Method of fundamental solutions for partial‐slip fibrous filtration flows

Abstract

SUMMARYIn this study a Stokeslet-based method of fundamental solutions (MFS) for two-dimensional low Reynolds number partial-slip flows has been developed. First, the flow past an infinitely long cylinder is selected as a benchmark. The numerical accuracy is investigated in terms of the location and the number of the Stokeslets. The benchmark study shows that the numerical accuracy increases when the Stokeslets are submerged deeper beneath the cylinder surface, as long as the formed linear system remains numerically solvable. The maximum submergence depth increases with the decrease in the number of Stokeslets. As a result, the numerical accuracy does not deteriorate with the dramatic decrease in the number of Stokeslets. A relatively small number of Stokeslets with a substantial submergence depth is thus chosen for modeling fibrous filtration flows. The developed methodology is further examined by application to Taylor-Couette flows. A good agreement between the numerical and analytical results is observed for no-slip and partial-slip boundary conditions. Next, the flow about a representative set of infinitely long cylindrical fibers confined between two planar walls is considered to represent the fibrous filter flow. The obtained flowfield and pressure drop agree very well with the experimental data for this setup of fibers. The developed MFS with submerged Stokeslets is then applied to partial-slip flows about fibers to investigate the slip effect at fiber-fluid interface on the pressure drop. The numerical results compare qualitatively with the analytical solution available for the limit case of infinite number of fibers.

On the importance of fibers' cross-sectional shape for air filters operating in the slip flow regime

“…Such studies include, but are not limited to, numerical simulations of Maze et al [1], Hosseini and Tafreshi [2][3][4], Wang and Pui [5], Wang et al [6], Zhao and Povitsky [7], Przekop and Gradon [8] as well as the experimental work of Podgorski et al [9], Wang et al [10], and Shin and Chase [11]. Since the infancy of filtration theory about fifty years ago, fibers have always been assumed to be circular.…”

Boundary singularity method for Stokes flow of droplet-fiber interaction

“…The analysis of geometrical setup of the Stokes flow about spherical droplet touching a fiber solved with the BSM leads to elevated condition number of the matrix M caused by near-parallel vectors directed from Stokeslets to collocation points [1][2][3][4][5]. This requires allocation of Stokeslets close to the surface.…”

“…In the past decades, boundary element methods (BEM) and its variant, Boundary singularity method (BSM), have proven their efficiency in numerous fields of computational physics including micro-and nano-scale Stokes flows about particles, fibers and their ensembles (Zhao and Povitsky [1][2][3][4] and Zhao [5]) and became more advantageous over traditional mesh-based methods (Wrobel [6]). BEM and BSM require optimization of allocation of boundary elements to reduce the computational time and increase solution convergence.…”

Numerical Simulation and Experimental Validation for the Filtration Performance of Fibrous Air Filter Media with LB Method

“…Some researchers have found that fluids flowing past fiber surfaces experience a slip which could reduce the flow resistance in a microscale channel. The slip phenomenon in porous media has been vastly studied in recent literatures (Zhao and Povitsky, 2009;Hosseini and Tafreshi, 2010;Chai et al, 2011;Hosseini and Tafreshi, 2011;Kirsh and Shabatin, 2015).…”