Exploring k and ϵ with R–Equation Model Using Elliptic Relaxation Function

Abstract

An extended version of the isotropic R-equation model accompanied by an elliptic relaxation approach to account for the distinct effects of low-Reynolds number (LRN) and wall proximity is proposed. The turbulent kinetic energy k and the dissipation rate are evaluated using the R (= k 2 /˜ ) transport equation together with some empirical relations. The eddy viscosity formulation maintains the positivity of normal Reynolds stresses and the Schwarz' inequality for turbulent shear stresses. The model coefficients/functions preserve the anisotropic characteristics of turbulence in the sense that they are sensitized to rotational and nonequilibrium flows. The model is validated against a few well-documented flow cases, yielding predictions in good agreement with the direct numerical simulation (DNS) and experimental data. Comparisons indicate that the present model offers some improvement over the Spalart-Allmaras one-equation model and competitiveness with the SST k-ω model.

Wall-Distance-Free Version of Spalart–Allmaras Turbulence Model

“…In the past several decades, considerable research has been devoted to improving the accuracy of one-equation models, for both equilibrium and nonequilibrium flows [2][3][4][5][6][7][8][9]. The Baldwin-Barth (BB) model [2] derived using the k-ϵ closure is one of the first oneequation models that does not explicitly use the algebraic length scales.…”

Development of a One-Equation Turbulence Model based on Epsilon-Equation

“…1 Concerning the complexity of calculation and increased cost, a non-linear one-equation turbulence model can provide solutions of similar and sometimes better predictive accuracy than the conventional two-equation models . [2][3][4][5][6] However, one-equation RANS (Reynolds-averaged Navier-Stokes) turbulence models that use a geometrically prescribed turbulent length scale have often shown limited success . 7 Therefore, accurate evaluations of velocity and length scales are required in turbulence modeling that are obtained from the transport equation of turbulent kinetic energy k and an algebraic length-scale determining quantity such as the dissipation ǫ or the specific dissipation ω.…”

An Improved Version of One-Equation RAS Turbulence Model

“…The motivation for this approach is that the BB model is constrained by assumptions inherited from the k-ǫ model. Recently, Rahman et al 9,10 have devised new models, called the RAS and Rahman-Wallin-Siikonen models that address the weakness of BB model and account for the non-equilibrium and anisotropic effects, a feature that is missing in the single-equation models developed so far.…”