Statistical Theory and Modeling for Turbulent Flows (eBook)

P. A. Durbin, Stanford University, USA and B. A. Pettersson Reif, Norwegian Defence Research Establishment, Norway Paul Durbin is a research professor within the flow physics and computational engineering department at Stanford University. He and his students carry out computational and modeling research on turbulent and transitional flows, exploring new analytical formulations and testing models in a wide range of applications with the practical aim of improving existing methods for computing engineering flows. Björn Anders Pettersson Reif spent 4 years post-doc working as an R&D engineer at Kongsberg Defence and Aerospace (Norway) until he started his present position as a senior scientist at the Norwegian Defence Research Establishment. He was also appointed Adjunct Professor in Turbulence Modeling between 2003 and 2009. His research has mainly been dedicated to numerical fluid mechanics, turbulence physics and single-point turbulence modeling.

Preface

Motivation

Epitome

Acknowledgments

I Fundamentals of Turbulence

1 Introduction

1.1 The Turbulence Problem

1.2 ClosureModeling

1.3 Categories of Turbulent Flow

2 Mathematical and Statistical Background

2.1 Dimensional Analysis

2.2 Statistical Tools

2.3 Cartesian Tensors

3 Reynolds Averaged Navier-Stokes Equations

3.1 Reynolds Averaged Equations

3.2 The Terms of the Kinetic Energy and Reynolds Stress Budgets

3.3 Passive Contaminant Transport

4 Parallel and Self-Similar Shear Flows

4.1 Plane Channel Flow

4.2 The Boundary Layer

4.3 Free Shear Layers

4.4 Heat and Mass Transfer

5 Vorticity and Vortical Structures

5.1 Structures

5.2 Vorticity and Dissipation

II Single Point Closure Modeling 103

6 Models with Scalar Variables

6.1 Boundary Layer Methods

6.2 The k-epsilon Model

6.3 The k-omega Model

6.4 The Stagnation-PointAnomaly

6.5 The Question of Transition

6.6 Eddy Viscosity Transport Models

7 Models with Tensor Variables

7.1 Second Moment Transport

7.2 Analytic Solutions to SMC Models

7.3 Non-homogeneity

7.4 Reynolds Averaged Computation

8 Advanced Topics

8.1 FurtherModeling Principles

8.2 Second Moment Closure and Langevin equations

8.3 Moving EquilibriumSolutions of SMC

8.4 Passive Scalar Flux Modeling

8.5 Active Scalar Flux Modeling: Effects of Buoyancy

III Theory of Homogeneous Turbulence

9 Mathematical Representations

9.1 Fourier Transforms

9.2 The 3-D Energy Spectrum of Homogeneous Turbulence

10 Navier-Stokes Equations in Spectral Space

10.1 Convolution Integrals as Triad Interaction

10.2 Evolution of Spectra

IV Turbulence Simulation

11 Eddy Resolving Simulation

11.1 Direct Numerical Simulation

11.2 Illustrations

11.3 Pseudo-spectral method

12 Simulation of Large Eddies

12.1 Large Eddy Simulation

12.2 Detached Eddy Simulation

Index