Experimental observations of a rupture induced underwater sound source Open Access

Underwater acoustic experiments often require a repeatable, predictable, broadband sound source. In many instances, a high amplitude, impulsive source is utilized to produce a waveform capable of deeply penetrating the seabed and propagating to long ranges in the water column. Impulsive waveforms have proven useful in providing broadband signatures to test propagation models and to perform geoacoustic characterization of the seabed.¹ Various devices such as airguns,² explosive charges,³ a combustive sound source,⁴ glass spheres,^5,6 and even light bulbs⁷ have historically been utilized in an attempt to produce a singular impulse in the time domain; however, in reality each source produces a transient event characterized by multiple time-domain impulses with decaying peak amplitudes. Recent experimentation has demonstrated the viability of a device known as the rupture induced underwater sound source (RIUSS) that aims to minimize this residual bubble activity and produce a source signature more closely resembling that of an ideal impulse.⁸ A schematic diagram of the experimental configuration and dimensions of the device can be found in Ref. 8.

The RIUSS relies on a rupture disk, which is an expendable diaphragm used in industrial applications, designed to break at a specified pressure differential between the two faces of the disk. Placing a rupture disk over an evacuated chamber and mechanically breaking the disk (either by striking on demand or via hydrostatic pressure) at a specified depth was found to produce high amplitude, broadband waveforms as the disk ruptures and inflowing water impacts the bottom of the chamber. Residual oscillations are greatly reduced due to the fact that the chamber is initially evacuated. This source also has the advantage that before the chamber is evacuated it is solely comprised of inert materials—no explosives or flammable gases are required—making it a potentially safer alternative to some other high amplitude impulsive sources. This work builds on that of a previous study⁹ whereby imploding cavities were deemed useful, safe, and portable underwater sound sources. In the following, an analysis of the bubble activity produced by a RIUSS in relation to the acoustic output through the use of high speed underwater video is provided. A comparison between preliminary modeling efforts and field measurements is presented as an initial step toward predictive modeling for the scaling of such a device, similar to that which has previously been done for explosive events.¹ 

A high-speed underwater video camera operating at 10 000 frames per second and an acoustical recording apparatus sampling at 225 kHz was configured along with the RIUSS in a deployment framework to observe the relationship between the rupturing of the disk, the resulting fluid flow, and the acoustic time series. This test was completed in an outdoor water tank, which has dimensions of approximately 15-m-diameter and a 12-m-depth. A photograph of the system is shown in Fig. 1(a). The camera was positioned such that an oblique view of the rupture disk mounted in the top of the RIUSS could be captured during the rupturing event and the subsequent cavity collapse. A hydrophone was suspended from the top of the framework (not shown in the figure) at 1.25 m from the RIUSS. The data acquisition system utilized to capture the acoustic event was time synced to the start of the high speed video. A Mersen Series 3 graphite rupture disk with a pressure rating of 138 kPa (20 psi) was utilized for this test, such that it ruptured due to the total overburden pressure at a depth of approximately 3.5 m. The procedure for this test was to mount the rupture disk in the top of the RIUSS, evacuate the air within the chamber with a vacuum pump, initiate the recording sequence, and lower the deployment framework into the tank until the disk was ruptured due to the overburden pressure. The high-speed video was combined with a time-synced plot of the recorded acoustic time series and is included as supplementary material.¹⁰ The vertical black line indicates the time associated with each frame of the high-speed video. The difference in acoustic propagation time between the chamber and the hydrophone has been removed. Two still images from this video are also shown in Figs. 1(b) and 1(c), one of which corresponds to a time before the rupturing of the disk (b) and one which corresponds to the peak pressure of the time series (c).

In the high speed video,¹⁰ one will note that the initial acoustic event [at zero seconds in Figs. 1(b) and 1(c)] and subsequent acoustic pressure fluctuation (also see the inset of Fig. 2) is due to the fracturing of the disk. This is followed by an inrush of the graphite disk and surrounding water into the chamber, whereby one will note the occurrence of cavitation around the opening. The inrushing water and cavitation field, with bubbles composed of a mixture of water vapor and air abruptly stops at the moment the first high amplitude pulse is observed in the time series [labeled α in Fig. 1(b)]. Immediately following, the cavitation field begins to coalesce into a torodial structure, which propagates back to the chamber opening. This is followed by a secondary high amplitude pulse at the collapse of the toroidal structure near the opening of the chamber [labeled β in Fig. 1(b)]. The torodial cavitation structure evolves into more of a spherically shaped cavitation cluster that oscillates, radiating acoustic pulses when the cluster reaches volume minima [points χ, δ, and ϵ in Fig. 1(b)]. Individual cavitation bubble collapses, and other cavitation clusters not visible in the video, may be responsible for other acoustic pulses in the recorded time series, such as those between β and χ in Fig. 1(b).

In addition to the event utilized to produce the high speed video, free-field acoustic measurements were obtained in a fresh water lake to investigate the source signature produced by the RIUSS as a function of depth using the same chamber. The chamber was lowered into the water column by a winch through the moon pool of a moored barge until the hydrostatic pressure caused the rupture disk to break. Mersen Series 3 graphite rupture discs with pressure ratings of 414, 689, 1034, and 1379 kPa (commonly marketed as pressure ratings of 60, 100, 150, and 200 psi) were utilized to initiate the events at various depths. A hydrophone was attached to the winch deployment line 2 m above the RIUSS, and this source-receiver distance remained constant for all events. Additional details of the data collection and signal processing steps utilized for this field test is provided in Ref. 8.

The repeatability of the acoustic output of the events at each depth is described in Ref. 8, where it is shown that the peak pressure varied by ±3 dB and the energy source level varied by ±1.5 dB from the mean value for a given depth. Additionally, each of the recorded time series were found to contain specific features that can be quantified in terms of period and amplitude as a function of depth. Figure 2(a) shows the period, T₁, between the rupturing of the disk, seen at approximately t = 0.002 s, and the first of the two high amplitude pulses occurring within a period of less than 1 ms, seen at approximately t = 0.013 s. These pulses are then followed by a subsequent set of lower amplitude peaks a few milliseconds later, seen at approximately t = 0.017 s. The occurrence of these features are consistently observed throughout the data; however, the amplitude and period between some of the features was found to be depth dependent.

Figure 2(b) shows the energy spectral density (ESD) of the event. The event contains significant acoustic energy across three decades from 30 Hz to 30 kHz. The hydrophones and recording system utilized for these measurements contain a known but uncalibrated roll-off about 30 kHz. Thus, it is difficult to comment on the true acoustic output above this frequency range for these measurements. The following section focuses on the trend found between the period, T₁, and the peak pressure of the first pulse, P₁, in the time series as a function of depth.

The period, T₁, was found to decrease with depth. This trend is generally expected from Lord Rayleigh's analysis of a spherical cavity immersed in a surrounding liquid¹¹ that predicted the cavity collapse time to be inversely proportional to the square root of the hydrostatic pressure,

where A is the maximum cavity radius (m), ρ is liquid density (kg/m³), P₀ is the total pressure (Pa) at depth, and T is the period of oscillation (s). For the purposes discussed here it is convenient to write the total pressure, P₀, as a function of depth such that

where P_atm is the atmospheric pressure (101 300 Pa), ρ is liquid density (1000 kg/m³ for fresh water), g is the gravitational acceleration (9.81 m/s²), and h is the depth of the source (m). For a given chamber volume and surrounding fluid density, the period of bubble oscillation becomes inversely proportional to the square root of the total pressure. Thus, with these assumptions combining Eqs. (1) and (2) yields

where C is a proportionality constant that can be empirically determined for a given set of conditions. Figure 3(b) shows the period, T₁, between the rupturing of the disk and the initial volume collapse for each of the events captured during the field test and the event from the high speed underwater video recording as a function of depth, as well as a curve produced by Eq. (3) whereby C was found to equal 10.3 from a best fit algorithm. As seen in this figure, the data follow this trend quite well, even though the geometry of the bubble collapse and oscillation is quite different than that of a spherical cavity.

A comparison between the measured peak pressure of the first pulse, P₁, and the predictions of a model based on the nonlinear Keller-Miksis bubble dynamics equation¹² which includes acoustic radiation, viscous damping, surface tension, and, as implemented here, gas thermodynamic effects,^12,13 is included here as an additional step toward a predictive model. An example of this comparison is provided in Fig. 3(a), which shows the modeled peak acoustic pressure as a function of depth for an equivalent chamber volume along with the measured peak pressure values of the first pulse, P₁, from the measurements described previously. For this application, the model computes the radiated acoustic pressure due to free oscillations of a spherical bubble with a volume equivalent to the collapse chamber. Initial conditions are specified to match the high external hydrostatic pressure and the low internal pressure of the chamber. The model does not attempt to include features resultant from cavitation, such as the secondary high amplitude pulse and subsequent bubble oscillations.

The initial bubble radius was set to the radius of a sphere with the same volume as the collapse chamber, and the initial internal pressure of the bubble was set to 2.5 kPa simulating the partial vacuum conditions at the beginning of the experiment. The external pressure was defined as the hydrostatic pressure in the water column at the depth of rupture with zero acoustic drive pressure. After solving the ordinary differential equations for the time history of bubble radius R as well as the first and second time derivatives of the bubble radius. One can compute the radiated acoustic pressure p(t) at a distance of 1 m from the source by

where ρ is the density of the surrounding water and the dot and double-dot indicate the first and second time derivatives. The peak pressure was then obtained from p(t) for comparison with the experimentally measured peak pressure, P₁. In Fig. 3(a), it can be seen that these preliminary modeling efforts generally show good agreement with the measured data. Both measurements and model show the peak pressure, P₁, tending to increase as a function of depth for a given volume.

It should be noted that although the events were generally found to be repeatable, the data do show some significant deviations in the acoustic features resultant from the bubble cloud produced by cavitation. For example, the secondary pulse occurring directly after P₁ was found to vary in amplitude throughout the data. For some events, this secondary pulse would be higher in amplitude than P₁ as seen in Fig. 2; however, this was not always found to be the case. Furthermore, the features resultant from the residual bubble oscillations [features labeled χ, δ, and ϵ in Fig. 1(b)] were found to show significant differences in amplitude and period between events as well. The initial modeling efforts described here do not attempt to include the complexities of cavitation and the resultant acoustic features observed throughout the data. Rather focus of the present modeling was on the most repeatable features of this source, the initial collapse period described by T₁ and collapse pressure P₁.

The relationship between the acoustic output and some characteristics of the bubble activity during a RIUSS event was investigated using high-speed video and a co-recorded hydrophone signal. In addition, free-field source signatures were measured and preliminary modeling steps were taken to quantify the collapse period and peak pressure of the collapse as a function of depth. It was found that the period of the collapse and peak pressure are scalable, thus allowing the RIUSS to be tailored to the requirements of a particular experiment or survey. The models described can thus be useful as a first-order design tool for future RIUSS implementations and as a starting point for more complete models in the future.

This research was supported by ARL:UT's Independent Research and Development Program and ONR Ocean Acoustics program.