S. Ollivier

An analytical prediction of the oscillation and extinction thresholds of a clarinet

This paper investigates the dynamic range of the clarinet from the oscillation threshold to the extinction at high pressure level. The use of an elementary model for the reed-mouthpiece valve effect combined with a simplified model of the pipe assuming frequency independent losses (Ramans model) allows an analytical calculation of the oscillations and their stability analysis. The different thresholds are shown to depend on parameters related to embouchure parameters and to the absorption coefficient in the pipe. Their values determine the dynamic range of the fundamental oscillations and the bifurcation scheme at the extinction.

Random focusing of nonlinear N‐waves in fully developed turbulence: Laboratory scale experiment and theoretical analysis.

The high‐amplitude shock wave generated by a supersonic aircraft propagates through the atmosphere toward the ground and generates an acoustic field with non‐uniform pressure distributions strongly influenced by atmospheric turbulence. Recent numerical simulations based on generalized KZK‐type equation including the effects of moving inhomogeneous media will be discussed. Formation of multiple focusing and defocusing zones is predicted. Nonlinear effects are significant not only in the random focusing zones but also in shadow zones of lower‐pressure levels due to scattering of high frequencies from the areas of focusing. A statistical analysis is performed, and the results are compared to experimental data obtained in the controlled laboratory scale experiments conducted in the ECL anechoic wind tunnel. A high‐power spark source is used to generate N‐waves. Correlation length scales and spectra of the turbulent velocity field are measured. Statistical distributions and mean values for peak positive pressure and shock arrival time are obtained and found to be in a good agreement with modeling. In focusing areas, waveforms with amplitudes more than four times higher than those measured without turbulence are observed. Pressure amplitude probability density distributions are shown to possess autosimilarity properties when changing the intensity of turbulence. [Work supported by RFBR, French Government.]

Nonlinear reflection of weak shock waves from a rough surface in air

Irregular reflection of weak acoustic shock waves occurs under the framework of the von Neumann paradox. In this study, the influence of the surface roughness on the reflection pattern was studied experimentally using spark-generated spherically divergent N-waves of 1.4 cm length reflecting from rigid rough surfaces in air. Dimensions of the roughness were varied from 20 up to 500 μm for different surfaces. A Mach-Zehnder interferometry method was used to reconstruct the pressure waveforms near the surface. The reconstruction was performed by applying the inverse Abel transform to the phase of the signal measured by the interferometer. It was shown that the height of the Mach stem became shorter for surfaces with larger dimensions of the roughness and disappeared when the surface roughness was large enough. Such tendency was also observed in simulations based on the Euler equations where the acoustic source was introduced as a Gaussian-envelope energy injection and the roughness was either sinusoidal or random and described by a Gaussian correlation function. [Work supported by RSF-17-72-10277 and by the Labex CeLyA of Universite de Lyon, operated by the French National Research Agency (ANR-10-LABX-0060/ ANR-11-IDEX-0007).]Irregular reflection of weak acoustic shock waves occurs under the framework of the von Neumann paradox. In this study, the influence of the surface roughness on the reflection pattern was studied experimentally using spark-generated spherically divergent N-waves of 1.4 cm length reflecting from rigid rough surfaces in air. Dimensions of the roughness were varied from 20 up to 500 μm for different surfaces. A Mach-Zehnder interferometry method was used to reconstruct the pressure waveforms near the surface. The reconstruction was performed by applying the inverse Abel transform to the phase of the signal measured by the interferometer. It was shown that the height of the Mach stem became shorter for surfaces with larger dimensions of the roughness and disappeared when the surface roughness was large enough. Such tendency was also observed in simulations based on the Euler equations where the acoustic source was introduced as a Gaussian-envelope energy injection and the roughness was either sinusoidal or r...

Nonlinear reflection of a spherically divergent N-wave from a plane surface: Optical interferometry measurements in air

Mach stem is a well-known structure typically observed in the process of strong (acoustic Mach numbers greater than 0.4) step-shock waves reflection from a rigid boundary. However, this phenomenon has been much less studied for weak shocks in nonlinear acoustic fields where Mach numbers are in the range from 0.001 to 0.01 and pressure waveforms have more complicated waveforms than step shocks. The goal of this work was to demonstrate experimentally how nonlinear reflection occurs in air for very weak spherically divergent acoustic spark-generated pulses resembling an N-wave. Measurements of reflection patterns were performed using a Mach-Zehnder interferometer. A thin laser beam with sub-millimeter cross-section was used to obtain the time resolution of 0.4 µs, which is 6 times higher than the time resolution of the condenser microphones. Pressure waveforms were reconstructed using the inverse Abel transform applied to the phase of the signal measured by the interferometer. The Mach stem formation was obs...

High frequency calibration of MEMS microphones using spherical N-waves

In the context of the scientific program SIMMIC supported by the French National Agency for Research (SIMI 9, ANR 2010 BLANC 0905 03), new wide band MEMS piezoresistive microphones have been designed and fabricated for weak shock wave measurements. The fabricated microphones have a high frequency resonance between 300 to 800 kHz depending on the membrane size. In order to characterize the frequency response of the fabricated sensors up to 1 MHz, new calibration methods based on an N-wave source were designed and tested. Short duration spherical N-waves can be generated by an electric spark source. To estimated a constant sensitivity coefficient, a known method is based on the estimation of the peak pressure from the lengthening of N-waves induced by non linear propagation. However, to obtain the sensitivity as a function of frequency, the output voltage must be compared to the incident pressure waveform, which must be accurately characterized. Taking advantage of recent works on the characterization of pr...