Near-Wall Formulation of the Partially Averaged Navier Stokes Turbulence Model

The variable-resolution partially averaged Navier-Stokes bridging strategy is applied to the four-equation k-epsilon-zeta-f turbulence model. In this approach, the popular two-equation model is enhanced with an additional transport equation for the velocity scale ratio zeta and an equation for the elliptic relaxation function f for the purpose of improved near-wall behavior. By using the elliptic relaxation technique to model the wall blocking effect, the new four-equation partially averaged Navier-Stokes model retains the simplicity of the previous two-equation partially averaged Navier-Stokes versions but significantly improves predictions in the near-wall region. The proposed partially averaged Navier-Stokes k-epsilon-zeta-f model is evaluated in a turbulent channel flow and flow around a three-dimensional circular cylinder mounted vertically on a flat plate. The results clearly show benefits of the improved near-wall modeling and extend partially averaged Navier-Stokes applicability to a broader range of smooth bluff-body separated flows.