An Improved Version of One-Equation RAS Turbulence Model

Abstract

An improved version of a recently developed one-equation turbulence model called RAS (Rahman-Agarwal-Siikonen) is proposed to account for the distinct effects of low-Reynolds number (LRN) and wall proximity. The turbulent kinetic energy k and the dissipation rate ǫ are evaluated using the R = (k 2 /ǫ)-transport equation together with the Bradshaw and other empirical relations. The associated coefficients are constructed such as to preserve the anisotropic characteristics of turbulence encountered in non-equilibrium flows. In the current version, several improvements to the original RAS model are made which include the introduction of a nearwall eddy-viscosity damping function. An anisotropic destruction coefficient is used to obtain a faster decaying behavior of turbulence destruction in the outer region of the boundary/shear layer, thereby precluding the free-stream dependency. The source term in the transport equation is independent of the Reynolds stress tensor. A comparative assessment of the improved RAS model with the Spalart-Allmaras (SA) one-equation model and the shear stress transport (SST) k-ω model is provided for welldocumented non-equilibrium turbulent flows.

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.…”

Consistently formulated eddy-viscosity coefficient for k-equation model

“…Conceptually, both scales can be obtained from the transport equation of turbulent kinetic energy k and the algebraic length-scale determining quantity such as the dissipation ǫ or the specific dissipation ω. The k-equation (one-equation) model proposed by some researchers [1][2][3][4] accounts for history effects on the turbulent kinetic energy and is therefore considered an improvement over the algebraic model . 5 However, this model still uses the same ad-hoc assumptions as used in the algebraic model and most researchers have abandoned the k-equation model in the favor of one-equation models based on the transport equations for the eddy viscosity µ T .…”

“…Hence, further study of an improved k-equation model is encouraged . [2][3][4] A one-equation turbulence model is attractive due to its simplicity of implementation and less demanding computational requirements when compared with the standard twoequation k-ǫ and k-ω models. In addition, a one-equation model includes the transport effect of turbulent kinetic energy and can be considered as a good compromise between algebraic and two-equation models.…”

“…In principle, the turbulent kinetic energy transport equation is with the least number of unclosed terms in which ǫ is the only unclosed term having a particular concern. Recently, modified versions of Norris-Reynolds 1 k-equation turbulence model has been proposed by Rahman et al 2,3 to account for the distinct effects of low-Reynolds number (LRN) and wall proximity. The k and ǫ are evaluated using the k-transport equation in conjunction with the Bradshaw 15 and other empirical relations.…”

“…The newly formulated C µ is used in conjunction with an improved version of the kequation model. This version has several desirable attributes relative to the k-equation models developed by Rahman et al : 2,3 (a) the turbulence structure parameter Bradshaw-relation) is extended down to the wall with a non-equilibrium function f k that depends non-linearly on both the rotational and irrotational strains; (b) the production term P k resulting from a combination of R b and P k /ǫ is capable of capturing partially some features of stress-strain misalignment on the evolution of turbulence levels in a linear eddy-viscosity model; (c) the eddy-viscosity formulation resembles the Menter SST k-ω model and (d) the linear/non-linear Reynolds-stress relation can be used to compute Reynolds stresses.…”