An immersed boundary method for computing heat and fluid flow in porous media

D.J. Lopez Penha, L. Ghazaryan, Bernardus J. Geurts, S. Stolz, Steffen Stolz, Markus Nordlund

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    Abstract

    A volume-penalizing immersed boundary (IB) method is presented that facilitates the computation of fluid flow in complex porous media. The computational domain is composed of a uniform Cartesian grid, and solid bodies are approximated on this grid using a series of grid cells (i.e., a ''staircase'' approximation). Solid bodies are distinguished from fluid regions using a binary phase-indicator function: Taking the value of ''1'' in the solid parts of the domain and ''0'' in the fluid parts. The effect of solid bodies on the flow is modeled using a source term in the momentum equations. The source term is active only within solid parts of the domain, and enforces the no-slip boundary condition. Fluid regions are governed by the incompressible Navier-Stokes equations. An extension of the IB method is proposed to tackle coupled fluid-solid heat transfer. The extended IB method is validated for Poiseuille flow, which allows for a direct comparison of the numerical results against a closed analytical solution. We subsequently apply the extended IB method to flow in a structured porous medium and focus on bulk properties such as the gradient of the average pressure and the Nusselt number. Reliable qualitative results were obtained with 16-32 grid points per singly-connected fluid region.
    Original languageEnglish
    Title of host publicationProceedings of the V European Conference on Computational Fluid Dynamics, ECCOMAS CFD 2010
    EditorsJ.C.F Pereira, A. Sequeira, J.M.C. Pereira
    Place of PublicationLisbon
    PublisherTechnical University of Lisbon
    Number of pages16
    ISBN (Print)978-989-96778-1-4
    Publication statusPublished - Jun 2010
    Event5th European Conference on Computational Fluid Dynamics, ECCOMAS ECFD 2010 - Lisbon, Portugal
    Duration: 14 Jun 201017 Jun 2010
    Conference number: 5

    Conference

    Conference5th European Conference on Computational Fluid Dynamics, ECCOMAS ECFD 2010
    Abbreviated titleECCOMAS ECFD 2010
    CountryPortugal
    CityLisbon
    Period14/06/1017/06/10

    Keywords

    • Incompressible Navier-Stokes equations
    • Immersed boundary method
    • Numerical simulation
    • Porous media
    • Volume penalization
    • Conjugate heat transfer

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