Reynolds Stress Anisotropy Based Turbulent Eddy Viscosity Model Applied to Numerical Ocean Models

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Subhendu Maity ◽  
Hari Warrior
Keyword(s):  
Reynolds Stress ◽  
Eddy Viscosity ◽  
State Of The Art ◽  
Test Case ◽  
Turbulent Eddy ◽  
Ocean Turbulence ◽  
Stress Anisotropy ◽  
Eddy Viscosity Model ◽  
Degree Of Anisotropy ◽  
Ocean Models

The present state-of-the-art ocean models use an eddy viscosity that depends on structure parameter (Cμ). In this paper we use a Reynolds stress anisotropy based formulation for the eddy viscosity because in addition to the value of turbulent kinetic energy, it also depends on the degree of anisotropy. The formulation is incorporated into the General Ocean Turbulence Model (GOTM) and simulated using the famous test case of Ocean Weather Station (OWS) Papa experiment. Even if there is not much of an improvement in terms of results with this model, it can be very easily incorporated into the ocean models removing cumbersome equations for structure parameters.

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.

Measurement Investigation of Complex Eddy Viscosity Model in Non-Equilibrium Wavy Wall Turbulence with TRPIV

2013 ◽  
Vol 718-720 ◽  
pp. 1657-1662
Author(s):  
An Tong Zhang ◽  
Nan Jiang
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Strain Rate ◽  
Reynolds Stress ◽  
Eddy Viscosity ◽  
Wavy Wall ◽  
Streamwise Direction ◽  
Mean Velocity ◽  
Eddy Viscosity Model ◽  
Phase Differences

The spatial flow fields of turbulent boundary layer over a wavy wall were measured by TRPIV at three different Reynolds numbers in a water channel, the mean streamwise and wall-normal velocities near the wall were calculated from the time series of instantaneous spatial 2D-2C flow fields of turbulent boundary layer, and the periodic distributions of the streamwise and wall-normal velocity in streamwise direction influenced by the wavy wall were found. The spatial distributions of Reynolds stress and mean velocity strain rate were obtained by ensemble average. Using the spatial cross-correlation technique, the spatial phase relationship in streamwise direction between mean velocity strain rate and Reynolds stress was investigated. It is found that there exist spatial phase differences between Reynolds stress components and mean velocity strain rate components, the phase differences increase gradually after decrease gradually from zero away from the wavy wall in wall-normal direction and reach a minimum at 0.4~0.5 times the wavelength of wavy wall, and in a certain range the effect of the Reynolds number on the phase differences is very small. The reasonability of the complex eddy viscosity model is confirmed by these experimental evidences in order to forecast non-equilibrium turbulence accurately.

Reconstruction of RANS Model and Cross-Validation of Flow Field Based on Tensor Basis Neural Network

2019 ◽  
Author(s):  
Xudong Song ◽  
Zhen Zhang ◽  
Yiwei Wang ◽  
Shuran Ye ◽  
Chenguang Huang
Keyword(s):  
Neural Network ◽  
Flow Field ◽  
Reynolds Stress ◽  
Prediction Accuracy ◽  
Eddy Viscosity ◽  
Viscosity Model ◽  
Strain Rate Tensor ◽  
Rans Model ◽  
Eddy Viscosity Model ◽  
Tensor Basis

Abstract The solution of the Reynolds-averaged Navier-Stokes (RANS) equation has been widely used in engineering problems. However, this model does not provide satisfactory prediction accuracy. Because the widely used eddy viscosity model assumes a linear relationship between the Reynolds stress and the average strain rate tensor and these linear models cannot capture the anisotropic characteristics of the actual flow. In this paper, two kinds of flow field structures of two-dimensional cylindrical flow and circular tube jet are calculated by using the RANS model. Secondly, in order to improve the prediction accuracy of the RANS model, the Reynolds stress of the RANS model is reconstructed by the tensor basis neural network algorithm based on nonlinear eddy viscosity model. Finally, the model trained by neural network is cross-validated, and compare the cross-test results with the traditional RANS k-eps model. The results show that the multi-layer neural network method has achieved good results in turbulence model reconstruction.

Evaluation of Turbulence Closure Models for Large-Eddy Simulation over Complex Terrain: Flow over Askervein Hill

2009 ◽  
Vol 48 (5) ◽  
pp. 1050-1065 ◽  
Author(s):  
Fotini Katopodes Chow ◽  
Robert L. Street
Keyword(s):  
Eddy Viscosity ◽  
Mixed Model ◽  
Turbulence Models ◽  
Test Case ◽  
Closure Models ◽  
Eddy Simulation ◽  
Eddy Viscosity Model ◽  
Scale Similarity ◽  
Askervein Hill ◽  
The Hill

Abstract The evaluation of turbulence closure models for large-eddy simulation (LES) has primarily been performed over flat terrain, where comparisons with theory and observations are simplified. The authors have previously developed improved closure models using explicit filtering and reconstruction, together with a dynamic eddy-viscosity model and a near-wall stress term. This dynamic reconstruction model (DRM) is a mixed model, combining scale-similarity and eddy-viscosity components. The DRM gave improved results over standard eddy-viscosity models for neutral boundary layer flow over flat but rough terrain, yielding the expected logarithmic velocity profiles near the wall. The results from the studies over flat terrain are now extended to flow over full-scale topography. The test case is flow over Askervein Hill, an isolated hill in western Scotland, where a field campaign was conducted in 1983 with the purpose of capturing wind data representing atmospheric episodes under near-neutral stratification and steady wind conditions. This widely studied flow provides a more challenging test case for the new turbulence models because of the sloping terrain and separation in the lee of the hill. Since an LES formulation is used, a number of simulation features are different than those typically used in the Askervein literature. The simulations are inherently unsteady, the inflow conditions are provided by a separate turbulent flow database, and (uniquely herein) ensemble averages of the turbulent flow results are used in comparisons with field data. Results indicate that the DRM can improve the predictions of flow speedup and especially turbulent kinetic energy (TKE) over the hill when compared with the standard TKE-1.5 model. This is the first study, to the authors’ knowledge, in which explicit filtering and reconstruction (scale similarity) and dynamic turbulence models have been applied to full-scale simulations of the atmospheric boundary layer over terrain. Simulations with the lowest level of reconstruction are straightforward. Increased levels of reconstruction, however, present difficulties when used with a dynamic eddy-viscosity model. An alternative mixed model is proposed to avoid the complexities associated with the dynamic procedure and to allow higher levels of reconstruction; this mixed model combines a standard TKE-1.5 eddy-viscosity closure with velocity reconstruction to form a simple and efficient turbulence model that gives good results for both mean flow and turbulence over Askervein Hill. The results indicate that significant improvements in LES over complex terrain can be obtained by the use of mixed models that combine scale-similarity and eddy-viscosity components.

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.

Assessment of a Reynolds Stress Closure Model for Appendage-Hull Junction Flows

1995 ◽  
Vol 117 (4) ◽  
pp. 557-563 ◽  
Author(s):  
Hamn-Ching Chen
Keyword(s):  
Reynolds Stress ◽  
Eddy Viscosity ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Moment Closure ◽  
Superior Performance ◽  
Navier Stokes ◽  
Second Moment ◽  
Eddy Viscosity Model ◽  
Second Moment Closure

A multiblock numerical method, for the solution of the Reynolds-Averaged Navier-Stokes equations, has been used in conjunction with a near-wall Reynolds stress closure and a two-layer isotropic eddy viscosity model for the study of turbulent flow around a simple appendage-hull junction. Comparisons of calculations with experimental data clearly demonstrate the superior performance of the present second-order Reynolds stress (second-moment) closure over simpler isotropic eddy viscosity models. The second-moment solutions are shown to capture the most important features of appendage-hull juncture flows, including the formation and evolution of the primary and secondary horseshoe vortices, the complex three-dimensional separations, and interaction among the hull boundary layer, the appendage wake and the root vortex system.

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