Sensitivity analysis of the aeroacoustic response of turbomachinery blade rows
A method for computing the sensitivity of the aeroacoustic response of a cascade to small changes in airfoil and cascade geometry is presented. The steady flow is modeled by the full potential equation, which is discretized using a variational finite element technique. A streamline computational grid is generated as part of the steady solution. Newton iteration is used to solve the nonlinear steady flow and grid equations with LU decomposition used at each iteration to factor the resulting matrix equations. The unsteady small disturbance flow is modeled by the linearized potential equation together with rapid distortion theory to account for vortical gusts. These equations are discretized using finite elements and solved with a single LU decomposition. The sensitivities of the steady and unsteady flow fields to small changes in geometry are computed by perturbing the discretized equations about the nominal solution. The resulting linear system of equations can be solved very efficiently since the LU factors of the matrices have already been computed as part of the nominal steady and unsteady solution. Results are presented to show the accuracy and efficiency of the method, and the implications for aeroacoustic design of turbomachinery blades are discussed.
