An Experimental and Theoretical Investigation of Two-Dimensional Centrifugal Pump Impellers

Abstract

In the past most of the experimental work in the field of hydraulic machinery has been conducted on complete machines. Because of the mechanical difficulties involved, relatively little work has been done to determine the performance and behavior of the individual components. Roughly, a hydraulic machine may be considered to be composed of three parts; a stationary inlet or guide d e vice, a rotating component or impeller, and volute or stationary collecting device. With a view to obtaining component performances, much experimental work has been done in testing combinations of impellers in various volutes. Individual performance is then inferred from changes in over-all behavior. A separate study of the components permits a more ready understanding of the processes occurring and through simplification allows analysis to be undertaken. If the complete characteristics of the individual elements of the machine were then either known or predictable, design would become more straightforward. Since the impeller is responsible for energy input to the flow, it seems clear that it should be the item of first interest. It would be highly desirable to be able to predict the head developed and the distributions of pressure which occur by methods other than the empirical cut and try. However, a satisfactory theory embracing all of the effects of real fluids and the complex geometries found in practice is not yet available. For that reason the problem must be simplified as far as possible, retaining only the essentials. To this end the impeller is assumed to be two dimensional, that is, the flow is restricted to depend only on radial and angular coordinates. For analysis, it is further assumed to be inviscid, incompressible and irrotational so that the methods of potential theory may be employed. This approach is familiar in fluid mechanics and much success has been obtained with it. However, it should be noted at the outset that the limitations of potential theory for flows of the sort described above are as yet unknown. The line of thought followed in this work is not novel. It is to be found in References 1 to 3, to mention a few of the current efforts. However, in most of these works the configurations studied are such that analysis or comparison with a theory in any systematic way is difficult. The blade shape chosen for analysis is a logarithmic spiral. This shape is the only one that is mathematically convenient but, fortunately, most blades used in practice are closely represented by such shapes.

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