Assessment of Eddy Viscosity Models in 2D and 3D Shock/Boundary-Layer Interactions

In this contribution we consider large-eddy simulation (LES) using the high-pass filtered (HPF) Smagorinsky model of a spatially developing supersonic turbulent boundary layer at a Mach number of 2.5 and momentum-thickness Reynolds numbers at inflow of ∼4500. The HPF eddy-viscosity models employ high-pass filtered quantities instead of the full velocity field for the computation of the subgrid-scale (SGS) model terms. This approach has been proposed independently by Vreman (Vreman, A. W., 2003, Phys. Fluids, 15, pp. L61–L64) and Stolz et al. (Stolz, S., Schlatter, P., Meyer, D., and Kleiser, L., 2003, in Direct and Large Eddy Simulation V, Kluwer, Dordrecht, pp. 81–88). Different from classical eddy-viscosity models, such as the Smagorinsky model (Smagorinsky, J., 1963, Mon. Weath. Rev, 93, pp. 99–164) or the structure-function model (Métais, O. and Lesieur, M., 1992, J. Fluid Mech., 239, pp. 157–194) which are among the most often employed SGS models for LES, the HPF eddy-viscosity models do need neither van Driest wall damping functions for a correct prediction of the viscous sublayer of wall-bounded turbulent flows nor a dynamic determination of the coefficient. Furthermore, the HPF eddy-viscosity models are formulated locally and three-dimensionally in space. For compressible flows the model is supplemented by a HPF eddy-diffusivity ansatz for the SGS heat flux in the energy equation. Turbulent inflow conditions are generated by a rescaling and recycling technique in which the mean and fluctuating part of the turbulent boundary layer at some distance downstream of inflow is rescaled and reintroduced at the inflow position (Stolz, S. and Adams, N. A., 2003, Phys. Fluids, 15, pp. 2389–2412).

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Evaluation of algebraic eddy-viscosity models in three-dimensional turbulent boundary-layer flows

AIAA Journal ◽

10.2514/3.11813 ◽

1993 ◽

Vol 31 (9) ◽

pp. 1545-1554 ◽

Cited By ~ 9

Author(s):

M. Semih Olcmen ◽

Roger L. Simpson

Keyword(s):

Boundary Layer ◽

Turbulent Boundary Layer ◽

Eddy Viscosity ◽

Three Dimensional ◽

Boundary Layer Flows ◽

Viscosity Models

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

Volume 1D, Symposia: Transport Phenomena in Mixing; Turbulent Flows; Urban Fluid Mechanics; Fluid Dynamic Behavior of Complex Particles; Analysis of Elementary Processes in Dispersed Multiphase Flows; Multiphase Flow With Heat/Mass Transfer in Process Technology; Fluid Mechanics of Aircraft and Rocket Emissions and Their Environmental Impacts; High Performance CFD Computation; Performance of Multiphase Flow Systems; Wind Energy; Uncertainty Quantification in Flow Measurements and Simulations ◽

10.1115/fedsm2014-21700 ◽

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.

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Explicit Filtering and Reconstruction Turbulence Modeling for Large-Eddy Simulation of Neutral Boundary Layer Flow

Journal of the Atmospheric Sciences ◽

10.1175/jas3456.1 ◽

2005 ◽

Vol 62 (7) ◽

pp. 2058-2077 ◽

Cited By ~ 131

Author(s):

Fotini Katopodes Chow ◽

Robert L. Street ◽

Ming Xue ◽

Joel H. Ferziger

Keyword(s):

Boundary Layer ◽

Boundary Layer Flow ◽

Eddy Viscosity ◽

Wall Stress ◽

Stress Model ◽

Viscosity Models ◽

Neutral Boundary Layer ◽

Large Eddy ◽

Layer Flow ◽

Near Wall

Abstract Standard turbulence closures for large-eddy simulations of atmospheric flow based on finite-difference or finite-volume codes use eddy-viscosity models and hence ignore the contribution of the resolved subfilter-scale stresses. These eddy-viscosity closures are unable to produce the expected logarithmic region near the surface in neutral boundary layer flows. Here, explicit filtering and reconstruction are used to improve the representation of the resolvable subfilter-scale (RSFS) stresses, and a dynamic eddy-viscosity model is used for the subgrid-scale (SGS) stresses. Combining reconstruction and eddy-viscosity models yields a sophisticated (and higher order) version of the well-known mixed model of Bardina et al.; the explicit filtering and reconstruction procedures clearly delineate the contribution of the RSFS and SGS motions. A near-wall stress model is implemented to supplement the turbulence models and account for the stress induced by filtering near a solid boundary as well as the effect of the large grid aspect ratio. Results for neutral boundary layer flow over a rough wall using the combined dynamic reconstruction model and the near-wall stress model show excellent agreement with similarity theory logarithmic velocity profiles, a significant improvement over standard eddy-viscosity closures. Stress profiles also exhibit the expected pattern with increased reconstruction level.

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High-Pass Filtered Eddy-Viscosity Models for Large-Eddy Simulations of Compressible Wall-Bounded Flows

Volume 2, Parts A and B ◽

10.1115/ht-fed2004-56540 ◽

2004 ◽

Cited By ~ 2

Author(s):

Steffen Stolz

Keyword(s):

Boundary Layer ◽

Turbulent Boundary Layer ◽

Eddy Viscosity ◽

Large Eddy Simulations ◽

Scale Model ◽

Subgrid Scale ◽

Smagorinsky Model ◽

Viscosity Models ◽

Large Eddy ◽

High Pass

Eddy-viscosity models such as the Smagorinsky model [1] are the most often employed subgrid-scale (SGS) models for large-eddy simulations (LES). However, for a correct prediction of the viscous sublayer of wall-bounded turbulent flows van-Driest wall damping functions or a dynamic determination of the constant [2] have to be employed. Alternatively, high-pass filtered (HPF) quantities can be used instead of the full velocity field for the computation of the subgrid-scale model terms. This approach has been independently proposed by Vreman [3] and Stolz et al. [4]. In this contribution we consider LES of a spatially developing supersonic turbulent boundary layer at a Mach number of 2.5 and momentum-thickness Reynolds numbers at inflow of approximately 4500, using the HPF Smagorinsky model. The model is supplemented by a HPF eddy-diffusivity ansatz for the SGS heat flux in the energy equation. Turbulent inflow conditions are generated by a rescaling and recycling technique proposed by [5] where the mean and fluctuating part of the turbulent boundary layer at some distance downstream of inflow is rescaled and reintroduced at inflow.

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The Improvement of k-ε Model in the Turbulent Wave Boundary Layer

Volume 4: Ocean Engineering; Ocean Renewable Energy; Ocean Space Utilization, Parts A and B ◽

10.1115/omae2009-79815 ◽

2009 ◽

Author(s):

Yuliang Zhu ◽

Jing Ma ◽

Peipei Dong

Keyword(s):

Boundary Layer ◽

Eddy Viscosity ◽

Wave Boundary Layer ◽

Viscosity Models ◽

Velocity Equation ◽

Layer Flow ◽

Wave Boundary ◽

Advanced Model ◽

Turbulent Wave ◽

Empirical Constants

Numerical model is one of the means for investigating turbulent wave boundary layer. Many scholars have used various eddy-viscosity models to simulate wave turbulent boundary layer flow. On the basis of analyzing existing models, the article uses more reasonable boundary condition to establish an advanced model of turbulent wave boundary layer by k-ε model. Past models have two problems. Firstly, the calculation area is not united since one of the calculation areas is all-water depth and another is boundary layer thickness. Aimed at this problem, this model makes a sensitivity analysis of velocity and eddy-viscosity for various calculation area, which turns out that velocity inside the boundary layer is low-sensitive while the eddy-viscosity is high-sensitive to the change of calculation area. Secondly, a new integration adjust coefficient p is presented to solve the five empirical constants which are difficult to adjust in k-ε model. Although these five empirical constants have recommended value, the universality is not good. In order to obtain better eddy-viscosity value, many methods were suggested to get these five empirical constants, however, most are very complicated. In this article, adjust coefficient p is put before the diffusion item in the velocity equation, and p is a little bit smaller than 1. The result indicates that a reasonable eddy-viscosity can be easily adjusted using this method. The modified model has overcome some shortcomings of the previous models, and gets a better simulation effect.

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An Examination of Eddy Viscosity Models for Turbulent Free Shear Flows

Journal of Basic Engineering ◽

10.1115/1.3425318 ◽

1971 ◽

Vol 93 (4) ◽

pp. 624-630

Author(s):

R. J. Elassar ◽

P. P. Pandolfini

Keyword(s):

Experimental Data ◽

Boundary Layer ◽

Difference Scheme ◽

Eddy Viscosity ◽

Shear Flows ◽

Coordinate Plane ◽

Boundary Layer Equations ◽

Viscosity Models ◽

Calculated Velocity ◽

Empirical Constants

The boundary layer equations based on an eddy viscosity concept are solved numerically in the Crocco coordinate plane. A multilevel linear difference scheme is employed. Four different viscosity models are examined and the resulting solutions are compared. The empirical constants in the viscosity models are evaluated by comparing the calculated velocity profiles with experimental data in the similarity region.

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Numerical Study of Vortical Separation From a Three-Dimensional Hill Using Eddy-Viscosity Models

Volume 1: Symposia ◽

10.1115/ajkfluids2015-3223 ◽

2015 ◽

Author(s):

Varun Chitta ◽

Tausif Jamal ◽

Keith Walters

Keyword(s):

Boundary Layer ◽

Turbulent Boundary Layer ◽

Eddy Viscosity ◽

Three Dimensional ◽

Flow Transition ◽

Mean Flow ◽

New Model ◽

Streamline Curvature ◽

Viscosity Models ◽

Rans Models

Turbulent flow over an axisymmetric hill is highly three-dimensional (3D) due to the presence of both streamwise and spanwise pressure gradients. Complex vortical separations and reattachments of the turbulent boundary layer are observed on the lee side, accurate prediction of which presents a demanding task for linear eddy-viscosity models (EVMs) when compared to attached boundary layer flows. In this study, an axisymmetric hill is investigated using three Reynolds-averaged Navier-Stokes (RANS) models — fully turbulent model (SST k-ω), transition-sensitive model (k-kL-ω), and a new four-equation model (k-kL-ω-v2). The new model is designed to exhibit physically correct responses to flow transition, streamline curvature, and system rotation effects. The test case includes a hill mounted in a channel with hill height H = 2δ, where δ is the approach turbulent boundary layer thickness. The flow Reynolds number (Re) based on the hill height is ReH = 1.3 × 105. Computational fluid dynamics (CFD) simulation results obtained using the new model are compared with the other two RANS models and with experimental data. Improved mean flow statistics are obtained using the new model that match well with the experiments. The results from this study highlight the need for a model that is able to resolve both flow transition and streamline curvature effects over blunt/curved bodies with reasonable engineering accuracy and computational cost.

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