Turbulence Modeling for CFD (Third Edition) 3rd Edition by David C. Wilcox (PDF)

Description

As in the first and second editions, the book revolves around the fact that turbulence modeling is one of three key elements in CFD. Very precise mathematical theories have evolved for the other two, viz., grid generation and algorithm development. By its nature, i.e., creating a mathematical model that approximates the physical behavior of turbulent flows, far less precision has been achieved in turbulence modeling. This text addresses the problem of selecting/devising such models. The fundamental premise is, in the spirit of G. I. Taylor, an ideal model should introduce the minimum amount of complexity while capturing the essence of the relevant physics. The text begins with the simplest models and charts a course leading to some of the most complex models that have been applied to a nontrivial flow. Along the way, a systematic methodology is presented for developing and analyzing turbulence models. The methodology makes use of tensor calculus, similarity solutions, singular perturbation methods, and numerical procedures. The text stresses the need to achieve a balance amongst the physics of turbulence, mathematical tools required to solve turbulence-model equations, and common numerical problems attending their use (i.e., what good is a model if it makes your program crash?). Several user friendly programs and detailed user’s guides are provided on the Compact Disk that accompanies the text. Many of the applications are used throughout the text to permit comparison of complicated models with simpler models. A completely objective point of view is taken in assessing the merits of models and their range of applicability. The text includes an extensive Bibliography, a detailed Index and well thought out homework problems of varying degrees of difficulty.

User’s Reviews

Editorial Reviews: From the Publisher Publication of the Third Edition of Turbulence Modeling for CFD has been motivated by its continuing popularity and Dr. Wilcox’s desire to document his recent contributions to the field. It has been adopted for course use in universities all around the world and Dr. Wilcox has presented a short course based on the book many times in the United States and beyond. Demand for the book continues to exceed all expectations. What’s New?… All chapters and appendices have undergone improvement and expansion. Most notably, Chapter 4 presents a new version of the k-omega model that includes cross diffusion and a stress limiter. These innovations, inspired by the research of Johan Kok and George Huang, have led to significant improvement of predictive accuracy. The new k-omega model yields close agreement with measurements for boundary layers with pressure gradient, classical free shear flows and separated flows. The improved k-omega model should provide improved predictive accuracy for complex turbulent flows as well as being a source of fresh research ideas. Inclusion of a stress limiter in a unique way yields excellent agreement between computed and measured properties of shock-separated flows from transonic to hypersonic speeds. Recent advances and successes in devising and applying nonlinear stress/strain-rate relations are included in Chapter 6, which also presents a revised stress-transport (second-order closure) model based on the omega equation. The discussion of DNS and LES in Chapter 8 has been expanded and DES has been added. Finally, to enhance the book’s utility in the classroom, the number of homework problems has increased by 25%. As with previous editions, the book comes with a companion Compact Disk (CD) that contains source code and documentation for several useful computer programs. In addition to the software provided with the first and second editions, the CD includes a two-dimensional/axisymmetric Navier-Stokes program and some simple grid-generation software. The CD also contains experimental and DNS data in digital form to aid users who wish to compare their own turbulent-flow predictions with measurements. The software on the CD has been modernized and optimized for personal computers running the Microsoft Windows operating system. All programs have menu-driven input-data preparation and plotting utilities, written entirely in Visual C++, that provide a user-friendly environment. From the Author For me, this edition represents a mission accomplished. It’s a mission I scoped out for myself three decades ago when I was fresh out of Caltech. What was that mission? To develop a set of turbulence-model equations that, with an absolute minimum of complexity, would accurately compute properties of a series of roughly 100 test cases. Over the years I have assembled a set of test cases that I deem essential for validating a useful engineering tool. The test cases include attached boundary layers, free shear flows, backward-facing steps and shock-separated flows to mention a few, most dealing with Mach numbers from incompressible speeds to hypersonic. The third edition presents a version of the k-omega model that yields close agreement with measurements for all 100 test cases. And it does all of this with just 6 closure coefficients and no compressibility corrections! About the Author David C. Wilcox was born in Wilmington, Delaware. He was educated as an aeronautical engineer at the Massachusetts Institute of Technology (BS 1966) and the California Institute of Technology (PhD 1970). After spending the early part of his career with several Southern California aerospace companies, in 1973, he founded DCW Industries, Inc., for which he is currently the President. He has taught several aerospace and mechanical engineering courses at both USC and UCLA. In the early 1990s, Dr. Wilcox shifted the focus of his corporation from defense contracting to book publishing. Building on an international reputation based on numerous scientific-journal publications, he has written and published two undergraduate fluid-mechanics texts entitled Basic Fluid Mechanics (1997, 2000, 2007) and Elements of Fluid Mechanics (2005). He has also written two graduate-level texts entitled Turbulence Modeling for CFD (1993, 1998, 2006) and Perturbation Methods in the Computer Age (1995). These books are currently in use at universities throughout the world. Dr. Wilcox has also written three nontechnical books, the most recent of which is a partial autobiography entitled An Improbable Life (2007). The other two books are a fictional novel about a political compaign, . . . And the Donkey They Rode in On (2001), and collection of essays about politics entitled Cliches of Liberalism (1999). Excerpt. © Reprinted by permission. All rights reserved. Chapter 1. Introduction This book has been described by many writers as the “how-to guide for engineers interested in computing turbulent flows.” This description is consistent with the contents of the book in the following sense. While the text provides some discussion of the physics of turbulent flows, it is by no means a thorough treatise on the complexities of the phenomenon. Rather, the discussion focuses on the most significant aspects of turbulence that underlie the engineering approximations introduced over the decades to facilitate affordable numerical computations. In other words, the book presents as much of the physics of turbulence as necessary to understand why existing modeling approximations have been made—but no more. This is true because the theme of the book is the modeling of turbulence, which begins with understanding the physics involved. However, it also involves correlation of measurements, engineering judgment, a healthy dose of mathematics and a lot of trial and error. The field is, to some extent, a throwback to the days of Prandtl, Taylor, von Karman and all the many other clever engineers who spent a good portion of their time devising engineering approximations and models describing complicated physical flows. The best efforts in turbulence modeling have been an attempt to develop a set of constitutive equations suitable for application to general turbulent flows, and to do it in as elegant and physically sound a manner as possible. These three fluid mechanics pioneers helped establish a solid framework for several generations of engineers to work in. 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 — in creating a mathematical model that approximates the physical behavior of turbulent flows — far less precision has been achieved in turbulence modeling. This is not really a surprising event since our objective has been to approximate an extremely complicated phenomenon. Two key questions we must ask at the outset are the following. What constitutes the ideal turbulence model and how complex must it be? 1.1 Definition of an Ideal Turbulence Model Simplicity combined with physical insight seems to have been a common denominator of the work of great men like Prandtl, Taylor and von Karman. Using their work as a gauge, an ideal model should introduce the minimum amount of complexity while capturing the essence of the relevant physics. This description of an ideal model serves as the keystone of this text. 1.2 How Complex Must a Turbulence Model Be? Aside from any physical considerations, turbulence is inherently three dimensional and time dependent. Thus, an enormous amount of information is required to completely describe a turbulent flow. Fortunately, we usually require something less than a complete time history over all spatial coordinates for every flow property. Thus, for a given turbulent-flow application, we must pose the following question. Given a set of initial and/or boundary conditions, how do we predict the relevant properties of the flow? What properties of a given flow are relevant is generally dictated by the application. For the simplest applications, we may require only the skin-friction and heat-transfer coefficients. More esoteric applications may require detailed knowledge of energy spectra, turbulence fluctuation magnitudes and scales. Certainly, we should expect the complexity of the mathematics required for a given application to increase as the amount of required flowfield detail increases. On the one hand, if all we require is skin friction for an attached flow, a simple mixing-length model (Chapter 3) may suffice. Such models are well developed and can be implemented with very little specialized knowledge. On the other hand, if we desire a complete time history of every aspect of a turbulent flow, only a solution to the complete Navier-Stokes equation will suffice. Such a solution requires an extremely accurate numerical solver and may require use of subtle transform techniques, not to mention vast computer resources. Most engineering problems fall somewhere between these two extremes. Thus, once the question of how much detail we need is answered, the level of complexity of the model follows, qualitatively speaking. (This is not a foolproof criterion, however. For example, a complicated model may be required to predict even the simplest properties of a very complex flow.) In the spirit of Prandtl, Taylor and von Karman, the conscientious engineer will strive to use as conceptually simple an approach as possible to achieve his ends. Overkill is often accompanied by unexpected difficulties that, in CFD applications, almost always manifest themselves as numerical difficulties! Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This text covers the fundamentals of turbulence very thoroughly and dives deeply into methods for developing and verify turbulence models. While, the author is fairly opinionated, his insight is quite invaluable. Sometimes, in a complicated subjects such as this, it is difficult for the reader, without intensive study, to make valid and insightful conclusions on what/how equations behave for variety of condition. The author provides many of the useful comments that facilitates that understanding. He also provides the ground work for being able to understand how to develop your own models and what is important to capture in a flow. Overall, this text comes highly recommend.It should be noted that turbulence modelling is a very rapidly changing field, so with any text, it will fall behind only month out of print. Journal papers are always a good way to keep up with the advancement, but that’s not within reach for most folk. However, the latest edition does bring up newer topics, like Large Eddy Simulation, but regardless of what *is* missing, this text is invaluable to grasping other models the reader will encounter.

⭐My aim is to use CFD to design ejectors (jet pumps) for incompressible and compressible fluids, steam above all. These are simple devices but I learned that it is very difficult to take properly into account the turbulent mixing of the supersonic motive jet with the aspirated flow. I knew I needed to know about the different turbulence models more than it is given in the CFD texts I refer to. After receiving Wilcox’ book and giving it a first look I believe that it is what I needed. I very much like how Wilcox uses perturbative methods to explain formulas that would otherwise seem fallen from the blue sky. But I feel that Appendix B, “Rudiments of Perturbation Methods”, could have been clearer. However up to now I have not yet found a really clear explanation of singular perturbations, inner and outer expansions; it’s probably up to me. The accompanying software is even more than advertised: the disk also contains a full Navier-Stokes 2D and axisymmetric compressible code.

⭐The best about these turbulence models.

⭐Awesome book! Super service!

⭐Having learned fluid mechanics from this author’s fluid mechanics text I was really happy when I discovered that he had written a book on the topic I need in my work. There is no other book like this one. It explains why some models do so poorly while others do very well. Wilcox teaches you how to analyze turbulence models to discover why they predict what they do. The boundary layer code on the CD is the best I’ve ever used and is truly industrial strength. Although the numerics in the Navier Stokes code are a little dated, the program is extremely accurate for the flows it was designed for — supesonice and hypersonic. Best of all, the software on the CD is very easy to use beacuse of the Visual C++ pre and post processors. This is a fabulous book that should be on the book shelf of every serious CFD researcher.

⭐If you study CFD for any real problem, Wilcox book is a must-read option. It covers the basics of turbulence modeling without being simplistic and get into the ‘complicated’ things in a didactic manner. Different from many others classic books, that cover an issue deeply, every chapter has a problems section at the end. This is very important for the book to be adopted in classroom.

⭐It is a very good book about RANS turbulence models. The LES part was improved over the last edition, but it is still only a small part.

⭐It is really a great book and a must-to-have for anyone who is doing CFD. Turbulence modeling is well explained with sufficient physical background. A great job indeed.

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