Transition of chaotic flow in a radially heated Taylor-Couette system

Numerical simulations have been performed to study the stability of heated incompressible Taylor-Couette flow for a radius ratio of 0.7 and a Prandtl number of 0.7, As Gr is increased, the Taylor cell that has the same direct ion of circulation as the natural convection current increases in size and the counterrotating cell becomes smaller. The flow remains axisymmetric and the average heat transfer decreases with the increase in Gr. When the cyli nder is impulsively heated, the counterrotating cell vanishes and n = 1 spi ral is formed for Gr = 1000. This transition marks an increase in the hear transfer due to an increase in the radial velocity component of the fluid. By slowly varying the Grashof number, the simulations demonstrate the exist ence of a hysteresis loop. Two different stable states with same heat trans fer are found to exist at the same Grashof number. A time-delay analysis of the radial velocity and the local heat transfer coefficient time is perfor med to determine the dimension at two Grashof numbers. For a fixed Reynolds number of 100, the two-dimensional projection of the reconstructed attract or shows a limit cycle for Gr = -1700. The limit cycle behavior disappears at Gr = -2100, and the reconstructed attractor becomes irregular. The attra ctor dimension increases to about 3.2 from a value of I for the limit cycle case, similar values were determined for both the local hear transfer and the local radial velocity, indicating that the dynamics of the temperature variations can be inferred from that of the velocity variations.