Application of POD and DMD to Study Flow in Porous Media

Abstract

Abstract Fluid flows in porous media exhibit diverse spatially and temporally complex structures arising from intricate interactions between fluid motion and solid interfaces/flow paths. While numerous experimental studies have aimed to quantify these complex flow structures, recent technological advancements have facilitated the widespread adoption of data-driven analysis approaches. These approaches offer invaluable insights into flow physics and can also be used for low-order modeling. The two primary objectives of this study are to apply Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) to velocity flow field data to predict the flow phenomena, develop low-order models, and apply DMD onflow visualization Planar Laser-Induced Fluorescence (PLIF) data to identify the temporal evolution of flow structures for recirculation region in porous media. An in-house refractive index-matched flow loop system was designed for the experiments, where a gear pump was used for fluid circulation, and a syringe pump was used for dye injection. The Reynolds numbers (Re) and the average porosity for the experiment were 42 and 0.39. Irregularly shaped 3 mm Tetrafluoroethylene hexafluoropropylene vinylidene fluoride (THV) beads were used as the porous media. 2D-PIV measurements were made at the center plane of the models to obtain a velocity flow field, which revealed a recirculation region. Applying POD in the PIV dataset, the energy distribution in the first twenty-five POD modes revealed key insights at Re. First twenty-five POD modes captured 74% of the recirculation region’s total energy. DMD provided dynamic insights into the velocity flow field, including frequency and growth rate associated with the frequencies in the recirculation region. Dominant frequencies were obtained using DMD, which were related to the occurrence of vortex in velocity flow field data. Low-order models were created using twenty-five POD modes and three DMD with modes with mean flow mode. The reconstructed velocity flow field data was compared with PIV velocity flow field data, resulting in an average Root Mean Square Error (RMSE) of 0.06% for POD across all regions and 1.37% for DMD low-order models for the recirculation region. Additionally, PLIF measurements using Rhodamine-B dye were used for flow visualization in the recirculation region. PLIF data offered qualitative information complementary to PIV. DMD results from flow visualization provided information about the flow dynamics of dye at Re = 42 in the recirculation region. The frequencies associated with the growth rate closer to zero in the frequency trend could capture the diffusion of dye, and the remaining frequencies captured the advection of dye. In conclusion, this study highlights the applicability of POD and DMD in unraveling the intricate dynamics of fluid flow in porous media, paving the way for future advancements in understanding and modeling these complex systems.