A Three-Equation Variant of the SST k-ω Model Sensitized to Rotation and Curvature Effects

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Tej P. Dhakal ◽  
D. Keith Walters
Keyword(s):  
Fluid Flow ◽  
Transport Equation ◽  
Rotation Rate ◽  
Eddy Viscosity ◽  
Test Cases ◽  
New Model ◽  
Streamline Curvature ◽  
Curvature Effects ◽  
Velocity Scale ◽  
Heat And Fluid Flow

A new variant of the SST k-ω model sensitized to system rotation and streamline curvature is presented. The new model is based on a direct simplification of the Reynolds stress model under weak equilibrium assumptions [York et al., 2009, “A Simple and Robust Linear Eddy-Viscosity Formulation for Curved and Rotating Flows,” International Journal for Numerical Methods in Heat and Fluid Flow, 19(6), pp. 745–776]. An additional transport equation for a transverse turbulent velocity scale is added to enhance stability and incorporate history effects. The added scalar transport equation introduces the physical effects of curvature and rotation on turbulence structure via a modified rotation rate vector. The modified rotation rate is based on the material rotation rate of the mean strain-rate based coordinate system proposed by Wallin and Johansson (2002, “Modeling Streamline Curvature Effects in Explicit Algebraic Reynolds Stress Turbulence Models,” International Journal of Heat and Fluid Flow, 23, pp. 721–730). The eddy viscosity is redefined based on the new turbulent velocity scale, similar to previously documented k-ɛ- υ2 model formulations (Durbin, 1991, “Near-Wall Turbulence Closure Modeling without Damping Functions,” Theoretical and Computational Fluid Dynamics, 3, pp. 1–13). The new model is calibrated based on rotating homogeneous turbulent shear flow and is assessed on a number of generic test cases involving rotation and/or curvature effects. Results are compared to both the standard SST k-ω model and a recently proposed curvature-corrected version (Smirnov and Menter, 2009, “Sensitization of the SST Turbulence Model to Rotation and Curvature by Applying the Spalart-Shur Correction Term,” ASME Journal of Turbomachinery, 131, pp. 1–8). For the test cases presented here, the new model provides reasonable engineering accuracy without compromising stability and efficiency, and with only a small increase in computational cost.

A Three Equation Curvature and Rotation Sensitive Variant of the SST K-Omega Turbulence Model

2010 ◽  
Author(s):  
Tej Prasad Dhakal ◽  
D. Keith Walters
Keyword(s):  
Transport Equation ◽  
Eddy Viscosity ◽  
Reynolds Stress Model ◽  
Turbulent Velocity ◽  
Turbulence Structure ◽  
New Model ◽  
Streamline Curvature ◽  
History Effects ◽  
System Rotation ◽  
Velocity Scale

To date, eddy viscosity models are the most accepted and widely used RANS-based turbulence closures, attributable to their computational efficiency and relative robustness. One notable shortcoming of these models is their insensitivity to system rotation and streamline curvature. In this article, we present a variation of the SST k-ω model properly sensitized to system rotation and streamline curvature. The new model is based on a direct simplification of the Reynolds Stress Model under weak equilibrium conditions. To enhance stability and include history effects, an additional transport equation for a transverse turbulent velocity scale is added to the model. The new transport equation incorporates the physical effect of curvature and rotation on the turbulence structure. The eddy viscosity is then redefined based on the new turbulent velocity scale. The model is calibrated based on rotating homogeneous shear flow and implemented for a number of test cases including rotating channel, U-duct, and hump model flow. Compared to popular two equation models, the new model shows improved performance in system rotation and/or streamline curvature dominated flows.

Sensitization of a Transition-Sensitive Linear Eddy-Viscosity Model to Rotation and Curvature Effects

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Varun Chitta ◽  
Tej P. Dhakal ◽  
D. Keith Walters
Keyword(s):  
Transport Equation ◽  
Eddy Viscosity ◽  
Computational Cost ◽  
Turbulence Models ◽  
Viscosity Model ◽  
Flow Transition ◽  
New Model ◽  
Streamline Curvature ◽  
Curvature Effects ◽  
Eddy Viscosity Model

A new scalar eddy-viscosity turbulence model is proposed, designed to exhibit physically correct responses to flow transition, streamline curvature, and system rotation effects. The eddy-viscosity model (EVM) developed herein is based on the k–ω framework and employs four transport equations. The transport equation for a structural variable (v2) from a curvature-sensitive Shear Stress Transport (SST) k–ω–v2 model, analogous to the transverse turbulent velocity scale, is added to the three-equation transition-sensitive k–kL–ω model. The physical effects of rotation and curvature (RC) enter the model through the added transport equation. The new model is implemented into a commercial computational fluid dynamics (CFD) solver and is tested on a number of flow problems involving flow transition and streamline curvature effects. The results obtained from the test cases presented here are compared with available experimental data and several other Reynolds-Averaged Navier-Stokes (RANS) based turbulence models. For the cases tested, the new model successfully resolves both flow transition and streamline curvature effects with reasonable engineering accuracy, for only a small increase in computational cost. The results suggest that the model has potential as a practical tool for the prediction of flow transition and curvature effects over blunt bodies.

Application of a Transition-Sensitive Two-Equation Turbulence Model to CFD Simulations of Missile Nose-Cone Geometries

2007 ◽  
Author(s):  
J. M. Jones ◽  
D. K. Walters
Keyword(s):  
Experimental Data ◽  
Turbulence Model ◽  
Eddy Viscosity ◽  
Transitional Flow ◽  
Test Cases ◽  
Freestream Turbulence ◽  
Model Framework ◽  
Modeling Framework ◽  
Flow Solver ◽  
New Model

This paper presents results from an ongoing effort to develop and validate a two-equation eddy-viscosity turbulence model for computational fluid dynamics (CFD) prediction of transitional and turbulent flow. The new model is based on a k-ω model framework, making it more easily implemented into existing general-purpose CFD solvers than other recently proposed model forms. The model incorporates inviscid and viscous damping functions for the eddy viscosity, as well as a production damping term, in order to reproduce the appropriate effects of laminar, transitional, and turbulent boundary layer flow. The new model has been implemented into a Mississippi State University (MSU) Computational Simulation and Design Center (SimCenter) developed flow solver (U2NCLE), as well as a commercially available CFD code (FLUENT). For model validation, comparisons were made to experimental data for an incompressible, zero-pressure gradient, flat plate geometry over a range of freestream turbulence quantities, using both of the flow solvers. Additional test cases were performed with the in-house flow solver and compared to experimental data for two sharp-cone geometries. The Mach number for the cone cases ranged from 0.4 to 2. The results presented in this document show that the new model performed well for the 2-D test cases and showed agreement with the experimental data of the 3-D geometries. The results illustrate the ability of the model to yield reasonable predictions of transitional flow behavior using a very simple modeling framework, including an appropriate response to freestream turbulence quantities.

scholarly journals Modeling of Flow Transition Using an Intermittency Transport Equation

2000 ◽  
Vol 122 (2) ◽  
pp. 273-284 ◽  
Author(s):  
Y. B. Suzen ◽  
P. G. Huang
Keyword(s):  
Experimental Data ◽  
Transport Equation ◽  
Eddy Viscosity ◽  
Test Cases ◽  
Flow Transition ◽  
Transitional Flows ◽  
Intermittent Behavior ◽  
Wall Flows ◽  
Sst Model ◽  
Intermittency Factor

A new transport equation for intermittency factor is proposed to model transitional flows. The intermittent behavior of the transitional flows is incorporated into the computations by modifying the eddy viscosity, μt, obtainable from a turbulence model, with the intermittency factor, γ:μt*=γμt. In this paper, Menter’s SST model is employed to compute μt and other turbulent quantities. The proposed intermittency transport equation can be considered as a blending of two models—Steelant and Dick and Cho and Chung. The former was proposed for near-wall flows and was designed to reproduce the streamwise variation of the intermittency factor in the transition zone following Dhawan and Narasimha correlation and the latter was proposed for free shear flows and a realistic cross-stream variation of the intermittency profile was reproduced. The new model was used to predict the T3 series experiments assembled by Savill including flows with different freestream turbulence intensities and two pressure-gradient cases. For all test cases good agreements between the computed results and the experimental data were observed. [S0098-2202(00)02302-6]

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

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.

An Eddy-Viscosity Model Sensitized to Curvature and Wall-Roughness Effects for Reynolds-Averaged Closure

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Yang Zhang ◽  
Gang Chen ◽  
Jiakuan Xu
Keyword(s):  
Richardson Number ◽  
Eddy Viscosity ◽  
Plane Channel ◽  
Wall Roughness ◽  
Roughness Effects ◽  
New Model ◽  
Streamline Curvature ◽  
Eddy Viscosity Model ◽  
System Rotation ◽  
Rotating Channel

Abstract This paper presents a new extension of the realizable K−ε model that accounts for streamline curvature, system rotation, and surface roughness. The model is a type of realizable K−ε model, but the transport equations and the eddy-viscosity damping functions are modified, based on the Richardson number and roughness height; the roughness correction covers both the transitional and fully rough regimes. Flows in a rotating channel and a U-bend duct are used to validate the response of the new model to the system rotation and streamline curvature. The flow in a plane channel and the flow over a dune are used to validate the roughness extension. Finally, a rotating channel with rough walls is studied, to test the new model when both rotation and roughness are present.

Modelling the Streamline Curvature Effects in Turbomachinery Flows

2006 ◽  
Author(s):  
Dragan Kozˇulovic´ ◽  
Thomas Ro¨ber
Keyword(s):  
Turbulence Models ◽  
Tip Vortex ◽  
Test Cases ◽  
Aerodynamic Design ◽  
Complex Flows ◽  
New Approach ◽  
Streamline Curvature ◽  
Curvature Effects ◽  
Multistage Compressor ◽  
End Wall

Turbomachinery flows show significant streamline curvature with corresponding effects on turbulence development. Generally, linear eddy viscosity turbulence models, which are widely used in industrial aerodynamic design, do not predict these effects accurately, leading to less reliable RANS-simulations. In this work, therefore, a modification is made to the two-equation turbulence model of Wilcox [1]. Although this extension is a simple and pragmatic approach, the effects of streamline curvature are accurately reproduced for many presented applications, ranging from simple generic test cases to multistage compressor flows. Improved predictions of performance maps are achieved, which is mainly due to improved modelling in regions with higher streamline curvature, e.g. tip vortex and end-wall boundary layers. The curvature correction enables a greater mass flow range to be simulated and increases the numerical stability. Furthermore, the new approach requires only local variables, which makes it applicable to complex flows and easy to implement in existing codes.

Modular Turbulence Modelling Applied to an Engine Intake

2013 ◽  
Author(s):  
Ugochukwu R. Oriji ◽  
Paul G. Tucker
Keyword(s):  
Surface Roughness ◽  
Richardson Number ◽  
Eddy Viscosity ◽  
Fluid Dynamic ◽  
Test Cases ◽  
Laminar Separation ◽  
Streamline Curvature ◽  
Flow Features ◽  
Unsteady Rans ◽  
The One

The one equation Spalart Allamaras (SA) turbulence model in an extended modular form is employed for the prediction of cross wind flow around the lip of a 90 degree sector of an intake with and without surface roughness. The flow features around the lip are complex. There exists a region of high streamline curvature. For this the Richardson number would suggest complete degeneration to laminar flow. Also there are regions of high favourable pressure gradient (FPG) sufficient to laminarize a turbulent boundary layer (BL). This is all terminated by a shock and followed by a laminar separation. Under these severe conditions, the SA model is insensitive to capturing the effects of laminarization and the reenergization of eddy viscosity which promotes the momentum transfer and correct reattachment prior to the fan face. Through distinct modules, the SA model has been modified to account for the effect of laminarization and separation induced transition. The SA modules have been implemented in Rolls-Royce HYDRA Computational Fluid Dynamic (CFD) solver. They have been validated over a number of experimental test cases involving laminarization and also surface roughness. The validated modules are finally applied in unsteady RANS mode to flow around an engine intake and comparisons made with measurements. Encouraging agreement is found and hence advances made towards a more reliable intake design framework.

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