Abstract
In this article, a concept named double decomposition, which is used to model turbulent flows in porous media, is examined. This concept is based on the idea that in a turbulent flow through a porous matrix, local instantaneous variables can be averaged in time and space, simultaneously. Depending on how these operators are applied, averaged equations take different forms. In this article, instantaneous local equations are averaged using both operators and a different set of equations resulting from such operations are commented upon. Additional terms proposed for the averaged equations are discussed.
Highlights
Other studies in the literature dealing with modeling turbulence in porous media include a review on methodologies [9], Direct Numerical Simulations (DNS) [10], two-scale models [11] and flow in channels with permeable walls [12]
In this paper we have revisited a methodology for the analysis of turbulent flow in permeable media, which was first published in the early 2000’s
A novel concept, called the double-decomposition idea, is revisited, showing how a variable can be decomposed in both time and volume in order to simultaneously account for fluctuations and deviations around mean values
Summary
The order of the averaging is immaterial if the variables are split using the double-decomposition theory, which is fully described in [4] and briefly revisited here. This new concept sheds some light on the existing controversy about which order mathematical operators should be applied to governing equations when double averaging the equation set. Other studies in the literature dealing with modeling turbulence in porous media include a review on methodologies [9], Direct Numerical Simulations (DNS) [10], two-scale models [11] and flow in channels with permeable walls [12]. The study of turbulence though porous media can find application in several areas, including engineering and environmental research.
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