Airblast TNT equivalence for a range of commercial blasting explosives.

Blast characteristics and TNT equivalence values for some commercial explosives detonated at ground level

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.

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

The purpose of this paper is to discuss from a historical point of view the classical Rankine-Hugoniot (RH) relations in more detail than usually done in standard textbooks. Particularly focusing on the last seventy years, this paper (i) reviews their validity and limitations as interpreted by numerous users; (ii) summarizes their enormous extension also to other branches of science and engineering; and (iii) discusses the nontrivial problem of error estimation. Originally, the RH relations were derived for a plane-parallel steadily propagating aerial shock with a step wave profile; i.e., a wave with zero rise-time and constant thermodynamic as well as kinematic parameter values behind the shock front. But real shock waves are in most cases three-dimensional, have finite rise-times, and in almost all cases are unsteady waves. These real properties must produce a systematic error when applying the RH relations and the cardinal question arises how large this error will be in comparison with a random error caused by the applied high-speed diagnostics. However, numerical procedures of studying systematic errors of unsteady wave propagation are difficult to carry out because of various reasons and still pending.

The classical Rankine-Hugoniot jump conditions, an important cornerstone of modern shock wave physics: ideal assumptions vs. reality

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 Karman 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°, wh...

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

Effects of viscosity and vibrational nonequilibrium on the profile of a weak, spherical N-wave in air are experimentally and numerically studied. Weak blast waves were generated, in a quiescent air dome, by spark discharges and exploding wires and observed by high frequency response microphones over 40 meters. Some similarity relationships were obtained from the blast wave experiments. For observed N-waves having less than 100 Pa peak overpressure, the peak overpressure Δpfand the duration of the positive phasetd+are found to vary with the radial distance from the sourcer as Δpf∝r−1.38 andtd+ ∝r0.19, whilst the rise time of the blast wave Δtflinearly increases with distance. Similar trends were also found for the negative phase of the blast wave. Numerical simulations were carried out to compare with the blast wave data. The Navier-Stokes equations for spherical symmetric flows were solved by coupling with a relaxation equation for vibrational excitation of oxygen using the random choice method (RCM) adapted to supercomputing with an operator splitting technique. The resultant N-wave profiles are in good agreement with the experimental results. The numerical results clearly indicate that the wave-easing process due to the dispersive effect of vibrational relaxation plays a dominant role in determining the rise time of the N-wave.

Experimental and numerical studies of weak blast waves in air

Numerical analysis of the nonstationary oblique reflection of weak shock waves

A numerical method for a kinetic equation and its application to propagating shock waves

The double-peak characteristic of radiation intensity behind shock waves above 10 km/s in a low-density air are studied by carrying out a numerical analysis for one-dimensional, steady hypersonic flows with nonequilibrium chemical reactions. The gas model is based on 11 gas species, 3 temperatures and 47 chemical reactions. The radiation model includes all possible types of emissions from bound-bound, free-bound and free-free transitions. The result indicates that the double-peak characteristic of the radiation profile can be attributed to the increase of the radiation intensity of the atomic line spectra and the continuum spectra from the free-bound and free-free transitions in the near equilibrium region far downstream of the shock front

A numerical analysis for radiation profile behind strong shock waves about 10 km/s in low-density air

Experimental and numerical results of weak oblique shock reflections from ramp surfaces are given in carbon dioxide. The results are shown for several combinations of the shock Mach number M s and ramp angle θ :M s , θ) = (1.027, 30°), (1.027, 20°), (1.047, 10°), (1.070, 20°) and (1.133, 30°). The maximum density just behind the stem shock increases with distance as the wave proceeds along the ramp surface, and approaches a finite value far downstream. This nonstationary phenomenon is attributed to the finite thickness of dispersed shock waves. The relaxation distance of the maximum density is defined from its exponential behaviour and found to depend mainly on the ramp angle rather than the incident shock Mach number.

H. Honma

Papers

Experimental and numerical studies of weak blast waves in air

Numerical analysis of the nonstationary oblique reflection of weak shock waves

A numerical method for a kinetic equation and its application to propagating shock waves

A numerical analysis for radiation profile behind strong shock waves about 10 km/s in low-density air

Nonstationary reflection of dispersed waves in carbon dioxide