The Third Two-Dimensional Problem of Three-Dimensional Blade Systems of Hydraulic Machines—Part 1: Theoretical Analysis

[+] Author and Article Information
P. K. Agarwal

Department of Mechanical Engineering, M.L.N. Engineering College, Allahabad, India

G. V. Viktorov

Department of Hydraulic Machines, Moscow Power Institute, Moscow, USSR

J. Fluids Eng 103(1), 33-41 (Mar 01, 1981) (9 pages) doi:10.1115/1.3240778 History: Received January 27, 1977; Online October 26, 2009


This is the first part of a study of “third” two-dimensional problem of three-dimensional blade systems of hydraulic machines. Proposed herein is a method of obtaining and evaluating the three-dimensional effect on a system of hydraulic machine blades with arbitrary geometry. An analysis method indicating the velocity distributions on surfaces perpendicular to the mean axisymmetric stream surfaces has been formulated to help create a general understanding and awareness of the flow conditions in the runner passage. An application of generalized analytic functions for inviscid, incompressible flow has been made to find out the general solution on an auxiliary plane, transformed conformally from the physical plane. Integral equation systems for the tangential velocity and the velocity potential function have been deduced. Thus, the solution of the three-dimensional flow problem is supplied by two-dimensional computation methods.

Copyright © 1981 by ASME
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