Vibration and sound generation in a cascade of flat plates in subsonic flow

Abstract

The report gives particulars of a method of calculation, which has been programmed for a digital computer, for linearized two-dimensional subsonic unsteady flow through a cascade of flat plates operating at zero mean incidence. Inputs to the calculation are motion of the blades due to either bending or torsional vibration, wakes from moving obstructions upstream of the cascade, and incoming acoustic waves. For each of these inputs the output gives the force and moment on the blades, the wakes shed from the trailing edges, and the outgoing acoustic waves. The program therefore provides all the information necessary for calculation of forced and self-excited vibration of the blades, and for the generation, transmission, and reflection of acoustic waves by a cascade. Two kinds of acoustic resonance are found, one corresponding to resonance of an annular duct without blades, and the other being an acoustic resonance in the passages between the blades. Results are presented which illustrate the generation of acoustic waves by wakes. Results on torsional flutter indicate that compressibility has a very important effect• Whereas at low Mach number the worst position for the torsional axis is at about 75 per cent chord, as the Mach number is increased this position moves forward to the leading edge.