Régis Marchiano

Three-dimensional acoustic radiation force on an arbitrarily located elastic sphere

This work aims to model the acoustic radiation forces acting on an elastic sphere placed in an inviscid fluid. An expression of the axial and transverse forces exerted on the sphere is derived. The analysis is based on the scattering of an arbitrary acoustic field expanded in the spherical coordinate system centered on the spherical scatterer. The sphere is allowed to be arbitrarily located. The special case of high order Bessel beams, acoustical vortices, are considered. These types of beams have a helicoidal wave front, i.e., a screw-type phase singularity and hence, the beam has a central dark core of zero amplitude surrounded by an intense ring. Depending on the spheres radius, different radial equilibrium positions may exist and the sphere can be set in rotation around the beam axis by an azimuthal force. This confirms the pseudo-angular moment transfer from the beam to the sphere. Cases where the axial force is directed opposite to the direction of the beam propagation are investigated and the potential use of Bessel beams as tractor beams is demonstrated. Numerical results provide an impetus for further designing acoustical tweezers for potential applications in particle entrapment and remote controlled manipulation.

A coupled time-reversal/complex differentiation method for aeroacoustic sensitivity analysis: towards a source detection procedure

Defining and identifying the aeroacoustic sources in a turbulent flow is a great challenge especially for noise control strategy. The purpose of the present Study consists in proposing a new methodology to localize regions associated with sound generation. These regions are associated, in the present work, with those of high sensitivity of the acoustic field, using the heuristic argument that modifying the flow in these regions would lead to a very significant change in the radiated noise. The proposed method relies on the efficient coupling between the time-reversal theory applied to the Euler equations and the complex differentiation method to compute the sensitivity variable. To the knowledge of the authors, tills is the first time that the time-reversal technique is applied to vectorial hydrodynamic equations, in place of the classical scalar wave equation. Subsequently, regions associated with sound generation are related to spatiotemporal events which exhibit the maximum of sensitivity to acoustical disturbances measured in far field. The proposed methodology is then successively tested on three cases for which the nature of the Source is different: injection of mass, vibrating surfaces and flow instabilities arising in a plane mixing layer flow. For each test case, the two-dimensional Euler equations are solved using a numerical solver based on a pseudo-characteristies formulation. During these computations flow, variables are stored only at the Computational boundaries. These variables are time reversed and relevant information concerning the acoustical disturbances is tagged using complex differentiation in order to lead the sensitivity analysis. The same numerical solver is used to access the evolution of the time-reversed variables. In each test case, the proposed methodology allows to localize successfully zones associated with noise generation.

Nonlinear reflection of grazing acoustic shock waves: unsteady transition from von Neumann to Mach to Snell-Descartes reflections

We study the reflection of acoustic shock waves grazing at a small angle over a rigid surface. Depending on the incidence angle and the Mach number, the reflection patterns are mainly categorized into two types, namely regular reflection and irregular reflection. In the present work, using the nonlinear KZ equation, this reflection problem is investigated for extremely weak shocks as encountered in acoustics. A critical parameter, defined as the ratio of the sine of the incidence angle and the square root of the acoustic Mach number, is introduced in a natural way. For step shocks, we recover the self-similar (pseudo-steady) nature of the reflection, which is well known from von Neumanns work. Four types of reflection as a function of the critical parameter can be categorized. Thus, we describe the continuous but nonlinear and non-monotonic transition from linear reflection (according to the Snell-Descartes laws) to the weak von-Neumann-type reflection observed for almost perfectly grazing incidence. This last regime is a new, one-shock regime, in contrast with the other, already known, two-shock (regular reflection) or three-shock (von Neumann-type reflection) regimes. Hence, the transition also resolves another paradox on acoustic shock waves addressed by von Neumann in his classical paper. However, step shocks are quite unrealistic in acoustics. Therefore, we investigate the generalization of this transition for N-waves or periodic sawtooth waves, which are more appropriate for acoustics. Our results show an unsteady reflection effect necessarily associated with the energy decay of the incident wave. This effect is the counterpart of step-shock propagation over a concave surface. For a given value of the critical parameter, all the patterns categorized for the step shock may successively appear when the shock is propagating along the surface, starting from weak von-Neumann-type reflection, then gradually turning to von Neumann reflection and finally evolving into nonlinear regular reflection. This last one will asymptotically result in linear regular reflection (Snell-Descartes). The transition back to regular reflection is one of two types, depending on whether a secondary reflected shock is observed. The latter case, here described for the first time, appears to be related to the non-constant state behind the incident shock, which prevents secondary reflection.

Spherical vortex beams of high radial degree for enhanced single-beam tweezers

We present, in our knowledge, the first theoretical demonstration of the possibility to trap and manipulate particles in three dimensions with the radiation pressure exerted by a single acoustical beam. Numerical examples demonstrate that single-beam acoustical tweezers operating in three dimensions are feasible with a large variety of materials and may widely extend the range of forces and operation regions that are currently available with optical tweezers. To do so, a method to model the focusing properties of acoustical beams with complex wavefronts using a spherical transducer is proposed. Then, the radiation forces exerted by various beams going from the classical vortex to the high radial degree spherical vortex beam that we introduce here are studied. While the first is shown to trap moderately small particles, the latter will stiffly trap large solid spheres in three dimensions. Even though this demonstration is carried out using a formalism suited to acoustics, it is easily applicable to trap no...

Acoustic shock wave propagation in a heterogeneous medium: A numerical simulation beyond the parabolic approximation

Numerical simulation of nonlinear acoustics and shock waves in a weakly heterogeneous and lossless medium is considered. The wave equation is formulated so as to separate homogeneous diffraction, heterogeneous effects, and nonlinearities. A numerical method called heterogeneous one-way approximation for resolution of diffraction (HOWARD) is developed, that solves the homogeneous part of the equation in the spectral domain (both in time and space) through a one-way approximation neglecting backscattering. A second-order parabolic approximation is performed but only on the small, heterogeneous part. So the resulting equation is more precise than the usual standard or wide-angle parabolic approximation. It has the same dispersion equation as the exact wave equation for all forward propagating waves, including evanescent waves. Finally, nonlinear terms are treated through an analytical, shock-fitting method. Several validation tests are performed through comparisons with analytical solutions in the linear case and outputs of the standard or wide-angle parabolic approximation in the nonlinear case. Numerical convergence tests and physical analysis are finally performed in the fully heterogeneous and nonlinear case of shock wave focusing through an acoustical lens.

Nonlinear focusing of acoustic shock waves at a caustic cusp

The present study investigates the focusing of acoustical weak shock waves incoming on a cusped caustic. The theoretical model is based on the Khokhlov-Zabolotskaya equation and its specific boundary conditions. Based on the so-called Guirauds similitude law for a step shock, a new explanation about the wavefront unfolding due to nonlinear self-refraction is proposed. This effect is shown to be associated not only to nonlinearities, as expected by previous authors, but also to the nonlocal geometry of the wavefront. Numerical simulations confirm the sensitivity of the process to wavefront geometry. Theoretical modeling and numerical simulations are substantiated by an original experiment. This one is carried out in two steps. First, the canonical Pearcey function is synthesized in linear regime by the inverse filter technique. In the second step, the same wavefront is emitted but with a high amplitude to generate shock waves during the propagation. The experimental results are compared with remarkable agreement to the numerical ones. Finally, applications to sonic boom are briefly discussed.

One-way approximation for the simulation of weak shock wave propagation in atmospheric flows

A numerical scheme is developed to simulate the propagation of weak acoustic shock waves in the atmosphere with no absorption. It generalizes the method previously developed for a heterogeneous medium [Dagrau, Rénier, Marchiano, and Coulouvrat, J. Acoust. Soc. Am. 130, 20-32 (2011)] to the case of a moving medium. It is based on an approximate scalar wave equation for potential, rewritten in a moving time frame, and separated into three parts: (i) the linear wave equation in a homogeneous and quiescent medium, (ii) the effects of atmospheric winds and of density and speed of sound heterogeneities, and (iii) nonlinearities. Each effect is then solved separately by an adapted method: angular spectrum for the wave equation, finite differences for the flow and heterogeneity corrections, and analytical method in time domain for nonlinearities. To keep a one-way formulation, only forward propagating waves are kept in the angular spectrum part, while a wide-angle parabolic approximation is performed on the correction terms. The numerical process is validated in the case of guided modal propagation with a shear flow. It is then applied to the case of blast wave propagation within a boundary layer flow over a flat and rigid ground.

Experimental observation of azimuthal shock waves on nonlinear acoustical vortices

Thanks to a new focused array of piezoelectric transducers, experimental results are reported here to evidence helical acoustical shock waves resulting from the nonlinear propagation of acoustical vortices (AVs). These shock waves have a three-dimensional spiral shape, from which both the longitudinal and azimuthal components are studied. The inverse filter technique used to synthesize AVs allows various parameters to be varied, especially the topological charge which is the key parameter describing screw dislocations. Firstly, an analysis of the longitudinal modes in the frequency domain reveals a wide cascade of harmonics (up to the 60th order) leading to the formation of the shock waves. Then, an original measurement in the transverse plane exhibits azimuthal behaviour which has never been observed until now for acoustical shock waves. Finally, these new experimental results suggest interesting potential applications of nonlinear effects in terms of acoustics spanners in order to manipulate small objects.

Design and implementation of a multi-octave-band audio camera for realtime diagnosis

Noise pollution investigation takes advantage of two common methods of diagnosis: measurement using a Sound Level Meter and acoustical imaging. The former enables a detailed analysis of the surrounding noise spectrum whereas the latter is rather used for source localization. Both approaches complete each other, and merging them into a unique system, working in realtime, would offer new possibilities of dynamic diagnosis. This paper describes the :design of a complete system for this purpose: imaging in realtime the acoustic field at different octave bands, with a convenient device. The acoustic field is sampled in time and space using an array of MEMS microphones. This recent technology enables a compact and fully digital design of the system. However, performing realtime imaging with resource-intensive algorithm on a large amount of measured data confronts with a technical challenge. This is overcome by executing the whole process on a Graphic Processing Unit, which has recently become an attractive device for parallel computing.

A Nonlinear Computational Method for the Propagation of Shock Waves in Aero-engine Inlets Towards a new Model for Buzz-saw Noise Prediction

The nonlinear propagation of finite amplitude acoustic waves in hard-walled guides is treated in the following paper. A convected nonlinear wave equation is derived, and a quasianalytical solution based on axially varying modal amplitudes is presented for a no-flow case. Plane and non-planar finite amplitude wave propagation is investigated, and nonlinear interactions of higher order modes are studied in two-dimensional and three-dimensional cylindrical configurations.