Abstract
A wall-distance-free modification to Wray-Agarwal (WA) one-equation turbulence model is convoked using an elliptic relaxation approach to accurately accounting for non-local characteristics of near-wall turbulence. Model coefficients/functions are parameterized with the elliptic relaxation function to preserve the combined effects of near-wall turbulence and nonequilibrium. The characteristic length scale associated with the elliptic relaxation equation is formulated in terms of viscous and turbulent length scales in conjunction with the invariant of strain-rate tensor. Consequently, non-local effects are explicitly influenced by the mean flow and turbulent variables. A near-wall damping function is introduced to relax the viscous length-scale coefficient adhering to the elliptic relaxation model. Comparisons indicate that the new model improves the accuracy of flow simulations compared to the widely used Spalart-Allmar as model and remains competitive with the SST model.A good correlation is obtained between the current model and DNS/experimental data.
Highlights
One-equation turbulence models solve directly for the eddy-viscosity without computing the full range of turbulent time and length scales
This paper proposes wall-distance-free modifications to the WA model with an elliptic blending function
The one-equation Wray-Agarwal (WA) model is modified to replace the blending function f1 by an elliptic relaxation method that accounts for the non-local characteristics of near-wall turbulence
Summary
C1 model closure coefficient Cb model closure coefficient Cw model closure coefficient Cf skin-friction coefficient C1kǫ closure coefficient C2kω closure coefficients C2kǫ closure coefficient d distance to the nearest wall fμ eddy-viscosity damping function f1 blending function fR elliptic blending function h channel height k turbulent kinetic energy R undamped eddy-viscosity; k/ω Re Reynolds number S mean strain-rate invariant. W mean vorticity invariant χ undamped turbulent-to-laminar viscosity ratio u+ non-dimensional flow velocity ω specific turbulent dissipation rate y+ non-dimensional wall distance. ΜT laminar and turbulent eddy viscosities T turbulent condition ν kinematic viscosity i,j variable numbers ρ density ref reference condition σ Schmidt number
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