On the diffraction of acoustic waves by a quarter-plane

This paper follows the work of A.V. Shanin on diffraction by an ideal quarter-plane. Shanin's theory, based on embedding formulae, the acoustic uniqueness theorem and spherical edge Green's functions, leads to three modified Smyshlyaev formulae, which partially solve the far-field problem of scattering of an incident plane wave by a quarter-plane in the Dirichlet case. In this paper, we present similar formulae in the Neumann case, and describe a numerical method allowing a fast computation of the diffraction coefficient using Shanin's third modified Smyshlyaev formula. The method requires knowledge of the eigenvalues of the Laplace-Beltrami operator on the unit sphere with a cut, and we also describe a way of computing these eigenvalues. Numerical results are given for different directions of incident plane wave in the Dirichlet and the Neumann cases, emphasising the superiority of the third modified Smyshlyaev formula over the other two. © 2011 Elsevier B.V.

Guided propagation of surface acoustic waves and piezoelectric field enhancement in ZnO/GaAs systems

The characteristics and dispersion of the distinct surface acoustic waves (SAWs) propagating in ZnO/GaAs heterostructures have been studied experimentally and theoretically. Besides the Rayleigh mode, strong Sezawa modes, which propagate confined in the overlayer, arise due to the smaller sound velocity in ZnO than in the substrate. The design parameters of the structure providing the strongest piezoelectric field at a given depth within the layered system for the different modes have been determined. The piezoelectric field of the Rayleigh mode is shown to be more than 10 times stronger at the interface region of the tailored ZnO/GaAs structure than at the surface region of the bulk GaAs, whereas the same comparison for the first Sezawa mode yields a factor of 2. This enhancement, together with the capacity of selecting waves with different piezoelectric and strain field depth profiles, will facilitate the development of SAW-modulated optoelectronic applications in GaAs-based systems. © 2011 American Institute of Physics.

Measurements of triggering and transient growth in a model lean-premixed gas turbine combustor

Instability triggering and transient growth of thermoacoustic oscillations were experimentally investigated in combination with linear/nonlinear flame transfer function (FTF) methodology in a model lean-premixed gas turbine combustor operated with CH 4 and air at atmospheric pressure. A fully premixed flame with 10kW thermal power and an equivalence ratio of 0.60 was chosen for detailed characterization of the nonlinear transient behaviors. Flame transfer functions were experimentally determined by simultaneous measurements of inlet velocity fluctuations and heat release rate oscillations using a constant temperature anemometer and OH */CH * chemiluminescence emissions, respectively. The phase-resolved variation of the local flame structure at a limit cycle was measured by planar laser-induced fluorescence of OH. Simultaneous measurements of inlet velocity, OH */CH * emission, and acoustic pressure were performed to investigate the temporal evolution of the system from a stable to a limit cycle operation. This measurement allows us to describe an unsteady instability triggering event in terms of several distinct stages: (i) initiation of a small perturbation, (ii) exponential amplification, (iii) saturation, (iv) nonlinear evolution of the perturbations towards a new unstable periodic state, (v) quasi-steady low-amplitude periodic oscillation, and (vi) fully-developed high-amplitude limit cycle oscillation. Phase-plane portraits of instantaneous inlet velocity and heat release rate clearly show the presence of two different attractors. Depending on its initial position in phase space at infinitesimally small amplitude, the system evolves towards either a high-amplitude oscillatory state or a low-amplitude oscillatory state. This transient phenomenon was analyzed using frequency- and amplitude-dependent damping mechanisms, and compared to subcritical and supercritical bifurcation theories. The results presented in this paper experimentally demonstrate the hypothesis proposed by Preetham et al. based on analytical and computational solutions of the nonlinear G-equation [J. Propul. Power 24 (2008) 1390-1402]. Good quantitative agreement was obtained between measurements and predictions in terms of the conditions for the onset of triggering and the amplitude of triggered combustion instabilities. © 2011 The Combustion Institute.