Optimal Growth of Linear Perturbations in Low Pressure Turbine Flows

This paper presents a numerical algorithm for the linearized flow initial value problem involving complex geometries where analytical solution is impossible. The method centres around the calculation of an eigenvalue problem involving the linearised flow and its spatial adjoint, and yields the flow perturbations that grow the most in a prescribed time, the magnitude of that growth and the perturbations after the growth has occurred. Previous work has shown that classical stability analysis of flow past a low-pressure turbine blade gives only stable eigenvalues, which cannot explain transition to turbulence in this flow. The inital value problem for this fan blade is presented and demonstrates significant perturbation growth, indicating that this growth may be the facilitator for transition in this case.