9781402006715

Variable Density Fluid Turbulence: Preamble

(10)

Introduction

(1)

Some expected incidences of density variation in turbulence

(2)

Stability and transition

(1)

Compressibility

(1)

Mixing

(1)

Monograph roadmap

(1)

Outline of the Chapters

(3)

The authors

(3)

Examples of Variable Density Effects in Turbulent Flows

(38)

General definitions

(2)

Different types of variable density fluid motions

(1)

Variable density fluid turbulence

(1)

Specific density effects in the transition to turbulence

(4)

Rayleigh-Taylor and Richtmyer-Meshkov instabilities

(2)

Density effects on the transition in low speed free shear flows

(2)

Density / compressibility effects in homogeneous turbulence

(14)

The concept of homogeneous turbulence

(1)

Homogeneous buoyancy-driven turbulence

(1)

Compressed isotropic turbulence

(2)

Compressible isotropic turbulence

(3)

Compressible homogeneous shear flow

(2)

Shock/Homogeneous turbulence interaction

(4)

Density / compressibility effects in fully developed turbulent shear flows

(18)

Compressible Boundary layer

(7)

Variable density effects in mixing layers and jets

(1)

The variable density mixing layer

(5)

The low speed jet

(4)

Approximate Models for Variable Density Fluid Motions

(30)

Introduction

(1)

The role of the pressure in compressible turbulence

(4)

Pressure in incompressible flows: Poisson's equation

(1)

Pressure in compressible flow: The generalized wave equation

(1)

Lighthill's acoustic analogy

(2)

Decomposition of velocity and pressure fields

(5)

Helmholtz decomposition

(1)

Decomposition of the pressure field

(2)

Pressure decomposition in turbulent flow

(2)

The Kovasznay modes decomposition

(3)

Flows in bounded domains

(4)

Mansour-Lundgren's model

(1)

Fedorchenko's non local model

(2)

Approximated models for low speed free buoyant flows

(5)

Boussinesq's approximations

(3)

Rehm-Baum's model

(1)

Isovolume approximations to the continuity equation

(3)

Anelastic approximation

(2)

Pseudo-incompressible approximation

(1)

Incompressible limits to the general equations

(5)

General Equations and Classification of Variable Density Fluid Motions

(40)

General assumptions and equations

(7)

Thermodynamics elements on mixtures of fluids

(3)

Balance equations of a compressible binary mixture

(1)

The equation of state

(1)

Physical properties and transport coefficients

(2)

Non dimensional parameters in variable density motions

(1)

Incompressibility and isovolume conditions

(5)

Definitions

(3)

Approximations to the isovolume condition for air and water flows

(2)

Density fluctuations in turbulent flows

(10)

Turbulent density intensity in low-speed flows

(3)

Turbulent density intensity in high-speed flows

(4)

The density variance transport equation

101

(1)

Non-isovolume evolution

102

(4)

The general equation

102

(1)

Discussion

103

(3)

Solenoidal condition in variable density turbulent flows

106

(6)

Mean and fluctuating divergence linkage

107

(2)

Approximation to the fluctuating divergence

109

(3)

Variable density situations in turbulent fluid motions

112

(7)

Normalization of the pressure

112

(1)

Typical time-scales ratios

113

(3)

Length-scale interpretation

116

(1)

Turbulent flows classification of variable density fluid

117

(2)

Statistical Averaging in Variable Density Fluid Turbulent Motion

119

(26)

Introduction

119

(1)

Averaging of variable density transport equations

120

(1)

Mean motion in variable density fluid turbulence

121

(7)

Binary regrouping

121

(2)

Transport selected regrouping

123

(1)

Ternary regrouping

123

(1)

Kinetic energy averaging

124

(1)

Comparision between binary and ternary regrouping

125

(3)

Mean flow equations

128

(5)

Binary regrouping

129

(2)

Ternary regrouping

131

(2)

Turbulent mass flux equation

133

(1)

Reynolds stress transport equation

133

(3)

Binary regrouping

134

(1)

Ternary regrouping

135

(1)

Turbulence kinetic energy

136

(1)

Binary regrouping

136

(1)

Ternary regrouping

136

(1)

Energy transfer in compressible turbulent flows

137

(5)

Binary regrouping

137

(2)

Ternary regrouping

139

(3)

Averaging the constitutive schemes

142

(3)

Some Basic Variable Density Mechanisms in Turbulent Flows

145

(22)

Introduction

145

(1)

Vorticity in variable density fluid motion

146

(5)

The instantaneous vorticity equation

146

(4)

Baroclinic generation in a stratified duct flow

150

(1)

Baroclinic generation through a curved shock

150

(1)

D.f.c. and turbulent mass flux

151

(6)

Exact expressions of d.f.c. in low speed flows

152

(2)

Analysis of d.f.c. in low speed flows

154

(3)

Energetic peculiarities in variable density turbulence

157

(5)

Instantaneous situation

157

(1)

Mean Energy linkage

158

(1)

Pressure-coupling

159

(1)

Dilatation dissipation

160

(2)

Shocklets

162

(5)

Relative Behaviour of Velocity and Scalar Structure functions in Turbulent Flows

167

(34)

Introduction

167

(2)

Analytical Framework

169

(5)

A Few Questions which Arise from Section 2

174

(1)

Rλ Dependence of ⟨(δα*)2⟩ and ⟨(δθ*)2⟩

175

(10)

A Framework for Comparing Velocity and Sclar Fields

185

(6)

Further Implications of the Spectral Analogy

191

(6)

Effect of large Scale Anisotropy in the Inertial Range: Some Recent Developments

197

(1)

Concluding Remarks

198

(3)

The Structure of Some Variable-Density Lowspeed Shear Flows

201

(34)

Introduction

201

(3)

The baroclinic torques

204

(2)

The two-dimensional mixing layer

206

(14)

The two-dimensional roll-up

206

(5)

The variable-density shear and strain fiels

211

(4)

The two-dimensional baroclinic secondary instability

215

(3)

The spatially evolving variable-density mixing-layer

218

(2)

The The structure of the 3-D shear-layer

220

(5)

The structure of variable-density jets

225

(10)

The two-dimensional jet

225

(5)

Corrugated axisymmetric light jets

230

(5)

The High-Speed Turbulent Shear Layer

235

(26)

Introduction to compressible turbulence

235

(2)

Mathematical preliminaries

237

(2)

Introduction to the compressible shear layer

239

(3)

A direct simulation of the temporally-evolving shear layer

242

(3)

The stabilizing effect of Mach number

245

(6)

The thickness growth rate

245

(1)

Turbulence intensities

246

(2)

An explanation of the Mach number effect

248

(3)

Variable-density effect in the high-speed shear layer

251

(7)

Momentum and vorticity thickness growth rate

252

(3)

The thermodynamic fluctuations

255

(2)

The mass flux

257

(1)

Turbulent stresses

258

(1)

Concluding remarks

258

(3)

First-Order Modeling

261

(50)

Introduction

261

(1)

Synopsis of one-point turbulence modeling status

262

(2)

Constant density flows

262

(1)

Variable density flows

263

(1)

The first-order modeling issue

264

(3)

The open set of equations and the closure issue

267

(3)

Pressure-dilatation correlation

269

(1)

Dilation dissipation

269

(1)

The closure problem

270

(1)

Turbulent momentum transport modeling

270

(7)

Eddy-viscosity representation of Reynolds stresses

270

(2)

Eddy-viscosity expressions

272

(1)

Compressibility effects on the eddy-viscosity concept

273

(2)

Non-linear constitutive relationship

275

(2)

Turbulent heat/mass transport moderling

277

(2)

Gradient diffusion assumption

277

(1)

Alternative to gradient diffusion schemes

277

(2)

Modeling d.f.c terms

279

(6)

Modeling density effects

285

(9)

Pressure-dilatation correlation

285

(6)

Dilatation dissipation

291

(3)

Examples of zero-equation models

294

(2)

One-equation models

296

(5)

Eddy-viscosity transport equation

297

(2)

Turbulence kinetic energy model equation

299

(2)

Two-equation models

301

(2)

The (κ - ε) model

301

(2)

Three-equation models

303

(4)

Density variance equation

304

(2)

Pressure variance equation

306

(1)

Closure models for buoyant flows

307

(1)

Final discussion and concluding remarks

308

(3)

Second-Order Modeling

311

(34)

Introduction

311

(1)

The modeling issue of RST equation

311

(2)

The open transport equation

312

(1)

Closure peculiarities in variable density flows

313

(1)

RST equation closure schemes

313

(16)

Diffusion in incompressible flows

313

(2)

Diffusion in variable density flows

315

(4)

Pressure-strain correlation in incompressible flows

319

(5)

Low turbulence Reynolds number corrections

324

(1)

Redistribution in variable density flows

325

(4)

Dissipation

329

(1)

Turbulent scalar fluxes modeling

329

(5)

Gradient diffusion schemes

329

(1)

Transport equation

330

(4)

Examples of second-order models predictions of variable density flows

334

(8)

Buoyant flows

334

(2)

Variable composition mixing

336

(3)

Compressible flows

339

(3)

Concluding remarks

342

(3)

References

345

(24)

Index

369

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Variable Density Fluid Turbulence

1402006713

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