Similarity criteria for vane pumps

Abstract

Engineers in the development of new technology usually use ready-made samples that are scaled by applying similarity criteria. Such an approach makes it possible to reduce the number of parameters by which the design is optimized. The performance curves of vane pumps are determined by two dimensionless quantities: q (dimensionless flow rate) and r (an analogue of the Reynolds number). The similarity criteria began to be applied even when the shaft rotation frequency and fluid viscosity practically did not change during operation, and the influence of the dimensionless parameter r was weak. In fact, when designing pumps, only parameter q was used, although it was known that in this case the effect of frequency and viscosity on the characteristics of the pumps was described poorly, the approximation error was more than 30–50%. Currently, the operating conditions of the pumps have changed significantly. Using of a frequency-controlled pump drive has become commonplace. Increasingly, multiphase fluids of variable composition (oil products, gas-liquid mixtures, suspensions) are being pumped. Now in industry, the frequency of rotation of the shaft and the viscosity of the pumped liquid vary widely. It is necessary to generalize the similarity criterion of pumps in the case of taking into account both dimensionless quantities q and r. Our approach is based on the hypothesis that in the limit of high frequencies (large r), the influence of viscosity decreases, and the performance of the pump only becomes a function of the dimensionless flow rate q. This made it possible to record the dependencies of pump performance through the composition of functions of one variable. To test this hypothesis, experimental studies of the performance curves of the stages of three centrifugal pumps were carried out, in which both dimensionless values q and r were varied. It is shown that the error in the approximation of the performance curves of the stages by the proposed composition of functions of one variable does not exceed the measurement error.