison of friction coefficient impairment and enhancement
in ascending mixed convection flows. ____________________________________ 193
Figure 5.9 – Mean flow and turbulence profiles obtained using the Launder-Sharma
model in CONVERT. _________________________________________________ 194
Figure 5.10 – Budgets of the turbulent kinetic energy [m2/s3] obtained using the
Launder-Sharma model in CONVERT (a) case A (b) case C.__________________ 196
Figure 5.11 – Effects of including the buoyancy production term on the heat transfer
and friction coefficient impairment/enhancement.___________________________ 197
Figure 5.12 – Effects of the heat flux models on the buoyancy production term [m2/s3]
using (a) Generalized Gradient Diffusion Hypothesis (GGDH) and (b) Simple Gradient
Diffusion Hypothesis (SGDH).__________________________________________ 198
Figure 5.13 – Effects of including the Yap term on the local Nusselt number and friction
coefficient.__________________________________________________________ 199
Figure 5.14 – Mean flow and turbulence profiles obtained using the Cotton-Ismael
model in CONVERT. _________________________________________________ 200
Figure 5.15 – Budgets of the turbulent kinetic energy [m2/s3] obtained using the Cotton-
Ismael model in CONVERT (a) case A (b) case C. __________________________ 203
Figure 5.16 – Mean flow and turbulence profiles obtained using the Suga model in
CONVERT._________________________________________________________ 204
~
Figure 5.17 – Distribution of C and non-dimensional strain rate S for case (D) using
µ
the Suga model in CONVERT.__________________________________________ 206
Figure 5.18 – Budgets of the turbulent kinetic energy [m2/s3] obtained using the Suga
model in CONVERT (a) case A (b) case C ________________________________ 207
Figure 5.19 – Comparison of the results for case (A) obtained using the Suga model in
CONVERT and STAR-CD. ____________________________________________ 208
Figure 5.20 – Comparison of the results for case (B) obtained using the Suga model in
CONVERT and STAR-CD. ____________________________________________ 209
Figure 5.21 – Comparison of the results for case (C) obtained using the Suga model in
CONVERT and STAR-CD. ____________________________________________ 210
List of Figures 9
Figure 5.22 – Mean flow and turbulence profiles obtained using the LCL k-ε model in
STAR-CD.__________________________________________________________ 211
Figure 5.23 – Mean flow and turbulence profiles obtained using the v2-f model in
STAR-CD.__________________________________________________________ 212
Figure 5.24 – Mean flow and turbulence profiles obtained using the standard k-ω-SST
model in STAR-CD.__________________________________________________ 213
Figure 5.25 – Mean flow and turbulence profiles obtained using the standard k-ω-SST
model in Code_Saturne. _______________________________________________ 214
Figure 5.26 – Comparison of mean flow and turbulence profiles for case (A) obtained
using the standard k-ω-SST model in STAR-CD vs. Code_Saturne._____________ 215
Figure 5.27 – Comparison of mean flow and turbulence profiles for case (D) obtained
using the standard k-ω-SST model in STAR-CD vs. Code_Saturne._____________ 216
Figure 5.28 – Mean flow and turbulence profiles for case (C) at different streamwise
locations obtained using the Launder-Sharma model in CONVERT. ____________ 217
Figure 5.29 – Nusselt number development against the experiments of Polyakov and
Shindin (1988) (Runs 1-5 in Table 5.11) __________________________________ 219
Figure 5.30 – Normalized Nusselt number impairment and enhancement against the
buoyancy parameter for different Reynolds numbers. ________________________ 221
Figure 5.31 – Normalized Friction coefficient impairment and enhancement against the
buoyancy parameter for different Reynolds numbers. ________________________ 221
Figure 6.1 – Schematic diagram of a rib-roughened surface.___________________ 267
Figure 6.2 – The computational domains used in the present work for 1s configuration.
___________________________________________________________________ 267
Figure 6.3 – The computational domains used in the present work for 2s configuration.
___________________________________________________________________ 267
Figure 6.4 – Schematic of the 3D mesh (P/k = 9; 2s). ________________________ 268
Figure 6.5 – Plan view contours of the streamwise velocity for the 3D case (P/k = 9; 2s)
at the y/k = 0.1 plane using the v2-f model. ________________________________ 268
Figure 6.6 – Spanwise plane contour plot of the streamwise velocity for the 3D case
(P/k = 9; 2s) at the mid-section between the two ribs (x/k = 4.5) using the v2-f model.
___________________________________________________________________ 269
Figure 6.7 – Spanwise flow structure. (a) Present v2-f model for the 3D case (P/k = 9;
2s) at x/k = 4.5 (b) LDV measurements of Liou et al. (1993b) for P/k = 9:2s at x/k = 2
plane.______________________________________________________________ 269
Figure 6.8 – Plan view contour of Nu/Nu on the floor of the channel for the 3D case
0
(P/k = 9; 2s) using the v2-f model. _______________________________________ 270
Figure 6.9 – Contour plot of Nu/Nu on the side wall for the 3D case (P/k = 9; 2s) (a)
0
experimental data of Rau et al. (1998) (b) the present v2-f model. ______________ 270
List of Figures 10
Figure 6.10 – Nusselt number distribution on the side wall of the 3D case (P/k = 9; 2s)
at a distance k upstream from a rib using the v2-f model.______________________ 271
Figure 6.11 – 2D very coarse mesh (P/k=9; 2s)._____________________________ 272
Figure 6.12 – 2D coarse mesh (P/k = 9; 2s).________________________________ 272
Figure 6.13 – 2D medium mesh (P/k = 9; 2s). ______________________________ 272
Figure 6.14 – 2D fine mesh (P/k = 9; 2s).__________________________________ 272
Figure 6.15 – Mesh sensitivity test and comparison of 2D vs 3D case (P/k = 9; 2s) for
the Nusselt distribution using the v2-f model._______________________________ 273
Figure 6.16 – Mesh sensitivity test and comparison of 2D vs 3D case (P/k = 9; 2s) for
the streamwise velocity distribution at y/k = 0.1 using the v2-f model. ___________ 273
Figure 6.17 – Mesh sensitivity test and comparison of 2D vs 3D case (P/k = 9; 2s) for
the wall-normal velocity distribution at y/k = 1 using the v2-f model.____________ 274
Figure 6.18 – Mesh sensitivity test and comparison of 2D vs 3D case (P/k = 9; 2s) for
the friction coefficient distribution using the v2-f model.______________________ 274
Figure 6.19 – The computational domains used for 2s configuration with different rib
thermal boundary conditions (a) Heated ribs (b) Insulated ribs_________________ 275
Figure 6.20 – Nusselt distribution for P/k = 9; 2s and two different rib thermal boundary
conditions.__________________________________________________________ 275
Figure 6.21 – Contour plots of temperature in the vicinity of the rib with different rib
thermal boundary condition (a) Uniform heat flux at the ribs (b) Insulated ribs____ 275
Figure 6.22 – Nusselt distribution for P/k = 9; 1s and various turbulence models. __ 276
Figure 6.23 – Streamlines for P/k = 9; 1s and various turbulence models. ________ 276
Figure 6.24 – Streamwise velocity distributions for P/k = 9; 1s at y/k = 0.1 for various
turbulence models. ___________________________________________________ 277
Figure 6.25 – Wall-normal velocity distributions for P/k = 9; 1s at y/k = 1 for various
turbulence models. ___________________________________________________ 277
Figure 6.26 – Friction coefficient distributions for various turbulence models._____ 277
Figure 6.27 – Streamwise velocity profiles for P/k = 9; 1s on the rib-top (x/k = 0) for
various turbulence models. _____________________________________________ 278
Figure 6.28 – Streamwise velocity profiles for P/k = 9; 1s at x/k = 4 for various
turbulence models. ___________________________________________________ 278
Figure 6.29 – Pressure coefficient distributions for P/k = 9; 1s for various turbulence
models. ____________________________________________________________ 278
Figure 6.30 – Contour plots of the streamwise velocity for P/k = 9; 1s for various
turbulence models. ___________________________________________________ 279