Flow Between Finite Rotating Disks and its Linear Stability
Abstract
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 quasisimilar 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 Bspline 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 spirallike 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) }.
 Publication:

Ph.D. Thesis
 Pub Date:
 1992
 Bibcode:
 1992PhDT........23F
 Keywords:

 ASYMPTOTICS;
 CRITICAL REYNOLDS NUMBER;
 Applied Mechanics; Physics: Fluid and Plasma;
 Computational Fluid Dynamics;
 Flow Stability;
 Rotating Disks;
 Aspect Ratio;
 Reynolds Number;
 Vortices;
 Wall Flow;
 Fluid Mechanics and Heat Transfer