Numerical Analysis of the Pressure Drop in Porous Media Flow using the Lattice Boltzmann Computational Technique
In this paper, we describe detailed simulations of low mach number Newtonian flow through randomly generated porous media for a wide range of Reynolds numbers. The simulations were carried out using the lattice Boltzmann method, which has become an establ
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C&C Research Laboratories, NEC Europe Ltd., Rathausallee 10, D - 53757 Sankt Augustin, Germany Institute of Fluid Mechanics (LSTM), University of Erlangen - Nuremberg, Cauerstr.4, D - 91058 Erlangen, Germany
Abstract. In this paper, we describe detailed simulations of low mach number Newtonian How through randomly generated porous media for a wide range of Reynolds numbers. The simulations were carried out using the lattice Boltzmann method, which has become an established tool for predicting Hows in highly complex geometries. Several quantities were determined by an a posteriori analysis of the How-fields: The pressure drop, the dissipation caused by shear and by elongation of the Huid, and the tortuosity. We were able to show that the pressure drop is mainly caused by the dissipation due to shear and elongation, and that the tortuosity is not related to the total dissipation, but to the relationship of dissipation and shear.
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Introduction
For simulations of flows through highly complex geometries, the lattice Boltzmann method has several advantages when compared to Navier Stokes based methods. Due to its cellular automata based algorithm and the simple and efficient treatment of wall boundary conditions, simulations can be efficiently carried out on high performance vector-parallel computers with a very high discretization on simple equidistant orthogonal lattices. This simple lattice type allows one to implement arbitrary complex geometries by the marker and cell method, were geometry-covered cells of the lattice are marked as being occupied. The marker and cell geometry information can be automatically generated from CAD-data, three dimensional computer tomography or, as in the present paper, by computer programs. In this paper, we used the lattice Boltzmann method for the prediction of flow through beds of randomly distributed cubes. The simulations were carried out for a wide range of Reynolds numbers, and the friction factor, which is a dimensionless quantity for the total dissipation, was determined from the pressure drop, the Reynolds number and the porosity of the porous media. A detailed a posteriori analysis ofthe velocity field gave the two parts adding up to the total dissipation of the fluid when passing through the porous media: the dissipation caused by sher and the dissipation caused by elongation. By integrating the path of the fluid inside the porous media, i.e., by measuring the length of the streamlines, N. Satofuka (ed.), Computational Fluid Dynamics 2000 © Springer-Verlag Berlin Heidelberg 2001
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Jorg Bernsdorf et &1.
the tortuosity, defined as the relationship of the length of the flow paths and the edge length of the porous media, was directly measured. In the following section, we give a short introduction to the lattice Boltzmann method. The capillaric theory for predicting pressure losses in porous media flow will be reviewed in the third section and compared to other experimental and numerical results. In the fourth section we present the results of our simulations and ad
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