Foreword: What is this Book About, and for Whom? |
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vii | |
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1 Statistical Viewpoint of Turbulence --- Motivation and Rationale |
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1 | (6) |
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2 What Makes Turbulence Tick? |
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7 | (26) |
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2.1 Eddies, vortices and their scales |
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7 | (13) |
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2.2 A semblance of order and organisation |
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20 | (5) |
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2.3 Forcing turbulence --- a first look |
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25 | (5) |
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30 | (3) |
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33 | (16) |
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3.1 Decomposition and time-integration |
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33 | (4) |
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3.2 The Reynolds-averaged Navier--Stokes (RANS) equations for steady flow |
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37 | (2) |
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3.3 The Reynolds-averaged Navier--Stokes equations for unsteady flow (URANS) |
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39 | (6) |
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3.4 Spatial averaging and statistical homogeneity |
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45 | (1) |
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46 | (3) |
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4 Fundamentals of Stress/Strain Interactions |
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49 | (16) |
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4.1 A rational framework for describing the Reynolds stresses |
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50 | (4) |
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4.2 The case of simple shear |
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54 | (3) |
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4.3 Manifestations of stress anisotropy |
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57 | (4) |
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61 | (4) |
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5 Fundamentals of Near-Wall Interaction |
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65 | (14) |
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5.1 Turbulence in the viscous sublayer |
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66 | (5) |
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5.2 Turbulence processes in the `buffer layer' |
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71 | (2) |
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5.3 The velocity distribution in the near-wall region |
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73 | (3) |
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76 | (3) |
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6 Fundamentals of Scalar-Flux/Scalar-Gradient Interactions |
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79 | (8) |
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6.1 The exact equations for the turbulent fluxes |
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80 | (1) |
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6.2 Some key interactions |
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81 | (5) |
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86 | (1) |
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87 | (28) |
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7.1 Conceptual foundation |
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87 | (5) |
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7.2 Quantification of the eddy viscosity --- a first attempt |
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92 | (5) |
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7.3 The turbulent-velocity scale |
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97 | (5) |
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7.4 The turbulent length scale |
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102 | (8) |
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7.5 Length-scale transport |
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110 | (3) |
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113 | (2) |
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8 One-Equation Eddy-Viscosity Models |
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115 | (20) |
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8.1 Introductory comments |
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115 | (2) |
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8.2 Turbulence-energy-based models |
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117 | (5) |
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8.2.1 The Wolfshtein (1969) model |
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118 | (2) |
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8.2.2 The Norris--Reynolds (1975) model |
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120 | (2) |
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8.3 Eddy-viscosity-transport models |
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122 | (10) |
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8.3.1 The Spalart--Allmaras (1992) model |
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123 | (5) |
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8.3.2 Models combining the k- and ε-equations |
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128 | (4) |
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132 | (3) |
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135 | (46) |
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9.1 Options for length-scale surrogates |
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135 | (2) |
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9.2 The basic k --- ε model |
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137 | (12) |
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9.3 Low-Reynolds-number k --- ε-model extensions |
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149 | (12) |
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9.3.1 The Lam--Bremhorst (1981), Chien (1982) and Launder--Sharma (1974) models |
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155 | (4) |
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9.3.2 The Lien--Leschziner model (1994, 1996) |
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159 | (2) |
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9.4 Alternative k --- φ models |
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161 | (15) |
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9.4.1 The basic k --- ω model |
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164 | (5) |
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9.4.2 Low-Reynolds-number k --- ω-model extensions |
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169 | (3) |
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9.4.3 Hybrid k --- ω/k --- ε modelling --- the SST model |
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172 | (4) |
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9.5 Reductions of two-equation models to one-equation forms |
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176 | (3) |
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179 | (2) |
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10 Wall Functions for Linear Eddy-Viscosity Models |
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181 | (18) |
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10.1 The purpose of `wall functions' |
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181 | (1) |
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10.2 Log-law-based wall functions |
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182 | (7) |
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10.3 Eddy-viscosity-based wall functions |
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189 | (2) |
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10.4 Numerical wall functions |
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191 | (2) |
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10.5 More general wall functions |
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193 | (2) |
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10.6 Wall functions for heat transfer |
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195 | (1) |
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196 | (3) |
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11 Defects of Linear Eddy-Viscosity Models, Their Sources and (Imperfect) Corrections |
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199 | (9) |
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11.1 The need for corrections |
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199 | (3) |
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202 | (6) |
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208 | (19) |
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214 | (3) |
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217 | (2) |
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11.6 Body forces --- buoyancy |
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219 | (4) |
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11.7 Length-scale corrections |
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223 | (2) |
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225 | (2) |
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12 Reynolds-Stress-Transport Modelling |
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227 | (76) |
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12.1 Rationale and motivation |
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227 | (4) |
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12.2 The exact Reynolds-stress equations |
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231 | (3) |
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12.3 Closure --- some basic rules |
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234 | (1) |
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12.4 Realisability and its implications for modelling |
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235 | (4) |
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239 | (5) |
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244 | (13) |
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12.7 Pressure-velocity interaction |
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257 | (42) |
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12.7.1 Basic considerations |
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257 | (5) |
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12.7.2 Modelling of the slow term Φij,1 |
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262 | (3) |
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12.7.3 Modelling of the rapid term Φij,2 |
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265 | (10) |
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12.7.4 Modelling Φij,1 + Φij,2 collectively |
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275 | (5) |
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280 | (10) |
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12.7.6 Effects of body forces |
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290 | (1) |
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12.7.7 Elliptic relaxation of pressure-strain correlation |
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291 | (8) |
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299 | (4) |
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13 Scalar/Heat-Flux-Transport Modelling |
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303 | (12) |
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13.1 The case for flux-transport closure |
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303 | (5) |
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13.2 Closure of the flux-transport equations |
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308 | (4) |
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312 | (3) |
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315 | (12) |
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14.1 Relationship to second-moment closure and elliptic relaxation |
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315 | (2) |
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14.2 υ2 - f model formulation and variants |
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317 | (9) |
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326 | (1) |
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15 Algebraic Reynolds-Stress and Non-Linear Eddy-Viscosity Models |
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327 | (52) |
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15.1 Rationale and motivation |
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327 | (5) |
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15.2 Explicit algebraic Reynolds-stress models (EARSMs) |
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332 | (21) |
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334 | (4) |
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15.2.2 The model of Pope (1975) |
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338 | (1) |
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15.2.3 The model of Gatski and Speziale (1993) |
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339 | (3) |
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15.2.4 The model of Wallin and Johansson (2000) |
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342 | (6) |
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15.2.5 Near-wall behaviour |
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348 | (4) |
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15.2.6 Scale-governing equations |
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352 | (1) |
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15.3 Approximations to rigorous EARSMs |
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353 | (13) |
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15.3.1 The Model of Abe et al. (1997, 2003) |
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354 | (5) |
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15.3.2 The Model of Apsley and Leschziner (1998) |
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359 | (7) |
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15.4 Non-linear eddy-viscosity models (NLEVMs) |
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366 | (10) |
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15.4.1 The model of Shih et al. (1995) |
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367 | (2) |
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15.4.2 The model of Craft et al. (1996) |
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369 | (7) |
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376 | (3) |
Appendix: Basic Tensor Algebra and Rules |
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379 | (4) |
References |
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383 | (14) |
Index |
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397 | |