Axisymmetric rotational stagnation-point flow impinging on a rotating disk

Abstract

Agrawal’s (Q J Mech Appl Math, 10:42–44, 1957) stagnation-point flow problem is extended to flow impingement normal to a uniformly rotating disk. This is the analog of the extension of Homann’s (Z Angew Math Mech (ZAMM), 16:153–164, 1936) stagnation flow when impinging on a rotating disk as reported by Hannah (Rep Mem Aerosp Res Coun Lond 2772, 1947). While both oncoming stagnation flows are axisymmetric, in the far field Homann’s stagnation flow is irrotational while Agrawal’s is rotational. A similarity reduction of the Navier–Stokes equations yields a pair of coupled ordinary differential equations governed by a dimensionless rotation rate σ. Integrations were carried out up to σ = 30 beyond which the equations become stiff and solution independence of integration length cannot be ensured. Results for the radial and azimuthal shear stresses are presented along with the strength of the flow induced into the boundary layer and the thickness of the azimuthal flow boundary layer. Analytic results found at σ = 0 are shown to be in excellent agreement with the numerical calculations. Sample velocity profiles for the radial and azimuthal flows are presented.