Data-driven modal analysis of turbulent momentum exchange and heat transfer in composite porous fluid systems

Abstract

This paper investigates the dynamics governing turbulent momentum exchange and heat transfer between pore flow within porous media and the turbulent flow passing over it. Employing high-fidelity pore-scale large eddy simulation, our investigation explores the fundamental mechanisms driving these phenomena. Modal analysis based on snapshot proper orthogonal decomposition (POD) is employed to quantify the modes of interaction between porous and non-porous regions, providing a comprehensive understanding of the underlying processes. Spatial and temporal modes reveal the existence of localized flow structures at the pore scale, contributing to time-varying patterns of information exchange. At the commencement of the porous block, the mean flow (Mode = 0) from the porous to non-porous region is the dominant mechanism in momentum exchange and heat transfer. This mode facilitates convective heat transfer from the porous to the non-porous region through upward and forward flow movements, showcasing positive flow leakage. In addition to the mean flow, the turbulent flux inherent in alternate POD modes (Mode ≠ 0) plays a substantial role in information propagation, influencing diverse directions. Spatial modes, complemented by statistical analysis, uncover a significant likelihood of observing negative vertical velocity values in the wake of the porous ligaments at the porous-fluid interface, indicative of negative flow leakage. This negative flow leakage precisely corresponds to the local penetration of fluid from the non-porous region into the porous region. Furthermore, our study reveals that information exchange via turbulence fluctuations manifests through complex outward and inward interactions in regions characterized by substantial positive flow leakage. Notably, these regions exhibit a distinct tendency for high-momentum streamwise-oriented flow to migrate outward from the porous region into the non-porous region (outward interactions). Conversely, inward interactions arise in these regions when the instantaneous magnitude of positive flow leakage is smaller than the mean value of positive flow leakage, emphasizing the pulsating nature of positive flow leakage. Finally, the distribution of the Nusselt number highlights that more than 60% of total heat transfer occurs within the initial one-third of the porous block length. Significantly, a notable portion of the porous ligaments experiences insufficient cooling due to positive flow leakage, underlining the critical implications of these findings for the understanding of turbulent momentum exchange and heat transfer in a composite porous-fluid system.