An investigation of unsteady disturbances in swirling flows in an annulus

The acoustic wave propagation due to a swirling flow within a coannular duct is investigated where the swirling flow is assumed to be a combination of both a free and forced vortex. The acoustic frequency, based on the swirling velocity function, is computed as the solution of a characteristic value problem using the fourth-order Runge-Kutta method. A small swirl velocity approximation is also derived, to generate starting values for the numerical solution, and proves to be particularly accurate for estimating the effect of the free vortex on the acoustic frequency.

In general, the acoustic frequency increases as the magnitude of the swirling flow, moving opposite to the acoustic waves, is increased. As the ratio of outer to inner radius is increased the effect of the free vortex diminishes while the effect of the forced vortex remains essentially constant. Finally, the effect of the circumferential wave number is that of a multiplicative constant over the base value when that wave number equals one.