Preliminary Assessment of Geometric Variability Effects Through a Viscous Through-Flow Model Applied to Modern Axial-Flow Compressor Blades

An important question for turbomachine designers is how to deal with blade and flowpath geometric variabilities stemming from the manufacturing process or erosion during the component lifetime. The challenge consists of identifying where stringent manufacturing tolerances are absolutely necessary and where looser tolerances can be used as some geometric variations have little or no effects on performance while others do have a significant impact. Because numerical simulations based on Reynolds-averaged Navier–Stokes (RANS) equations are computationally expensive for a stochastic analysis, an alternative approach is proposed in which these simulations are complemented by cheaper through-flow simulations to provide a finer exploration of the range of variations, in particular in the context of robust design. The overall goal of the present study is to evaluate the adequacy of a viscous time-marching through-flow solver to predict geometric variability effects on compressor performance and, in particular, to capture the main trends. Although the computational efficiency of such a low-fidelity solver is useful for parametric studies, it is known that the involved assumptions and approximations associated with the through-flow (TF) approach introduce errors in the performance prediction. Thus, we first evaluate the model with respect to its underlying assumptions and correlations. To accomplish this, TF simulations are compared to RANS simulations applied to a modern low-pressure compressor designed by Safran Aero Boosters. On the one hand, the TF simulations are fed with the exact radial distribution of the correlation parameters using RANS input data in order to isolate the modeling error from correlation empiricism. Moreover, in the context of multi-fidelity optimization, such distributions can be predicted using the more detailed RANS simulations that are performed on selected operating points. On the other hand, correlations from the literature are assessed and improved. It is shown that the solver provides realistic predictions of performance but is highly sensitive to the underlying correlations. Then, two modeling aspects linked to the blade leading edge, namely incidence correction and camber line computation, are discussed. As geometric variability precisely at the blade leading edge has a significant impact on the performance, we assess how these two aspects influence the variability propagation in this region. Moreover, we propose a strategy to mitigate these model uncertainties, and geometric variabilities are introduced at the blade leading edge in order to quantify the resulting variation in performance. Finally, within the scope of this preliminary study, perturbations of the three-dimensional position of undeformed stator blades and deformations of the hub and shroud contours are introduced one factor at a time per simulation. Their range is defined based on the tolerance limits typically imposed in the industry and on observed manufacturing variability. It is found that the through-flow model broadly provides realistic predictions of performance variations resulting from the imposed geometric variations. These results are a promising first step towards the use of the through-flow modeling approach for geometric uncertainty quantification.