An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows

Some new developments of explicit algebraic Reynolds stress turbulence models (EARSM) are presented. The new developments include a new near-wall treatment ensuring realizability for the individual stress components, a formulation for compressible flows, and a suggestion for a possible approximation of diffusion terms in the anisotropy transport equation. Recent developments in this area are assessed and collected into a model for both incompressible and compressible three-dimensional wall-bounded turbulent flows. This model represents a solution of the implicit ARSM equations, where the production to dissipation ratio is obtained as a solution to a nonlinear algebraic relation. Three-dimensionality is fully accounted for in the mean flow description of the stress anisotropy. The resulting EARSM has been found to be well suited to integration to the wall and all individual Reynolds stresses can be well predicted by introducing wall damping functions derived from the van Driest damping function. The platform for the model consists of the transport equations for the kinetic energy and an auxiliary quantity. The proposed model can be used with any such platform, and examples are shown for two different choices of the auxiliary quantity.

[1]  J. Lumley,et al.  A Realizable Reynolds Stress Algebraic Equation Model , 1993 .

[2]  J. Lumley,et al.  Remarks on turbulent constitutive relations , 1993 .

[3]  I. Lindblad,et al.  The engineering of multiblock/multigrid software for Navier-Stokes flows on structured meshes , 1993 .

[4]  Stavros Tavoularis,et al.  Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. Part 2. The fine structure , 1981, Journal of Fluid Mechanics.

[5]  Shigeki Imao,et al.  Turbulent characteristics of the flow in an axially rotating pipe , 1996 .

[6]  Suad Jakirlić,et al.  Computation of Oscillating Turbulent Flows at Transitional Re-Numbers , 1995 .

[7]  Sharath S. Girimaji,et al.  A Galilean invariant explicit algebraic Reynolds stress model for turbulent curved flows , 1997 .

[8]  D. Wilcox.  Reassessment of the scale-determining equation for advanced turbulence models , 1988 .

[9]  Dale B. Taulbee,et al.  Stress relation for three‐dimensional turbulent flows , 1994 .

[10]  Ronald M. C. So,et al.  Second-Order Near-Wall Turbulence Closures: A Review , 1991 .

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

[12]  D. Naot,et al.  Two‐point correlation model and the redistribution of Reynolds stresses , 1973 .

[13]  John L. Lumley,et al.  Computational Modeling of Turbulent Flows , 1978 .

[14]  J. Rotta,et al.  Statistische Theorie nichthomogener Turbulenz , 1951 .

[15]  P. Henrik Alfredsson,et al.  Curvature- and rotation-induced instabilities in channel flow , 1990, Journal of Fluid Mechanics.

[16]  A.J.M. Spencer,et al.  The theory of matrix polynomials and its application to the mechanics of isotropic continua , 1958 .

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

[18]  S. Pope.  A more general effective-viscosity hypothesis , 1975, Journal of Fluid Mechanics.

[19]  T. Shih,et al.  Constitutive Relations and Realizability of Single-Point Turbulence Closures , 1996 .

[20]  F. Menter.  ZONAL TWO EQUATION k-w TURBULENCE MODELS FOR AERODYNAMIC FLOWS , 1993 .

[21]  Wolfgang Rodi,et al.  The prediction of free turbulent boundary layers by use of a two-equation model of turbulence , 1973 .

[22]  K. Chien,et al.  Predictions of Channel and Boundary-Layer Flows with a Low-Reynolds-Number Turbulence Model , 1982 .

[23]  Arne V. Johansson,et al.  A New Explicit Algebraic Reynolds Stress Model , 1996 .

[24]  D. Wilcox.  Simulation of Transition with a Two-Equation Turbulence Model , 1994 .

[25]  Paul A. Durbin,et al.  Application of a near-wall turbulence model to boundary layers and heat transfer , 1993 .

[26]  S. Girimaji.  Fully explicit and self-consistent algebraic Reynolds stress model , 1995 .

[27]  S. Girimaji.  Improved algebraic Reynolds stress model for engineering flows , 1996 .

[28]  Egon Stanewsky,et al.  Documentation of two-dimensional impinging shock/turbulent boundary layer interaction flow , 1996 .

[29]  T. Shih,et al.  Critical assessment of Reynolds stress turbulence models using homogeneous flows , 1993 .

[30]  Arthur Rizzi,et al.  Reynolds Stress Transport Modeling of Transonic Flow Around the RAE2822 Airfoil , 1994 .

[31]  P. Durbin.  SEPARATED FLOW COMPUTATIONS WITH THE K-E-V2 MODEL , 1995 .

[32]  F. P. Bertolotti,et al.  Compressibility effects due to turbulent fluctuations , 1996 .

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

[34]  P. Spalart.  Direct simulation of a turbulent boundary layer up to Rθ = 1410 , 1988, Journal of Fluid Mechanics.

[35]  Torbjörn Sjögren.  Development and validiation of turbulence models through experiment and computation , 1997 .

[36]  J. Lumley,et al.  A new Reynolds stress algebraic equation model , 1994 .

[37]  W. Rodi.  A new algebraic relation for calculating the Reynolds stresses , 1976 .

[38]  John Kim,et al.  On the structure of pressure fluctuations in simulated turbulent channel flow , 1989, Journal of Fluid Mechanics.

[39]  Charles G. Speziale,et al.  Towards the development of second-order closure models for nonequilibrium turbulent flows , 1996 .

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

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

[42]  Dale B. Taulbee,et al.  An improved algebraic Reynolds stress model and corresponding nonlinear stress model , 1992 .

[43]  T. Gatski,et al.  On explicit algebraic stress models for complex turbulent flows , 1992, Journal of Fluid Mechanics.