Predicting the pressure drop of gas-liquid flows through porous media

Understanding gas-liquid flows through porous media such as packed-bed reactors (PBRs) under microgravity conditions is important for long-duration space journeys, specifically in designing life-support systems such as for water and air reclamation. These two-phase flows traverse the tortuous interstitial voids between the tightly packed solids comprising the PBR. Usually the liquid phase completely wets the solid packing, and hence, an Ergun-type correlation can be used for liquid-solid drag force, f_ls. The physics governing the gas-liquid interphase drag force, f_gl, is complex, and coming up with a reduced-order description is more challenging. To this end, we start from a two-fluid model (TFM), assuming steady flow and uniform velocities. These assumptions allow us to rewrite the TFM with f_gl as the unknown. Next, we leverage the pressure-drop data from NASA's microgravity packed-bed reactor experiment (PBRE) to fit the proposed 1D TFM formulation and obtain a correlation of f_gl as a function of the gas and liquid Reynolds numbers, Re_gs and Rel_s, via composite fits. The developed correlation can then be used to predict the pressure drop of two-phase flow under microgravity conditions. We demonstrate its use by incorporating the proposed f_gl(Re_gs,Re_ls) correlation into a 2D transient simulation of a two-phase flow through a PBR via an Euler-Euler formulation in ANSYS Fluent. The predicted pressure drop shows good agreement with the PBRE data.