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. This study has three primary objectives: (1) applying Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) to velocity flow field data to predict the flow phenomena and develop low-order models, (2) this study will apply DMD on flow visualization Planar Laser-Induced Fluorescence (PLIF) data to identify the temporal evolution of flow structures, and (3) use physics-based DMD to velocity flow field vectors 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) for these experiments were 14, 38, 42, and 77, and the average porosity was 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 distinct regions such as channel, impinging, and recirculation. An increase in Re influenced the fluid flow structures within pores, increasing vortex size in the recirculation zone from Re = 42 to 77. Advanced data analysis techniques, including POD and DMD, were applied to quantify flow behavior. The energy distribution in the first twenty-five POD modes revealed key insights at Re. Re = 14 captured 47% and 56% of the total energy for impinging and channel region. The higher Re of 38 captured lower energy than Re = 14 of 31% and 38% for impinging and channel regions. The recirculation region captured the highest amount of energy of 74% for Re = 42 and 58% for Re = 77. Furthermore, the POD modes could also identify the three-dimensional regions in the porous media flow. 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. A physics-based DMD called orthogonal DMD, which was based on the conservation of energy, was used in the recirculation region. A low-order model was created using orthogonal DMD, resulting in an average RMSE of 1.2%, which was less than the traditional DMD by a factor of 1.1. 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 and 77 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.