Alternative Modeling for Turbulent Flow in Porous Media

Abstract

The development of models for turbulent flows in porous media is an active area of research with diverse and practical applications. Following the steps to model turbulence in clear flows, porous media models have appeared in the last three decades to capture the turbulence phenomenon at macroscopic scales. The fact that, in the porous media approximation, we are representing a region of the space with single values, obligate us to introduce space-fluctuating quantities in addition to the time decomposition or Reynolds decomposition. This issue has yielded some controversies in the way that turbulence quantities are defined and therefore, in the resulting turbulence models for porous media that have been already developed following the well known k-ε model. In this paper an alternative model is developed to address turbulent flows in porous media. This new set of k-ε equations for rigid and isotropic porous media is developed treating spatial and time fluctuations as a unique identity. This feature leads to a natural construction of the k and ε equations with the same terms found in the corresponding equations for clear flow plus additional terms resulting from the interaction between solid walls of the porous media and the fluid. These extra terms arise in an integral form allowing their evaluation from microscopic or clear flow calculations. Assuming the eddy viscosity approximation and simple models to represent the interaction between solid walls and fluid, the model is closed. The resulting equations are simplified and numerically solved for fully developed flow in one dimensional porous media. Results are compared with those obtained using existing models.