Linearized unsteady aerodynamic analysis of supersonic cascades with subsonic axial velocity
Abstract
An analysis was developed that is capable of predicting the linearized unsteady aerodynamics of real blade cascades operating with supersonic inflow and/or outflow velocities, but with subsonic axial velocity. The numerical prediction of the unsteady flow in cascades in which the inlet and/or exit flow is supersonic presents several serious difficulties. If the mean flow has a subsonic axial velocity, then the acoustic response far upstream and/or downstream of the cascade is discontinuous. In addition, and perhaps more troublesome, oblique shocks or Mach waves in the cascade passage are reflected by adjacent blades. The flow discontinuities associated with these phenomena make accurate numerical prediction of unsteady aerodynamic response difficult. The first difficulty was addressed by matching the numerical near-field solution to an analytic far-field solution for the velocity potential. The velocity potential is continuous, but has discontinuous first derivatives, leading to a spatial Fourier spectrum that decays like 1/N$\sp2,$ whereas the discontinuous pressure has a Fourier spectrum that decays like 1/N. The second difficulty was addressed by using a variable amount of upwind differencing to control the amount of discontinuity smearing, i.e. numerical smoothing. Results for a flat plate cascade, where comparison with analytic solutions are possible, suggest that although the discontinuities are smeared and the high frequency content of the acoustic response is lost, reasonable predictions for the blade unsteady aerodynamic response are possible. The thickness of the numerically smeared Mach waves decreases slowly as the mesh is refined, as expected. However, the aerodynamic quantities of interest converge more quickly. Real blade and blade loading effects were investigated by comparing the unsteady aerodynamic responses of double circular arc airfoils, operating as a lightly loaded compressor cascade, with those of flat plate cascades. The dominant effect of real blade geometry and blade loading on the unsteady aerodynamic response for supersonic flows is the shock impulse due to the unsteady motion of the finite strength mean shock. This additional shock impulse can be stabilizing or destabilizing.
Degree
Ph.D.
Advisors
Fleeter, Purdue University.
Subject Area
Mechanical engineering|Aerospace materials
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