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A linearized unsteady aerodynamic analysis for transonic cascades

A linearized potential-flow analysis is presented for predicting the unsteady airloads produced by the vibrations of turbomachinery blades operating at transonic Mach numbers. The unsteady aerodynamic model includes the effects of blade geometry, non-zero mean-pressure variation across the blade row, high-frequency blade motion, and shock motion within the framework of a linearized frequency-domain formulation. The unsteady equations are solved using an implicit least-squares finite-difference approximation which is applicable on arbitrary grids. A numerical solution for the entire unsteady flow field is determined by matching a solution determined on a rectilinear-type cascade mesh, which covers an extended blade-passage region, to a solution determined on a detailed polar-type local mesh, which covers and extends well beyond the supersonic region(s) adjacent to a blade surface. Results are presented for cascades of double-circular-arc and flat-plate blades to demonstrate the unsteady analysis and to partially illustrate the effects of blade geometry, inlet Mach number, blade-vibration frequency and shock motion on unsteady response.