The effects of external acoustic pressure fields on a free-running supercavitating projectile
A side-view schematic of the experiment setup showing key apparatus. The projectile trajectory is shown originating at the firing mechanism, going through induction coil sets and the acoustic transducer array, and terminating at the backstop on the tank base. The induction coil sets are devices for measuring projectile speed.
(Color online) Side-view drawing (top) and photograph (bottom) of the projectile used in the experiments. Length = 2.5 in. (63.5 mm), cavitator diameter = 0.115 in. (2.92 mm), tail diameter = 0.453 in. (11.5 mm).
Schematic of the annular transducer array (approximately 1 m diameter).
(Color online) Maximum sound pressure amplitude plot. Comparison between free and confined environment cases.
(Color online) Plot showing an output trace from the signal generator for the 12 kHz, 3 ms duration pulse (36 cycles).
Images from the high-speed digital camera showing disruptions to the shape of the supercavity. The projectile was traveling vertically downward in all images. Top row: 7.5 kHz (kd c = 0.09), middle row: 12 kHz (kd c = 0.15), bottom row: 17.5 kHz (kd c = 0.22). In each row the left image shows a shot where the projectile was centered in the cavity and the right image shows an instant when the projectile was experiencing tail-slap. For each image showing tail-slap, the tail of the projectile was impacting with the cavity wall coming toward the viewer and is located at the very bottom of the image (indicated by an arrow in the figure).
Image from the high-speed digital camera showing a typical cavity from a control shot. The projectile was traveling vertically downward and the cavity was formed at the tip. The projectile body is enveloped by the supercavity in this image.
(Color online) Plot showing effect of acoustic pressure signal on cavity shape predicted by Logvinovich’s model. The case shown here assumes that liquid medium can sustain negative pressures.
(Color online) Plot showing the effect of an acoustic pressure signal on the cavity shape predicted by Logvinovich’s model. The case shown here assumes that cavitation in the liquid medium causes clipping of the signal at the water vapor pressure.
Percentage p-values for the circular error probable. High, medium, and low denote the acoustic pressure amplitude, and the frequency values denote the acoustic signal frequency. Bold type denotes a statistically significant result.
Summary of the projectile accuracy results. A check mark represents a significant reduction in accuracy.
Drag coefficients calculated from measured speeds. C D is the drag coefficient, n is the number of measurements, s is the sample standard deviation. The t value calculated is the difference between the sample mean and the control mean in units of the standard error. Bold type denotes a statistically significant result.
Measurements of circular error probable (CEP) for shots identified as having or not having an incidence of tail-slap in the recorded view. N is the number of data points. The column headed “Tail-slap” indicates whether that row represents all of the shots (Yes and No) or the subset with (Yes) or without (No) tail-slap. Bold type denotes a statistically significant result.
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