Taylor-Couette flow in an elliptical enclosure generated by an inner rotating circular cylinder

Abstract

Taylor-Couette flow between rotating cylinders is a classical problem in fluid mechanics and has been extensively studied in the case of two concentric circular cylinders. There have been relatively small number of studies in complex-shaped cylinders with one or both cylinders rotating. In this paper, we study the characteristics of Taylor cells in an elliptical outer cylinder with a rotating concentric inner circular cylinder. We numerically solve the three-dimensional unsteady Navier-Stokes equations assuming periodicity in the axial direction. We use a Fourier-spectral meshless discretization by interpolating variables at scattered points using polyharmonic splines and appended polynomials. A pressure-projection algorithm is used to advance the flow equations in time. Results are presented for an ellipse of aspect ratio two and for several flow Reynolds numbers (Re=ωri(b−ri))/ν, where ω = angular velocity [rad/s], ri = radius of inner cylinder, b = semi-minor axis, and ν = kinematic viscosity) from subcritical to 300. Streamlines, contours of axial velocity, pressure, vorticity, and temperature are presented along with surfaces of Q criterion. The flow is observed to be steady until Re=300 and unsteady at Re=350.