Assessing Turbomachinery Performance Sensitivity to Boundary Conditions Using Control Theory

Abstract

The adjoint method is extended to assess the sensitivity of turbomachinery performance with respect to inlet and exit boundary conditions. The derivation of the adjoint and sensitivity equations are briefly derived in general form, such that they can be applied to any set of flow-governing equations. In this paper, the Reynolds-averaged Navier–Stokes equations have been used, where the turbulence model has been selected. A compressor rotor blade test case is studied for verification and demonstration of the methodology. The adjoint-based sensitivities are verified using finite differences. The sensitivities of efficiency and pressure ratio with respect to the boundary condition parameters prescribed at each computational grid node at the inlet and exit faces of the blade passage are illustrated in the form of contour plots. Circumferentially averaged values and sensitivities demonstrate that fuller, more uniform profiles lead to improved performance, in line with basic thermodynamic principles. Two examples of modifying either inlet or exit boundary profiles, according to the sensitivity data obtained, show that performance tuning can be achieved. The sensitivity assessment approach presented is shown to be accurate and extremely efficient, while providing the designer with valuable information and insights to achieve a robust design.