Sébastien Ollivier

Nonlinear characteristics of single-reed instruments: quasistatic volume flow and reed opening measurements.

A wind instrument can be described as a closed feedback loop made up of a linear passive element-the resonator-and a lumped nonlinear element-the mouthpiece. A method for measuring the nonlinear characteristics of the mouthpiece-nonlinear flow relationship-in static condition is given. An artificial mouth is used in which the volume flow is deduced from the pressure difference between both sides of a constriction (orifice) which takes place in the resonator. The orifice also plays the role of a nonlinear absorber, thwarting possible reed oscillations. This allows the measurement of the complete characteristics. In addition, the reed opening is measured using an optical device. Results are compared to a model in which the reed is reduced to its stiffness and the flow is governed by the Bernoulli equation. It is shown that the reed stiffness and the ratio of the effective surface of the jet and the reed opening are constant in a large range of openings. Standard range values of embouchure parameters are given.

Nonlinear propagation of spark-generated N-waves in air: Modeling and measurements using acoustical and optical methods

The propagation of nonlinear spherically diverging N-waves in homogeneous air is studied experimentally and theoretically. A spark source is used to generate high amplitude (1.4 kPa) short duration (40 μs) N-waves; acoustic measurements are performed using microphones (3 mm diameter, 150 kHz bandwidth). Numerical modeling with the generalized Burgers equation is used to reveal the relative effects of acoustic nonlinearity, thermoviscous absorption, and oxygen and nitrogen relaxation on the wave propagation. The results of modeling are in a good agreement with the measurements in respect to the wave amplitude and duration. However, the measured rise time of the front shock is ten times longer than the calculated one, which is attributed to the limited bandwidth of the microphone. To better resolve the shock thickness, a focused shadowgraphy technique is used. The recorded optical shadowgrams are compared with shadow patterns predicted by geometrical optics and scalar diffraction model of light propagation. It is shown that the geometrical optics approximation results in overestimation of the shock rise time, while the diffraction model allows to correctly resolve the shock width. A combination of microphone measurements and focused optical shadowgraphy is therefore a reliable way of studying evolution of spark-generated shock waves in air.

Random focusing of nonlinear acoustic N-waves in fully developed turbulence: Laboratory scale experiment

A laboratory experiment was conducted to study the propagation of short duration (25 μs) and high amplitude (1000 Pa) acoustic N-waves in turbulent flow. Turbulent flows with a root-mean-square value of the fluctuating velocity up to 4 m/s were generated using a bidimensional nozzle (140 × 1600 mm(2)). Energy spectra of velocity fluctuations were measured and found in good agreement with the modified von Kármán spectrum for fully developed turbulence. Spherical N-waves were generated by an electric spark source. Distorted waves were measured by four 3 mm diameter microphones placed beyond the turbulent jet. The presence of turbulence resulted in random focusing of the pulse; more than a threefold increase of peak pressures was occasionally observed. Statistics of the acoustic field parameters were evaluated as functions of the propagation distance and the level of turbulence fluctuations. It is shown that random inhomogeneities decrease the mean peak positive pressure up to 30% at 2 m from the source, double the mean rise time, and cause the arrival time about 0.3% earlier than that for corresponding conditions in still air. Probability distributions of the pressure amplitude possess autosimilarity properties with respect to the level of turbulence fluctuations.

Mach stem formation in reflection and focusing of weak shock acoustic pulses

The aim of this study is to show the evidence of Mach stem formation for very weak shock waves with acoustic Mach numbers on the order of 10(-3) to 10(-2). Two representative cases are considered: reflection of shock pulses from a rigid surface and focusing of nonlinear acoustic beams. Reflection experiments are performed in air using spark-generated shock pulses. Shock fronts are visualized using a schlieren system. Both regular and irregular types of reflection are observed. Numerical simulations are performed to demonstrate the Mach stem formation in the focal region of periodic and pulsed nonlinear beams in water.

Laboratory-scale experiment to study nonlinear N-wave distortion by thermal turbulence

The nonlinear propagation of spark-generated N-waves through thermal turbulence is experimentally studied at the laboratory scale under well-controlled conditions. A grid of electrical resistors was used to generate the turbulent field, well described by a modified von Kármán model. A spark source was used to generate high-amplitude (~1500 Pa) and short duration (~50 μs) N-waves. Thousands of waveforms were acquired at distances from 250 to 1750 mm from the source (~15 to 100 wavelengths). The mean values and the probability densities of the peak pressure, the deviation angle, and the rise time of the pressure wave were obtained as functions of propagation distance through turbulence. The peak pressure distributions were described using a generalized gamma distribution, whose coefficients depend on the propagation distance. A line array of microphones was used to analyze the effect of turbulence on the propagation direction. The angle of deviation induced by turbulence was found to be smaller than 15°, which validates the use of the parabolic equation method to model this kind of experiment. The transverse size of the focus regions was estimated to be on the order of the acoustic wavelength for propagation distances longer than 50 wavelengths.

Mach-Zehnder interferometry method for acoustic shock wave measurements in air and broadband calibration of microphones

A Mach-Zehnder interferometer is used to measure spherically diverging N-waves in homogeneous air. An electrical spark source is used to generate high-amplitude (1800 Pa at 15 cm from the source) and short duration (50 μs) N-waves. Pressure waveforms are reconstructed from optical phase signals using an Abel-type inversion. It is shown that the interferometric method allows one to reach 0.4 μs of time resolution, which is 6 times better than the time resolution of a 1/8-in. condenser microphone (2.5 μs). Numerical modeling is used to validate the waveform reconstruction method. The waveform reconstruction method provides an error of less than 2% with respect to amplitude in the given experimental conditions. Optical measurement is used as a reference to calibrate a 1/8-in. condenser microphone. The frequency response function of the microphone is obtained by comparing the spectra of the waveforms resulting from optical and acoustical measurements. The optically measured pressure waveforms filtered with the microphone frequency response are in good agreement with the microphone output voltage. Therefore, an optical measurement method based on the Mach-Zehnder interferometer is a reliable tool to accurately characterize evolution of weak shock waves in air and to calibrate broadband acoustical microphones.

Bulk micro-machined wide-band aero-acoustic microphone and its application to acoustic ranging

A wide-band aero-acoustic microphone was realized using a bulk micro-machining process based on the deep reactive-ion etching of silicon. The sensing diaphragm is completely sealed, thus eliminating the loss of low-frequency response resulting from pressure equalization through the release etch-holes present on the diaphragm of a previously reported microphone implemented using a surface-micro-machining process. A dynamic sensitivity of ∼0.33 μV/V/Pa was estimated using an acoustic shockwave (‘N-wave’) generated using a custom-built high-voltage electrical spark-discharge system. This value is comparable to the effective static sensitivity of ∼0.28 μV/V/Pa measured using a commercial nano-indenter system. The response of the microphone is relatively flat from 6 to 500 kHz, with a resonance frequency of ∼715 kHz. An array of three microphones was also constructed and tested to demonstrate the application of these microphones to the localization of high frequency and short duration acoustic sources. (Some figures may appear in colour only in the online journal)

Model experiments to study acoustic N-waves propagation through turbulent media

Turbulence plays a role in the propagation and the distortion of sonic booms but its influence is still not modelled accurately. One reason for this situation is the lack of controlled experimental data. For this purpose laboratory-scale experiments has been done. An electrical spark source has been designed to generate N-waves, and two setups are used to study separately the influence of temperature or velocity random fluctuations. For both setups the spectrum and characteristic lengths of the turbulence have been measured. We then performed the statistical analysis of the peak pressure and of the rise time of thousands pressure waveforms measured after propagation through thermal or kinetic turbulence. Data show that the increase of the mean rise time and the decrease of the mean peak pressure is linked to the occurrence of caustics.

Characterization of spark-generated N-waves in air using an optical schlieren method

Accurate measurement of high-amplitude, broadband shock pulses in air is an important part of laboratory-scale experiments in atmospheric acoustics. Although various methods have been developed, specific drawbacks still exist and need to be addressed. Here, a schlieren optical method was used to reconstruct the pressure signatures of nonlinear spherically diverging short acoustic pulses generated using an electric spark source (2.5 kPa, 33 μs at 10 cm from the source) in homogeneous air. A high-speed camera was used to capture light rays deflected by refractive index inhomogeneities, caused by the acoustic wave. Pressure waveforms were reconstructed from the light intensity patterns in the recorded images using an Abel-type inversion method. Absolute pressure levels were determined by analyzing at different propagation distances the duration of the compression phase of pulses, which changed due to nonlinear propagation effects. Numerical modeling base on the generalized Burgers equation was used to evaluate the smearing of the waveform caused by finite exposure time of the high-speed camera and corresponding limitations in resolution of the schlieren technique. The proposed method allows the study of the evolution of spark-generated shock waves in air starting from the very short distances from the spark, 30 mm, up to 600 mm.

Wide-band piezoresistive microphone for aero-acoustic applications

A surface micro-machined microphone employing recrystallized metal-induced-laterally crystallized (RC-MILC) polycrystalline silicon (Poly-Si) piezoresistor is developed for aero-acoustic applications. A static sensitivity of ~0.4μV/V/Pa is measured using a nano-indentation technique and a useful bandwidth starting from ~100kHz with a resonance peak at ~400kHz has been obtained using shock waves generated using a the high-voltage electrical spark discharge.