One Point Statistical Turbulence Models
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| Author | : Michael Leschziner |
| Publisher | : World Scientific |
| Total Pages | : 424 |
| Release | : 2015-08-20 |
| Genre | : Science |
| ISBN | : 1783266635 |
This book is intended for self-study or as a companion of lectures delivered to post-graduate students on the subject of the computational prediction of complex turbulent flows. There are several books in the extensive literature on turbulence that deal, in statistical terms, with the phenomenon itself, as well its many manifestations in the context of fluid dynamics. Statistical Turbulence Modelling for Fluid Dynamics — Demystified differs from these and focuses on the physical interpretation of a broad range of mathematical models used to represent the time-averaged effects of turbulence in computational prediction schemes for fluid flow and related transport processes in engineering and the natural environment. It dispenses with complex mathematical manipulations and instead gives physical and phenomenological explanations. This approach allows students to gain a 'feel' for the physical fabric represented by the mathematical structure that describes the effects of turbulence and the models embedded in most of the software currently used in practical fluid-flow predictions, thus counteracting the ill-informed black-box approach to turbulence modelling. This is done by taking readers through the physical arguments underpinning exact concepts, the rationale of approximations of processes that cannot be retained in their exact form, and essential calibration steps to which the resulting models are subjected by reference to theoretically established behaviour of, and experimental data for, key canonical flows.
| Author | : P. A. Durbin |
| Publisher | : John Wiley & Sons |
| Total Pages | : 347 |
| Release | : 2011-06-28 |
| Genre | : Science |
| ISBN | : 1119957524 |
Providing a comprehensive grounding in the subject of turbulence, Statistical Theory and Modeling for Turbulent Flows develops both the physical insight and the mathematical framework needed to understand turbulent flow. Its scope enables the reader to become a knowledgeable user of turbulence models; it develops analytical tools for developers of predictive tools. Thoroughly revised and updated, this second edition includes a new fourth section covering DNS (direct numerical simulation), LES (large eddy simulation), DES (detached eddy simulation) and numerical aspects of eddy resolving simulation. In addition to its role as a guide for students, Statistical Theory and Modeling for Turbulent Flows also is a valuable reference for practicing engineers and scientists in computational and experimental fluid dynamics, who would like to broaden their understanding of fundamental issues in turbulence and how they relate to turbulence model implementation. Provides an excellent foundation to the fundamental theoretical concepts in turbulence. Features new and heavily revised material, including an entire new section on eddy resolving simulation. Includes new material on modeling laminar to turbulent transition. Written for students and practitioners in aeronautical and mechanical engineering, applied mathematics and the physical sciences. Accompanied by a website housing solutions to the problems within the book.
| Author | : P. A. Durbin |
| Publisher | : Wiley-Blackwell |
| Total Pages | : 312 |
| Release | : 2001-03-12 |
| Genre | : Mathematics |
| ISBN | : |
Most natural and industrial flows are turbulent. The atmosphere and oceans, automobile and aircraft engines, all provide examples of this ubiquitous phenomenon. In recent years, turbulence has become a very lively area of scientific research and application, and this work offers a grounding in the subject of turbulence, developing both the physical insight and the mathematical framework needed to express the theory. Providing a solid foundation in the key topics in turbulence, this valuable reference resource enables the reader to become a knowledgeable developer of predictive tools. This central and broad ranging topic would be of interest to graduate students in a broad range of subjects, including aeronautical and mechanical engineering, applied mathematics and the physical sciences. The accompanying solutions manual to the text also makes this a valuable teaching tool for lecturers and for practising engineers and scientists in computational and experimental and experimental fluid dynamics.
| Author | : P.-L. Viollet |
| Publisher | : |
| Total Pages | : 23 |
| Release | : 1987 |
| Genre | : |
| ISBN | : |
| Author | : Manuel D. Salas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 385 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 9401147248 |
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.
| Author | : Rodney O. Fox |
| Publisher | : Cambridge University Press |
| Total Pages | : 156 |
| Release | : 2003-10-30 |
| Genre | : Mathematics |
| ISBN | : 9780521659079 |
| Author | : Stefan Heinz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 232 |
| Release | : 2013-03-09 |
| Genre | : Science |
| ISBN | : 3662100223 |
The simulation of technological and environmental flows is very important for many industrial developments. A major challenge related to their modeling is to involve the characteristic turbulence that appears in most of these flows. The traditional way to tackle this question is to use deterministic equations where the effects of turbulence are directly parametrized, i. e. , assumed as functions of the variables considered. However, this approach often becomes problematic, in particular if reacting flows have to be simulated. In many cases, it turns out that appropriate approximations for the closure of deterministic equations are simply unavailable. The alternative to the traditional way of modeling turbulence is to construct stochastic models which explain the random nature of turbulence. The application of such models is very attractive: one can overcome the closure problems that are inherent to deterministic methods on the basis of relatively simple and physically consistent models. Thus, from a general point of view, the use of stochastic methods for turbulence simulations seems to be the optimal way to solve most of the problems related to industrial flow simulations. However, it turns out that this is not as simple as it looks at first glance. The first question concerns the numerical solution of stochastic equations for flows of environmental and technological interest. To calculate industrial flows, 3 one often has to consider a number of grid cells that is of the order of 100 .
| Author | : |
| Publisher | : |
| Total Pages | : 139 |
| Release | : 2001 |
| Genre | : |
| ISBN | : |
The Reynolds stresses alone are not sufficient to characterize complex turbulent flows adequately. Complementary information, contained in the structure dimensionality tensor, must also be included in one-point turbulence models. This work uses hypothetical turbulent eddies to bring awareness of turbulence structure into the turbulence model. Averaging over a large ensemble of eddies produces a set of one-point statistics, representative of the eddy field, and a set of equations of state relating the Reynolds stresses and the structure dimensionality to the eddy statistics. An algebraic model for the eddy statistics is constructed in terms of the local mean deformation and two turbulent scales; the turbulent kinetic energy and the large-scale enstrophy. The algebraic model is further sensitized to the presence of walls by a blocking scheme, which ensures proper asymptotic behavior for the Reynolds stresses in the vicinity of walls. Contrary to existing ad-hoc definitions of a second scale equation, the large-scale enstrophy equation has a fundamental background; it is derived from the large-scale vorticity equation. Its terms represent large-scale processes, and their exact form provides valuable guidance when making choices for their closure, and when matching their asymptotic behavior in the vicinity of walls. The algebraic model produces physically realistic Reynolds stresses and structure tensors for different combinations of mean strain and mean rotation, with and without frame rotation. The complete model, with evolution equations for the turbulent scales and algebraic equations for the turbulence structure, was successfully implemented. The full model was found to produce excellent results for a set of channel flows in fixed frames and in spanwise-rotating frames of reference.
| Author | : Jean Piquet |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 767 |
| Release | : 2013-04-17 |
| Genre | : Technology & Engineering |
| ISBN | : 3662035596 |
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.
| Author | : Martin Oberlack |
| Publisher | : Springer |
| Total Pages | : 377 |
| Release | : 2014-05-04 |
| Genre | : Science |
| ISBN | : 3709125642 |
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.
