Flow Between Finite Rotating Disks and its Linear Stability

The flow between finite rotating disks with a large aspect ratio (beta = R/d, where d is the gap between the disks and R is the radius of the disk) and its linear stability are the subjects of study of this thesis. Through an analysis of the singular points of the governing equations, some quasi-similar properties of basic flow with respect to certain of parameters are obtained. Extensive numerical experiments on the basic flows are conducted by projecting governing equations onto a polynomial subspace with a B-spline basis. The numerical results have very good agreement with the experimental data of Szeri ^{(1)}, and strongly support the theoretical predictions. The linear stability of the basic flow, with beta ^2 = 406.5 and beta^2 = 1975.3, is studied in detail. The perturbation equations which characterize the stability of the finite disk flow are derived and solved numerically. Three types of unstable modes are found. These are: (1) S _{rm W}, introduced by and located near the side wall; (2) S_{ rm L}, consisting of spiral-like vortices, which occurs at mid radius; and (3) S_{ rm R}, appearing when the Reynolds number of the basic flow is large. The numerical predictions for critical Reynolds number are in good agreement with the experimental data of Sirivat^{(2) }.