Near-Wall Formulation of the Partially Averaged Navier-Stokes Turbulence Model

The variable-resolution partially averaged Navier-Stokes bridging strategy is applied to the four-equation k-epsilon-zeta-f turbulence model. In this approach, the popular two-equation model is enhanced with an additional transport equation for the velocity scale ratio zeta and an equation for the elliptic relaxation function f for the purpose of improved near-wall behavior. By using the elliptic relaxation technique to model the wall blocking effect, the new four-equation partially averaged Navier-Stokes model retains the simplicity of the previous two-equation partially averaged Navier-Stokes versions but significantly improves predictions in the near-wall region. The proposed partially averaged Navier-Stokes k-epsilon-zeta-f model is evaluated in a turbulent channel flow and flow around a three-dimensional circular cylinder mounted vertically on a flat plate. The results clearly show benefits of the improved near-wall modeling and extend partially averaged Navier-Stokes applicability to a broader range of smooth bluff-body separated flows.

[1]  Sharath S. Girimaji,et al.  PANS Turbulence Model for Seamless Transition Between RANS and LES: Fixed-Point Analysis and Preliminary Results , 2003 .

[2]  M. Germano,et al.  Turbulence: the filtering approach , 1992, Journal of Fluid Mechanics.

[3]  Sunil Lakshmipathy,et al.  Partially-averaged Navier-Stokes method for turbulent flows: k-w model implementation , 2006 .

[4]  Pierre Sagaut,et al.  Multiscale And Multiresolution Approaches In Turbulence , 2006 .

[5]  Sinisa Krajnovic,et al.  Flow around a tall finite cylinder explored by large eddy simulation , 2011, Journal of Fluid Mechanics.

[6]  Branislav Basara,et al.  A nonlinear eddy-viscosity model based on an elliptic relaxation approach , 2009 .

[7]  Sinisa Krajnovic,et al.  Numerical Simulation of the Flow around a Tall Finite Cylinder Using LES and PANS , 2009 .

[8]  S. Girimaji.  Partially-Averaged Navier-Stokes Model for Turbulence: A Reynolds-Averaged Navier-Stokes to Direct Numerical Simulation Bridging Method , 2006 .

[9]  Marcel Lesieur,et al.  Direct numerical simulations of high velocity ratio coaxial jets: mixing properties and influence of upstream conditions , 2007 .

[10]  Sinisa Krajnovic,et al.  Superiority of PANS compared to LES in predicting a rudimentary landing gear flow with affordable meshes , 2012 .

[11]  Cheol Woo Park,et al.  Flow structure around a finite circular cylinder embedded in various atmospheric boundary layers , 2002 .

[12]  Branislav Basara,et al.  Simulation of single‐ and two‐phase flows on sliding unstructured meshes using finite volume method , 2004 .

[13]  Eunhwan Jeong,et al.  Partially averaged navier-stokes method for turbulence : Fixed point analysis and comparison with unsteady partially averaged navier-stokes , 2006 .

[14]  S. Krajnović.  Flow Around a Surface-Mounted Finite Cylinder: A Challenging Case for LES , 2008 .

[15]  Dominique Laurence,et al.  Large Eddy Simulation of Turbulent Flow for Wall Mounted Cantilever Cylinders of Aspect Ratio 6 and 10 , 2007 .

[16]  P. Durbin.  Near-wall turbulence closure modeling without “damping functions” , 1991, Theoretical and Computational Fluid Dynamics.

[17]  Cheol Woo Park,et al.  Effects of free-end corner shape on flow structure around a finite cylinder , 2004 .

[18]  Remi Manceau,et al.  A SEAMLESS HYBRID RANS-LES MODEL BASED ON TRANSPORT EQUATIONS FOR THE SUBGRID STRESSES AND ELLIPTIC BLENDING , 2010, Proceeding of Fifth International Symposium on Turbulence and Shear Flow Phenomena.

[19]  Seung-O Park,et al.  Numerical simulation of flow past a square cylinder using Partially-Averaged Navier–Stokes model , 2009 .

[20]  I. Demirdzic,et al.  Numerical method for coupled fluid flow, heat transfer and stress analysis using unstructured moving meshes with cells of arbitrary topology , 1995 .

[21]  T. Gatski,et al.  Modelling the pressure–strain correlation of turbulence: an invariant dynamical systems approach , 1991, Journal of Fluid Mechanics.

[22]  Kelly Cohen,et al.  Filtered POD‐based low‐dimensional modeling of the 3D turbulent flow behind a circular cylinder , 2011 .

[23]  Cheol Woo Park,et al.  Free end effects on the near wake flow structure behind a finite circular cylinder , 2000 .

[24]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[25]  P. Sweby.  High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws , 1984 .

[26]  M. Hadžiabdić,et al.  A robust near-wall elliptic-relaxation eddy-viscosity turbulence model for CFD , 2004 .

[27]  Sharath S. Girimaji,et al.  Flow Past a Backward-Facing Step: Comparison of PANS, DES and URANS Results with Experiments , 2006 .

[28]  Bruno Chaouat,et al.  From single-scale turbulence models to multiple-scale and subgrid-scale models by Fourier transform , 2007 .

[29]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[30]  D. Sujudi,et al.  Identification of Swirling Flow in 3-D Vector Fields , 1995 .

[31]  Branislav Basara,et al.  Employment of the second‐moment turbulence closure on arbitrary unstructured grids , 2004 .

[32]  S. Girimaji,et al.  Partially-averaged Navier Stokes Model for Turbulence: Implementation and Validation , 2005 .

[33]  Nobuhide Kasagi,et al.  Reynolds Number Effect on Wall Turbulence: Toward Effective Feedback Control , 2002 .

[34]  Bruno Chaouat,et al.  Progress in subgrid-scale transport modelling for continuous hybrid non-zonal RANS/LES simulations , 2009 .

[35]  J. Murthy,et al.  A PRESSURE-BASED METHOD FOR UNSTRUCTURED MESHES , 1997 .

[36]  K. Hanjalic,et al.  Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer , 2007 .

[37]  Branislav Basara,et al.  Eddy viscosity transport model based on elliptic relaxation approach , 2006 .

[38]  P. Spalart.  Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach , 1997 .

[39]  Eunhwan Jeong,et al.  Partially Averaged Navier–Stokes (PANS) Method for Turbulence Simulations—Flow Past a Square Cylinder , 2010 .

[40]  Bruno Chaouat,et al.  A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows , 2005 .

[41]  Branislav Basara,et al.  BOUNDED CONVECTION SCHEMES FOR UNSTRUCTURED GRIDS , 2001 .