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Numerical studies of slow viscous rotating flow past a sphere. III
Author(s) -
Raghavarao C. V.,
Pramadavalli K.
Publication year - 1989
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650091103
Subject(s) - streamlines, streaklines, and pathlines , vorticity , mathematics , stream function , reynolds number , navier–stokes equations , partial differential equation , flow (mathematics) , mathematical analysis , drag , physics , classical mechanics , mechanics , compressibility , geometry , vortex , turbulence
The flow of steady incompressible viscous fluid rotating about the z ‐axis with angular velocity ω and moving with velocity u past a sphere of radius a which is kept fixed at the origin is investigated by means of a numerical method for small values of the Reynolds number Re ω . The Navier–Stokes equations governing the axisymmetric flow can be written as three coupled non‐linear partial differential equations for the streamfunction, vorticity and rotational velocity component. Central differences are applied to the partial differential equations for solution by the Peaceman–Rachford ADI method, and the resulting algebraic equations are solved by the ‘method of sweeps’. The results obtained by solving the non‐linear partial differential equations are compared with the results obtained by linearizing the equations for very small values of Re ω . Streamlines are plotted for Ψ = 0·05, 0·2, 0·5 for both linear and non‐linear cases. The magnitude of the vorticity vector near the body, i.e. at z = 0·2, is plotted for Re ω = 0·05, 0·24, 0·5. The correction to the Stokes drag as a result of rotation of the fluid is calculated.