Direct measurement of the eddy viscosity tensor in a canonical separated flow: What is the upper bound of accuracy for local Reynolds stress models?

2022 ◽  
Author(s):  
Danah Park ◽  
Ali Mani
Keyword(s):  
Reynolds Stress ◽  
Direct Measurement ◽  
Upper Bound ◽  
Eddy Viscosity ◽  
Separated Flow ◽  
Stress Models

Applications of EARSM Turbulence Models to Internal Flows

2012 ◽  
Author(s):  
O. Z. Mehdizadeh ◽  
L. Temmerman ◽  
B. Tartinville ◽  
Ch. Hirsch
Keyword(s):  
Reynolds Stress ◽  
High Performance ◽  
Eddy Viscosity ◽  
Computational Cost ◽  
Turbulence Models ◽  
Industrial Applications ◽  
Mean Flow ◽  
Viscosity Models ◽  
Stress Models ◽  
Corner Flows

Turbulence modeling remains an active CFD development front for turbomachinery as well as for general industrial applications. While DNS and even LES still seem out of reach within the typical industrial design cycle due to their high computational cost, RANS-based models remain the workhorse of CFD. Currently, the most widely used models are Linear Eddy-Viscosity Models (LEVM), despite their known limitations for certain flow complexities. Therefore, extending the reliability of eddy-viscosity models to more complex flows without significantly increasing the computational cost can immediately contribute to more reliable CFD results for wider range of applications. This, in turn, can further reduce the need for costly tests and consequently can reduce the product development cost. A promising approach to achieve this goal is using Explicit Algebraic Reynolds Stress Models (EARSM), obtained through a simplification of the full Differential Reynolds Stress Models (DRSM), and can be perceived as an extension of LEVMs by including the non-linear relation between the turbulence stress tensor, the mean-flow gradient and the turbulence scales. These models are thus less demanding than DRSM, yet capable of capturing more complex turbulence features, compared to LEVM, such as anisotropy in the normal stresses. This may be particularly important in corner flows, for instance, in the hub-blade regions or in diffusers. This work explores the application of EARSM models to a double diffuser and a high-performance centrifugal compressor stage (HPCC). The results are compared to available experimental data [1,2] showing the importance of including the anisotropy of turbulence in the model, particularly in presence of turbulent corner flows in a diffuser. Furthermore, the EARSM results are also compared to results from the commonly used SST turbulence model. The CFD comparison includes details of the flow structure in the diffuser, where the most noticeable impact from the use of EARSM turbulence models is expected.

Modeling Of Turbulent Transport Equations

1996 ◽  
Author(s):  
Charles G. Speziale
Keyword(s):  
Turbulent Flows ◽  
Reynolds Stress ◽  
Time Scales ◽  
Eddy Viscosity ◽  
Ad Hoc ◽  
Stokes Equations ◽  
Transport Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stress Models

The high-Reynolds-number turbulent flows of technological importance contain such a wide range of excited length and time scales that the application of direct or large-eddy simulations is all but impossible for the foreseeable future. Reynolds stress models remain the only viable means for the solution of these complex turbulent flows. It is widely believed that Reynolds stress models are completely ad hoc, having no formal connection with solutions of the full Navier-Stokes equations for turbulent flows. While this belief is largely warranted for the older eddy viscosity models of turbulence, it constitutes a far too pessimistic assessment of the current generation of Reynolds stress closures. It will be shown how secondorder closure models and two-equation models with an anisotropic eddy viscosity can be systematically derived from the Navier-Stokes equations when one overriding assumption is made: the turbulence is locally homogeneous and in equilibrium. A brief review of zero equation models and one equation models based on the Boussinesq eddy viscosity hypothesis will first be provided in order to gain a perspective on the earlier approaches to Reynolds stress modeling. It will, however, be argued that since turbulent flows contain length and time scales that change dramatically from one flow configuration to the next, two-equation models constitute the minimum level of closure that is physically acceptable. Typically, modeled transport equations are solved for the turbulent kinetic energy and dissipation rate from which the turbulent length and time scales are built up; this obviates the need to specify these scales in an ad hoc fashion. While two-equation models represent the minimum acceptable closure, second-order closure models constitute the most complex level of closure that is currently feasible from a computational standpoint. It will be shown how the former models follow from the latter in the equilibrium limit of homogeneous turbulence. However, the two-equation models that are formally consistent with second-order closures have an anisotropic eddy viscosity with strain-dependent coefficients - a feature that most of the commonly used models do not possess.

Blending the Eddy-Viscosity and Reynolds-Stress Models Using Uniform High-Order Discretization

AIAA Journal ◽  
2020 ◽  
Vol 58 (12) ◽  
pp. 5361-5378
Author(s):  
Shengye Wang ◽  
Xiaogang Deng ◽  
Guangxue Wang ◽  
Xiaoliang Yang
Keyword(s):  
Reynolds Stress ◽  
Eddy Viscosity ◽  
High Order ◽  
Stress Models

Modeling Separation-Induced Transition Using a Non-Linear Three Equation Turbulence Model and a Reynolds Stress Turbulence Model

2010 ◽  
Author(s):  
Zinon Vlahostergios ◽  
Kyros Yakinthos
Keyword(s):  
Transport Equation ◽  
Reynolds Stress ◽  
Turbulence Model ◽  
Eddy Viscosity ◽  
Turbulence Models ◽  
Viscosity Model ◽  
Transitional Flows ◽  
Eddy Viscosity Model ◽  
Non Linear ◽  
Stress Models

This paper presents an effort to model separation-induced transition on a flat plate with a semi-circular leading edge, by using two advanced turbulence models, the three equation non-linear model k-ε-A2 of Craft et al. [16] and the Reynolds-stress model of Craft [13]. The mechanism of the transition is governed by the different inlet velocity and turbulence intensity conditions, which lead to different recirculation bubbles and different transition onset points for each case. The use of advanced turbulence models in predicting the development of transitional flows has shown, in past studies, good perspectives. The k-ε-A2 model uses an additional transport equation for the A2 Reynolds stress invariant and it is an improvement of Craft et al. [12] non-linear eddy viscosity model. The use of the third transport equation gives improved results in the prediction of the longitudinal Reynolds stress distributions and especially, in flows where transitional phenomena may occur. Although this model is a pure eddy-viscosity model, it borrows many aspects from the more complex Reynolds-stress models. On the other hand, the use of an advanced Reynolds-stress turbulence model, such as the one of Craft [13], can predict many complex flows and there are indications that it can be applied to transitional flows also, since the crucial terms of Reynolds stress generation are computed exactly and normal stress anisotropy is resolved. The model of Craft [13], overcomes the drawbacks of the common used Reynolds-stress models regarding the computation of wall-normal distances and vectors in order to account for wall proximity effects. Instead of these quantities, it employs “normalized turbulence lengthscale gradients” which give the ability to identify the presence of strong inhomogeneity in a flow development, in an easier way. The final results of both turbulence models showed acceptable agreement with the experimental data. In this work it is shown that there is a good potential to model separation-induced transitional flows, with advanced turbulence modeling without any additional use of ad-hoc modifications or additional equations, based on various transition models.

scholarly journals Reynolds stress models of convection in convective cores

2006 ◽  
Vol 2 (S239) ◽  
pp. 77-79 ◽  
Author(s):  
Ian W Roxburgh ◽  
Friedrich Kupka
Keyword(s):  
Reynolds Stress ◽  
Algebraic Closure ◽  
Spherical Geometry ◽  
Turbulent Convection ◽  
Closure Models ◽  
Non Local ◽  
Stress Models

AbstractWe investigate the properties of non-local Reynolds stress models of turbulent convection in a spherical geometry. Regularity at the centre r=0 places constraints on the behaviour of 3rd order moments. Some of the down-gradient and algebraic closure models have inconsistent behaviour at r=0. A combination of down-gradient and algebraic closures gives a consistent prescription that can be used to model convection in stellar cores.

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