Comparison of Two Methods for Sensitivity Analysis of Compressor Blades

Abstract

This paper will compare two approaches of sensitivity analysis, namely (i) the adjoint method which is used to obtain an initial estimate of the geometric sensitivity of the gas-washed surfaces to aerodynamic quantities of interest and (ii) a Monte Carlo-type simulation with an efficient sampling strategy. For both approaches the geometry is parameterized using a modified NACA parameterization. First the sensitivity of those parameters is calculated using the linear (first order) adjoint model. Since the effort of the adjoint CFD solution is comparable to that of the initial flow CFD solution and the sensitivity calculation is simply a postprocessing step, this approach yields fast results. However, it relies on a linear model which may not be adequate to describe the relationship between relevant aerodynamic quantities and actual geometric shape variations for the derived amplitudes of shape variations. In order to better capture nonlinear and interaction effects, secondly a Monte Carlo-type simulation with an efficient sampling strategy is used to carry out the sensitivity analysis. The sensitivities are expressed by means of the Coefficient of Importance, which is calculated based on modified polynomial regression and therefore able to describe relationships of higher order. The methods are applied to a typical high pressure compressor stage. The impact of a variable rotor geometry is calculated by 3D CFD simulations using a steady RANS model. The geometric variability of the rotor is based on the analysis of a set of 400 blades which have been measured using high-precision 3D optical measurement techniques.