CALCULATION OF 3-DIMENSIONAL UNSTEADY FLOWS IN TURBOMACHINERY USING THE LINEARIZED HARMONIC EULER EQUATIONS

An efficient three-dimensional Euler analysis of unsteady flows in tur bomachinery is presented. The unsteady flow is modeled as the sum of a steady or mean flow field plus a harmonically varying small perturbat ion flow. The linearized Euler equations, which describe the small per turbation unsteady flow, are found to be linear, variable coefficient differential equations whose coefficients depend on the mean flow. A p seudo-time time-marching finite-volume Lax- Wendroff scheme is used to discretize and solve the linearized equations for the unknown perturb ation flow quantities. Local time stepping and multiple-grid accelerat ion techniques are used to speed convergence. For unsteady flow proble ms involving blade motion, a harmonically deforming computational grid , which conforms to the motion of the vibrating blades, is used to eli minate large error-producing extrapolation terms that would otherwise appear in the airfoil surface boundary conditions and in the evaluatio n of the unsteady surface pressure. Results are presented for both lin ear and annular cascade geometries, and for the latter, both rotating and nonrotating blade rows.