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 |  موضوع: كتاب Computational Fluid Dynamics - A Practical Approach الإثنين 03 فبراير 2020, 11:33 pm | |
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أخوانى فى الله
أحضرت لكم كتاب
Computational Fluid Dynamics
A Practical Approach
Third Edition
Jiyuan Tu
RMIT University, Australia
University of New South Wales, Australia
Tsinghua University, P.R. China
Guan-Heng Yeoh
Australian Nuclear Science and Technology Organisation
University of New South Wales, Australia
Chaoqun Liu
University of Texas at Arlington, USA
و المحتوى كما يلي :
Chapter 1 Introduction
Chapter 2 CFD Solution Procedure: A Beginning
Chapter 3 Governing Equations for CFD: Fundamentals
Chapter 4 CFD Mesh Generation: A Practical Guideline
Chapter 5 CFD Techniques: The Basics
Chapter 6 CFD Solution Analysis: Essentials
Chapter 7 Practical Guidelines for CFD Simulation and Analysis
Chapter 8 Some Applications of CFD With Examples
Chapter 9 Some Advanced Topics in CFD
Chapter e1 CFD Case Studies
Appendix A Full Derivation of Conservation Equations
Appendix B Upwind Schemes
Appendix C Explicit and Implicit Methods
Appendix D Learning Program
Appendix E CFD Assignments and Guideline for CFD Project
Index
Note: Page numbers followed by f indicate figures, and t indicate tables.
A
Acceleration, 77–78
force balance, 73
stagnation streamline, 80, 80f
Accuracy
channel flow, 242–244
grid convergence, 230
solution errors
control, 236–238
discretisation error, 231–234, 232–233f
human error, 236
iteration/convergence error, 235
physical modelling error, 235–236
round-off error, 234–235
verification and validation, 238–239
truncation error, 229
Adaptive mesh, 145–146
redistribution, 145–146
refinement, 145–146
Adiabatic wall temperature, 119
Advantages, 4–5
Advection, 66–67, 77–78, 156, 420
Aerodynamic helmet, 26–27, 27f
Aerodynamics, 10, 11f
Aerofoil, 348–349, 350f, 443
lift curve slope, 443, 443f
plain flap, 443, 443f
Aerospace, 9–10, 9f
Ahmed model, 325–326, 326f, 437
drag coefficient for, 438, 439f
lift coefficient, 438, 439f
two-dimensional geometry of, 437, 437f
Algebraic equations
direct methods, 185–189
iterative methods, 189–193
Algebraic multigrid (AMG) algorithm, 47–48
Alternating direction implicit (ADI), 193, 371
Animation, 60–61
ANSYS CFX software, 35–36, 36f
ANSYS FLUENT software, 35–36, 37f, 268
Applications
aerospace, 9–10, 9f
air/particle flow in human nasal cavity,
331–337, 332–337f
automotive engineering, 10–12, 11f
biomedical science and engineering, 12–15,
12–14f
buoyant free-standing fire, 320–325, 321f,
323–324f
chemical and mineral processing, 15–17,
16–17f
civil and environmental engineering, 17–19,
18–19f
conjugate and radiation heat transfer,
312–320, 313–315f, 319t, 319–320f
as design tool, 8–9
as educational tool, 7–8
flow over vehicle platoon, 325–330,
326–327f, 329–331f
heat exchanger, 305–312, 306f, 308f, 309t,
310–312f
high speed flows, 338–360, 339–340f, 341t,
342f, 344–360f, 344t
indoor airflow distribution, 292–298
metallurgy, 19–20, 20–21f
nuclear safety, 20–22, 22f
power generation and renewable energy,
22–25, 23–25f
as research tool, 6–7
gas-particle flow in 90 degrees bend,
299–305, 300f, 301t, 303–304f
sports, 25–27, 26–27f
Artificial compressibility, 371
Automotive engineering
aerodynamics, 10, 11f
CFD in, 10
diesel internal combustion engine, 10–12, 11f
numerical simulations, 10–12
B
Backward-facing step geometry, 142, 143f, 435
local mesh refinement, 142, 143f
turbulent flow over, 444–445
Bernoulli’s equation, 79
467Black boxes, 33
Block-structured grids, 144–145
Body-fitted mesh, 128–133
Cartesian coordinates, 131
computational geometry, 130f
elliptic grid generation method, 132–133
Hermite interpolation, 132
staircase-like steps, 130f
transfinite interpolation method, 131
Body forces, 74
Boundary conditions
for an external flow problem, 43–44, 43f
buoyancy driven flows, 44
combusting flows, 44
cyclic, 44, 45f
for external flows, 278
inflow and outflow boundaries, 42
inlet, 258–260, 259–260f
for internal flows, 42–43, 43f, 278
for k–? model, 278
outlet, 260–261, 261f
overview, 256–258
periodic, 262–263, 263–264f
solid walls, 43–44
for solid walls, 278
subsonic fluid flows, 44–45
supersonic fluid flows, 44–45
symmetry, 44, 45f, 262–263, 263–264f
turbulent kinetic energy, 277–278
wall, 261–262, 262f
Boundedness, 180
Bronchial tree geometry, pulmonary system, 13,
14f
Buoyant fire
bulge structure, 321–322
buoyant plume, 320–321, 321f
CFD simulation, 322
flickering behaviour, 322–324, 323f
intermittent flame, 320–321, 321f
LES, 322
persistent flame, 320–321, 321f
puffing effect, 321–322, 323f
SGS, 322
soot model, 322, 324f, 325
vortex, 321–322
Buoyant plume, 320–321, 321f
C
Carbon dissolution, 20
Cartesian mesh, 127–129
Central processing units (CPUs), 241, 384,
387
Channel flow
accuracy, 242–244
collocated grid arrangement, 242
consistency, 242–244
double precision, 244
grid convergence, 242
horizontal velocity, convergence histories of,
242, 243f
SIMPLE scheme, 242
single-precision, 244
solution error, 244, 244t
Channel length
horizontal velocity, 71f
vertical velocity, 71–72, 72f
Chebyshev polynomials, 156
Chimera grids. See Block-structured grids
Codes
commercial CFD, 35–36
elements, 34
Shareware CFD, 34
Combustion, 400–402
Commercial CFD codes, 35–36, 51–52
internet links, 35–36, 36t
Compressible flows, 6
adaptive meshing, 378–380, 379f
embedded shock waves, 373
explicit method, 373
high resolution schemes
MUSCL, 375
PPM, 375
propagating wave, 374–375, 374f
TVD, 375
implicit method, 373
pressure drag, 373
r-refinement technique, 378–380, 379f
wave drag, 373
Computational aeroelasticity (CAE), 402–403
Computational domain, 36–38
Computational efficiency, 372
Computational models, advances in
combustion, 400–402
DEM, 413–415
DNS, 390–393
fluid–structure interaction, 402–404
LBM, 407–408
LES, 393–396
Monte Carlo method, 409–410
multiphase flows, 398–400
particle methods, 411–413
physiological fluid dynamics, 404–406
RANS–LES coupling, 396–398
Computational simulations, 3–4
468 IndexComputational solutions, 155, 157–158, 157f
channel flow, 242–245
consistency, 212–216
convergence
accelerating, 228–229
definition, 222–224
difficulty, 227–228
residuals and, 224–226
underrelaxation factors, 227–228
efficiency, 239–241
flow over 90o bend, 245–250, 245f
solution errors
control, 236–238
discretisation error, 231–234, 232–233f
human error, 236
iteration/convergence error, 235
physical modelling error, 235–236
round-off error, 234–235
verification and validation, 238–239
stability, 216–222
Compute unified device architecture (CUDA),
241
Conservation equations
advection term, 420
control volume, 421
Newton’s law of viscosity, 422
Stokes’ hypothesis, 422
substantial derivative, 419
Conservativeness, 181
Consistency
control volume, for two-dimensional
structured grid, 213, 213f
face velocities, 213
one-dimensional transient diffusion equation,
214
steady-state solutions, 215, 215–216f
Taylor series expansion, 213–215
truncation error, 212
Continuity equation
comments, 72–73
mass conservation, 65–68
physical interpretation, 69–72
Continuous forcing approach, 389
Contour line, 56
Contour plots
flooded contours, 56, 56–57f, 59f
isolines, 56
isosurface, 56
line contours, 58f
rainbow-scale colour map, 56, 56–57f
Convergence
acceleration, 228–229
ANSYS CFX GUIs, 48–50, 49f
definition, 222–224
difficulty, 227–228
error(s), 235
error estimation, 50
FLUENT GUIs, 48–50, 49f
grid, 223–224
imbalances, 48–50
iterative, 223–224
lift coefficient, 48–50
one-dimensional transient diffusion equation,
223, 223f
parabolic laminar velocity, 51f
residuals and, 48–50, 223–226
tolerance values, 48–50
underrelaxation factors, 50, 227–228
Cooling, electronic components within
computer, 448–449
Cooling tower, plume dispersion, 18f
Courant–Friedrichs–Lewy (CFL) condition,
218
Courant number, 228–229
CPUs. See Central processing units (CPUs)
Crank–Nicolson methods, 429–430
CUDA processing flow paradigm, 386, 386f
Cyclic boundary condition, 44, 45f
D
Delaunay triangulation, 134
Density fluctuation, 347–348, 348f
Design tool, 8–9
Diesel internal combustion engine, 10–12, 11f
Diffuser grill, 296, 297f
Direct methods
back substitution process, 186–187
forward elimination, 186–187
Gaussian elimination, 185
Thomas algorithm, 186–188
Direct numerical simulation (DNS), 28,
264–265
explicit methods, 391–392
implicit methods, 391–392
k-? two-equation turbulence model,
100–101
Kolmogorov microscales, 390
numerical issues, 391
RANS, 392–393
Reynolds number, 391
supersonic flow, over flat plate, 340–341,
347, 347f
turbulence models, 264–265
turbulent flow, 390
Index 469Direct simulation Monte Carlo (DSMC),
409–410
Dirichlet boundary condition, 118,
256–257
Disciplines, 1–2, 2f
Discontinuous Galerkin method, 156
Discrete element method (DEM), 413–415
Discrete forcing approach, 389
Discrete random walk (DRW) model, 302
Discretisation approach, 126
Discretisation error, 237, 237f
convection-type equation, 233f
Euler explicit method, 232
global, 231, 232f
leapfrog method, 233
local, 231, 232f
Distorted air diffusion, 296, 297f
Diverging residuals, 227
DNS. See Direct numerical simulation (DNS)
Domain decomposition, 384–385
Donor-cell concept, 178–179
Drag coefficient, 328–330, 328f, 438–439, 439f
DSMC. See Direct simulation Monte Carlo
(DSMC)
Dynamic mesh model, 18–19
E
Eddy-lifetime model, 301
Efficiency
CPUs, 241
explicit marching methods, 240
GPUs, 241
implicit methods, 240–241
parallel computing, 240
steepest descent methods, 239–240
Elliptic grid generation method, 132–133
Embedded Cartesian mesh, 144, 144f
Energy cascade, 99–100
Energy conservation
for compressible flow, 90
conservative form, 90
dissipation function, 90
energy fluxes, 89
first law of thermodynamics, 88
for incompressible flow, 90–91
nonconservative form, 88–89
surface forces, 88, 89f
Energy equations
acceleration, 91–97
advection, 91, 97
comments, 88–91
diffusion, 91, 97
dimensionless temperature profiles, 95–96,
95–96f
energy conservation, 87–88
friction, 97
physical interpretation, 88–98
Errors
defined, 230–231
discretisation, 231–234, 232–233f
high frequency, 382–383
human, 236
iteration/convergence, 235
low-frequency, 382–383
physical modelling, 235–236
round-off, 234–235
Essentially non-oscillatory (ENO) schemes, 376
Explicit methods, 182, 183f, 429–430
compressible flows, 373
DNS, 391–392
Stability, 222
External flow, 38
F
Finite difference method
algebraic equation system, 170–171
backward difference, 161–162
Cartesian grids, 158–159
central difference, 160–161
forward difference, 161–162
grid lines, 159
partial differential equations, 159–160
second-order derivative, 162
Taylor series expansions, 158, 160, 162
truncation error, 160–161
uniform grid spacing, 170f
uniform spacing, 159–160
Finite element method
Galerkin method, 168–169
governing equations, 168–169
linear shape functions, 168–169
Finite-volume discretization
control volumes, 174–175, 175f
of large brick plate domain, 174–175, 175f
Finite volume method, 47
algebraic equation system, 171–173
control volume, 163–165, 171, 171f
diffusive fluxes, 172
discretized continuity equation, 166
first-order derivative, 164–167
Gauss’s divergence theorem, 164–167
heat conduction problem, 174
interpolation, 163
second-order derivative, 167
470 Indexstructured mesh, 163–164, 164f, 168f
two-dimensional structured grid, 165, 166f
unstructured mesh, 163–164, 164f
F18 jet, 9, 9f
Flat plate
boundary layer thickness, 70, 70f
two-dimensional flow, 69, 69f
velocity ratio, 70, 70f
Flickering behaviour, 322–324, 323f
Flooded contours
on grey-scale colour map, 57–58, 59f
on rainbow-scale colour map, 56, 56–57f
Flow
external, 38
internal, 38
Fluid flow
flow between two stationary parallel plates,
36–38, 37f
heat transfer coupled with, 305–320
passing over two cylinders, 36–38, 38f
vehicle platoon, 325–330
Fluidized coal bed, 23–24, 24f
Fluid motion
circular cylinder, 78, 78f
in piston mechanism, 77, 77f
venturi, 77–78
Fluid–structure interaction, 402–404
Force balance
body forces, 74
substantial derivative, 75
surface forces, 74, 74f
Friction coefficients, 115–116, 116f
Friction forces, 87
Fully coupled model, 403
G
Gaphical user interface (GUI)
ANSYS CFX software, 35–36, 36f
ANSYS FLUENT software, 35–36, 37f
Gas cyclones, 15–16, 17f
Gas-particle flows, 298–299
in 90 degrees bend
ANSYS FLUENT, 299
computational meshes, 299, 300f
DRW model, 302
eddy-lifetime model, 301
Eulerian approach, 301–305
gas tracers, 304
grid, 299
Lagrangian approach, 300–301
LDA system, 299
mean streamwise gas velocity, 303, 303f
Reynolds number, 301
Stokes number, 302–304, 304f
transport equations, 301, 301t
solid particles, 298–299, 298f
Gas-sparged stirred tank reactor, 15, 16f
Gas tracers, 304
Gaussian elimination, 185
Gauss’s divergence theorem, 65–66, 164–167
Gauss–Seidel method, 190–192
Geometry creation
computational domain, 36–38
fluid flow cases, 36–38, 37f
Global solution algorithm, 285–286
Governing equations
for compressible flow in Cartesian
coordinates, 109, 112t
continuity
comments, 72–73
mass conservation, 65–68
physical interpretation, 69–72
conversion to algebraic equation system
finite difference method, 170–171
finite difference vs. finite volume
discretizations, 173–184
finite volume method, 171–173
discretization
finite difference method, 158–163
finite element method, 168–169
finite volume method, 163–167
spectral method, 169
energy
comments, 88–91
energy conservation, 87–88
physical interpretation, 88–98
generic form, 108–117
for incompressible flow in Cartesian
coordinates, 109, 110t, 112t
momentum
comments, 77–87
force balance, 73–88
physical interpretation, 73–76
numerical solutions
direct methods, 185–189
iterative methods, 189–193
multigrid method, 204–206
pressure–velocity coupling, 193–204
physical boundary conditions, 117–120
turbulent flow
comments, 108
k-? two-equation turbulence model,
100–107
turbulence, 98–100
Index 471Graphics processing units (GPUs), 241,
385–387
Grid distortion, 150
GRIDGEN, 126–127
Grid generation, 148
Grid independence, 151–152, 237–238
GRIDPRO, 126–127
Guidelines
for boundary conditions
inlet, 258–260, 259–260f
outlet, 260–261, 261f
overview, 256–258
symmetry and periodic, 262–263,
263–264f
wall, 261–262, 262f
global solution algorithm, 285–286
on problem definition, 284–285
on solution strategy, 285–286
for turbulence modeling
hydrofoil flows, two-equation turbulence
modeling for, 279–284
near wall treatments, 273–277, 275f
overview, 264–267, 265f
selection strategy, 267–273
setting boundary conditions, 277–279
on validation, 286
H
Hagen–Poiseuille flow, 83–84
Hard-sphere model, 414
Heat conduction, 174
solid slab, 91–92, 92f
Heat exchanger
CFD simulation, 315–316
conjugate, 312–320
cyclic boundary conditions, 307
dimensionless parameters, 305
hybrid mesh, 308–309
in-line arrangement, 305–307, 306f, 309t,
310f
momentum equation, 316
radiation, 312–320
Reynolds number, 310–311, 310–311f
single plate-type molybdenum target,
312–313, 313f
smoke seeding, 318–319
smoke traces, 318–319, 318f
SST model, 317–318
staggered arrangement, 305–307, 306f, 309t,
311f
symmetric boundary conditions, 307
target plate, 313–315, 314–315f
temperature contours, 319, 319f
tube banks, 305, 306f
Hermite interpolation, 132
H-grid, 136–137, 138f
High speed flows
subsonic and supersonic flows over wing
aerofoil, 348–349, 350f
boundary conditions, 357
CFD simulation, 351
C-type mesh scheme, 351–352, 352f
free-slip condition, 351–352
instantaneous spanwise vorticity,
357–360, 357f, 359f
local Mach number, 352–354, 353–354f
multiblock mesh, 351, 351f
no-slip condition, 351–352
RANS, 350–351
stall position, 354–356
temperature contours, 356–357, 356f
velocity vectors, 354–356, 355f
supersonic flow, over flat plate
boundary conditions, 342–343, 342f
boundary layer, 338
CFD simulation, 341
density fluctuation, 347–348, 348f
DNS, 340–341, 347, 347f
laminar flow, 339–340, 343, 344t
local Mach number, 343–346, 346f
Navier–Stokes equations, 341
normalized component velocity, 343–346,
345f
normalized temperature, 343–346, 345f
parameters, 341t
Reynolds number, 339–340
Sutherland’s law, 342
temperature contours, 343, 344f
three-dimensional computational domain,
340–341, 340f
two-dimensional computational domain,
339–340, 339f
velocity vectors, 343, 344f
viscous dissipation, 338
wall-normal vorticity, 349f
Human error
computer programming, 236
usage, 236
Human nasal cavity
airflow rate, 335–336
air/particle flow in, 331–337
CFD simulation, 333–334
internal walls, 334
QUICK scheme, 333–334
472 Indexspray cone angles, 336–337, 336–337f
spray particle deposition, 331
surface topology, 332, 333f
velocity profiles, 332–333, 334f
Hybrid grids, 140
Hybrid RANS–LES models, 397–398
Hydrocyclone, 15–16, 17f
Hydrodynamic entry length, 84, 84f
I
Ice–water interface, 381, 382f
Immersed boundary methods, 387–390
Implicit method, 183, 184f, 429–430
compressible flows, 373
DNS, 391–392
efficiency, 240–241
residuals, 226–227
stability, 222
Incompressible flows, 6
artificial compressibility approach, 371
definition, 369–370
fractional step procedure, 370–371
Poisson’s equation, 370
pressure iteration, 370
Indoor airflow
computational mesh, 293, 294f
diffuser grill, 296, 297f
distorted air diffusion, 296, 297f
grid, 293
LES, 293–294
LRN turbulence, 292–293
model room, 293, 293f
model validation, 294–295
pressure–velocity coupling, 293–294
RANS approach, 293–294
RNG-based LES model, 295–296
room ventilation system, 296
simulation features, 293–294
symmetrical air diffusion, 296, 297f
ventilated compartment, 296, 296f
vertical inlet velocity, 293–296, 295f
Inhomogeneous multiphase model, 20–22
Inlet boundary conditions
backward-facing step geometry, 259–260, 260f
flow between two stationary parallel plates,
258–259, 259f
parameters, 258
Intelligent transport systems (ITS), 325
Interface capturing, 399–400
Interface-tracking methods, 399–400
Intermittent flame, 320–321, 321f
Internal flow, 38
Intervehicle spacing, 328–329, 329f
Inviscid fluid flows, 41–42
Iteration errors, 235
Iterative methods
Gauss–Seidel method, 190–192
Jacobi method, 189
steady heat conduction problem, 190
successive overrelaxation, 192–193
Iterative solvers, 47–48
Itsukushima torii, 18–19, 19f
J
Jacobi method, 189
Kk-?
two-equation turbulence model
Cartesian tensor notation, 102
conservative form, 104
DNS, 100–101
laminar velocity profiles, 105–108, 106f
laminar viscosity, 105–108, 106f
Newton’s law of viscosity, 102
nonconservative form, 104
Reynolds stresses, 100–102
turbulent momentum transport, 102
turbulent velocity profiles, 105–108, 106f
turbulent viscosity, 105–108, 106f
Kolmogorov microscales, 390
k–? model, 272–273
L
Laminar viscosity, 105–108, 106f
Large-eddy simulation (LES), 28, 264–265,
389, 393–396
Laser Doppler anemometry (LDA) system, 299
Lattice Boltzmann equation (LBE), 407–408
Lattice Boltzmann method (LBM), 407–408
operations, 408
Lax method, 218
Lead model, 326–328, 327f
Learning program, 431–434
LES. See Large-eddy simulation (LES)
Lift coefficient, 48–50
Load balancing, 384–385
Local mesh refinement
backward-facing step geometry, 142, 143f
boundary layer, 141
embedded Cartesian mesh, 144, 144f
stretched grid, 140–141
truncation error, 141–142
upward stagnation flow, 142
viscous-like velocity profile, 141
Index 473Log-law layer, 274
Longitudinal mean velocity, 246–247, 247f
Loosely coupled model, 403
Low-Reynolds-number (LRN), 292
M
Marker-and cell (MAC) method, 370–371
Mass conservation, 65–68, 66–67f
Mass residual, 199
convergence history of the, 202f
Medical simulations, 12–13
Menter’s model, 272–273
Mesh generation, 39–40
adaptive mesh with solution, 145–146, 146f
definition, 125
discretization approach, 126
local refinement, 140–144, 142–144f
moving meshes, 146–148, 148f
overlapping grids, 144–145, 145f
quality and design, 148–152, 150–151f
rectangular Cartesian meshes, 126
topology, 136–140, 137–141f
types
body-fitted, 128–133, 130f
structured, 127–128, 128–129f
unstructured, 133–135, 133f, 136f
Metallurgy, 19–20
Mineral processing, 15–16
Molten iron, flow pattern of, 20
Momentum equations
comments, 77–87
force balance, 73–88
physical interpretation, 73–76
Monitor function, 147
Monotone upwind scheme for conservation
laws (MUSCL), 375
Monte Carlo method, 409–410
Moving grids, 380–381
Moving meshes, 146–148, 148f
for swinging limb, 147, 148f
Multiblock mesh, 136–137, 138f, 351, 351f
Multigrid methods, 381–384
highfrequency errors, 382–383
low-frequency errors, 382–383
Poisson-like pressure, 204
V-cycle, 204–206, 205f, 381–383
W-cycle, 204–206, 383–384
Multiphase flows, 398–400
N
Nasal cavity, particle transport/deposition,13, 14f
Nasal sprayers, particle formation/dispersion,
13, 14f
Navier–Stokes equations, 156, 174–177
physical modelling error, 235–236
Near-wall models, 273
Neumann boundary condition, 118, 257
Newton’s law of viscosity, 102
Non-linear disturbance equation (NLDE)
approach, 397
Nonuniform grid distribution, 173
Nonuniform rectangular mesh, 127–128, 129f
No-time-counter technique, 410
Nuclear safety, 20–22
Numerical errors, 236–237
Numerical methods
compressible flows, 373–380
CUDA processing flow paradigm, 386–387,
386f
GPU, 385–387
immersed boundary methods, 387–390
incompressible flow, 369–372
LBM, 407–408
moving grids, 380–381
multigrid methods, 381–384
parallel computing, 384–385
Numerical solutions
to algebraic equations
direct methods, 185–189
iterative methods, 189–193
convergence, monitoring, 48–51, 49–51f
initialization and solution control, 46–48
O
Off-gas combustion, 20, 21f
O-grid, 136–137, 139f
Olympic bikes, 26–27
Optimum stroke, 25–26, 26f
Ordinary differential equations (ODEs), 411
Outlet boundary conditions, 260–261, 261f
Overlapping grids, 144–145, 145f
Overlapping mesh techniques, 144–145,
145f
P
Parabolic laminar velocity, 51f
Parabolic profile, 83–84
Parallel computing, 240, 384–385
Partial differential equations, 155, 159–160
Particle methods, 411–413
ODEs, 411
SPH, 411
truncation errors, 411
VMs, 411–412
Peclet numbers, 180–181
474 IndexPeriodic boundary conditions, 263, 264f
Persistent flame, 320–321, 321f
Physical modelling error, 235–236
Physiological fluid dynamics, 404–406
Pickup trucks
with open/closed tubs, 446–447
recirculation flow region, 330, 331f
Piecewise parabolic method (PPM), 375
Poisson’s equation, 199
Poject-based learning (PBL), 8
Polyhedral cells, 135, 136f, 145–146
Population balance approach, 399
Power generation, 22–25
Power-law differencing scheme, 181
Prandtl number, 97–98
Pressure
coefficient values for patient with and
without asthma, 13, 14f
convergence history of, 201f
correction, 202f
drag, 373
iteration, 370
Pressure–velocity coupling, 293–294
collocated grid arrangement, 195–196, 195f
control volume, velocity components on,
195–196, 195f
pressure-correction equation, 196
SIMPLE, 194, 197f
iterative steps, 196–203
pressure-correction equation, 196
staggered grid arrangement, 194, 195f
Problem definition, 284–285
Problem setup
boundary conditions, 42–45, 43f, 45f
geometry creation, 36–39
mesh generation, 39–40
physics and fluid properties selection, 40–42,
41f
Puffing effect, 321–322, 323f
Pure diffusion process, 170
Q
Quadratic upstream interpolation convective
kinetics (QUICK), 47
Quadrilateral cell, 149–150, 150f
QUICK schemes, 427–428
R
Realizable k-? model, 269–271
Rectangular Cartesian meshes, 126
Research tool, 6–7
Residuals
in CFD, 224
convergence tolerance, 225–227
implicit methodology, 226–227
qualitative convergence, 225–227
quantitative convergence, 225–227
Reynolds averaged Navier-Stokes (RANS),
100–101
Reynolds stresses, 100–102
Reynolds stress model, 246–250, 266
RNG k-? model, 268–271
Robust solvers, 47–48
Round-off error, 234–235, 237, 237f
double precision, 234
single precision, 234
S
Scalability, 384
Semi-implicit method for pressure-linkage
equations (SIMPLE)
iterative steps, 196–203
pressure-correction equation, 196
Shareware CFD, 34
Shear-stress transport (SST), 273, 317–318
Side-by-side cylinders, CFD simulations, 6–7,
6–7f
Simple chemical reacting system (SCRS),
401–402
SIMPLE-consistent (SIMPLEC) algorithm,
203–204
SIMPLE-revised (SIMPLER) algorithm,
203–204
Single instruction multiple data (SIMD),
386–387
Skewness, 150
Smagorinsky subgrid-scale (SGS) turbulence
model, 322
Smoke seeding, 318–319
Smoke traces, 318–319, 318f
Smooth particle hydrodynamics (SPH),
411–413
Soft-sphere model, 413–414
SolarFox 3, 25, 25f
Solid modeller packages, 39
Solution errors
control, 236–238
discretisation error, 231–234, 232–233f
human error, 236
iteration/convergence error, 235
physical modelling error, 235–236
round-off error, 234–235
verification and validation, 238–239
Index 475Solution strategy, 285–286
Solvers, 46
iterative, 47–48
robust, 47–48
Soot model, 322, 324f, 325
Spectral method, 169
Sports Engineering Research Group (SERG),
26–27
Stability
convection-type equation, 220
Courant–Friedrichs–Lewy condition, 218,
220–222
Euler method, 218–220
explicit method, 222
finite-difference discretization, 218–220
implicit method, 222
latter criterion, 217–218
Lax method, 218
for linear problems, 216–222
matrix method, 216–222
one-dimensional transient diffusion equation,
218–219
time advancement, 219f, 220, 221f, 222
von Neumann method, 216–222
Stagnation streamline
acceleration, 80, 80f
pressure difference, 80, 80f
velocity profile, 79–80, 79f
Standard k–? model, 266–267, 271–272
weakness, 267–272
STAR-CD, 51–52
Steady convection-diffusion process, 177
Steady heat conduction problem
Gauss–Seidel method, 191–192
Jacobi method, 190
in large brick plate, 174, 174f
Thomas algorithm, 188
Stenosed artery, 12–13, 12f
Stokes number, 302–304, 304f
Streamlines, 58–59
Stress–strain relationships, 75–76
Strongly implicit procedure (SIP), 47–48, 193
Structured mesh, 127–128, 157–158, 163–164,
164f, 168f
elemental cells, 136, 137f
H-grid, 136–137, 138f
multiblock, 136–137, 138f
nonuniform rectangular mesh, 127–128,
129f
O-grid, 136–137, 139f
uniform rectangular mesh, 127, 128f
Subgrid-scale (SGS) model, 393–394
Subsonic fluid flows, 44–45
Successive overrelaxation, 192–193
Supersonic fluid flows, 44–45
Surface forces, 74, 74f
Sutherland’s law, 342
Symmetry boundary condition, 44, 45f,
262–263, 263f
T
Taylor series expansion, 155–156, 178
TECPLOT, 51–53
Test runs, 148–149. See also Mesh generation
Thermal entry length, 94–95, 94f
Thomas algorithm, 184–185
direct methods, 186–188
Three-dimensional turbulent flow, over 90o
bend, 245–250, 245f
Total error, 237, 237f
Transfinite interpolation method, 131
Transportiveness, 179–180
Triangular mesh, 133f
Truncation error, 141–142
accuracy, 229
consistency, 212
finite difference method, 160–161
local mesh refinement, 141–142
particle methods, 411
Turbulence, 98–100
random fluctuations, 98–100
Turbulence models
advanced techniques, 264–265
DNS, 264–265
hydrofoil flows, two-equation turbulence
modeling for, 279–284
LES, 264–265
near wall treatments, 273–277, 275f
practical techniques, 265–267
selection strategy, 267–273
setting boundary conditions, 277–279
turbulent motion, 264–265, 265f
two-dimensional hydrofoil geometry
boundary conditions, 281
grid, 280
model description, 280
pressure-surface boundary-layer velocity
profiles, 282–284, 283f
simulation features, 280–281
wall treatment analysis, 282, 282–283f
Turbulent boundary layer, 273–274, 275f
Turbulent flow
comments, 108
k-? two-equation turbulence model, 100–107
RANS-LES coupling for, 396–398
turbulence, 98–100
476 IndexTurbulent fluctuations, 99–100
Turbulent viscosity, 394
Two-dimensional laminar flow, 200, 200f
U
Underrelaxation factors, 149–150, 227–228
Uniform rectangular mesh, 127, 128f
Unsteady convection-diffusion process, 181
Unstructured mesh, 137–139, 157–158,
163–164, 164f
for circular cylinder, 140f
Delaunay triangulation, 134
polyhedral, 135, 136f
quadtree/octree method, 135
vs. structured mesh, 139–140
for three-dimensional grid generation, 135
triangular mesh, 133f
Upwind differencing scheme, 179–180, 180f
Upwind schemes, 427–428
V
Validation, 239
guidelines, 286
V-cycle, 204–206, 205f, 381–383
Vector plots
localized wake recirculation zones, 55–56,
55f
parallel-plate channel, fluid flow, 54–55, 55f
Vehicle platoon
Ahmed car geometry, 325–326, 326f
drag coefficient, 328–330, 328f
Ford Falcon EXT 2003 model, 330, 330f
high drag configuration, 329, 329f
intervehicle spacing, 328–329, 329f
ITS, 325
lead model, 326–328, 327f
pressure pathlines, 329–330, 330f
recirculation flow region, pickup truck, 330,
331f
trailing model, 327–328
turbulent flow, 328
wind-tunnel configuration, 327–328
Velocity profile
downstream locations, 84–86, 85–86f
stagnation streamline, 79–80, 79f
Verification, 239
Vertical inlet velocity, 293–296, 295f
Virtually stented arteries, 12–13, 12f
Viscous dissipation, 338
Viscous fluid flows, 41–42
Viscous sublayer, 272, 274
VMs. See Vortex methods (VMs)
Volume of fluid (VOF), 399–400
von Neumann method, 216–222
Vortex methods (VMs), 411–412
Vortex stretching, 99–100
W
Wall boundary conditions
fluid flow with moving or rotating walls, 262,
262f
solid walls, 261
stationary walls, 261–262
Wall functions
with low-Reynolds-number turbulence
models, 277
near-wall meshing guidelines on, 276
Wall shear stress (WSS), 12f
Warp angles, 151
Water tank, CFD simulation, 18f
Water turbulence, 25–26
Wave drag, 373
Wavy channel, 440, 440f
W-cycle, 204–206, 383–384
Weighted ENO (WENO), 376
Wind-tunnel configuration, 327–328
Wind-tunnel testing, 5
Wind turbine, 22–23, 23f
XX–
Y plots
laminar velocity profile, 51f, 53–54
normalized horizontal velocity, 53–54, 54f
two-dimensional velocity profiles, 53–54, 53f
Z
Zero prototype engineering, 27–28
Index 477
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