Sensitivity analysis of the aeroacoustic response of turbomachinery blade rows

A method for computing the change or 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 for the nonlinear steady flow and grid equations with lower-upper (LU) matrix decomposition plus one forward and one back substitution used to solve the resulting matrix equations. Similarly, the unsteady small disturbance flow about the nonlinear mean flow is modeled by the linearized potential equation together with rapid distortion theory to account for vortical gusts. These linearized equations are discretized using finite elements and solved with a single LU decomposition. The sensitivities of the steady and unsteady flowfields to small changes in geometry are computed by perturbing the discretized equations about the nominal solutions. The resulting linear system of equations can be solved very efficiently because the LU factors of the resulting matrix equations are computed as part of the nominal steady and unsteady solution. Results are presented in this paper to show the accuracy and efficiency of the method, and the implications for aeroacoustic design of turbomachinery blades are discussed.

Duke Scholars

Author Kenneth C. Hall Thomas Lord Department of Mechanical Engineering and Materia ...