On URANS Congruity with Time Averaging: Analytical Laws Suggest Improved Models

Abstract

The standard 1-equation model of turbulence was first derived by Prandtl and has evolved to be a common method for practical flow simulations. Five fundamental laws that any URANS model should satisfy are (Table Presented) This report proves that a kinematic specification of the model’s turbulence lengthscale by l(x,t)=√2k1/2(x,t)τ, where τ is the time filter window, results in a 1-equation model satisfying Conditions 1, 2, 3, 4 without model tweaks, adjustments or wall damping multipliers.