Nonlinear sound propagation in 2D curved ducts : a multimodal approach

A method for studying weakly nonlinear acoustic propagation in 2D ducts of general shape - including curvature and variable width - is presented. The method is based on a local modal decomposition of the pressure and velocity in the duct. A pair of nonlinear ODEs for the modal amplitudes of the pressure and velocity modes is derived. To overcome the inherent instability of these equations, a nonlinear admittance relation between the pressure and velocity modes is presented, introducing a novel `nonlinear admittance' term. Appropriate equations for the admittance are derived which are to be solved through the duct, with a radiation condition applied at the duct exit. The pressure and velocity are subsequently found by integrating an equation involving the admittance through the duct. The method is compared, both analytically and numerically, against published results and the importance of nonlinearity is demonstrated in ducts of complex geometry. Comparisons between ducts of differing geometry are also performed to illustrate the effect of geometry on nonlinear sound propagation. A new 'nonlinear reflectance' term is introduced, providing a more complete description of acoustic reflection that also takes into account the amplitude of the incident wave

Nonlinear acoustics in a viscothermal boundary layer over an acoustic lining

Sound within aircraft engines can be 120dB-160dB, pushing the validity of linearized governing equations. Moreover, some components of sound within a visco-thermal mean flow boundary layer over an acoustic lining may be amplified by a factor of ~100 (~40dB) in a typical aircraft engine compared with the sound outside the boundary layer, which may be expected to trigger nonlinear effects within the boundary layer. This is in addition to the well-known nonlinear effects within the holes of the perforated lining facing sheet. This paper presents a mathematical investigation into the effects of weak nonlinearity on the acoustics within a thin parallel mean flow boundary layer in flow over an acoustic lining in a cylindrical duct. (This is the first investigation of nonlinear acoustics in a boundary layer flow over a non-rigid surface, to our knowledge.) The analysis combines the effects of sheared mean flow, viscosity, and nonlinearity into an effective impedance boundary condition. In certain cases, a surprisingly large acoustic streaming effect is found that escapes the mean flow boundary layer and pervades well out into the interior of the duct

The impedance boundary condition for acoustics in swirling ducted flow

The acoustics of a straight annular lined duct containing a swirling mean flow is considered. The classical Ingard–Myers impedance boundary condition is shown not to be correct for swirling flow. By considering behaviour within the thin boundary layers at the duct walls, the correct impedance boundary condition for an infinitely thin boundary layer with swirl is derived, which reduces to the Ingard–Myers condition when the swirl is set to zero. The correct boundary condition contains a spring-like term due to centrifugal acceleration at the walls, and consequently has a different sign at the inner (hub) and outer (tip) walls. Examples are given for mean flows relevant to the interstage region of aeroengines. Surface waves in swirling flows are also considered, and are shown to obey a more complicated dispersion relation than for non-swirling flows. The stability of the surface waves is also investigated, and as in the non-swirling case, one unstable surface wave per wall is found

Meta-analysis of curvature trends in asymmetric rolling

This paper investigates curvature in asymmetric rolling by combining existing results from eight experimental and nine numerical previous studies. These previous results are digitised and a linear regression model fitted which explains 65% of the variance in these data. It is found that conclusions from several previous studies are contradicted by other previous studies, and that there is no consensus on the fundamental mechanism of curvature generation in rolling. Results from an existing curvature-predicting analytic slab model are also compared with the previous results, and the agreement is shown to be adequate at best. Future work is clearly needed to enable accurate curvature prediction, and it is hoped that the evidence collected here will inform future investigations and models to ensure the relevant range of parameters are considered