Fig 1.
The representative incident shock wave profiles generated using helium as a driver gas and Mylar membrane (thickness of 1.016 mm), with accompanying secondary reflected shock and underpressure waves are presented (A). The profile of the secondary wave depends on the gap between the end plate reflector and the exit of the shock tube (B): 1. 0.625-inch, 2. 2-inch, 3. 4-inch, and 4. open end. C. Schematics of the 9-inch square cross section shock tube indicating the breech (I), transition (II), test section (III) and end plate (IV). Distribution of pressure sensor locations is also illustrated. Typically sensors B1, C1, T4, C2, D2 and D4 were used in our experiments to track the shock wave profile evolution along the entire length of the shock tube. The scale bar indicates the distance of specific sensor from the breech, i.e. Mylar membranes installation port.
Fig 2.
Peak overpressure inside of the shock tube as a function of sensor location and membrane thickness: A) 0.02”, B) 0.04”, and C) 0.06”. Peak overpressure values averaged among experiments preformed using the same Mylar membrane thickness (D): differences of average BOPs for sensors C1 and T4 are not statistically significant (marked with ampersand &, p > 0.05) in respective test groups.
Fig 3.
Calculated shock wave velocities at different sensor locations as a function of BOPs generated using Mylar membranes with thicknesses of: A) 0.02”, B) 0.04”, and C) 0.06”. Shock wave velocities were averaged for all experiments preformed using the same Mylar membrane thickness (D). Individual data points were horizontally shifted for clarity of presentation. The B1 sensor was used as a reference for all calculations.
Fig 4.
Positive phase impulse measured for the shock waves traveling inside of the shock tube as a function of sensor location and membrane thickness: A) 0.02”, B) 0.04”, and C) 0.06”. The average impulse of shock waves recorded for three respective Mylar membrane thicknesses used as a function of sensor location along the shock tube (D). Asterisk indicates impulse value recorded by the C1 sensor, which shows statistically significant difference in respective data sets (p < 0.003, power: >0.95).
Fig 5.
The ratios of peak overpressure between incident and reflected shock wave measured at different locations inside of the shock tube as a function of sensor distance from the breech and blast intensity: A) 0.625” gap, B) 2” gap between end of the shock tube and reflector plate. The ratios between incident peak overpressure and the lowest level (through) of measured reflected underpressure for blasts generated when the gap between the end of the shock tube and reflector plate was 4” (C) and with open end (D). The data points were horizontally shifted for clarity of presentation.
Fig 6.
Velocities of reflected underpressure (A, B) and overpressure (C, D) waves generated with: A) open end, B) 4” gap, C) 2” gap and D) 0.625” gap. The straight arrow indicates the direction of the reflected waves’ propagation. The red and green horizontal lines indicate sound speed in the air. The velocity of reflected waves increases with the distance from the end of the shock tube, which is caused by increased helium (driver gas) concentration closer to the breech. The D4 sensor was used as reference.
Fig 7.
The optimization of the end plate to the shock tube gap distance.
A. Reflected peak overpressure values measured at the D4 location for three different membrane thicknesses (0.02, 0.04 and 0.06 inch) and two different end plate gap sizes (0.625 and 2.0 inches) were used to identify the optimal gap size, i.e. the point on the plot where all linear functions converge (x0 = 2.85 inch). Overpressure profiles recorded using optimized end plate position at three different blast intensities generated using: B. 0.02”, C. 0.04” and D. 0.06”.
Fig 8.
Numerical simulations: A) isometric view of the full scale model of the 9 inch square cross section shock tube, B) comparison of pressure traces recorded experimentally and obtained as results of numerical simulations with Abacus software for shock wave generated using 0.020” thick Mylar membrane and 2 inches end plate gap. Input feed for simulations was composed using initial 15 ms of the incident overpressure recorded by T4 sensor and 10 ms of baseline signal. This was done to eliminate secondary loading waveform from input data, which leads to erroneous calculations.
Fig 9.
The distance-time (x-t) diagrams for incident and reflected waves based on experimental arrival times obtained at membrane thicknesses of: A) 0.02, B) 0.04, and C) 0.06 inches, respectively. The traces representing reflected waves are from experiments when the tube was fully closed and the underpressure waves observed when no endplate was present. Speed of sound for reflected wave domain is marked as dotted line.