Development of k-R turbulence model for wall-bounded flows

Abstract

A new low-Reynolds-number turbulence model is formulated based on the turbulent kinetic energy k and eddy-viscosity parameter R=k2/ϵ. In the derivation, most of the diffusion terms emerging from the transformation have been preserved in the proposed model, maintaining the closest relationship with its parent k-ϵ model; the near-wall viscous balance is guaranteed by including a far-wall damping function. The turbulent structure parameter (i.e., Bradshaw-relation) that may enhance the predicted accuracy for non-equilibrium flows, is incorporated into the current model. The coefficients and functions are constructed such as to preserve the anisotropic characteristics of turbulence, encountered in rotational and irrotational flows. Fully-developed turbulent channel and flat-plate flows are computed to validate the model ability in replicating the near-wall turbulence. Two-dimensional asymmetric plane diffuser and airfoil flows are simulated to verify the model accuracy in capturing non-equilibrium flows with separation and reattachment. Computation of a three-dimensional wing with shock-wave is presented, rectifying the model competency in predicting large adverse-pressure-gradient flows. Furthermore, model predictions are compared with other two frequently-used turbulence models; a good correlation is obtained between the current model and experimental data.