Formulation of time and volume averaged two-fluid model considering structural materials in a control volume

Time–volume averaged two-fluid model considering structural materials in a control volume (porous media approach) is formulated for two-phase flow analyses. The time–volume averaged two-fluid model is obtained rigorously by averaging local time-averaged two-fluid model over a control volume including structural materials. The volume porosity based model obtained by the simple time–volume averaging is converted into the surface porosity based model by introducing the directional surface porosity concept. The covariance approach is adopted to consider distributions of various variables in the control volume. The obtained porous media formulation is consistent with existing two-fluid model. Existing constitutive equations may be applicable to the porous media formulation provided they are properly time–volume averaged in the control volume. The strategy to obtain time–volume averaged constitutive equations is briefly discussed.