Darcy's law and the Brinkman equation are two main models used for creepingfluid flows inside moving permeable particles. For these two models, the timederivative and the nonlinear convective terms of fluid velocity are neglectedin the momentum equation. In this paper, a new momentum equation includingthese two terms are rigorously derived from the pore-scale microscopicequations by the volume-averaging method, which can reduces to Darcy's law andthe Brinkman equation under creeping flow conditions. Using the latticeBoltzmann equation method, the macroscopic equations are solved for the problemof a porous circular cylinder moving along the centerline of a channel.Galilean invariance of the equations are investigated both with the intrinsicphase averaged velocity and the phase averaged velocity. The resultsdemonstrate that the commonly used phase averaged velocity cannot serve as thesuperficial velocity, while the intrinsic phase averaged velocity should bechosen for porous particulate systems.
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