Direct simulation of structured wall bounded packed beds using hybrid FE/FV methods

Abstract

Direct numerical simulations are conducted for regular or structured porous media represented by packed beds of spheres enclosed in square cross-section channels for different channel-to-sphere diameter ratios (Ds/dp=1 to ∞) using hybrid finite element/volume (FE/FV) methods. The hybrid flow solver methodology is based on the pressure correction or projection method, which involves a fractional step approach to obtain an intermediate velocity field by solving the original momentum equations with the matrix-free, implicit, cell-centered finite volume method. The poisson equation resulting from the fractional step approach is then solved by node based Galerkin finite element method for an auxiliary variable which is closely related to pressure and is used to update the velocity field and pressure field.The hybrid flow solver has been extended for applications in structured packed beds for both infinite and also wall bounded porous media. The packed spheres representing the porous media are shrunk by 2% dp so that there is a finite, but very small spacing between spheres and also between sphere and wall to avoid highly skewed elements. Studies are conducted to test our novel hybrid FE/FV solver for porous media flows and also to analyze wall effects in detail for regular, structured porous media in Simple Cubic (SC) configuration. Three dimensional numerical simulations are conducted for different channel to sphere diameter ratios (Ds/dp) and also for infinite porous media over wide range of Reynolds numbers (1⩽ReE⩽5000) so that the dimensionless pressure drop or friction factor dependence on the Reynolds number and Ds/dp ratio is clearly understood. Results are validated with available empirical correlations and experimental data. Friction factor correlations for random beds are suitable for structured beds only at very low Reynolds numbers (ReE⩽20), but deviate significantly beyond that due to the channeling present in regular porous media which becomes increasingly significant at higher Reynolds numbers. For structured beds, wall influence was observed to be significant on the friction factor calculation in both laminar and turbulent regimes. Compared to infinite beds, friction factors increased as the channel-to-sphere diameter ratio (Ds/dp) decreased in the entire flow regime. This is unlike the behavior for random porous media where walls have contrasting effects at lower and higher Reynolds numbers when compared to the infinite random beds. Dimensionless pressure drop and friction factor results obtained from our simulations for a wide range of ReE and Ds/dp are curve-fitted to provide generalized correlations for predicting the friction factors in Simple Cubic (SC) structured packed beds.