Shear-Driven Flow in an Elliptical Enclosure Generated by an Inner Rotating Circular Cylinder

TL;DR

This study investigates shear-driven flow in an elliptical enclosure with a rotating inner cylinder using a meshless method, analyzing vortex formation and flow characteristics across different aspect ratios and Reynolds numbers.

Contribution

Introduces a meshless interpolation method for simulating shear-driven flow in elliptical enclosures with detailed vortex analysis and benchmark data.

Findings

Vortex formation varies with aspect ratio and eccentricity.

Moffatt-like vortices observed in wide-gap regions.

Flow characteristics documented for Reynolds numbers 200-2000.

Abstract

Shear-driven flow between a rotating cylinder and a stationary elliptical enclosure is studied in this paper. Two-dimensional time-dependent Navier Stokes equations are solved using a meshless method where interpolations are done with Polyharmonic Spline Radial Basis Functions. The fluid flow is analyzed for various aspect ratios of the ellipse and eccentric placements of the inner cylinder. Contour plots of vorticity with streamlines, plots of non-dimensional torque, and the angle of eye of the primary vortex are presented in the paper for Reynolds numbers between 200 and 2000. Formation of Moffatt like vortices in the wide-gap region of the model is observed and some benchmark data are provided for various cases that are simulated.