A √k-l Turbulence Model for Fluids Engineering Applications

Abstract

A turbulence closure based on transport equations for the square-root of the kinetic energy of turbulence, q=k^1/2 and the length-scale, , is proposed and tested. The model is topography parameter free (no wall distance needed), uses local wall proximity indicators instead, and is meant to be applicable to both wall-bounded and free shear flows. Solving directly for the turbulence length-scale, invoking Dirichlet boundary conditions for both q and  and the fact that q varies linearly across the viscous sublayer contribute to reduced sensitivity of this model to near-wall grid concentration (as long as the sublayer is resolved) and to less numerical stiffness, hence faster convergence. A variable C_m parameter is featured in this model to account for non-simple shear where mean strain and vorticity rates are different. Several cases, covering a wide variety of flows, are presented to demonstrate the model’s performance. Fluids engineers whose work involves complex 3D topologies, particularly with non-stationary grids which require re-computing wall distance arrays at each time-step (a heavy demand on time and budget) may appreciate the fact that no distance arrays are needed for the q-  model.