WALL-BOUNDED BLADE-TIP VORTEX INTERACTION NOISE

An analytical treatment is given of the canonical problem of the gener ation of sound when a locally rectilinear vortex is drawn through the clearance gap between a wall and the square tip of a rigid blade at lo w Mach number. The mean flow in the neighborhood of the blade tip is a ssumed to be locally two-dimensional, and is modelled by free streamli ne potential flow theory, according to which the flow into the gap on the pressure side emerges as a wall jet on the suction side. The addit ional vorticity shed from the tip (in accordance with the unsteady Kut ta condition) during the passage of the vortex is assumed to convect a t constant speed along the free streamline boundary of the jet. Sound is generated by a dipole source, the magnitude and orientation of whic h are determined by the unsteady lift experienced by the blade. We cal culate the separate contributions to the radiation (i.e., to the dipol e strength) from the vortex and the shed vorticity. The sound is gener ated while the vortex is within a distance from the blade tip comparab le to the clearance, and has wavelength which is order 1/M larger, whe re M is the characteristic Mach number of the flow. The conclusions of this analysis are supported by an alternative, simplified treatment i n which the vortex motion through the gap is assumed to be steady and the shed vorticity convects at a fixed distance from the duct wall rat her than along the free streamline. (C) 1997 Academic Press Limited.