Extension of perturbation series by computer: Viscous flow between two infinite rotating disks*1
Abstract
A digital computer is used to extend the lowReynoldsnumber perturbation series for viscous, incompressible flow between two infinite, concentric, rotating disks. Ten terms are found for the case of contrarotating disks and eight for the case of one disk fixed. Convergence is found to be limited by a square root branch point at R^{2} = 1747.24 and 215.63 for the contrarotating case and the one disk fixed case, respectively. Analytic continuation is used to extend the series for velocity profile and torque to high Reynolds numbers. Comparisons with published numerical solutions show excellent agreement. The link between the lowReynoldsnumber perturbation solution and the solution at highReynoldsnumber is discussed.
 Publication:

Journal of Computational Physics
 Pub Date:
 November 1974
 DOI:
 10.1016/00219991(74)90093X
 Bibcode:
 1974JCoPh..16..240H
 Keywords:

 Computer Techniques;
 Perturbation Theory;
 Reynolds Number;
 Rotating Disks;
 Velocity Distribution;
 Viscous Flow;
 Boundary Value Problems;
 Flow Velocity;
 Incompressible Flow;
 NavierStokes Equation;
 Parallel Plates;
 Series (Mathematics);
 Steady Flow;
 Fluid Mechanics and Heat Transfer