Leakage Uncertainties in Compressors: The Case of Rotor 37

Abstract

This paper revisits an old problem of validating computational fluid dynamics simulations with experiments in turbomachinery. The case considered here is NASA rotor 37. Prior computational fluid dynamics studies of this blade have been unable to predict a total pressure deficit at the hub as observed in the experiments. A possible explanation for this discrepancy is a small hub leakage flow emanating fore of the leading edge, between the forward stationary center body and the rotating disk. In this work, a large-scale high-fidelity uncertainty quantification study is carried out to investigate whether this indeed was the case. Computations are carried out on a 4.5-million-cell rotor 37 mesh with a small cavity fore of the leading edge. This cavity has an inlet with three boundary conditions: all assumed to be uncertain. A nonintrusive, orthogonal polynomial-based technique using sparse grids is used to propagate these three uncertainties, namely, leakage mass flow, leakage whirl velocity, and radial flow angle. A total of 158 sparse-grid-based design-of-experiment computations are carried out at two flow conditions. The results of the uncertainty quantification study show that a small amount of leakage flow can account for the hub pressure deficit at both on- and off-design conditions. For the uncertainty supports selected, the total pressure that best matched experiment was found to lie between the second and third standard deviations over the assumed uncertainties.