Singular treatment of viscous flow near the corner by using matched eigenfunctions

Abstract

In this paper, the local singular behavior of Stokes flow is solved near the salient and re-entrant corners by the matching eigenfunction method. The flow in a rectangular and an L-shaped cavity are considered as a model for the flow generated by the motion of the upper lid. The solutions of the Stokes equation in polar coordinates are matched with a velocity vector components obtained by analytic or numerical solution for the streamfunction developed for any values of the heights of the rectangular and an L-shaped cavity. Streamline patterns near the corner are simulated for a different aspect ratio A. The techniques are tested on a flow problem undergoing Stokes or Navier–Stokes equations in a square cavity. It is seen that the method appears to be cheaper and more accurate than the numerical and analytical methods. It is expected that the study will lead to useful insights into the understanding of the flow topology near a re-entrant corner from a combined analytical-numerical method. Attention is then focused on the topological behavior near the re-entrant corner of the L-shaped cavity. Careful analysis of the streamlines of streamfunction near the re-entrant corner by using wall shear stress allows us to give a possible flow bifurcation of dividing streamline.

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“…Sprittles and Shikhmurzaev [6] considered the numerical issues arising in computations of viscous flows in corners formed by a liquid-fluid free surface and a solid boundary. In addition, Deliceoglu, et al [7] solved the local singular behavior of Stokes flow near the salient and re-entrant corners by the matching eigenfunction method.…”

Laws of Nature and their Supporting Casts

“…Navier-Stokes equations regarding our system. For examples of this approach, seeGupta, Manohar, and Noble [1981] andDeliceoglu, C ¸elik, and Gürcan [2019].…”

Data-driven control of discrete-phase concentration in a vortex involved two-phase flow with optimized energy consumption

“…For example, the stream function of the corner flow was modelled by mirrored-driven point vortices plus a stagnation flow as a quarter of the spinup model with potential flow assumption [78,80]. The stream function of a liddriven corner flow was solved numerically by the matched eigenfunction method for a Stokes flow [81]. The similar crosswise velocity distribution pattern in the boundary layer was found by Rubin [3] between an incompressible corner flow and a quarter-infinite flat flow.…”