A study of supersonic flow past vibrating shells and cascades

Abstract

Supersonic flow past oscillating cylindrical shells and oscillating flat-plate cascades is analyzed using linearized characteristics methods. Pressure distributions and generalized aerodynamic forces are computed for arbitrary radius to length ratios, axial and circumferential wave numbers, Mach numbers, and reduced frequencies. Excellent agreement is obtained with a previous solution of the complete unsteady linearized potential equation by Dowell and Widnall using Laplace transform techniques. Also, pressure distributions are computed for flat-plate cascades with subsonic leading edge locus for arbitrary solidity, stagger angle, frequency, and interblade phase angle. For comparison, a two-blade solution is developed using the method of singularities. Good agreement is obtained for this special case.