TY - JOUR

T1 - Laminar compressible flow between close rotating disks. An asymptotic and numerical study

AU - Israeli, Moshe

AU - Ungarish, Marius

PY - 1983

Y1 - 1983

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0019652977&partnerID=8YFLogxK

U2 - 10.1016/0045-7930(83)90007-5

DO - 10.1016/0045-7930(83)90007-5

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AN - SCOPUS:0019652977

SN - 0045-7930

VL - 11

SP - 145

EP - 157

JO - Computers and Fluids

JF - Computers and Fluids

IS - 2

ER -