NUMERICAL INVESTIGATION OF INSTABILITY OF AN ANNULAR ROTATING CAVITY

Abstract: A direct two-dimensional numerical simulation has been performed to study the tran-sition flow in an annual rotating cavity. The spectral collocation method based on the Chebyshev polynomial is used to solve the incompressible Navier-Stokes equation. The time scheme is semi-implicit and second-order accurate; it corresponds to a combination of the second-order backward differentiation formula for the viscous diffusion term and the Adams-Bashforth scheme for the non-linear terms. The method uses a projection scheme to maintain the incompressibility constrain. The numerical computations, performed for an annular cavity of the aspect ratio L=2 and 5 and for the curvature parameters Rm=(R1+R0)/(R1−R0) = 5, exhibit instability structures in the form of cir-cular rolls. These structures are in good agreement with the other investigations, both experimental and theoretical