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.

Modeling Complex Turbulent Flows

Modeling Complex Turbulent Flows
Author: Manuel D. Salas
Publisher: Springer Science & Business Media
Total Pages: 402
Release: 1999-04-30
Genre: Science
ISBN: 9780792355908

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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.

Reynolds Stress Modeling of Turbulent Open-channel Flows

Reynolds Stress Modeling of Turbulent Open-channel Flows
Author: Sung-Uk Choi
Publisher:
Total Pages: 116
Release: 2009
Genre: Mathematics
ISBN:

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This book presents numerical simulations of three-dimensional turbulent open-channel flows. In the simulations, Reynolds-averaged Navier-Stokes equations are solved with the Reynolds stress model for turbulence closure. The overall solution strategy is the SIMPLER algorithm, and the power-law scheme is used to discretise the convection and diffusion terms in the governing equations. The Reynolds stress model is applied to rectangular open-channel flows, partly-vegetated open-channel flows, and compound open-channel flows. The simulated mean flow and turbulence structures including streamwise mean velocity, secondary currents, turbulence intensity, and Reynolds stress, are provided and compared with measure data in the literature. As shown in this book, these comparisons reveal that the proposed Reynolds stress model successfully predicts the mean flow and turbulence statistics of turbulent open-channel flows.

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...

Modeling Complex Turbulent Flows

Modeling Complex Turbulent Flows
Author: Manuel D. Salas
Publisher: Springer Science & Business Media
Total Pages: 385
Release: 2012-12-06
Genre: Science
ISBN: 9401147248

Download Modeling Complex Turbulent Flows Book in PDF, Epub and Kindle

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.