Eddy viscosity models for free turbulent flows

1973 ◽  
Vol 16 (2) ◽  
pp. 174 ◽  
Author(s):  
T. S. Lundgren
Keyword(s):  
Turbulent Flows ◽  
Eddy Viscosity ◽  
Viscosity Models

Numerical Investigation of Low-Reynolds Number Airfoil Flows Using Transition-Sensitive and Fully Turbulent RANS Models

2014 ◽  
Author(s):  
Varun Chitta ◽  
Tausif Jamal ◽  
D. Keith Walters
Keyword(s):  
Boundary Layer ◽  
Turbulent Flows ◽  
Eddy Viscosity ◽  
Boundary Layer Transition ◽  
Transition Flow ◽  
Layer Transition ◽  
Laminar Separation ◽  
Viscosity Models ◽  
Separation Bubbles ◽  
Laminar Separation Bubbles

A numerical analysis is performed to study the pre-stall and post-stall aerodynamic characteristics over a group of six airfoils using commercially available transition-sensitive and fully turbulent eddy-viscosity models. The study is focused on a range of Reynolds numbers from 6 × 104 to 2 × 106, wherein the flow around the airfoil is characterized by complex phenomena such as boundary layer transition, flow separation and reattachment, and formation of laminar separation bubbles on either the suction, pressure or both surfaces of airfoil. The predictive capability of the transition-sensitive k-kL-ω model versus the fully turbulent SST k-ω model is investigated for all airfoils. The transition-sensitive k-kL-ω model used in this study is capable of predicting both attached and separated turbulent flows over the surface of an airfoil without the need for an external linear stability solver to predict transition. The comparison between experimental data and results obtained from the numerical simulations is presented, which shows that the boundary layer transition and laminar separation bubbles that appear on the suction and pressure surfaces of the airfoil can be captured accurately by the use of a transition-sensitive model. The fully turbulent SST k-ω model predicts a turbulent boundary layer on both surfaces of the airfoil for all angles of attack and fails to predict boundary layer transition or separation bubbles. Discrepancies are observed in the predictions of airfoil stall by both the models. Reasons for the discrepancies between computational and experimental results, and also possible improvements in eddy-viscosity models, are discussed.

Review: Adapting Scalar Turbulence Closure Models for Rotation and Curvature

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Paul Durbin
Keyword(s):  
Growth Rate ◽  
Turbulent Flows ◽  
Equilibrium Solution ◽  
Eddy Viscosity ◽  
Turbulent Energy ◽  
Streamline Curvature ◽  
Viscosity Models ◽  
Scalar Turbulence ◽  
Convective Derivative ◽  
Effects Of Rotation

Scalar, eddy viscosity models are widely used for predicting engineering turbulent flows. System rotation, or streamline curvature, can enhance or reduce the intensity of turbulence. Methods to incorporate the effects of rotation and streamline curvature consist of introducing parametric variation of model coefficients, such that either the growth rate of turbulent energy is altered; or such that the equilibrium solution bifurcates from healthy to decaying solution branches. For general use, parameters must be developed in coordinate invariant forms. Effects of rotation and of curvature can be unified by introducing the convective derivative of the rate of strain eigenvectors as their measure.

scholarly journals Modification of the Marquardt method for training a neural network predictor in eddy viscosity models

2021 ◽  
pp. 27-34
Author(s):  
Vladimir Viktorovich Pekunov
Keyword(s):  
Neural Network ◽  
Turbulent Flows ◽  
Eddy Viscosity ◽  
Random Search ◽  
Optimization Techniques ◽  
Marquardt Method ◽  
Viscosity Models ◽  
The Neural Network ◽  
Limited Series ◽  
Speed Up

The subject of this article is the numerical optimization techniques used in training neural networks that serve as predicate components in certain modern eddy viscosity models. Qualitative solution to the problem of training (minimization of the functional of neural network offsets) often requires significant computational costs, which necessitates to increase the speed of such training based on combination of numerical methods and parallelization of calculations. The Marquardt method draws particular interest, as it contains  the parameter that allows speeding up the solution by switching the method from the descent away from the solution to the Newton’s method of approximate solution. The article offers modification of the Marquardt method, which uses the limited series of random samples for improving the current point and calculate the parameter of the method. The author demonstrate descent characteristics of the method in numerical experiments, both on the test functions of Himmelblau and Rosenbrock, as well as the actual task of training the neural network predictor applies in modeling of the turbulent flows. The use of this method may significantly speed up the training of neural network predictor in corrective models of eddy viscosity. The method is less time-consuming in comparison with random search, namely in terms of a small amount of compute kernels; however, it provides solution that is close to the result of random search and is better than the original Marquardt method.

Multiscale subgrid models of large eddy simulation for turbulent flows

2016 ◽  
Vol 26 (5) ◽  
pp. 1380-1390
Author(s):  
Jianying Jiao ◽  
Ye Zhang
Keyword(s):  
Strain Rate ◽  
Turbulent Flows ◽  
Eddy Viscosity ◽  
Scale Model ◽  
Wall Region ◽  
Strain Rate Tensor ◽  
Content Type ◽  
Eddy Viscosity Model ◽  
Viscosity Models ◽  
Near Wall

Purpose – The purpose of this paper is to propose three modified subgrid-scale (SGS) eddy-viscosity models to improve their original eddy-viscosity models (the Smagorinsky model (SM), the mixed-scale model (MSM), and the wall-adapted local eddy-viscosity model (WALE)) in the simulation of turbulent flows in near-wall region. Design/methodology/approach – The subgrid viscosity is related to the norm of strain rate tensor of the smallest resolved scales, instead of the norm of the resolved strain rate tensor of the large scales. Findings – All the SGS viscosity of the modified eddy-viscosity models (small-large model, modified MSM, and modified WALE) is closer to y+3 behavior than those of the original eddy-viscosity models (SM, MSM, and WALE) near the wall. Originality/value – The norm of strain rate tensor of the smallest scales used in eddy-viscosity models, instead of the norm of strain rate tensor, makes the eddy viscosity in near-wall region approach to zero in a physical sense.

INCREASE OF HEAT TRANSFER AND NEGATIVE EDDY VISCOSITY IN TURBULENT FLOWS INFLUENCED BY A MAGNETIC FIELD

1990 ◽  
Author(s):  
C. Henoch ◽  
Martin Hoffert ◽  
A. Baron ◽  
D. Klaiman ◽  
Semion Sukoriansky ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Turbulent Flows ◽  
Eddy Viscosity

scholarly journals Optimal nonlinear eddy viscosity in Galerkin models of turbulent flows

2015 ◽  
Vol 766 ◽  
pp. 337-367 ◽  
Author(s):  
Bartosz Protas ◽  
Bernd R. Noack ◽  
Jan Östh
Keyword(s):  
Turbulent Flows ◽  
High Speed ◽  
Eddy Viscosity ◽  
Broad Class ◽  
Constitutive Relations ◽  
Body Height ◽  
Mixing Layer ◽  
The Body ◽  
Stream Velocity ◽  
Initial Vorticity

AbstractWe propose a variational approach to the identification of an optimal nonlinear eddy viscosity as a subscale turbulence representation for proper orthogonal decomposition (POD) models. The ansatz for the eddy viscosity is given in terms of an arbitrary function of the resolved fluctuation energy. This function is found as a minimizer of a cost functional measuring the difference between the target data coming from a resolved direct or large-eddy simulation of the flow and its reconstruction based on the POD model. The optimization is performed with a data-assimilation approach generalizing the 4D-VAR method. POD models with optimal eddy viscosities are presented for a 2D incompressible mixing layer at $\mathit{Re}=500$ (based on the initial vorticity thickness and the velocity of the high-speed stream) and a 3D Ahmed body wake at $\mathit{Re}=300\,000$ (based on the body height and the free-stream velocity). The variational optimization formulation elucidates a number of interesting physical insights concerning the eddy-viscosity ansatz used. The 20-dimensional model of the mixing-layer reveals a negative eddy-viscosity regime at low fluctuation levels which improves the transient times towards the attractor. The 100-dimensional wake model yields more accurate energy distributions as compared to the nonlinear modal eddy-viscosity benchmark proposed recently by Östh et al. (J. Fluid Mech., vol. 747, 2014, pp. 518–544). Our methodology can be applied to construct quite arbitrary closure relations and, more generally, constitutive relations optimizing statistical properties of a broad class of reduced-order models.

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