Philippe Blanc-Benon

Propagation of finite amplitude sound through turbulence: Modeling with geometrical acoustics and the parabolic approximation

Sonic boom propagation can be affected by atmospheric turbulence. It has been shown that turbulence affects the perceived loudness of sonic booms, mainly by changing its peak pressure and rise time. The models reported here describe the nonlinear propagation of sound through turbulence. Turbulence is modeled as a set of individual realizations of a random temperature or velocity field. In the first model, linear geometrical acoustics is used to trace rays through each realization of the turbulent field. A nonlinear transport equation is then derived along each eigenray connecting the source and receiver. The transport equation is solved by a Pestorius algorithm. In the second model, the KZK equation is modified to account for the effect of a random temperature field and it is then solved numerically. Results from numerical experiments that simulate the propagation of spark-produced N waves through turbulence are presented. It is observed that turbulence decreases, on average, the peak pressure of the N waves and increases the rise time. Nonlinear distortion is less when turbulence is present than without it. The effects of random vector fields are stronger than those of random temperature fields. The location of the caustics and the deformation of the wave front are also presented. These observations confirm the results from the model experiment in which spark-produced N waves are used to simulate sonic boom propagation through a turbulent atmosphere.

Numerical Simulation of Stack-Heat Exchangers Coupling in a Thermoacoustic Refrigerator

The Navier‐Stokes equations for an unsteady and compressible flow are solved numerically to investigate the flow near the stack of a thermoacoustic refrigerator. The computational domain is a resonator “slice” including the resonator end but not the source. An incoming wave is introduced into the domain using the method of characteristics. Also included in the domain is a stack plate and two heat exchangers. The effects of the acoustic Mach number and geometrical parameters on refrigerator performance is investigated. Of special interest are some nonlinear temperature oscillations, which are not predicted by linear models and are due to acoustic propagation, and coupling between the stack plate and the heat exchangers. It is shown that the maximum heat pumping occurs fo ra stack/heat exchanger separation that is of the order of one particle displacement amplitude.

Time-Domain Impedance Boundary Conditions for Simulations of Outdoor Sound Propagation

B = Gaussian half-width, m c0 = speed of sound, m=s dL = porous layer thickness, m f = frequency, Hz Im = imaginary part j = imaginary unit k = complex wave number, m 1 p = pressure, Pa q = tortuosity Re = real part S = number of first-order systems in the impedance approximation sf = coefficient of the selective filter T = number of second-order systems in the impedance approximation t = time, s v = velocity component normal to impedance surface, m=s Z = complex impedance, kg=m=s = ratio of specific heats L = sound pressure level relative to the free field, dB t = time step, s x = spatial mesh size, m 0 = air density, kg=m 0, e = flow resistivity, Pa s=m = porosity ! = angular frequency, rad=s

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.

Outdoor sound propagation modeling in realistic environments: Application of coupled parabolic and atmospheric models

Predicting long-range sound propagation over a nonurban site with complex propagation media requires the knowledge of micrometeorological fields in the lower part of the atmospheric boundary layer, and more precisely its characteristics varying in both space and time with respect to local (“small-scale”) and average (“long-term”) conditions, respectively. Thus in this study, a mean-wind wide-angle parabolic equation (MW-WAPE) code is coupled with a dedicated micrometeorological code (SUBMESO) which simulates wind and temperature fields over moderately complex terrain with high resolution. Its output data are used as input data for the MW-WAPE code, which can also deal with different boundary conditions, such as the introduction of impedance jumps, thin screens or complex topography. Both codes are presented in the present paper. Comparisons between numerical predictions, and experimental data are also presented and discussed. Finally, we present an example of such a coupling method (MW-WAPE/SUBMESO) for t...

Computation of the temperature distortion in the stack of a standing-wave thermoacoustic refrigerator

The numerical computation of the flow and heat transfer in the vicinity of a stack plate in a standing wave refrigerator is performed. Temperature distortion is observed, which appears only in the stack region, even if the acoustic standing wave outside the stack is itself sinusoidal. The distortion takes place above the whole plate surface when the length of the plate is equal to or shorter than four times the particle displacement. This condition may occur at high drive ratios and is favored by plate positions close to the velocity antinode. The thermal distortion decreases the thermoacoustic heat pumping along the plate. At high drive ratios, if the length of the plate is not large enough, the thermal distortion can typically explain a difference of about 10% between the calculated heat flux and the heat flux predicted using linear theory.

Nonlinear and diffraction effects in propagation of N-waves in randomly inhomogeneous moving media.

Finite amplitude acoustic wave propagation through atmospheric turbulence is modeled using a Khokhlov-Zabolotskaya-Kuznetsov (KZK)-type equation. The equation accounts for the combined effects of nonlinearity, diffraction, absorption, and vectorial inhomogeneities of the medium. A numerical algorithm is developed which uses a shock capturing scheme to reduce the number of temporal grid points. The inhomogeneous medium is modeled using random Fourier modes technique. Propagation of N-waves through the medium produces regions of focusing and defocusing that is consistent with geometrical ray theory. However, differences up to ten wavelengths are observed in the locations of fist foci. Nonlinear effects are shown to enhance local focusing, increase the maximum peak pressure (up to 60%), and decrease the shock rise time (about 30 times). Although the peak pressure increases and the rise time decreases in focal regions, statistical analysis across the entire wavefront at a distance 120 wavelengths from the source indicates that turbulence: decreases the mean time-of-flight by 15% of a pulse duration, decreases the mean peak pressure by 6%, and increases the mean rise time by almost 100%. The peak pressure and the arrival time are primarily governed by large scale inhomogeneities, while the rise time is also sensitive to small scales.

Time-domain solver in curvilinear coordinates for outdoor sound propagation over complex terrain

The current work aims at developing a linearized Euler equations solver in curvilinear coordinates to account for the effects of topography on sound propagation. In applications for transportation noise, the propagation environment as well as the description of acoustic sources is complex, and time-domain methods have proved their capability to deal with both atmospheric and ground effects. First, equations in curvilinear coordinates are examined. Then time-domain boundary conditions initially proposed for a Cartesian coordinate system are implemented in the curvilinear solver. Two test cases dealing with acoustic scattering by an impedance cylinder in a two-dimensional geometry and by an impedance sphere in a three-dimensional geometry are considered to validate the boundary conditions. Accurate solutions are obtained for both rigid and impedance surfaces. Finally, the solver is used to examine a typical outdoor sound propagation problem. It is shown that it is well-suited to study coupled effects of topography, mixed impedance ground and meteorological conditions.

Nonperiodicity of the flow within the gap of a thermoacoustic couple at high amplitudes

The flow inside a thermoacoustic couple is investigated experimentally using particle image velocimetry. Measurements show the oscillation of the shear layers flowing out of a single stack, thus forming an asymmetric vortex street at high driving amplitudes. Development of vortices is also observed within the gap of a thermoacoustic couple. It causes the flow not to repeat from one acoustic period to another. The nonperiodicity of the flow will lead to unsteady heat transfer between the stack and heat exchangers and to the oscillation of the cooling load.

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.