An efficient frequency-domain algorithm for wave scattering problems with application to jet noise

This paper presents a pseudo-time-step method to calculate a (vector) Green function for the adjoint linearised Euler equations as a scattering problem in the frequency domain, for use as a jet-noise propagation prediction tool. A method of selecting the acoustics-related solution in a truncated spatial domain while suppressing any possible shear-layer-type instability is presented. Numerical tests for 3-D axisymmetrical parallel mean flows against semi-analytical reference solutions indicate that the new iterative algorithm is capable of producing accurate solutions with modest computational requirements.

On a classical problem of acoustic wave scattering by a free vortex: Numerical modelling

The scattering of sound from a point source by a Rankine vortex is investigated numerically by solving the Euler equations with the novel high-resolution CABARET method. For several Mach numbers of the vortex, the time-average amplitudes of the scattered field obtained from the numerical modeling are compared with the theoretical scaling laws' predictions. Copyright © 2009 by Sergey Karabasov.

Energy scattering in weakly non-linear systems.

The Chinese Tam-Tam exhibits non-linear behavior in its vibro-acoustic response. The frequency content of the response during free, unforced vibration smoothly changes, with energy being progressively smeared out over a greater bandwidth with time. This is used as a motivating case for the general study of the phenomenon of energy cascading through weak nonlinearity. Numerical models based upon the Fermi-Pasta-Ulam system of non-linearly coupled oscillators, modified with the addition of damping, have been developed. These were used to study the response of ensembles of systems with randomized natural frequencies. Results from simulations will be presented here. For un-damped systems, individual ensemble members exhibit cyclical energy exchange between linear modes, but the ensemble average displays a steady state. For the ensemble response of damped systems, lightly damped modes can exhibit an effective damping which is higher than predicated by linear theory. The presence of a non-linearity provides a path for energy flow to other modes, increasing the apparent damping spectrum at some frequencies and reducing it at others. The target of this work is a model revealing the governing parameters of a generic system of this type and leading to predictions of the ensemble response.

Fluid-structure interaction with mean flow: Over-scattering and unstable resonance growth

It is known theoretically [1-3] that infinitely long fluid loaded plates in mean flow exhibit a range of unusual phenomena in the 'long time' limit. These include convective instability, absolute instability and negative energy waves which are destabilized by dissipation. However, structures are necessarily of finite length and may have discontinuities. Moreover, linear instability waves can only grow over a limited number of cycles before non-linear effects become dominant. We have undertaken an analytical and computational study to investigate the response of finite, discontinuous plates to ascertain if these unusual effects might be realized in practice. Analytically, we take a "wave scattering" [2,4] - as opposed to a "modal superposition" [5] - view of the fluttering plate problem. First, we solve for the scattering coefficients of localized plate discontinuities and identify a range of parameter space, well outside the convective instability regime, where over-scattering or amplified reflection/transmission occurs. These are scattering processes that draw energy from the mean flow into the plate. Next, we use the Wiener-Hopf technique to solve for the scattering coefficients from the leading and trailing edges of a baffled plate. Finally, we construct the response of a finite, baffled plate by a superposition of infinite plate propagating waves continuously scattering off the plate ends and solve for the unstable resonance frequencies and temporal growth rates for long plates. We present a comparison between our computational results and the infinite plate theory. In particular, the resonance response of a moderately sized plate is shown to be in excellent agreement with our long plate analytical predictions. Copyright © 2010 by ASME.