Numerical Simulation Of Magnetohydrodynamics Taylor Vortex

The MHD Taylor vortex flow between two concentric cylinders in the presence of axial magnetic fields is numerically studied. The incompressible electrical conducting fluid confined between the rotating cylinders is assumed to be small magnetic Reynolds number and magnetic diffusion equation is replaced by electric potential equation. Lorentz force appears in Navier-Stokes equations as the source term.An improved projection method is used to solve the unsteady Navier-Stokes equations in primitive variable form. In the treatment of the governing equation, the Chebyshev-Fourier spectral method is used for spatial discretication. The time integration used is semi implicit second order accurate and is based on combination of Adams-Bashforth and backward difference schemes.Critical Reynolds numbers and transitions from rotating Couette flow to Taylor vortex flow in different Hartmann numbers are calculated in infinitely Taylor-Couette flow. The axisymmetric disturbances to the laminar flow is introduced and allowed to grow into steady-state Taylor vortex. In the numerical calculation, periodic boundary condition is used to avoid end plates effects.The Taylor vortex structure in a finite length annulus for symmetric end plates and asymmetric end plates are invested. The typical symmetrical vortical structure and an anomalous mode vortex are obtained for different end plates boundary conditions. The evolution of the MHD Taylor vortex in different Ha numbers is reproduced. At last, the direction of radial velocity near the end plates and the effect of axial magnetic field on the layers are analyzed respectively.