Laminar compressible flow between close rotating disks. An asymptotic and numerical study

Laminar steady compressible flow between close rotating thermally conducting axisymmetric disks with inflow was investigated by means of a numerical solution of the Navier-Stokes equation and an asymptotic analysis. The approximate solution, obtained for small ε{lunate}, E and H (Rossby and Ekman numbers, and height/radius, respectively) is valid for "merged", "close" and "separate" boundary layers on the disks, corresponding to β≪ 1, β {reversed tilde equals} 1 and β≫ 1, respectively (where β = H 2√ E ρ, and ρ is the non-dimensional density). These three cases may appear simultaneously in different regions of the same system due to the large variation of ρ in the radial direction. The small ε{lunate} (i.e. negligible convection terms) does not necessarily imply small perturbations of the pressure, and a special treatment of the pressure term was used in order to account for this feature, which sometimes culminates in inversion of the radial pressure gradient. Thenumerical solution was obtained by a finite-difference, modified Cheng-Allen method, using a non-uniform mesh. The numerical and the approximate solution are in good agreement.