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Numerical studies of slow viscous rotating flow past a sphere—1
Author(s) -
Raghavarao C. V.,
Valli K. Pramada
Publication year - 1987
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.1650070402
Subject(s) - stream function , vorticity , navier–stokes equations , stokes flow , rotational symmetry , physics , angular velocity , stokes' law , drag , flow (mathematics) , rotation (mathematics) , mathematics , vorticity equation , mathematical analysis , non dimensionalization and scaling of the navier–stokes equations , classical mechanics , mechanics , vortex , geometry , compressibility
Abstract The Navier‐Stokes equations for a steady, viscous rotating fluid, rotating about the z ‐axis with angular velocity ω are linearized using the Stokes approximation. The linearized Navier‐Stokes equations governing the axisymmetric flow can be written as three coupled partial differential equations for the stream function, vorticity and rotational velocity components. One parameter, R eω = 2ωa 2 /v, enters the resulting equations. For R eω « 1, the coupled equations are solved by the Peaceman‐Rachford A.D.I. (Alternating Direction Implicit) method and the resulting algebraic equations are solved by the ‘method of sweeps’. Stream lines for ψ = 0·05, 0·2, 0·5 and magnitude of the vorticity vector z = 0·2 are plotted for R eω = 0·1, 0·3, 0·5. Correction to the Stokes drag due to the rotation of fluid is calculated.