DCW Industries Online Bookstore

DCW Industries, Inc.
5354 Palm Drive
La Cañada, CA 91011

voice: (818) 790-3844
fax: (818) 952-1272

Comments from Attendees of the Short Course

"An excellent overview of the current state of turbulence modeling. An equally excellent way to go from theory to application with a thorough understanding of the strengths and weaknesses of the models." Timothy Madden, National Academy of Sciences
"Excellent speaker - able to keep your attention focused on the subject." Guy B. Spear, Atlantic Research Corp.
"Excellent lecture!" Kenji Yoshida, Kawasaki Heavy Industries Ltd.
"Dave's knowledge of the field was very impressive." Daniel Marcus, Lawrence Livermore National Lab

Course Description
Turbulence modeling is one of three key elements in Computational Fluid Dynamics (CFD). Very precise mathematical theories have evolved for the other two key elements, viz, grid generation and algorithm development. By its nature, i.e., creating a mathematical model which approximates the physical behavior of turbulent flows, far less precision has been achieved in turbulence modeling. This course addresses the problem of selecting and/or devising such a model for a given application. The fundamental premise of this short course is that, in the spirit of G. I. Taylor, a really good model should introduce the minimum amount of complexity while capturing the essence of the relevant physics.

The course begins with a careful discussion of turbulence physics in the context of modeling. The exact equations governing the extra turbulent (Reynolds) stresses, and the ways in which these equations can be closed, will be briefly outlined. We then discuss the behavior of length scales in turbulence, and the processes that govern the dissipation rate and other quantities used to provide model length (or time) scales. The section on modeling as such begins with the simplest turbulence models and charts a course leading to some of the most complex models that have been applied to a nontrivial turbulent flow problem.

Along the way, a systematic methodology involving use of similarity solutions, perturbation methods and numerical techniques, is presented for developing and/or analyzing a set of constitutive equations suitable for computation of turbulent flows. The course will stress the need to achieve a balance amongst the physics of turbulence, mathematical tools required to solve turbulence-model equations, and common numerical problems attending use of such equations (i.e., what good is a model if it makes your program crash?). Several state-of-the-art, user-friendly FORTRAN programs will be provided.

This short course was originally developed to satisfy a need identified by the NASA Johnson Space Center to help Lockheed and North American Rockwell engineers in their Computational Fluid Dynamics (CFD) activities. It has proven to be very popular and has been presented throughout the United States and Canada since June, 1993 as follows.

**Short Course History**
Date	Sponsor	Location
June 1993	Lockheed Engineering Company	Houston, TX
January, 1994	AIAA	Reno, NV
June, 1994	CERCA	Montreal, Quebec, CANADA
October, 1994	National Program Office	Palmdale, CA
January, 1995	AIAA	Reno, NV
June, 1995	CFDCS Meeting	Banff, BC, CANADA
March, 1996	AIAA	Washington, DC
March, 1996	Knolls Atomic Power Lab	Schenectady, NY
June, 1997	AIAA	Snowmass, CO
June, 1998	AIAA	Albuquerque, NM
June, 1998	Boeing	Seattle, WA
October, 1998	Boeing North American	Canoga Park, CA
January, 1999	AIAA	Reno, NV
February, 1999	University of Adelaide	Adelaide, AUSTRALIA
June, 1999	AIAA	Norfolk, VA
August, 1999	NASA Langley	Hampton, VA
May, 2000	NASA Glenn	Cleveland, OH
June, 2000	NLR	Amsterdam, Holland
June, 2000	AIAA	Denver, CO
June, 2001	AIAA	Anaheim, CA
June, 2002	AIAA	St. Louis, MO
June, 2007	AIAA	Miami, FL

Intended Audience
The course is designed for all research engineers, programmers and managers engaged in turbulent flow CFD. Managers will gain an appreciation of what constitutes a suitable turbulence model for a given application and will gain the ability to interact effectively with specialists. Research engineers and programmers will learn the truths and myths of turbulence modeling along with a systematic methodology for testing and validating turbulence models and associated software.

Course Materials

You will be provided with course notes. Optionally, you may purchase (at a discounted price) a copy of the hardback text, Turbulence Modeling for CFD, by David C. Wilcox, which includes a compact disk containing both source and executable code for the programs documented in the text. The book is now in its third edition and is used at universities all over the world. Course attendance also entitles you discounts on all DCW Industries publications for a limited time.

Instructor

Dr. David C. Wilcox is the President of DCW Industries, Inc., a California aerospace and book-publishing firm he founded in 1973. He is also a Lecturer at UCLA and USC. Dr. Wilcox did his undergraduate studies at the Massachusetts Institute of Technology and received his PhD in Aeronautics from the California Institute of Technology in 1970. He served as an AIAA Journal Associate Editor from 1989 to 1992.

Course Outline

The short course touches on highlights of each chapter of the text. The course involves approximately 20 hours of lectures with provision for discussion and software demonstration. It will be presented over a three-day period. The course also includes provision for focusing on topics of particular interest to your organization. Such topics are agreed to in advance, and Dr. Wilcox will make a special presentation followed by extended discussion. The general outline is as follows.

Day One

Introduction

The ideal turbulence model
Physics of turbulence
Kolmogorov theory
The law of the wall and the power-law controversy
History of turbulence modeling

The Closure Problem

Reynolds averaging
Reynolds-averaged equations
The Reynolds stress equation
Length scales and their behavior
Equations vs. unknowns
The scales of turbulence
Two-point statistics

Algebraic Models
1. Molecular transport of momentum
2. The mixing length hypothesis
3. How molecules and eddies are different
4. Free shear flows
5. Cebeci-Smith and Baldwin-Lomax models
6. Channel/pipe flow
7. Attached boundary layers
8. Separated flows
9. The half-equation model
10. Range of applicability

Day Two

Turbulence Energy Equation Models

The turbulence energy equation
One-equation models
Two-equation models/generic
k-omega and k-epsilon models
Closure coefficients
Free shear flows
The role of cross diffusion
Solution sensitivity to freestream conditions
Surface boundary conditions
Surface roughness and surface mass transfer
Channel/pipe flow
Perturbation analysis of the boundary layer
Attached boundary layers
Low-Reynolds-number corrections
Transition prediction
Separated flows
The stress-limiter concept
Range of applicability

Effects of Compressibility

Favre-averaging
Favre-averaged equations
Compressible-flow closure approximations
Compressible mixing layer
Compressible law of the wall
Shock induced separation
More on the role of the stress limiter
The reattachment-point heat-transfer anomaly

Beyond the Boussinesq Approximation
1. Nonlinear constitutive relations
2. Algebraic Stress Models
3. Why the stress-limiter works so well
4. Stress-transport models
5. Pressure-strain correlation modeling
6. LRR and Wilcox Stress-omega models
7. Free shear flows
8. Channel/pipe flow
9. Attached boundary layers
10. Streamline curvature
11. Rotating channel flow
12. Unsteady boundary layers
13. Separated flows
14. Range of Applicability

Day Three

Numerical Considerations

Multiple time scales and stiffness
Near-wall solution accuracy
Turbulent/nonturbulent interfaces
Parabolic marching methods
Elementary time-marching methods
Block-implicit methods
Iteration and grid convergence

New Horizons

Direct Numerical Simulation
Large Eddy Simulation
Detached Eddy Simulation
Chaos

Special Topics

Special Presentation
Extended Discussion
Open Forum Discussion