Modelling the Pore Level Heat Transfer in Porous Media Using the Immersed Boundary Method

Abstract:

This work presents the extension of a compact finite difference immersed boundary method for the detailed calculation of fluid flow and heat transfer in porous media. The unsteady incompressible Navier-Stokes and energy conservation equations are solved with fourth-order Runge-Kutta temporal discretization and fourth-order compact schemes for spatial discretization, which allows achieving highly accurate calculations. Verification proves that the method is higher than third-order accurate. Three test cases were used for the validation of the method: (i) isothermal flow around a square cylinder in a plane parallel channel, (ii) isothermal flow through an infinite row of square cylinders and iii) flow and heat transfer around a square cylinder in a plane parallel channel. The validation tests establish confidence in the application of the method to porous media. As an example of such an application, direct numerical simulations are conducted for a staggered array of equal size square cylinders. Although the problem is rather complex from the geometrical point of view, a Cartesian grid is employed, with all its advantages. The potential of applying an immersed boundary method to the solution of a multiphase problem with complex internal boundaries is demonstrated.

• Periodical: Diffusion Foundations (Volume 3)
• Pages: 63-85
• DOI: https://doi.org/10.4028/www.scientific.net/DF.3.63
• Online since: February 2015
• Authors: I. Malico, P.J.S.A. Ferreira de Sousa
• Keywords: Compact Finite Differences, Fluid Flow, Heat Transfer, Immersed Boundary Method, Ordered Porous Media

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