The Influence of Sweep on Axial Flow Turbine Aerodynamics in the Endwall Region

Sweep, when the stacking axis of the blade is not perpendicular to the axisymmetric stream surface in the meridional view, is often an unavoidable feature of turbine design. In a previously reported study, the authors demonstrated that sweep leads to an inevitable increase in midspan profile loss. In this paper, the influence on the flowfield close to the endwalls is investigated. Experimental data from two linear cascades, one unswept, and the other swept at 45 deg but having the same overall turning and midspan pressure distribution, are presented. It is shown that sweep causes the blade to become more rear loaded at the hub and fore loaded at the casing. This is further shown to reduce the penetration of the secondary flow at the hub, and to produce a highly unusual secondary flow structure, with low endwall overturning, at the casing. A computational study is then presented in which the development of the secondary flows of both blades is studied. The differences in the endwall flowfields are found to be caused by a combination of the effect of sweep on both the endwall blade loading distribution and on the bulk movements of the primary irrotational flow.

Application of an Inverse Design Procedure to Axial Compressor Blading

A blade-to-blade inverse design procedure is presented for use in a quasi-3-D design system for multistage axial flow compressors. The procedure is applicable to transonic rotor and stator airfoil sections along axisymmetric stream surfaces. It accounts for the streamtube thickness and radius variations, and can be used in the analysis, fully inverse, and mixed inverse modes. Steady state Euler equations are implemented and formulated in terms of density and local displacement normal to streamline as dependent variables. Three test cases are presented in this paper to illustrate the application of this inverse design technique for optimizing rotor and stator airfoils of highly loaded, high pressure ratio compressor stages. These test cases demonstrate the capability of this procedure to optimize airfoil geometry for minimizing shock and diffusion losses without compromising the airfoil structural integrity.

The Third Two-Dimensional Problem of Three-Dimensional Blade Systems of Hydraulic Machines—Part 2: Analytical Results

This is the second part of a study of the “third” two-dimensional problem of three-dimensional blade systems of hydraulic machines. Part I described the formulation of the problem and the proposed method of solution to determine the velocity field on surfaces orthogonal to mean axisymmetric stream surfaces. Part II presents the numerical method of solving the integral equations; a few numerical examples for actual impellers/runners are also given. The results are presented in a series of figures and tables showing the distribution of the velocity component c2 along the blade profile on the surface q1 = const. The purpose of these numerical examples is to demonstrate the method and to help create a general understanding and awareness of the flow conditions existing in the runner passage.

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

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.