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MULTI-SCALE k−ε MODELLING OF TURBULENCE FOR POROUS MEDIUM FLOWS

Yusuke Kuwata
Department of Mechanical Engineering, Osaka Prefecture University, 1-1, Gakuen-cho, Naka-ku, Sakai 599-8531, Japan

Kazuhiko Suga
Department of Mechanical Engineering, Osaka Prefecture University, Gakuen-cho 1-1, Naka-ku, Sakai, Osaka 599-8531, Japan

Résumé

To predict turbulence in porous media, a new approach is discussed. By double (both volume and Reynolds) averaging Navier-Stokes equations, there appear two unknown covariant terms in the momentum equation. They are namely the dispersive covariance and the volume averaged Reynolds stress which is split into the macro-scale Reynolds stress and the micro-scale Reynolds stress. To obtain the Reynolds stresses, two-equation eddy viscosity models are applied to the volume averaged Reynolds stress and the micro-scale Reynolds stress whilst the Smagorinsky model is applied to the dispersive covariance. The presently proposed multi-scale four-equation k − ε model is evaluated in porous wall channel flows and porous rib channel flows with good accuracy.