Development and application of a multi-scale k–ε model for turbulent porous medium flows

A multi-scale k – ε eddy viscosity model for turbulence in porous media is developed. When the double averaging is applied to the momentum equation, the dispersive covariance, the macro-scale and micro-scale Reynolds stresses appear and need modelling to close the equation. The conventional eddy viscosity modelling is applied to model the second moments for engineering applications. A k – ε two-equation eddy viscosity model is employed for obtaining the volume averaged Reynolds stress which consists of the macro-scale and the micro-scale Reynolds stresses. The micro-scale Reynolds stress is also independently modelled and obtained by solving another set of k and ε equations, whilst an algebraic model is developed for the dispersive covariance. The presently proposed multi-scale four equations eddy viscosity model is evaluated in developed turbulent flows in homogeneous porous media, porous wall channel flows and porous rib-mounted channel flows with satisfactory accuracy.