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Register a new userTraveling and standing thermoacoustic waves in solid media
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The most attractive application of fluid-based thermoacoustic (TA) energy conversion involves traveling wave devices due to their low onset temperature ratios and high growth rates. Recently, theoretical and numerical studies have shown that thermoacoustic effects can exist also in solids. However, these initial studies only focus on standing waves. This paper presents a numerical study investigating the existence of self-sustained thermoelastic oscillations associated with traveling wave modes in a looped solid rod under the effect of a localized thermal gradient. Configurations having different ratios of the rod radius $R$ to the thermal penetration depth $delta_k$ were explored and the traveling wave component (TWC) was found to become dominant as $R$ approaches $delta_k$. The growth-rate-to-frequency ratio of the traveling TA wave is found to be significantly larger than that of the standing wave counterpart for the same wavelength. The perturbation energy budgets are analytically formulated and closed, shedding light onto the energy conversion processes of solid-state thermoacoustic (SSTA) engines and highlighting differences with fluids. Efficiency is also quantified based on the thermoacoustic production and dissipation rates evaluated from the energy budgets.
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Continuing a line of investigation initiated in [11] exploring the connections between Jost and Evans functions and (modified) Fredholm determinants of Birman-Schwinger type integral operators, we here examine the stability index, or sign of the first nonvanishing derivative at frequency zero of the characteristic determinant, an object that has found considerable use in the study by Evans function techniques of stability of standing and traveling wave solutions of partial differential equations (PDE) in one dimension. This leads us to the derivation of general perturbation expansions for analytically-varying modified Fredholm determinants of abstract operators. Our main conclusion, similarly in the analysis of the determinant itself, is that the derivative of the characteristic Fredholm determinant may be efficiently computed from first principles for integral operators with semi-separable integral kernels, which include in particular the general one-dimensional case, and for sums thereof, which latter possibility appears to offer applications in the multi-dimensional case. A second main result is to show that the multi-dimensional characteristic Fredholm determinant is the renormalized limit of a sequence of Evans functions defined in [23] on successive Galerkin subspaces, giving a natural extension of the one-dimensional results of [11] and answering a question of [27] whether this sequence might possibly converge (in general, no, but with renormalization, yes). Convergence is useful in practice for numerical error control and acceleration.
When waves impinge on a disordered material they are back-scattered and form a highly complex interference pattern. Suppressing any such distortions in the free propagation of a wave is a challenging task with many applications in a number of different disciplines. In a recent theoretical proposal, it was pointed out that both perfect transmission through disorder as well as a complete suppression of any variation in a wave intensity can be achieved by adding a continuous gain-loss distribution to the disorder. Here we show that this abstract concept can be implemented in a realistic acoustic system. Our prototype consists of an acoustic waveguide containing several inclusions that scatter the incoming wave in a passive configuration and provide the gain or loss when being actively controlled. Our measurements on this non-Hermitian acoustic metamaterial demonstrate unambiguously the creation of a reflectionless scattering wave state that features a unique form of discrete constant-amplitude pressure waves. In addition to demonstrating that gain-loss additions can turn localised systems into transparent ones, we expect our proof-of-principle demonstration to trigger interesting new developments not only in sound engineering, but also in other related fields such as in non-Hermitian photonics.
We begin with the theoretical study of spectral energy cascade due to the propagation of high amplitude sound in the absence of thermal sources. To this end, a first-principles-based system of governing equations, correct up to second order in perturbation variables is derived. The exact energy corollary of such second-order system of equations is then formulated and used to elucidate the spectral energy dynamics of nonlinear acoustic waves. We then extend this analysis to thermoacoustically unstable waves -- i.e. amplified as a result of thermoacoustic instability. We drive such instability up until the generation of shock waves. We further study the nonlinear wave propagation in geometrically complex case of waves induced by the spark plasma between the electrodes. This case adds the geometrical complexity of a curved, three-dimensional shock, yielding vorticity production due to baroclinic torque. Finally, detonation waves are simulated by using a low-order approach, in a periodic setup subjected to high pressure inlet and exhaust of combustible gaseous mixture. An order adaptive fully compressible and unstructured Navier Stokes solver is currently under development to enable higher fidelity studies of both the spark plasma and detonation wave problem in the future.
We investigate the dispersion characteristics and the effective properties of acoustic waves propagating in a one-dimensional duct equipped with periodic thermoacoustic coupling elements. Each coupling element consists in a classical thermoacoustic regenerator subject to a spatial temperature gradient. When acoustic waves pass through the regenerator, thermal-to-acoustic energy conversion takes place and can either amplify or attenuate the wave, depending on the direction of propagation of the wave. The presence of the spatial gradient naturally induces a loss of reciprocity. This study provides a comprehensive theoretical model as well as an in-depth numerical analysis of the band structure and of the propagation properties of this thermoacoustically-coupled, tunable, one-dimensional metamaterial. Among the most significant findings, it is shown that the acoustic metamaterial is capable of supporting non-reciprocal thermoacoustic Bloch waves that are associated with a particular form of unidirectional energy transport. Remarkably, the thermoacoustic coupling also allows achieving effective zero compressibility and zero refractive index that ultimately lead to the phase invariance of the propagating sound waves. This single zero effective property is also shown to have very interesting implications in the attainment of acoustic cloaking.
We define a mapping of the QCD Balitsky-Kovchegov equation in the diffusive approximation with noise and a generalized coupling allowing a common treatment of the fixed and running QCD couplings. It corresponds to the extension of the stochastic Fisher and Kolmogorov-Petrovsky-Piscounov equation to the radial wave propagation in a medium with negative-gradient absorption responsible for anomalous diffusion,non-integer dimension and damped noise fluctuations. We obtain its analytic traveling wave solutions with a new scaling curve and in particular for running coupling a new scaling variable allowing to extend the range and validity of the geometric-scaling QCD prediction beyond the previously known domain.
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