Investigation of Natural Convection in Porous Medium by Immersed Boundary Method

Immersed boundary method (IBM) is utilized for investigation of natural convection in two-dimensional differentially heated cavity filled with porous medium (PM). The PM is modelled by single- and bi-modal cylinders randomly filling the cavity in accordance with a given porosity value. The IBM is implicitly embedded into the fully pressure velocity coupled (FPCD) time stepper [1] allowing for implicit coupling of all flow fields and singular body forces and heat fluxes in accordance with the IBM formalism. Discrete delta functions of Roma et al. [2] are implemented into the IBM regularization and interpolation operators. The study aims at conducting a theoretical analysis of natural non-Darcy convection flows through anisotropic porous media. The flow characteristics, obtained by direct numerical simulations (DNS) of Navier Stokes (NS), and the energy equations are used to understand the principal mechanisms of the flow through PM. This theoretical analysis facilitates the design of novel smart PM, which could potentially be adjusted for specific engineering applications. The study demonstrates the potential of the derived methodology to control efficiently the convective heat flux rate passing through the prescribed PM.

Figure: Temperature distribution with superimposed velocity vector field inside differentially heated PM cavity with thermally insulated horizontal boundaries. Porosity value : (a) bottom left; (b) top right; (c) overview.

References

[1] Feldman, Yu., Gelfghat, A., Comp.&Struct. 87(2009) 710-720.

[2] Roma, A., M., Peskin C., S., Berger, M., J., J. Comput. Phys. 153 (1999) 509–534.