Versteeg H., Malalasekra W. An Introduction to Computational Fluid Dynamics: The Finite Volume Method
Подождите немного. Документ загружается.
INDEX 497
ε
estimation 271
eddies 42
isotropic 44
large 44, 66
simulation 66
viscosity and diffusivity 67–8
see also large eddy simulation
eddy break-up model of combustion 385–8
eddy dissipation concept 388
effective mixing 41
electromagnetic waves 417
elliptic equations 27, 31–2
emitted intensity 418, 419
emitted radiative heat flux 418
endothermic reactions 351, 354
energy cascade in eddies 42
energy equation
for combustion 364–6
in 3D 16–20
source terms 420–3
energy flux 17–18
enthalpy 3, 20
of combustion 345, 349
equations in laminar diffusion flame 372
of formation 345–6, 349
entrainment 55
equations of fluid flow 24
equations of state 20–1
equilibrium
in combustion 351–5
condition for 352
problems of 27
equivalence ratio 348–9, 415
ERCOFTAC guidelines 299
errors 5, 285–6
Eulerian approach 12
explicit scheme 246–7
face velocity interpolation method 340–1
false diffusion 150
Favre average 377, 379, 380
Favre averaged equation 383, 403
Favre averaged reaction rates 385
finite difference methods 112
finite rate chemistry of laminar diffusion flame 374–5
finite volume method 115
for one-dimensional diffusion 115–29, 135–6
for three-dimensional diffusion 131–2
for two-dimensional diffusion 129–31
finite volume method in radiative heat transfer 437
fire in a test room 463–7
flame sheet model 384
flame structure, predicting 404–11
flame surface density models 415
flamelet-based NO modelling 402
flamelet equations in mixture fraction space 395–7
flamelets 389
FlameMaster 396, 397, 398
flow simulation 445–7
FLUENT 3, 156
fluid flow, boundary conditions of 24
fluid medium 419
fluid properties and input uncertainty 290–1
fluid properties of radiative heat transfer 419–20
flux, consistent representation of 141
flux limiter functions 170–1
forward elimination 213–14, 222
free turbulent flow 53–7
fully implicit scheme 246, 248–9
gaseous combustion 343
gaseous mixtures
properties 346–8
radiative properties in 442–3
gauge pressure 210
Gauss–Seidel iteration method 4, 212, 213, 225–6
with relaxation 228
Gauss’ theorem 314
Gaussian elimination 212
general transport equations 24–6
geometric multigrid method 241
Gibbs function 351, 352
governing equations
energy 16–20
mass conservation 10–12
momentum 14–16
rates of change 12–14
grid 2
and flow simulation 445–7
non-uniform 448–9
grid generation
in finite volume method 116
in multigrid methods 241
grid-independence 5
hairpin Λ-vortices 47
heat addition 18
heat conduction, energy flux due to 17–18
hexanogal ring geometry 329–36
higher-order finite difference methods 112
hybrid differencing scheme 151–5
assessment of 154
for multi-dimensional convection-diffusion 154–5
hybrid meshes 312
hydrodynamic instability 44–5
hyperbolic behaviour 35
ANIN_Z09.qxd 29/12/2006 10:12 AM Page 497
hyperbolic equations 27, 28–9
role of 29–32
I-DEAS 3
implicit scheme 246
for two- and three-dimensional problems 256
incident radiation 418
incident radiative heat flux 418, 422, 423
incompressible fluids
3D mass conservation in 12
equations of state 21
in planar nozzle 456–8
incompressible viscous flow
boundary conditions for 36
indirect methods 212
initial-boundary-value problems 28
inlet boundary conditions 268–71
perpendicular 271
reference pressure 270–1
input uncertainty 289–91
boundary conditions 290
domain geometry 289–90
fluid properties 290–1
quantification of 301
and validation 295–6
intermediate combustion reactions 355–6
intermittency 55
internal energy equation 18–20
interpolation practice 339
interpretation and reporting of results 300–2
inviscid instability 45
isotropic eddies 44
iterative convergence errors 287–9, 294
iterative methods 212
convergence in 229, 230
Jacobi iteration method 212, 213, 224–5
jet flow 46, 54
k–
ε
model 68, 72–80
boundary conditions 76–8
equations 75–6
non-linear model 95–7
performance 78–80
physical model uncertainty in 291
RNG 87–8
two-layer 86–7
k estimation 271
k–
ω
models 69
Menter SST model 91–2
Wilcox model 90–1
kinetic energy equation 18–20
498 INDEX
KIVA-3V 310
Kolmogorov microscales 43, 44
Lagrangian approach 12
laminar diffusion flame 370–5
combustion model 372–4
continuity 371
enthalpy equation 372
finite rate chemistry 374–5
momentum equations 372
laminar flamelet library 389
generation of 390–8
opposed flow diffusion flame configuration 390–5
laminar flamelet model 388–90
NO modelling of turbulent flame 403–14
non-equilibrium parameter 399–400
laminar flamelet profiles in physical space 393
laminar flamelet relationships 397–8
laminar flow 41, 275–6
hydrodynamic stability of 45
in pipe with pressure variations 467–71
random nature of 41
transition to turbulence 45–6, 48
large eddy simulations (LES) 98–110
accuracy and validity in 292
advanced models 105–6
in combustion 415
complex geometry of 108–9
continuity equation 100
higher-order SGS models 104
initial and boundary conditions 106–8
momentum equation 101
performance of 109–10
Smagorinksy-Lilly model 102–4
sub-grid-scale stresses in 101–2
unsteady Navier-Stokes equations 98–102
law-of-the-wake layer 60
lean mixture 369
least-squares gradient reconstruction 321
Leonard stresses 102
Lewis number 365, 374, 413–14
limiter functions in TVD schemes 169, 452–5
linear sub-layer 58, 275–6
linear upwind discretisation (LUD) schemes 165–6
local rate of strain of resolved flow 102
local SGS stresses 102
log-law layer 58–9
low Reynolds number flows 85
Mach number 34, 37
in combusting flows 364
and turbulent flow 49, 64
ANIN_Z09.qxd 29/12/2006 10:12 AM Page 498
INDEX 499
marching problems 27–9
mass conservation, 3D 10–12
mass flows 11
mean flow and turbulence 61–5
mean flow kinetic energy K 73–4
mean flow turbulent energy K 74–5
mean of any property 381
Menter SST k–
ω
models 91–2
mesh 2, 229, 230, 304
mesh refinement 294
mixing length model 68, 69–72
mixture fraction
flamelet equations in 395–7
in laminar flamelet libraries 394, 395
in SCRS 368, 369
moments
of different fluctuating variables 51
higher-order 51
momentum equations 183–6, 203–6
for combustion 363
in complex geometries 337–8
in laminar diffusion flame 372
momentum exchange 62
monotonicity preserving schemes 168
Monte Carlo (MC) method in radiative heat transfer
427–9
complex geometry in radiative heat transfer 441–2
furnace geometry in radiative heat transfer 440–1
heating of cold black plates 438
moving walls 278–9
multi-dimensional convection-diffusion 154–5
multigrid techniques 229–41
concept 230–1
cycles 239–41
example 232–9
grid generation in 241
outline 231–2
Navier-Stokes equations 21–4, 33–4
unsteady, spatial filtering of 98–102
near-wall flow 275
near-wall grid 283
near wall regions 86–7
near-wall turbulent flow 276
net progress reaction rate 357
Newtonian fluid 21–4
Newton’s second law 14
nitric oxide (NO) formation 401–2
nitric oxide (NO) modelling of turbulent flame
403–14
flame structure, predicting 404–11
NO, predicting 411–14
no-slip condition 273
nodes 3
non-conservative form 13
non-linear k–
ε
model 95–7
non-orthogonal grids 305, 306, 308
non-uniform grids 448–9
normalisation 230
numerical errors 286–9
discretisation 289
iterative convergence 287–9
roundoff 287
1-dimension
control volume 244
convection-diffusion
TVD scheme for 173
using QUICK differencing 258–62
finite volume method in 115–29, 135–6
flow, SIMPLE algorithm on 197–200
heating of cold black plates 437–40
incompressible flow through planar nozzle
456–8
QUICK scheme for convection-diffusion 158
solution of equations in 118–29
unbsteady heat conduction 243–9
opaque surfaces 418
OPPDIF 393
opposed flow diffusion flame configuration 390–5
order of the difference approximation 446
orthogonal grids 305, 306, 308
outer layer 59–60
outgoing heat flux 422, 423
outlet boundaries, positioning 283
outlet boundary conditions 271–3
over-relaxation 227
overall combustion reactions 355–6
‘P’ function 277, 280
parabolic equations 27–8, 31–2
partial pressure 346
participating medium 419, 424
PATRAN 3
Peclet numbers 151, 152, 154
perfect gas 21
periodic boundary condition 281
PHOENICS 3
photon streams 417
physical model uncertainty 291–3
accuracy and validity
of assumptions 292–3
of submodels 291–2
and validation 296
ANIN_Z09.qxd 29/12/2006 10:12 AM Page 499
pipe flow 57–60
with pressure variations 467–71
in sudden contraction 462–3
transition 48
PISO algorithm 193–6
point-iterative methods 223–8
post-processor 4
potential energy equation 18–20
power-law scheme 155–6
Prandtl number 276, 364
Prandtl’s mixing length model 70
pre-processor 2–3
predictor step 193
pressure correction equation 189, 203, 206–8
pressure gradients, adverse 86, 88–92
pressure interpolation 340
pressure-velocity coupling 336–7
presumed pdf approach 384
probability density function 52
probability density function (pdf ) 380–2
in non-premixed combustion 415
problem solving 4–6
pseudo-transient approach 265
quadratic upstream interpolation for convective kinetics
(QUICK) scheme 154, 156
assessment of 162
differencing scheme 156–62
in flow simulation 447
general comments 164
limiter function 171
non-uniform grids 448–9
stability problems 163–4
in transient convection-diffusion 258–62
RADCAL 443
radiative heat transfer 417
boundary conditions 423–4, 425
coupled problems 420
definitions 418
discrete ordinates method 433–7
discrete transfer method 429–32
engineering problems 417–18
equations governing 424–6
finite volume method 437
fluid properties 419–20
gaseous mixture properties 442–3
Monte Carlo method 427–9
1D heating of cold black plates 437–40
ray tracing 433
source terms 420–3
500 INDEX
surface properties 418–19
3D complex geometry 441–2
3D furnace geometry 440–1
radiative transfer equation (RTE) 424–7
incident intensity integrals 425–6
solution methods 426–7
rapidly changing flows 85–6
rate of change following fluid particle 12–14
ray tracing in radiative heat transfer 433
reaction rate of combustion 356–61
detailed mechanisms 361
net progress 357
reduced mechanisms 361–2
recirculation regions 86
reflected radiation 418
relaxation methods 226–8
residuals 227
average 229
resolved flow, local rate of strain 102
Reynold-averaged Navier–Stokes (RANS) equations 62–5,
65–6, 66–98
eddy viscosity and diffusivity 67–8
k–
ε
model 72–80
mixing length model 69–72
turbulence models 97–8
Reynold averaging 376
Reynolds decomposition 41, 376
Reynolds number 36, 40, 279
in k–
ε
model 75, 77
and turbulent flow 40, 42, 44, 47, 49
Reynolds stresses 62, 64
accuracy and validity in 292
algebraic stress equation model 93–4
in eddies 67
equation models 69, 80–5
in k–
ε
model 74, 76
in LES 102
in mixing length model 70
non-linear k–
ε
model 95–6
in turbulent combustion 379
rich mixture 369
RNG k–
ε
model 87–8
rough walls 278
roughness 275, 278
roundoff errors 287, 293–4
RUN-IDL 393, 396, 397, 398
scalar control volumes 182, 188, 337
scalar dissipation rate 389, 396, 399
scattering coefficient 419
scattering phase function 420
ANIN_Z09.qxd 29/12/2006 10:12 AM Page 500
INDEX 501
Schmidt number 364, 365, 378
second-order accuracy in TVD schemes 169
SIMPLE algorithm 4, 36
approximation of 187
method 190
and NO modelling 403
1-dimensional flow example 197–200
in pressure-velocity coupling 180, 186–90, 196
2-dimensional nozzle example 200–11
worked examples 197–211
simple chemical reacting system (SCRS) 367–70
for turbulent combustion 380
simple wave solutions 30
SIMPLEC algorithm 193, 196
SIMPLER algorithm 191–2, 196
Smagorinksy-Lilly SGS model 102–4
smooth walls 58–9
solid walls 106
solver 3–4
source-free heat conduction in finite volume method for
1-D diffusion 118–21
source terms 324
calculation of 450–1
in radiative heat transfer 420–3
in species transport equations 359, 364
Spalart-Allmaras model 60, 89–90, 292
spatial discretisation in DNS 112
spatial filtering of unsteady Navier-Stokes equations
98–102
functions 99–100
spatial resolution in DNS 112
species concentration flux 62
species transport equations 359, 361, 363–4, 365
specific energy equation 18–20
spectral element methods 112
staggered grid 180–3
stagnation plane 390
standard state Gibbs function change 352
STAR-CD 3
steady laminar flamelet model (SLFM) 396
steady state 265
steady-state temperature distribution in finite volume
method for 1-D diffusion 121–5
stoichiometric air requirement 348
stoichiometric mixture fraction 367, 368, 400
stoichiometric oxygen/fuel ratio 367
stoichiometry 348
strain rate 389
strain sensitivity 87–8
stress anisotropy 86
stress components 14–15
structured curvilinear grids 305, 308
and Cartesian co-ordinate system 306–7
difficulties with 308–9
sub-grid-scale stresses (SGS) 101–2
advanced models 105–6
dynamic models 105
higher-order models 104
local stresses 102
Smagorinksy-Lilly SGS model 102–4
turbulence model 102
successive over-relaxation (SOR) 228
SUPERBEE schemes 171
supersonic problems in compressible fluids 36–8
surface forces 14
work done by 16–17
surface properties of radiative heat transfer 418–19
surface stresses 17
sweep direction, alternating 216
symmetry boundary conditions 36, 38, 280, 284
symmetry property for limiter functions 169
T-S waves 47
Taylor Series Truncation error (TSTE) 289, 294
TDMA 4
temporal discretisation in DNS 112
temporal resolution in DNS 112–13
test room, fire in 463–7
thermal radiation 417
thermodynamic equilibrium 20
thermodynamics, first law of 344–5, 349
3-dimensions
complex geometry in radiative heat transfer
441–2
energy equation in 16–20
finite volume method in 131–2
furnace geometry in radiative heat transfer
440–1
implicit scheme 256
mass conservation 10–12
momentum equation 14–16
TDMA methods 215–16
turbulent flow in 41
time average momentum equations 63
time-average transport equation 64
time averaging 49–50
total enthalpy 20
total reaction rate 359
total variation in TVD schemes 167–8
transient convection-diffusion 257–8
using QUICK differencing 258–62
transient PISO algorithm 263–5
ANIN_Z09.qxd 29/12/2006 10:12 AM Page 501
transient schemes 265–6
transient SIMPLE 262–3
transmitted radiation 418
transonic problems in compressible fluids 36–8
transport equations for combustion 359, 363–4
in SCRS 367, 369
transport equations for enthalpy 364
transportiveness 143–4, 145, 149
tri-diagonal matrix algorithm (TDMA) 4, 212,
213–14
in one-dimension 216–17
in three-dimensions 215–16
in two-dimension 215, 218–22
turbulence 40–4
advanced models 85–97
production, high 60
turbulence kinetic energy 50, 82
turbulence model of SGS 102
turbulence models for aerospace applications 88–92
external aerodynamics 92
turbulent core 275
turbulent flow 41, 275, 276–8
boundary layer 59–60
calculations 65–6
descriptors of 49–52
energy losses in 43
free 53–7
length scales of 41
and mean flow 61–5
simple, characteristics of 52–61
transition from laminar 45–6, 48
turbulent heat 62
turbulent pre-mixed combustion 376–80
SCRS model for 380
turbulent spots 47, 48
TVD schemes 164–78
criteria for 168–70
evaluation of 175–6
implementation of 171–5
and total variation 167–8
in unstructured grids 323–4
upwind-biased discretisation schemes 165–7
2-dimensions
convection-diffusion, TVD scheme for 174–5
discrete ordinates method in radiative heat transfer
435–6
finite volume method in 129–31
implicit scheme 256
nozzle, SIMPLE algorithm on 200–11
TDMA methods 215
two-layer k–
ε
model 86–7
502 INDEX
UMIST scheme 175
unbsteady heat conduction 243–9
Crank–Nicholson scheme 246, 247–8
explicit scheme 246–7
fully implicit scheme 246, 248–9
thin plate examples 249–55
transient PISO algorithm 263–5
transient SIMPLE 262–3
uncertainty 285–6
of input 289–91
of physical model 291–3
validation 293, 295–6
verification 293–5
under-relaxation 189, 190, 208, 227
unsteady Navier–Stokes equations, spatial filtering of
98–102
functions 99–100
unstructured grids 305, 311–12
calculations with 329–36
and Cartesian grids 325–9
discretisation in 312–15
face velocity interpolation method 340–1
higher-order differencing in 321–3
pressure-velocity coupling in 336–7
TVD schemes in 323–4
upwind differencing in 321
upwind-biased discretisation schemes 165–7
upwind differencing 321
upwind differencing scheme 146–51
assessment of 149–51
validation 293, 295–6
data sources 296–8
result interpretation and reporting 301
verification 293–5
data sources 296–8
interpretation and reporting of results
301
vertex-centred method 312–13
viscous flow
boundary conditions for 35, 36
viscous instability 45
viscous stress 21–3
viscous sub-layer 58
von Karmen’s constant 275
vortex stretching 41, 42
wakes 53
wall, law of 57
wall boundary conditions 273–9
wall functions 275
ANIN_Z09.qxd 29/12/2006 10:12 AM Page 502
INDEX 503
walls
moving 278–9
rough 278
smooth, and sub-layers 58–9
solid, and LES 106
water-gas equilibrium equation 353
Wilcox k–
ω
model 90–1
x-component of momentum equation 15–16
y-component of momentum equation 16
z-component of momentum equation 16
Zel’dovich mechanism 401
zone of influence 30–1
ANIN_Z09.qxd 29/12/2006 10:12 AM Page 503