ALBERT

Description: The observed nonlinear saturation of crossflow vortices in the DLR swept-plate transition experiment, followed by the onset of high-frequency signals, motivated us to compute nonlinear equilibrium solutions for this flow and investigate their instability to high-frequency disturbances. The equilibrium solutions are independent of receptivity, i.e. the way crossflow vortices are generated, and thus provide a unique characterization of the nonlinear flow prior to turbulence. Comparisons of these equilibrium solutions with experimental measurements exhibit strong similarities. Additional comparisons with results from the nonlinear parabolized stability equations (PSE) and spatial direct numerical simulations (DNS) reveal that the equilibrium solutions become unstable to steady, spatial oscillations with very long wavelengths following a bifurcation close to the leading edge. Such spatially oscillating solutions have been observed also in critical layer theory computations. The nature of the spatial behaviour is herein clarified and shown to be analogous to that encountered in temporal direct numerical simulations. We then employ Floquet theory to systematically study the dependence of the secondary, high-frequency instabilities on the saturation amplitude of the equilibrium solutions. With increasing amplitude, the most amplified instability mode can be clearly traced to spanwise inflectional shear layers that occur in the wake-like portions of the equilibrium solutions (Malik et al. 1994 call it 'mode I' instability). Both the frequency range and the eigenfunctions resemble recent experimental measurements of Kawakami et al. (1999). However, the lack of an explosive growth leads us to believe that additional self-sustaining processes are active at transition, including the possibility of an absolute instability of the high-frequency disturbances.

Description: Acoustic resonances of simple three-dimensional finite-length structures in an infinitely long cylindrical pipe are investigated numerically by solving an eigenvalue problem. To avoid unphysical reflections at the finite grid boundaries placed in the uniform cross-sections of the pipe, perfectly matched layer absorbing boundary conditions are applied in the form of the complex scaling method of atomic and molecular physics. Examples of the structures investigated are sound-hard spheres, cylinders, cavities and closed side branches. Several truly trapped modes with zero radiation loss are identified for frequencies below the first cutoff frequency of the pipe. Such trapped modes can be excited aerodynamically by coherent vortices if the frequency of the shed vortices is close to a resonant frequency. Furthermore, numerical evidence is presented for the existence of isolated embedded trapped modes for annular cavities above the first cutoff frequency and for closed side branches below the first cutoff frequency. As applications of engineering interest, the acoustic resonances are computed for a ball-type valve and around a simple model of a high-speed train in an infinitely long tunnel. © 2008 Cambridge University Press.

Description: An open system or open resonator is a domain of wave activity separated from the exterior by a partly open or partly transparent surface. Such open resonators lose energy to infinity through radiation. The numerical computation of the corresponding resonances is complicated by spurious reflections of the outgoing waves at the necessarily finite grid boundaries. These reflections can be reduced to extremely low levels by applying perfectly matched layer (PML) absorbing boundary conditions, which separate the discrete resonances from the continuous spectrum. Using a simple one-dimensional model problem, the influence of the various PML parameters is determined by a numerical error analysis. In addition to one-dimensional open resonators, two-dimensional open resonators as well as various resonating structures in waveguides are considered, and the resonant spectra and selected modes are evaluated. For the first time, leaky modes are computed for several resonating structures in a waveguide in addition to the trapped modes published in the literature. In applications, leaky mode resonances are often more important than trapped mode resonances. Gap tones, observed in a model problem of high-lift configurations, are identified as transversal resonant modes with the lowest radiation losses. © 2004 Cambridge University Press.

Description: Low- and high-frequency acoustic resonances are computed numerically via a high-order finite-element code for a generic two-dimensional high-lift configuration with a leading-edge slat. Zero mean flow is assumed, approximating the low-Mach-number situation at aircraft landing and approach. To avoid unphysical reflections at the boundaries of the truncated computational domain, perfectly matched layer absorbing boundary conditions are implemented in the form of the complex scaling method of atomic and molecular physics. It is shown that two types of resonance exist: resonances of surface waves which scale with the total airfoil length and longitudinal cavity-type resonances which scale with the slat cove length. Minima exist in the temporal decay rate which can be associated with the slat cove resonances and depend on the slat cove geometry. All resonances are damped owing to radiation losses. However, if coherent noise sources exist, as observed in low-Reynolds-number experiments, these sources can be enhanced acoustically by the above resonances if the source frequency is close to a resonant frequency. © Cambridge University Press 2007.

Description: In contrast to completely open systems, laterally confined domains can sustain localized, truly trapped modes with nominally zero radiation loss. These discrete resonant modes cannot be excited linearly by the continuous propagating duct modes due to symmetry constraints. If the symmetry of the geometry is broken the trapped modes become highly localized quasi-trapped modes which can interfere with the propagating duct modes. The resulting narrowband Fano resonances with resonance and antiresonance features are a generic phenomenon in all scattering problems with multiple resonant pathways. This paper deals with the classical scattering of acoustic waves by various obstacles such as hard-walled single and multiple circular cylinders or rectangular and wedge-like screens in a two-dimensional duct without mean flow. The transmission and reflection coefficients as well as the (complex) resonances are computed numerically by means of the finite-element method in conjunction with two different absorbing boundary conditions, namely the complex scaling method and the Hardy space method. The results exhibit the typical asymmetric Fano line shapes near the trapped-mode resonances if the symmetry of the geometry is broken. © 2010 Cambridge University Press.

Description: Abstract Revisiting the classical acoustics problem of rectangular side-branch cavities in a two-dimensional duct of infinite length, we use the finite-element method to numerically compute the acoustic resonances as well as the sound transmission and reflection for an incoming fundamental duct mode. To satisfy the requirement of outgoing waves in the far field, we use two different forms of absorbing boundary conditions, namely the complex scaling method and the Hardy space method. In general, the resonances are damped due to radiation losses, but there also exist various types of localized trapped modes with nominally zero radiation loss. The most common type of trapped mode is antisymmetric about the duct axis and becomes quasi-trapped with very low damping if the symmetry about the duct axis is broken. In this case a Fano resonance results, with resonance and antiresonance features and drastic changes in the sound transmission and reflection coefficients. Two other types of trapped modes, termed embedded trapped modes, result from the interaction of neighbouring modes or Fabry-Pérot interference in multi-cavity systems. These embedded trapped modes occur only for very particular geometry parameters and frequencies and become highly localized quasi-trapped modes as soon as the geometry is perturbed. We show that all three types of trapped modes are possible in duct-cavity systems and that embedded trapped modes continue to exist when a cavity is moved off centre. If several cavities interact, the single-cavity trapped mode splits into several trapped supermodes, which might be useful for the design of low-frequency acoustic filters. © 2012 Cambridge University Press.