Theoretical Investigation of an Eddy-Viscosity-Type Representation of the Reynolds Stress

1994 ◽  
Vol 63 (6) ◽  
pp. 2102-2122 ◽  
Author(s):  
Masayoshi Okamoto
Keyword(s):  
Reynolds Stress ◽  
Theoretical Investigation ◽  
Eddy Viscosity ◽  
Type Representation

scholarly journals Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

2016 ◽  
Vol 807 ◽  
pp. 155-166 ◽  
Author(s):  
Julia Ling ◽  
Andrew Kurzawski ◽  
Jeremy Templeton
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Reynolds Stress ◽  
Network Architecture ◽  
Eddy Viscosity ◽  
Deep Neural Networks ◽  
Test Cases ◽  
Neural Network Architecture ◽  
Stress Anisotropy ◽  
Anisotropy Tensor

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. The Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.

Structural Parameters and Prediction of Adverse Pressure Gradient Turbulent Flows: An Improved k-ε Model

1995 ◽  
Vol 117 (3) ◽  
pp. 424-432 ◽  
Author(s):  
G. Chukkapalli ◽  
O¨. F. Turan
Keyword(s):  
Pressure Gradient ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Eddy Viscosity ◽  
Structural Parameters ◽  
Adverse Pressure Gradient ◽  
Reynolds Stress Model ◽  
Model Representation ◽  
Stress Model ◽  
Kinetic Diffusion

A modified k-ε model is proposed to predict complex, adverse pressure gradient, turbulent diffuser flows. The need for an eddy viscosity is eliminated by using three structural parameters. A fuller treatment of the rate of kinetic diffusion terms is incorporated with a Reynolds stress model representation. A thorough evaluation is given of the three structural parameters in three decreasing and one increasing adverse pressure gradient diffuser flows leading to a three-layer representation. The results indicate the need for better modeling of the ε-equation.

scholarly journals Rotating Flow and Heat Transfer in Cylindrical Cavities With Radial Inflow

2012 ◽  
Author(s):  
B. G. Vinod Kumar ◽  
John W. Chew ◽  
Nicholas J. Hills
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Reynolds Stress ◽  
Integral Method ◽  
Eddy Viscosity ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Rotating Disc ◽  
Flow And Heat Transfer ◽  
Viscosity Models

Design and optimization of an efficient internal air system of a gas turbine requires thorough understanding of the flow and heat transfer in rotating disc cavities. The present study is devoted to numerical modelling of flow and heat transfer in a cylindrical cavity with radial inflow and comparison with the available experimental data. The simulations are carried out with axi-symmetric and 3-D sector models for various inlet swirl and rotational Reynolds numbers upto 2.1×106. The pressure coefficients and Nusselt numbers are compared with the available experimental data and integral method solutions. Two popular eddy viscosity models, the Spalart-Allmaras and the k-ε, and a Reynolds stress model have been used. For cases with particularly strong vortex behaviour the eddy viscosity models show some shortcomings with the Spalart-Allmaras model giving slightly better results than the k-ε model. Use of the Reynolds stress model improved the agreement with measurements for such cases. The integral method results are also found to agree well with the measurements.

Performance Evaluation of a Non-Linear Explicit Algebraic Reynolds Stress Model for Surface Mounted Obstacles

2020 ◽  
Author(s):  
Benjamin H. Taylor ◽  
Tausif Jamal ◽  
D. Keith Walters
Keyword(s):  
Reynolds Stress ◽  
Eddy Viscosity ◽  
Numerical Data ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Rans Model ◽  
Non Linear ◽  
Additional Strain ◽  
Dynamic Hybrid ◽  
Algebraic Reynolds Stress Model

Abstract The presence of complex vortical structures, unsteady wakes, separated shear layers, and streamline curvature pose considerable challenges for traditional linear Eddy-Viscosity (LEV) models. Since Non-Linear Eddy Viscosity Models (NEV) models contain additional strain-rate and vorticity relationships, they can provide a better description for flows with Reynolds stress anisotropy and can be considered to be suitable alternatives to traditional EVMs in some cases. In this study, performance of a Non-Linear Explicit Algebraic Reynolds Stress Model (NEARSM) to accurately resolve flow over a surface mounted cube and a 3D axisymmetric hill is evaluated against existing experimental and numerical studies. Numerical simulations were performed using the SST k-ω RANS model, SST k-ω-NEARSM, SST-Multiscale LES model, and two variants of the Dynamic Hybrid RANS-LES (DHRL) model that include the SST k-ω and the SST k-ω-NEARSM as the RANS models. Results indicate that the SST k-ω RANS model fails to accurately predict the flowfield in the separated wake region and although the SST-NEARSM and SST-Multiscale LES models provide an improved description of the flow, they suffer from incorrect RANS-LES transition caused by Modeled Stress Depletion (MSD) and sensitivity to changes in grid resolution. The SST-DHRL and the SST-NEARSM-DHRL variants provide the best agreement to experimental and numerical data.

Reynolds stress and eddy viscosity in direct numerical simulations of sheared two-dimensional turbulence

2010 ◽  
Vol 657 ◽  
pp. 394-412 ◽  
Author(s):  
PATRICK F. CUMMINS ◽  
GREG HOLLOWAY
Keyword(s):  
Reynolds Stress ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Finite Domain ◽  
Spectral Space ◽  
Two Dimensional ◽  
Initial Value ◽  
Theoretical Predictions ◽  
Eddy Field ◽  
Scale Shear

The Reynolds stress associated with the adjustment of two-dimensional isotropic eddies subject to a large-scale shear flow is examined in a series of initial-value calculations in a periodic channel. Several stages in the temporal evolution of the stress can be identified. Initially, there is a brief period associated with quasi-passive straining of the eddy field in which the net Reynolds stress and the associated eddy viscosity remain essentially zero. In spectral space this is characterized by mutual cancellation of contributions to the Reynolds stress at high and low eddy wavenumbers. Subsequently, eddy–eddy interactions produce a tendency to restore isotropy at higher eddy wavenumbers, leading to an overall positive eddy viscosity associated with the dominant contribution to the Reynolds stress at low eddy wavenumbers. These results are consistent with theoretical predictions of positive eddy viscosity for initially isotropic homogeneous two-dimensional turbulence. Due to the inverse cascade, the accumulation with time of energy at the scale of the channel produces a competing tendency to negative eddy viscosity associated with linear shearing of the disturbances. This finite-domain effect may become dominant if the nonlinearity of the eddy field is relatively weak.

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.

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