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Taylor-Couette flow between rotating cylinders is a classical problem influid mechanics and has been extensively studied in the case of two concentriccircular cylinders. There have been relatively small number of studies incomplex-shaped cylinders with one or both cylinders rotating. In this paper, westudy the characteristics of Taylor cells in an elliptical outer cylinder witha rotating concentric inner circular cylinder. We numerically solve thethree-dimensional unsteady Navier-Stokes equations assuming periodicity in theaxial direction. We use a Fourier-spectral meshless discretization byinterpolating variables at scattered points using polyharmonic splines andappended polynomials. A pressure-projection algorithm is used to advance theflow equations in time. Results are presented for an ellipse of aspect ratiotwo and for several flow Reynolds numbers ($Re = \omega r_i (b-r_i))/\nu$,where $\omega$ = angular velocity [rad/s], $r_i$ = radius of inner cylinder,$b$ = semi-minor axis, and $\nu$ = kinematic viscosity) from subcritical to300. Streamlines, contours of axial velocity, pressure, vorticity, andtemperature are presented along with surfaces of Q criterion. The flow isobserved to be steady until $Re = 300$ and unsteady at $Re = 350$.

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