| An efficient numerical model is developed for solving the interaction of high frequency, unsteady, three-dimensional incident disturbances with an annular cascade of loaded blades in swirling flows. The numerical scheme is made efficient by split ting the velocity field into nearly-acoustic and nearly-convected vortical components. This leads to a coupled set of equations, which can be solved iteratively. Numerical results show that the number of iterations between the two sets of equations decreases as the frequency increases as predicted by asymptotic analysis.; The nearly-convected component of the velocity is analyzed using an initial value analysis which calculates its evolution in swirling flows. The pressure associated with the nearly-convected disturbance is small and can be neglected locally, however, its effects are significant over large propagation distances. Viscosity and entropy are included in the model and results show significant effects for disturbances with large azimuthal mode number and propagation distance.; Non-reflecting boundary conditions are developed to avoid wave reflection inside the computational domain. The method is based on the expansion of the downstream and upstream acoustic eigenmodes. Because the mean flow is non-uniform, a Gram-Schmidt procedure is used to express the acoustic pressure coefficients.; Unsteady aerodynamic and acoustic scattering problems are validated through extensive comparisons with known solutions in the narrow annulus and full annulus cases. Computations indicate that full three-dimensional calculations are essential at high frequency. Steady blade loading increases the acoustic pressure compared to the unloaded blades in swirling flows. Furthermore, spanwise blade loading and blade twist excite higher order acoustic modes and may contribute significantly to the sound level.; Passive noise reduction techniques are explored by increasing rotor/stator gap, applying blade lean and sweep and mean flow acceleration. Results indicate that blade lean and sweep are effective means for noise reduction, however, their effectiveness depends on the rotor/stator blade count, the incident Mach number and the reduced frequency. The effect of the rotor/stator gap is examined. Results indicate that significant reduction in unsteady lift and sound pressure is obtained by increasing the gap. This reduction is due to the modification of the blade upwash by the swirling flow and not by viscous forces as commonly thought. |
