Geometrical uncertainty in turbomachinery: Tip gap and fillet radius

Abstract

In turbomachinery, the prediction of component life is crucial. It has been found that the variability of gaps, fillets and small geometries, due to manufacturing process and in service operation, can be higher than expected. This has direct consequences on both component life and efficiency. The question arising is how to take into account the aleatory distribution due to manufacturing uncertainty during the design phase. The use of state of the art Computational Fluid Dynamics allows considering the uncertainties in the estimation of performance parameters. Uncertainty is treated including the statistical distribution of the variability in the geometrical models. In this work the methodology for the analysis of the impact of geometrical variations on components life and machine reliability is presented. A representative high pressure stage is used as a reference and fillet sizes and gaps are modified in order to generate the response surface to geometrical uncertainty. For that machine, the nominal rotor tip gap G 0 is 1.5% of the span. A preliminary analysis has been performed considering a value for the fillet radius r/ G 0 = 50%, to underline the high impact of geometrical variations on the flow field. Then, five fillet radii at the rotor tip and three tip gaps have been studied ( r/ G 0 = 0.0, 0.03, 0.075, 0.15, 0.3 and G/ G 0 = 1, 1.5, 2). A two dimensional Gaussian distribution for the fillet radius and tip gap is arbitrarily assumed. Starting from this distribution the probabilistic functions of corresponding mass-flow through the rotor gap and the heat loading of rotor tip are obtained. The overall variation of mass-flow can be more than 60% and the heat loading is modified by 15% if compared to nominal conditions. Moreover this work shows that by including the mean value without the probability distribution the discrepancy is about 6% for mass-flow and 7% of heat loading.