New correlations for the interphase drag in the two-fluid model of gas-liquid flows through packed-bed reactors

Understanding transport phenomena through porous media is essential for applications ranging from water treatment systems to heat pipes. In many of these systems, packed-bed reactors (PBRs) are crucial components, and understanding and quantifying the pressure drop due to flow through the PBR is critical to effective operation. Recent experiments conducted by NASA measured the pressure drop due to gas-liquid flow through a PBR under microgravity conditions. Based on these experiments, we develop correlations for the interphase drag in a two-fluid model (TFM). Specifically, two closure relations are needed for the TFM: the liquid-solid $f_{ls}$ and gas-liquid $f_{gl}$ interphase force. We use an Ergun-type closure for $f_{ls}$. Then, under a 1D flow assumption, the TFM equations are rewritten with $f_{gl}$ as the only unknown. We employ data-driven calculations to determine $f_{gl}$, which we correlate (via composite fits) as a function of the liquid and gas Reynolds numbers, $Re_{l}$ and $Re_{g}$, respectively, and the Suratman number $Su_{l}$. To validate the proposed $f_{gl}(Re_{l},Re_{g},Su_{l})$ closure, we perform two-dimensional (2D) transient, multiphase computational fluid dynamics (CFD) simulations at low $Re_{l}$ and $Re_{g}$ (laminar flow) in ANSYS Fluent employing an Euler-Euler formulation. We find good agreement between the CFD simulations based on the proposed $f_{gl}$ closure and the experimental data.