Nonlinear spherically divergent shock waves propagating in a relaxing medium

Yuldashev, Petr V.; Averiyanov, Mikhail; Khokhlova, Vera A.; Ollivier, Sébastien; Blanc‐Benon, Ph.

doi:10.1134/s1063771008010065

Cited by 19 publications

(45 citation statements)

References 10 publications

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“…17,18 Nevertheless, the N-wave model is widespread to describe pressure signatures of shock pulses during their propagation in air. 11,12,19 Even if the waveform is not restricted to have the N-wave shape in simulations of pulse propagation through homogeneous 12 and turbulent media, 20 the N-wave assumption is still often used to set a boundary condition to the model. This simplified assumption may introduce errors, for example, in the simulation of pulse propagation through a caustic, in which the resulting waveform resembles the derivative of an initial wave.…”

Section: Introductionmentioning

confidence: 99%

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

Karzova

Yuldashev

Khokhlova

et al. 2015

The Journal of the Acoustical Society of America

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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.

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Section: Introductionmentioning

confidence: 99%

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

Karzova

Yuldashev

Khokhlova

et al. 2015

The Journal of the Acoustical Society of America

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“…2(b) where ϵ = 1 × 10 −5 and there was good agreement between the asymptotic predictions and numerical results. Laboratory measurements for a spherically spreading shock generated by an electrical spark source [27] correspond to ϵ ≈ 1 × 10…”

Section: Discussionmentioning

confidence: 99%

“…Thus we have two separate predictions from the asymptotic analysis to be compared with the full numerical solutions. For smaller times we have the Taylor shock width (26), whereas for larger times we have the shock width obtained from the error function shock form (27).…”

Section: Spherical Casementioning

confidence: 99%

“…The first order correction term is also obtained, however it turns out that the two-term perturbation expansion is only a useful approximation for extremely small values of ϵ and, as such, is not presented here. Instead, we determine the shock width numerically from the asymptotic solution (27) in the same way that the width is obtained from the full numerical solution, as described in Section 4.1. Thus we have two separate predictions from the asymptotic analysis to be compared with the full numerical solutions.…”

Section: Spherical Casementioning

confidence: 99%

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Numerical and asymptotic solutions of generalised Burgers’ equation

Schofield

Hammerton

2014

Wave Motion

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h i g h l i g h t s• We generate a numerical scheme to solve Burgers' equation using a variable mesh scheme.• We validate asymptotic prediction for shock location and width for small times.• Show partial breakdown in spherical case from a tanh shock to an erf shock.• Offers validation of Enflo's old age form for cylindrical case. a r t i c l e i n f o b s t r a c tThe generalised Burgers' equation models the nonlinear evolution of acoustic disturbances subject to thermoviscous dissipation. When thermoviscous effects are small, asymptotic analysis predicts the development of a narrow shock region, which widens, leading eventually to a shock-free linear decay regime. The exact nature of the evolution differs subtly depending upon whether plane waves are considered, or cylindrical or spherical spreading waves. This paper focuses on the differences in asymptotic shock structure and validates the asymptotic predictions by comparison with numerical solutions. Precise expressions for the shock width and shock location are also obtained.

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“…Its front shock rise time which is unaffected by the turbulence interaction are less than approximately 3 μs, and it corresponds with a wave duration on the order of less than 1/10; thus, the short shock rise time is in high frequency domain. Wave attenuation, which is important factor for a shock wave propagation, depends on the frequency component which the pressure waveform has [31]. The frequency component of the short rise time does not correspond with that of the long rise time enable us to deduce that the same shock wave focusing/diffracting effects do not necessarily contribute to the long risetime pressure signature.…”

Section: Introductionmentioning

confidence: 99%

Turbulent jet interaction with a long rise-time pressure signature

2016

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Abstract:A sonic boom signature with a long rise time has the ability to reduce the sonic boom, but it does not necessarily minimize the sonic boom at the ground level because of the real atmospheric turbulence. In this study, an effect of the turbulence on a long rise-time pressure signature was experimentally investigated in a ballistic range facility. To compare the effects of the turbulence on the long and short rise-time pressure signatures, a cone-cylinder projectile that simultaneously produces these pressure signatures was designed. The pressure waves interacted with a turbulent field generated by a circular nozzle. The turbulence effects were evaluated using flow diagnostic techniques: high-speed schlieren photography, a point-diffraction interferometer, and a pressure measurement. In spite of the fact that the long and short rise-time pressure signatures simultaneously travel through the turbulent field, the turbulence effects do not give the same contribution to these overpressures. Regarding the long risetime pressure signature, the overpressure fluctuation due to the turbulence interaction is almost uniform, and a standard deviation 1.5 times greater than that of the no-turbulence case is observed. By contrast, a short rise-time pressure signature which passed through the same turbulent field is strongly affected by the turbulence. A standard deviation increases by a factor of 14 because of the turbulence interaction. Additionally, there is a non-correlation between the overpressure fluctuations of the long and short rise-time pressure signatures. These results deduce that the length of the rise time is important to the turbulence effects such as the shock focusing/diffracting.

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Nonlinear spherically divergent shock waves propagating in a relaxing medium

Cited by 19 publications

References 10 publications

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

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

Numerical and asymptotic solutions of generalised Burgers’ equation

Turbulent jet interaction with a long rise-time pressure signature

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