This work is devoted to the field of turbulence modeling. It is focused on the development of the complete second-order turbulence closure model. The alternative approach for obtaining the linear anisotropy invariant map based on the eigenvalues of the second-order tensors, which represent the important turbulent quantities like the Reynolds stress, turbulent dissipation tensor and pressure-strain correlation term, is proposed. The general modeling relationships between the corresponding tensors are derived using the kinematic constraints and validated for the particular classes of turbulent flows. The new modeling framework, based on application of the linear anisotropy invariant considerations, is placed in the context of the most recent Reynolds stress transport models, so that the innovation and advantages of the proposed methodology can be evaluated directly.

The term "turbulence” is used for a large variety of dynamical phenomena of fluids in motion whenever the details of the flow appear to be random and average properties are of primary interest. Just as wide ranging are the theoretical methods that have been applied towards a better understanding of fluid turbulence. In this book a number of these methods are described and applied to a broad range of problems from the transition to turbulence to asymptotic turbulence when the inertial part of the spectrum is fully developed. Statistical as well as nonstatistical treatments are presented, but a complete coverage of the subject is not attempted. The book will be of interest to scientists and engineers who wish to familiarize themselves with modern developments in theories of turbulence. The fact that the properties of turbulent fluid flow are addressed from very different points of view makes this volume rather unique among presently available books on turbulence.

This unique text provides engineering students and practicing professionals with a comprehensive set of practical, hands-on guidelines and dozens of step-by-step examples for performing state-of-the-art, reliable computational fluid dynamics (CFD) and turbulence modeling. Key CFD and turbulence programs are included as well. The text first reviews basic CFD theory, and then details advanced applied theories for estimating turbulence, including new algorithms created by the author. The book gives practical advice on selecting appropriate turbulence models and presents best CFD practices for modeling and generating reliable simulations. The author gathered and developed the book’s hundreds of tips, tricks, and examples over three decades of research and development at three national laboratories and at the University of New Mexico—many in print for the first time in this book. The book also places a strong emphasis on recent CFD and turbulence advancements found in the literature over the past five to 10 years. Readers can apply the author’s advice and insights whether using commercial or national laboratory software such as ANSYS Fluent, STAR-CCM, COMSOL, Flownex, SimScale, OpenFOAM, Fuego, KIVA, BIGHORN, or their own computational tools. Applied Computational Fluid Dynamics and Turbulence Modeling is a practical, complementary companion for academic CFD textbooks and senior project courses in mechanical, civil, chemical, and nuclear engineering; senior undergraduate and graduate CFD and turbulence modeling courses; and for professionals developing commercial and research applications.

Turbulence modeling both addresses a fundamental problem in physics, 'the last great unsolved problem of classical physics,' and has far-reaching importance in the solution of difficult practical problems from aeronautical engineering to dynamic meteorology. However, the growth of supercom puter facilities has recently caused an apparent shift in the focus of tur bulence research from modeling to direct numerical simulation (DNS) and large eddy simulation (LES). This shift in emphasis comes at a time when claims are being made in the world around us that scientific analysis itself will shortly be transformed or replaced by a more powerful 'paradigm' based on massive computations and sophisticated visualization. Although this viewpoint has not lacked ar ticulate and influential advocates, these claims can at best only be judged premature. After all, as one computational researcher lamented, 'the com puter only does what I tell it to do, and not what I want it to do. ' In turbulence research, the initial speculation that computational meth ods would replace not only model-based computations but even experimen tal measurements, have not come close to fulfillment. It is becoming clear that computational methods and model development are equal partners in turbulence research: DNS and LES remain valuable tools for suggesting and validating models, while turbulence models continue to be the preferred tool for practical computations. We believed that a symposium which would reaffirm the practical and scientific importance of turbulence modeling was both necessary and timely.

Advanced Approaches in Turbulence: Theory, Modeling, Simulation and Data Analysis for Turbulent Flows focuses on the updated theory, simulation and data analysis of turbulence dealing mainly with turbulence modeling instead of the physics of turbulence. Beginning with the basics of turbulence, the book discusses closure modeling, direct simulation, large eddy simulation and hybrid simulation. The book also covers the entire spectrum of turbulence models for both single-phase and multi-phase flows, as well as turbulence in compressible flow. Turbulence modeling is very extensive and continuously updated with new achievements and improvements of the models. Modern advances in computer speed offer the potential for elaborate numerical analysis of turbulent fluid flow while advances in instrumentation are creating large amounts of data. This book covers these topics in great detail. - Covers the fundamentals of turbulence updated with recent developments - Focuses on hybrid methods such as DES and wall-modeled LES - Gives an updated treatment of numerical simulation and data analysis

obtained are still severely limited to low Reynolds numbers (about only one decade better than direct numerical simulations), and the interpretation of such calculations for complex, curved geometries is still unclear. It is evident that a lot of work (and a very significant increase in available computing power) is required before such methods can be adopted in daily's engineering practice. I hope to l"Cport on all these topics in a near future. The book is divided into six chapters, each· chapter in subchapters, sections and subsections. The first part is introduced by Chapter 1 which summarizes the equations of fluid mechanies, it is developed in C~apters 2 to 4 devoted to the construction of turbulence models. What has been called "engineering methods" is considered in Chapter 2 where the Reynolds averaged equations al"C established and the closure problem studied (§1-3). A first detailed study of homogeneous turbulent flows follows (§4). It includes a review of available experimental data and their modeling. The eddy viscosity concept is analyzed in §5 with the l"Csulting ~alar-transport equation models such as the famous K-e model. Reynolds stl"Css models (Chapter 4) require a preliminary consideration of two-point turbulence concepts which are developed in Chapter 3 devoted to homogeneous turbulence. We review the two-point moments of velocity fields and their spectral transforms (§ 1), their general dynamics (§2) with the particular case of homogeneous, isotropie turbulence (§3) whel"C the so-called Kolmogorov's assumptions are discussed at length.