Fan Laws, the Use and Limits in Predicting Centrifugal Compressor off Design Performance

The fan laws, particularly what the limits are in their use is described. The derivation is covered very briefly. To help understand some of the fan law uses, centrifugal impeller characteristics are covered, particularly some of the things controlling the shape of the curve. A discussion of the fan law deviations in an individual impeller is covered. Multistage centrifugals are covered using two, four, and six stage configurations. A set of stage curves are made up for use of the study. These curves reflect two basic impeller designs. The designs result in a high (15 percent) and a low (five percent) head rise. Also included is a study where the effect of molecular weight is presented. Speed variations are covered and compared to the fan law prediction with the deviations being shown. INTRODUCTION The inspiration for this paper came from a question raised at one of the Performance Testing Discussion Groups during the 1990 91 Turbomachinery Symposium. While discussing the subject of doing a field performance test on an alternative gas, the fan law question was raised. Specifically, the question was "What are the limits of use of the fan laws?" There was silence, then the question was dismissed with a "it depends" kind of answer. After the session, it occurred to the author that this question deserved a better answer. The following will attempt to do just that. Before proceeding, it seems in order to issue a disclaimer or two. To give some idea of magnitude, a few numerical examples will be used. For comparison to the fan law, centrifugal stage curves will be used. Any resemblance of these curves to machines currently in service or being designed is purely coincidental. The author believes these to be typical of real curves, but these curves are the result of imagineering on the part of the author and some of his colleagues. The purpose here is to illustrate a point or two, not present a design dissertation. Having said all of this, it is time to address the subject. FAN LAWS The fan laws are derived from a dimensional analysis, using the Pi-theorem as a formal procedure. The reader is directed to Shepherd [I] for a complete derivation of the 1t-terms. The following three 1t-terms are used for the simplified fan law approach.