Application of a Full Reynolds Stress Model to High Lift Flows

A recently developed second-moment Reynolds stress model was applied to two challenging high-lift flows: (1) transonic flow over the ONERA M6 wing, and (2) subsonic flow over the DLR-F11 wing-body configuration from the second AIAA High Lift Prediction Workshop. In this study, the Reynolds stress model results were contrasted with those obtained from one- and two-equation turbulence models, and were found to be competitive in terms of the prediction of shock location and separation. For an ONERA M6 case, results from multiple codes, grids, and models were compared, with the Reynolds stress model tending to yield a slightly smaller shock-induced separation bubble near the wing tip than the simpler models, but all models were fairly close to the limited experimental surface pressure data. For a series of high-lift DLR-F11 cases, the range of results was more limited, but there was indication that the Reynolds stress model yielded less-separated results than the one-equation model near maximum lift. These less-separated results were similar to results from the one-equation model with a quadratic constitutive relation. Additional computations need to be performed before a more definitive assessment of the Reynolds stress model can be made.

[1]  W. K. Anderson,et al.  Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids , 1995 .

[2]  P. Spalart Strategies for turbulence modelling and simulations , 2000 .

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

[4]  Hassan Hassan,et al.  Simulation of a Variety of Wings Using a Reynolds Stress Model , 2014 .

[5]  Vamshi Togiti,et al.  Assessment of g-Equation Formulation for a Second-Moment Reynolds Stress Turbulence Model , 2015 .

[6]  Ralf Rudnik,et al.  EUROLIFT Test Case Description for the 2nd High Lift Prediction Workshop , 2012 .

[7]  P. Spalart A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[8]  L Krist Sherrie,et al.  CFL3D User''s Manual (Version 5.0) , 1998 .

[9]  D. Wilcox Turbulence modeling for CFD , 1993 .

[10]  Hassan Hassan,et al.  NASA Trapezoidal Wing Simulation Using Stress-w and One- and Two-Equation Turbulence Models , 2015 .

[11]  Boris Diskin,et al.  Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes , 2011 .

[12]  Boris Diskin,et al.  Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes , 2011 .

[13]  C. Rumsey,et al.  Second-Moment RANS Model Verification and Validation Using the Turbulence Modeling Resource Website (Invited) , 2015 .

[14]  Strategies for turbulence modelling and simulations , 2000 .

[15]  Shahyar Pirzadeh,et al.  Three-dimensional unstructured viscous grids by the advancing-layers method , 1996 .

[16]  김창성 Sensitivity analysis for the Navier-Stokes equations with two-equation turbulence models and its applications , 2001 .

[17]  B. Launder,et al.  Progress in the development of a Reynolds-stress turbulence closure , 1975, Journal of Fluid Mechanics.

[18]  C. Rumsey,et al.  Grid-Adapted FUN3D Computations for the Second High Lift Prediction Workshop , 2015 .

[19]  W. K. Anderson,et al.  Sensitivity Analysis for Navier-Stokes Equations on Unstructured Meshes Using Complex Variables , 2001 .

[20]  Francis H. Harlow,et al.  Transport Equations in Turbulence , 1970 .

[21]  Viktoria Schmitt,et al.  Pressure distributions on the ONERA M6 wing at transonic Mach numbers , 1979 .

[22]  W. K. Anderson,et al.  An implicit upwind algorithm for computing turbulent flows on unstructured grids , 1994 .

[23]  Vamshi Togiti,et al.  Second-Moment RANS Model Verification and Validation using the Turbulence Model Resource Website , 2015 .

[24]  P. Roe Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[25]  Michael Long,et al.  Summary of the First AIAA CFD High Lift Prediction Workshop , 2011 .

[26]  F. Menter Two-equation eddy-viscosity turbulence models for engineering applications , 1994 .

[27]  D. Darmofal,et al.  An implicit, exact dual adjoint solution method for turbulent flows on unstructured grids , 2004 .

[28]  V. Venkatakrishnan Convergence to steady state solutions of the Euler equations on unstructured grids with limiters , 1995 .

[29]  E. Nielsen,et al.  Aerodynamic design sensitivities on an unstructured mesh using the Navier-Stokes equations and a discrete adjoint formulation , 1998 .

[30]  Elizabeth M. Lee-Rausch,et al.  FUN3D and CFL3D Computations for the First High Lift Prediction Workshop , 2011 .

[31]  C. C. Shir,et al.  A Preliminary Numerical Study of Atmospheric Turbulent Flows in the Idealized Planetary Boundary Layer , 1973 .

[32]  P. Spalart,et al.  Turbulence Modeling in Rotating and Curved Channels: Assessing the Spalart-Shur Correction , 2000 .

[33]  Christopher L. Rumsey,et al.  Application of Reynolds Stress Models to Separated Aerodynamic Flows , 2015 .

[34]  A. Cain,et al.  An assessment of one- and two-equation turbulence models for internal and external flows , 1997 .

[35]  Olaf Brodersen,et al.  Advanced Turbulence Modelling and Stress Analysis for the DLR-F6 Configuration , 2005 .

[36]  Rolf Radespiel,et al.  Differential Reynolds-Stress Modeling for Aeronautics , 2015 .

[37]  Dimitri J. Mavriplis,et al.  NSU3D Results for the Second AIAA High-Lift Prediction Workshop , 2015 .

[38]  Christopher L. Rumsey,et al.  Overview and Summary of the Second AIAA High-Lift Prediction Workshop , 2015 .

[39]  Dieter Schwamborn,et al.  Development of the TAU-Code for aerospace applications , 2008 .

[40]  Christopher L. Rumsey,et al.  Verification and Validation of a Second-Moment-Closure Model , 2016 .

[41]  Bernhard Eisfeld,et al.  Differential Reynolds Stress Modeling for Separating Flows in Industrial Aerodynamics , 2015 .