Abstract

Numerical experiments were performed to assess the effect of numerical discretization error on the convergence rate of polynomial chaos (PC) approximations for a transonic axial compressor stage. A random variable with a uniform distribution and expected value of one was introduced into the expression for turbulent viscosity of the k-ω SST turbulence model. Model uncertainty was quantified from the expected value and standard deviation estimates obtained via univariate non-intrusive polynomial chaos. Spectral projection and point collocation were both used and their results were compared. The effect of discretization error on convergence of the PC approximation was investigated using a grid refinement study with four grids. The PC expansion was computed for each grid while maintaining the same boundary conditions, basis functions, model evaluations, random variable distribution, and polynomial order. The quantities of interest (QOIs) were total–to–total pressure ratio, total–to–total temperature, and adiabatic efficiency. The grid resolution was found to have an influence on resulting surrogate models and the estimates of expected value and standard deviation for all QOIs. However, the estimates converged towards final values as the mesh was refined. Point collocation provided different estimates from spectral projection and the difference was also found to depend on the mesh size.

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