Statistical and numerical study of the relationship between turbulence and sonic boom characteristics

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.

Section: Introductionmentioning

confidence: 99%

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

Salze

Yuldashev

Ollivier

et al. 2014

“…I, a similar discrepancy was noted in the 1970s for aircraft sonic booms; 6,7 molecular relaxation and propagation through atmospheric turbulence both contribute in amounts that depend on the exact geometry and environmental conditions of the propagation. [6][7][8][9]14 Reference 5 attempts to match smallcaliber ballistic shock rise times with molecular relaxation, obtaining order-of-magnitude agreement. However, their agreement is the worst for their indoor data set where turbulence is effectively absent.…”

Section: Observations Of Ballistic Shock Wavesmentioning

confidence: 97%

“…Rise times of these shocks, 5 as well as those of aircraft sonic booms, 6 are significantly larger then predicted from viscosity and still air. Atmospheric turbulence [7][8][9] and molecular relaxation 5, 10,11 have been used to explain this excess, and both are established as important mechanisms. We repeat some of the earlier ballistic shock wave measurements, confirm quantitative agreement with the weak-shock predictions of shock wave period and amplitude, and also measure the effects of atmospheric turbulence on wavefront shape and peak amplitude.…”

Section: Introductionmentioning

confidence: 99%

Measurements of small-caliber ballistic shock waves in air

Stoughton

1997

Megahertz bandwidth pressure measurements of airborne ballistic shock waves from bullets are presented which confirm weak-shock theoretical predictions of waveform shape, period, amplitude, and the scaling of these quantities with shock propagation distance. Wavefront distortions and amplitude variations are quantified versus shock propagation distances of 3-55 m and agree with predictions based on linear acoustic propagation through simple turbulence models. Observed rise times probably exhibit a mix of turbulence and molecular relaxation effects.

“…Although several efforts have been made to clarify this question, no definitive answer has been given yet. [27][28][29][30][31] In order to better understand different aspects of nonlinear pulse propagation in the turbulence, several laboratory scale experiments were performed. 27,[32][33][34] The main advantage of such experiments is that both the source of shock waves and the turbulence can be well controlled.…”

Section: Introductionmentioning

confidence: 99%

Statistics of peak overpressure and shock steepness for linear and nonlinear N-wave propagation in a kinematic turbulence

Yuldashev

Ollivier

Karzova

et al. 2017

Linear and nonlinear propagation of high amplitude acoustic pulses through a turbulent layer in air is investigated using a two-dimensional KZK-type (Khokhlov-Zabolotskaya-Kuznetsov) equation. Initial waves are symmetrical N-waves with shock fronts of finite width. A modified von Kármán spectrum model is used to generate random wind velocity fluctuations associated with the turbulence. Physical parameters in simulations correspond to previous laboratory scale experiments where N-waves with 1.4 cm wavelength propagated through a turbulence layer with the outer scale of about 16 cm. Mean value and standard deviation of peak overpressure and shock steepness, as well as cumulative probabilities to observe amplified peak overpressure and shock steepness, are analyzed. Nonlinear propagation effects are shown to enhance pressure level in random foci for moderate initial amplitudes of N-waves thus increasing the probability to observe highly peaked waveforms. Saturation of the pressure level is observed for stronger nonlinear effects. It is shown that in the linear propagation regime, the turbulence mainly leads to the smearing of shock fronts, thus decreasing the probability to observe high values of steepness, whereas nonlinear effects dramatically increase the probability to observe steep shocks.