Uncertainty analysis of global and local performance impact of inflow and geometric uncertainties using sparse grid-based non-intrusive polynomial chaos

Abstract

Flow variations at the inlet boundary due to the compressor operational condition changes and geometric variations of the realistic compressor blades due to the manufacturing variability cannot be absolutely avoided, the global and local performance impact of which requires to be considered in the mechanism study of performance change and the aerodynamic shape design. In this paper, a method to analyze the simultaneous impact of the inflow Mach number, inlet incidence and geometric uncertainties was proposed. To make the uncertainty modeling of geometric variations faster and closer to engineering practice, a parametric mathematical model based on scanning points on the blade was introduced to describing the profile and torsion errors in the method specially. Meanwhile, a sparse grid based-Non-Intrusive Polynomial Chaos (NIPC) was used for uncertainty quantification and uncertainty sensitivity analysis to alleviate the computational burden. Then, the method was combined with a loss source calculation method to estimate the global and local aerodynamic loss changes of a controlled diffusion compressor blade in a reference flow state of high inflow Mach number and large positive incidence, and the response performance of sparse grid-based NIPC was verified. The results show that inlet incidence and torsion error have a significance uncertainty effect on the boundary-layer separation above the suction surface, which is main reason for the fluctuation of global aerodynamic loss. The uncertainty effect of profile error on the boundary-layer separation is relatively weak, but profile error could have a certain uncertainty effect on the leading edge separation. The boundary-layer separation is insensitive to Inflow Mach number. Furthermore, a stochastic aerodynamic analysis in different reference inflow states was investigated, which reveals some laws that the uncertainty of the aerodynamic losses and the sensitivity of the inflow and geometric uncertainties change with reference inflow states.

A data-driven polynomial chaos method for uncertainty quantification of a subsonic compressor cascade with stagger angle errors

“…where μ denotes the raw moment matrix of discrete measurement data. The constant terms h can be determined by solving equation (7), and then the polynomial basis Ψ (k) (ξ) can be also determined. The polynomial chaos coefficient u i in equation ( 1) can be determined by the Galerkin projection method.…”

“…Firstly, given the discrete measurement data and the order p of polynomial chaos, the raw moment matrix (μ) can be calculated. Then the constant term h of the orthogonal polynomial basis function Ψ (ξ) can be determined by solving equation (7). The polynomial chaos coefficients u i can be calculated by equation (8).…”

“…With the rapid growth of computing capabilities, uncertainty quantification (UQ) of turbomachinery blades has attracted more and more attention from scholars. 2,[4][5][6][7][8] The goal of UQ is to quantitatively evaluate the effects of random inputs on system outputs. Through UQ analysis, the statistical results (e.g., mean value and standard deviation) of a certain performance parameter can be obtained.…”

Mechanism analysis and uncertainty quantification of blade thickness deviation on rotor performance

“…In the past decade, with the ability to quantitatively study the influence of different factors, Polynomial chaos expansions (PCE) method has been widely used in CFD uncertainty analysis. [13][14][15][16][17] Polynomial chaos expansions method is divided into Intrusive polynomial chaos (IPC) method and Non-Intrusive polynomial chaotic (NIPC) method. IPC method needs to modify the deterministic solver.…”