Kevin Leete and Faculty Mentor: Dr. Kent Gee, Physics and Astronomy
When a shock wave reflects off a rigid surface with certain combinations of incident shock strength and angle, a Mach reflection can occur. This is when portions of the incident and reflected waves merge to create a stronger shock called a Mach stem that travels parallel to the reflecting surface. This phenomenon has been studied extensively for two extreme cases: large outdoor explosions and small, laboratory experiments of weak shocks. The purpose of this project was to design and execute an outdoor experiment where this phenomenon could be observed by microphones as well as high speed video imaging to detect the distance from the source where Mach stem formation occurs.
The experiment conducted consisted of the detonation of 25 large, spherical balloons which were filled with a balanced mixture of acetylene and oxygen. The experiment configuration is displayed in figure 1. A tripod mounted metal cradle held the balloons a fixed distance above the pavement. Two pressure probes were located on tripods at fixed distances at about 45° on either side of the propagation line to be used as references. Over the 25 detonations, the mean peak sound pressure levels were 194.2 and 195.6 dB re 20 μPa. A tripod with an array of pressure microphones attached at several different heights was placed at 15 different locations throughout the test to scan the length of the propagation line. An additional probe was attached to the end of a tripod with an adjustable boom arm to provide additional resolution at areas of interest.
To visualize the shockwave propagation, a high-speed camera recorded four separate regions along the propagation line. In these regions, a checkerboard backdrop was placed behind the propagation line to provide additional contrast for the camera. In post processing, the position of the shock is emphasized by subtracting the pixel values of two adjacent frames of the video. These difference images were then converted to grayscale and their histograms readjusted so that all pixels above a certain threshold value were saturated to white and all remaining pixel values were linearly distributed from black to white. A median filter in a five by five pixel neighborhood was then applied to reduce noise. The position of the shock could then be seen in the video. Figure 2 shows a few frames of the processed video.
At each microphone location, analysis of the pressure waveform could give whether or not a Mach stem had passed over that point, which in turn allowed for me to graph the height of the Mach stem as a function of distance that the shock had propagated from the explosion. This data was least squares fit to a cubic polynomial and extrapolated back to the ground to determine where the Mach stem first formed.
Two models were used to determine the Mach stem formation point and thereafter compared to my experimental data. One model, derived for very weak shocks generated in a laboratory setting, is dependent on calculating a parameter from the properties of the shock front. The second model depends on scaling the explosive yield of the source to an equivalent yield in kilotons of TNT and comparing to many other scaled explosions. These two models were compared to our experimental results. The model that was based off of an analytic solution for very weak shocks overestimated the Mach stem formation distance, while the model derived from empirical fits to large scale explosions underestimates the measured value.
The strength of this project was that I was able to use acoustical and visual recordings which confirmed each other to map out how the Mach stem developed as it propagated away from the explosion. However, there were several methods that, if I were to repeat the experiment, would do better. This was our first attempt at high speed video recording, and even with the signal processing techniques used, it was still difficult to see the shock wave in the video. There are more advanced techniques such as Schleiren imaging that could yield much clearer results that we could implement in the future. To see the full explanation and analysis that was completed, see the paper that we published as a result of this project, called “Mach stem formation in outdoor measurements of acoustic shocks”.i
Figure 1 ) Mach-stem experiment setup with 1) gas-filled balloon in its metal cradle at z = 1.8 m; 2) two reference pressure gauges at 1.35 and 1.27 m; 3) vertical array of GRAS pressure microphones; 4) pressure probe attached to adjustable boom arm; 5) Phantom high-speed camera; 6) high-contrast checkerboard backdrop; 7) Line of propagation (x-axis). (Inset) balloon explosion.
Figure 2) Three frames of the processed high speed video. The shocks can be seen propagating from the left to the right with the reflected shock starting to merge with the incident shock to create the “Y” pattern of a Mach stem.
i K. M. Leete, K. L. Gee, T. B. Neilsen, T.T. Truscott, “Mach stem formation in outdoor measurements of acoustic shocks”, J. Acoust. Soc. Am. 138, EL522 (2015); http://dx.doi.org/10.1121/1.4937745