Analytical Solution and Flow Topology in a Lid-Driven S-Shaped Cavity


Bilgil H., Şafak İ., Öztürk Z.

PHYSICS OF FLUIDS, vol.34, no.12, pp.123113, 2022 (Peer-Reviewed Journal)

  • Publication Type: Article / Article
  • Volume: 34 Issue: 12
  • Publication Date: 2022
  • Doi Number: 10.1063/5.0134448
  • Journal Name: PHYSICS OF FLUIDS
  • Journal Indexes: Academic Search Premier, zbMATH
  • Page Numbers: pp.123113
  • Kayseri University Affiliated: Yes

Abstract

In this study, the Stokes flow problem in an S-shaped double lid-driven cavity filled with fluid was analyzed. The side edges of the cavity were considered as immovable walls.

The flow region was divided into two sub-regions, and the streamfunction in each sub-region was considered as an extension of the Papkovich–Faddle eigenfunctions. Parameters in the analytical solution were obtained using biorthogonality conditions. The Newton iteration method was used to obtain the eigenvalues of the problem and integrals were calculated with the Gaussian Quadrature Method.


It was ensured that the solutions made separately for the two sub-regions converge on the interface, which is the intersection of these sub-regions. The two parameters controlling the flow structure were determined as the speed ratio of the movable lids (S) and the aspect ratio of the cavity (A). The effects of these parameters on the flow structures were shown. New eddy formation mechanisms and bifurcations were observed in the cavity by keeping the speed ratio of the lids constant and slowly changing the aspect ratio.