A Realizable Reynolds Stress Algebraic Equation Model

A Realizable Reynolds Stress Algebraic Equation Model
Author: Tsan-Hsing Shih
Publisher:
Total Pages: 42
Release: 1993
Genre:
ISBN:

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The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.

A New Reynolds Stress Algebraic Equation Model

A New Reynolds Stress Algebraic Equation Model
Author: Tsan-Hsing Shih
Publisher:
Total Pages:
Release: 1994
Genre:
ISBN:

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A general turbulent constitutive relation is directly applied to propose a new Reynolds stress algebraic equation model. In the development of this model, the constraints based on rapid distortion theory and realizability (i.e. the positivity of the normal Reynolds stresses and the Schwarz' inequality between turbulent velocity correlations) are imposed. Model coefficients are calibrated using well-studied basic flows such as homogeneous shear flow and the surface flow in the inertial sublayer. The performance of this model is then tested in complex turbulent flows including the separated flow over a backward-facing step and the flow in a confined jet. The calculation results are encouraging and point to the success of the present model in modeling turbulent flows with complex geometries.

Fully-Explicit and Self-Consistent Algebraic Reynolds Stress Models

Fully-Explicit and Self-Consistent Algebraic Reynolds Stress Models
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
Total Pages: 32
Release: 2018-07-03
Genre:
ISBN: 9781722250218

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A fully-explicit, self-consistent algebraic expression for the Reynolds stress, which is the exact solution to the Reynolds stress transport equation in the 'weak equilibrium' limit for two-dimensional mean flows for all linear and some quasi-linear pressure-strain models, is derived. Current explicit algebraic Reynolds stress models derived by employing the 'weak equilibrium' assumption treat the production-to-dissipation (P/epsilon) ratio implicitly, resulting in an effective viscosity that can be singular away from the equilibrium limit. In the present paper, the set of simultaneous algebraic Reynolds stress equations are solved in the full non-linear form and the eddy viscosity is found to be non-singular. Preliminary tests indicate that the model performs adequately, even for three dimensional mean flow cases. Due to the explicit and non-singular nature of the effective viscosity, this model should mitigate many of the difficulties encountered in computing complex turbulent flows with the algebraic Reynolds stress models. Girimaji, Sharath S. Langley Research Center NAS1-19480; RTOP 505-90-52-01...

Progress in Propulsion Physics

Progress in Propulsion Physics
Author: Luigi T. DeLuca
Publisher:
Total Pages: 570
Release: 2012
Genre:
ISBN: 9782759806744

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La péface indique : "EUCASS (European Conference for Aero-Space Sciences) is a scientific association at the service of research scientists, engineers, and decision makers active in aeronautical and space sciences. EUCASS, which is an international nonprofit association under the Belgian law, addresses all topics of interest to aerospace, from research challenges to long-term programmes and prospective. It organizes regular conferences, workshops, and meetings. Its goal is to attract the best specialists from Europe and elsewhere, and to create a commonwealth of interest and challenges where in-formation and ideas circulate freely and swiftly, where the currently scattered European knowledge is exchanged much faster and cross-fertilised. EUCASS is the cradle that nurtures a friendly and lively community spirit among all players. It started its activities in 2005 by organizing the first-ever European conference in Moscow, followed at a biennial rate in Brussels and Versailles. In order to contribute to the dissemination of scientific knowledge, we have launched this EUCASS Book Series, the first and second volumes of which were dedicated to Propulsion Physics and presented a selection of the lectures given in Brussels in July 2007. EUCASS is organized in several permanent Technical Committees (TC). One of them is the Flight Physics TC. Within the broad EUCASS framework, the specificc purpose of the Flight Physics TC is to promote the technology, sciences, and arts of Flight physics and to help those engaged in these pursuits to develop their skills and those of their students. This third volume of the EUCASS Book Series on Advances in Aerospace Sciences is dedicated to Flight Physics. It comprises a selected collection of 43 papers presented at the 3rd European Conference for Aerospace Sciences held in Versailles, France, July 06-10, 2009. The current volume is the result of a long review process. About 1/3 of the total number of papers accepted for presentation at the conference was later selected by the volume editors, then edited by an international body of peer reviewers. The volume includes six chapters covering experimental, theoretical and numerical aspects of the fight physics: Chapter One Aerodynamics, Chapter Two Shock Interaction, Chapter Three High Enthalphy Flows, Chapter Four Heat Transfer, Chapter Five Aeroacoustics, Chapter Six Flow Control. To easily identify the material of interest, the reader is invited to consult the brief paper summaries compiled at the start of each chapter."