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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
![كتاب Computational Fluid Dynamics - A Practical Approach C_f_d_11](https://i.servimg.com/u/f61/15/36/74/14/c_f_d_11.jpg) 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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