The Elliptic Solution of the Secondary Flow Problem

[+] Author and Article Information
S. Abdallah

Applied Research Laboratory, Pennsylvania State University, State College, Pa. 16802

A. Hamed

Department of Aerospace Engineering and Applied Mechanics, University of Cincinnati, Cincinnati, Ohio 45221

J. Eng. Power 105(3), 530-535 (Jul 01, 1983) (6 pages) doi:10.1115/1.3227448 History: Received December 18, 1981; Online September 28, 2009


This paper presents the elliptic solution of the inviscid incompressible secondary flow in curved passages. The three-dimensional flow field is synthesized between 3 sets of orthogonal nonstream surfaces. The two-dimensional flow field on each set of surfaces is considered to be resulting from a source/sink distribution. The distribution and strength of these sources are dependent on the variation in the flow properties normal to the surfaces. The dependent variables in this formulation are the velocity components, the total pressure, and the main flow vorticity component. The governing equations in terms of these dependent variables are solved on each family of surfaces using the streamlike function formulation. A new mechanism is implemented to exchange information between the solutions on the three family surfaces, resulting into a unique solution. In addition, the boundary conditions for the resulting systems of equations are carefully chosen to insure the existence and uniqueness of the solution. The numerical results obtained for the rotational inviscid flow in a curved duct are discussed and compared with the available experimental data.

Copyright © 1983 by ASME
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