Turbulence
ME 7960

Pat McMurtry
2140 MEB

mcmurtry@eng.utah.edu

581 - 3889

COURSE OUTLINE

Introductory Background
Some General Comments and Observations about Turbulence
Math Background
Tensor Notation
Scale Analysis
The Probability Density Function

Governing Equations
Conservation of Mass
Conservation of Momentum
Fluid Deformation
Fourier Transforms
Fourier Transform of Governing Equations

Some Observations On Turbulent Flows
Laminar vs. Turbulent Flows
Turbulent Diffusivity
3-D Nature of Turbulence
Order and Randomness

Statistical Measures of Turbulent Flows
Mean Values
Higher Order Moments
Two-Point, Time Statistics
Homogeneous and Isotropic Turbulence

Vorticity Dynamics
Vorticity Equation
Mechanisms of Vorticity Generation
The Energy Cascade
Equilibrium Range Theories
Energy Spectrum in the Equilibrium Range

Length and Time Scales in Turbulent Flows
Turbulent Length Scales
Time Scales
Implications on the Numerical Solution of Turbulent Flows

Direct Numerical Simulations
Numerical Approaches
The Spectral Methods
Higher Order Finite Difference
Applications

Turbulent Transport
Reynolds Averaged Equations
An Estimate for the Reynolds Stress
Turbulent Kinetic Energy
Turbulent Transport of a Passive Scalar

Turbulence Modeling
The Closure Problem
Reynolds Stress Modeling
Modeling the Eddy Viscosity
One-Equation Models
Two-Equation Models
Reynolds Stress Transport Equation

Turbulent Scalar Mixing Process
Physical Mechanisms of Turbulent Mixing
Convection
Molecular Diffusion
Spectrum of the Scalar Field
Mixing Configurations

Predicting the Scalar Mixing Process
Moment Methods
Modeling Mean Reaction Rates
Probability Density Function Methods
Coalescence-Dispersion Modeling
Other Models

Linear Eddy Modeling of Turbulent Mixing
Linear Eddy Modeling Philosophy
Linear Eddy Model Formulation
Implementation of Linear Eddy
Applications of Linear Eddy

Discussions of Selected Turbulent Flows
Mixing in Pipe Flows
Application to Rapid Crystal Growth in Supersaturated Solutions
Turbulent Mixing Layers

One Dimensional Turbulence Modeling
Model Ideas
Model Formulation

Large Eddy Simulations
Basic Ideas
Filtering, Filtered Equations
Subgrid Modeling