An Assessment of Non-Intrusive Probabilistic Methods for Turbomachinery Problems

The ability to quantify the impact of uncertainty on performance is an important facet of engineering design. Computational Fluid Dynamics (CFD) studies during the design cycle typically utilize estimates of boundary conditions, geometry and model constants, all of which have uncertainty that could lead to variations in the estimated performance of the design. Traditionally, engineering environments have relied on Monte-Carlo (MC) simulations to obtain probabilistic estimates. But MC methods have poor convergence rate leading to prohibitive computational requirements when used in conjunction with medium to high fidelity computational tools. In this study, we will use an alternate probabilistic approach. We assume that the uncertainties in our computational system can be modeled as random variables with known/prescribed distributions, use CFD solvers to estimate the performance measures and then use a psuedo-spectral probabilistic collocation technique to determine regression/interpolation fits. The psuedo-spectral discrete expansion uses the orthogonal polynomials from the Askey-Wiener basis and finds the coefficients of the expansion [1]. We will restrict our attention to problems with one random variable and hence can without ambiguity choose the Gauss quadratures as the optimal choice to obtain statistical data (mean, variance, moments etc.) of the performance measures. The computational frame-work will be first validated against Monte-Carlo simulations to assess convergence of pdfs. It will then be used to assess the variability in compressor blade efficiency and turbine vane loss due to uncertainty in inflow conditions. The results will be used to answer the following questions. Do we need new probabilistic algorithms to quantify the impact of uncertainty? What is the optimal basis for standard performance metrics in turbomachinery? What are the computational and accuracy requirements of this probabilistic approach? Are there alternate (more efficient) techniques? We believe that the answers to the above questions will provide a quantitative basis to assess the usefulness of non-intrusive (and possibly intrusive) probabilistic methods to analyze variability in engineering designs.