Experimental Investigations on Leakages in Positive Displacement Machines

The clearance gaps in positive displacement machines such as compressors, pumps, expanders, and turbines are critical for their performance and reliability. The leakage flow through these clearances influences the volumetric and adiabatic efficiencies of the machines. The extent of the leakage flow depends on the size and shape of clearance paths and pressure differences across these paths. Usually, the mass flow through the gaps is estimated using the isentropic nozzle equation with the flow coefficients applied to correct for the real flow conditions. However, the flow coefficients applied generally do not take into account the shape and size of these leakage paths. For that reason, a proper understanding of the relationship between flow coefficients and shape parameters is crucial for an accurate prediction of leakage flows. The present study investigates the influence of the various dimensionless parameters such as Reynolds number, Mach number, and pressure ratio on the flow coefficients for circular and rectangular clearance shapes. The flow coefficients are determined by comparing the experimental values obtained in an experimental test rig and the flow rates obtained from the isentropic nozzle equation. It is observed that in the case of circular clearances, the mean deviation of the experimental leakage results (in comparison to the analytical results using isotropic nozzle equations) is +9.1%, which is significantly lower than the mean deviation (+20.5%) in the case of rectangular clearance leakages. The study indicates that the isentropic nozzle equation method is more suitable for predicting the leakages through the circular clearances and needs modifications for consideration of the rectangular clearances. Using regression analysis, empirical correlations are developed to predict the flow coefficient in terms of Reynolds number, Mach number, pressure ratio, aspect ratio, and β ratio, which are found to match within ±6.4 percent of the numerical results for the rectangular clearance and within the range of -3.6 percent to +5.1 percent of the numerical result for the circular clearance. The empirical relationships presented in this study can be extended to evaluate the flow coefficients in a positive displacement machine.