As in the First Edition, 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 are documented in the Appendices and provided on disk.
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.
All chapters and appendices have undergone improvement and expansion in the Second Edition. Most notably, the introduction includes an expanded discussion of the physics of turbulence. This makes the book a stand-alone text that can be used for teaching an introductory turbulence course. Chapter 2 now includes a discussion of two-point statistics as they pertain to engineering turbulence-model development. Chapter 3 subjects algebraic and 1/2-equation models to an increased number of baseline applications, which are repeated for other models in subsequent chapters.
Chapter 4 includes an expanded discussion of recent one-equation models, and presents a new version of the k-omega model that yields close agreement with measurements for both boundary layers with pressure gradient (for which the k-epsilon model is very inaccurate) and for classical free shear flows (for which the k-epsilon model is marginally accurate). The improved k-omega model should provide improved predictive accuracy for complex turbulent flows as well as being a source for fresh research ideas.
New insight into compressible turbulence gleaned from basic analyses is included to bring Chapter 5 up to date in this rapidly advancing field. The extensive efforts of Speziale and various co-authors in devising nonlinear stress/strain-rate relations are included in Chapter 6, which also presents a new stress-transport (second-order closure) model based on the omega equation. The discussion of DNS and LES in Chapter 8 has been expanded. Finally, to enhance the book's utility in the classroom, the number of homework problems has increased by 50%.
The material presented is appropriate for a one-semester, first or second year graduate course. Successful study of this material requires an understanding of viscous-flow and boundary-layer theory. Some degree of proficiency in solving partial differential equations is needed. A knowledge of FORTRAN will help the reader gain maximum benefit from the companion software.
The text will serve as an invaluable reference for years to come. While it is not a catalog of every turbulence model ever created, complete details of the most frequently used models ranging from algebraic to stress-transport models are given; references to most noteworthy models are included.
