Study of Taylor Couette flow between an elliptical enclosure and an inner rotating cylinder

Taylor-Couette flows have been extensively studied in a gap between concentric cylinders. However, fewer studies exist of Taylor cells in the gap between a non-circular enclosure and an inner rotating circular cylinder. In this study, a meshless method is used to study such Taylor cells in the gap formed by an elliptical enclosure and a cylinder. We have considered ellipses of aspect ratios two and three. The meshless method uses Polyharmonic spline radial basis functions (PHS-RBF) with appended polynomials for interpolating scattered data. In the periodic streamwise direction, Fourier expansions are used. The discrete equations are obtained by differentiation of radial basis functions and collocation of the partial-differential equations at the scattered points. A second-order accurate fractional step algorithm solves the discrete equations in time. The first onset of Taylor cells and their characteristics at increasing Reynolds numbers are studied for two aspect ratio of outer enclosure. The Taylor Couette cells are observed to stretch and compress to fit the varying gap between the outer enclosure and the inner cylinder. The torque on the inner cylinder and the velocity distributions are presented. These flow patterns can have important effects on mixing and particle dynamics.