Numerical study on inertial effects on liquid-vapor flow using lattice Boltzmann method

Liquid-vapor flow in porous media is studied in this article. To fulfill this goal, a double-distribution-function lattice Boltzmann (LB) model is proposed based on the separate-phase governing equations at the representative elementary volume (REV) scale. Importantly, besides the Darcy force and capillary force, which were commonly included in previous studies, the LB model in this article also considers the inertial force characterized by the Forchheimer term. This feature enables the model to offer an effective description of liquid-vapor flow in porous media at low, intermediate and even high flow rates. We validated the LB model by simulating a single-phase flow in porous media driven by a pressure difference and found its results are in good agreement with the available analytical solutions. We then applied the model to study water-vapor flow in a semi-infinite porous region bounded by an impermeable and heated wall. The numerical simulation reveals the flow and mass transfer characteristics under the compounding effects of inertial, Darcy and capillary forces. Through a comparison with the results given by the generalized Darcy's law, our numerical results directly evidence that the inertial force is a dominating factor when a fluid passes through porous media at an intermediate or high flow rate.