Modelling of the additional motion resistance term in CFD simulations using porosity distributed resistance (PDR)

Abstract

The numerical simulation of turbulent flows through groups of obstacles is essential in various industrial applications, particularly in the numerical modelling of accidental explosions. In such contexts, particular attention must be given to small-scale objects that impose flow resistance and contribute to turbulence generation. The Porosity Distributed Resistance (PDR) approach has been introduced as a practical method to address the complexity of simulating flow behaviour near small-scale objects. This study presents a novel model for the additional motion resistance term ($R_i$) within Computational Fluid Dynamics (CFD) simulations, specifically designed to enhance the PDR approach. Using CFD simulations conducted in CFX, we derived and validated the $R_i$ model by comparing simulation results with empirical correlations, demonstrating its dependence on cell volumetric porosity. This model was subsequently implemented and tested in STOKES, a CFD software tailored for explosion simulations that incorporates the PDR methodology. Our study also investigated the effects of computational mesh resolution on porosity distribution within the domain. Two key conclusions emerged: first, the proposed model significantly improves simulation accuracy when coarse computational meshes are employed—typical for large-scale industrial simulations, including gas dispersion and explosion scenarios; second, at finer mesh resolutions, the PDR concept renders the $R_i$ model impact negligible. Consequently, an influence radius is recommended for activating the $R_i$ term, ensuring optimal application within the computational domain.