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Unsteady Rotating Flow of a Compressible Fluid over a Finite Disk
Author(s) -
Bhattacharyya S.,
Pal A.,
Datta N.,
Nath G.
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199804)78:4<243::aid-zamm243>3.0.co;2-6
Subject(s) - mathematics , boundary layer , similarity solution , flow (mathematics) , stream function , radius , mathematical analysis , discretization , geometry , mechanics , physics , vortex , classical mechanics , vorticity , computer security , computer science
The semi‐similar formulation of the problem of an unsteady boundary layer over a stationary disk of finite radius induced by a time dependent rotating flow of compressible fluid is considered. The free stream swirling flow is assumed to be tangential and varies as a power of radial distance, i.e., v e ∼ r —n ϕ( t *), where ϕ( t *) is an arbitrary function of time t *. Several free stream velocity distributions have been examined. Near the outer edge of the disk the flow is described by the Stewartson edge similarity solutions and near the axis of rotation the solutions coincide with the Bödewadt's type of similarity solution. The velocity profiles are monotonic over the outer half of the finite disk but they exhibit oscillation over the inner half (for n < 1). Due to reversal in radial velocity over the inner half of the disk, the boundary layer equations become a kind of time dependent singular parabolic equation and the solution of which requires the conditions over all of its boundaries. Finite‐difference scheme using space‐centered differences in the axial direction and upwind differences in the radial direction is used for solving the governing equations. Crank‐Nicolson scheme is used for time‐wise discretisation. Numerical solutions have been obtained for the entire range of the radial distance. Solutions for the entire range of the radial distance exist upto a certain critical value of n. Boundary layer solutions do not exit over the inner half of the disk for the case of potential vortex flow ( n = 1). Effect of acceleration and oscillation of the free stream azimuthal velocity on the boundary layer flow and heat transfer have been investigated.