Numerical studies of slow viscous rotating flow past a sphere—1

✍ Scribed by C. V. Raghavarao; K. Pramada Valli

• Publisher: John Wiley and Sons
• Year: 1987
• Tongue: English
• Weight: 405 KB
• Volume: 7
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/fld.1650070402

✦ Synopsis

The Navier-Stokes equations for a steady, viscous rotating fluid, rotating about the z-axis with angular velocity w 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, Re, = 2wa2/v, enters the resulting equations. For Re, << 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 i +b =0.05, 0.2, 0.5 and magnitude of the vorticity vector z = 0.2 are plotted for Re, = 0.1, 0.3, 0.5. Correction to the Stokes drag due to the rotation of fluid is calculated.