Stationary solutions of incompressible viscous flow in a wall-driven semi-circular cavity

Ercan Erturk

doi:10.14311/ap.2021.61.0516

Abstract

Stationary numerical solutions of incompressible viscous flow inside a wall-driven semicircular cavity are presented. After a conformal mapping of the geometry, using a body-fitted mesh, the Navier-Stokes equations are solved numerically. The stationary solutions of the flow in a wall-driven semi-circular cavity are computed up to Re = 24000. The present results are in good agreement with the published results found in the literature. Our results show that as the Reynolds number increases, the sizes of the secondary and tertiary vortices increase, whereas the size of the primary vortex decreases. At large Reynolds numbers, the vorticity at the primary vortex centre increases almost linearly stating that Batchelor’s mean-square law is not valid for wall-driven semi-circular cavity flow. Detailed results are presented and also tabulated for future references and benchmark purposes.

Highlights

Flows in enclosures are studied very frequently in Computational Fluid Dynamics studies since they retain rich flow physics in rather simple geometries
We numerically investigate the behavior of the stationary solutions of an incompressible viscous flow in a wall-driven semi-circular cavity at large Reynolds numbers
As convergence criteria in our simulations, we use the change in the streamfunction and vorticity variables between two consecutive iterations, which is normalized by the previous values defined as the following

Summary

Introduction

Flows in enclosures are studied very frequently in Computational Fluid Dynamics studies since they retain rich flow physics in rather simple geometries. Similar to the flows in different enclosures mentioned above, Glowinski et al [10] studied the flow in a semi-circular cavity They ([10]) used an unsteady operator-splitting/finite elements method and solved the governing flow equations on an unstructured mesh and presented detailed stationary solutions of the semi-circular cavity flow. Mercan and Atalik [15] considered the arc-shaped cavity flow for the semi-circular case numerically using an unsteady finite difference method They ([15]) used an elliptic grid generator scheme in order to obtain a body-fitted general coordinates and solve the governing streamfunction and vorticity equations. We numerically investigate the behavior of the stationary solutions of an incompressible viscous flow in a wall-driven semi-circular cavity at large Reynolds numbers.

Numerical method

Numerical mesh

Governing equations in the computational domain

Mapping transformation metrics

Results and discussion

Conclusion