Some allied problems related to unsteady flow

In the first part of this investigation, an analysis is presented to determine the unsteady flow field produced by a harmonically oscillating airfoil which has the contour of a parabolic arc placed in a supersonic free stream. The analysis is based on the assumptions of an inviscid, two-dimensional flow field and accounts for the effect of airfoil thickness in the far field unsteady signals. By an approximation through the small perturbation method, the solution is reduced to the form of an integral equation which has been solved numerically. It is shown that, although the airfoil shape displays a negligible effect in the near field, it introduces s a non-negligible change to both the amplitudes and phases of the unsteady flow signal in the far field which differed from the results of the linear theory; the present analysis is a refined work recently published by Kurosaka.

In the second part, the acoustic wave propagation within. the cylindrical co-annular duct, where both the circumferentially swirling and axially convective flow are present, is also investigated. In predicting the acoustic frequency in terms of free vortex motion and axial flow, the characteristic value problem is solved using the fourth-order Runge-Kutta method.

To the investigator's knowledge, this is the first attempt to evaluate accurately the acoustic frequency as a function of swirl flow and radius ratio. The numerical results reveal that the frequency of unsteady disturbance increases with the swirl, but as the ratio of the outer and inner radius increases, the frequency becomes insensitive to the variations of the swirl.