Implosion-driven technique to create fast shockwaves in high-density gas

. Pressurized tubes surrounded by either one or two layers (separated by a secondary tube) of sensitized nitromethane and encased in a thick-walled tube (the tamper) were imploded. The distance between the detonation wave in the explosive and shock wave in the innermost tube were measured (the standoff). A simple model based on hoop stress and acoustic interactions between the tubing was developed and used to predict the standoff distance. At low initial pressures (on the order of 7 MPa), results indicate that the secondary tube and two layers of explosive did not prove to signiﬁcantly increase the standoff. However, at higher pressures (on the order of 10 MPa), standoff was noticeably greater when the secondary tube was inserted between the pressurized tube and the tamper. The measured values are in reasonable agreement with the predictions of the model.


INTRODUCTION
The extremely high energy density of explosives permits them to be used as drivers for shock tubes in which a pressurized tube of gas is imploded by a surrounding explosive layer. Shock waves can thus be driven through gas at very high initial pressure (10 MPa) to very high velocities (20 km/s). In addition to applications of high energy density physics, such devices can also be used as drivers for hypervelocity launchers. A recent study of the dynamics of implosion-driven shock waves and interaction with the resulting radial expansion of the tube identified the use of a thick-walled tamper surrounding the explosive as integral to effective operation of the device [1]. In addition to providing confinement of the detonation products and focusing more energy release inward to implode the tube, the tamper also plays an essential role in helping confine the dynamic expansion of the tube due to the gas shock, delaying rupture of the tube prior to the arrival of the detonation. Effective interaction between the pressurized tube and the tamper requires that the explosive layer be thin, so that compression waves can quickly communicate with the tamper across the explosive layer. However, imploding tubes pressurized to higher initial pressure (>10 MPa) may require thicker layers of explosive for a complete pinch. Thus, optimization of the device to produce large shock velocities and shock stand-off distances at high initial pressure requires a compromise between these two competing effects.
At higher fill pressures, the innermost tube is more likely to rupture mid-experiment, and the geometry within the apparatus has a greater impact on its performance. The use of an intermediate layer of high impedance material in the explosive to provide better dynamic confinement while enabling a greater total thickness of explosive is explored to achieve the enhanced tamping effect illustrated in Figure 1

MODEL
A simple model of the dynamics of the radial expansion of the pressurized tube and its interaction with the surrounding (liquid) explosive and tamper has been developed that uses acoustic wave tracking [1]. This model is justified since the radial motion of the tube (order of 100 m/s) is much less than the sound speed of the explosive (1500 m/s) into which it expands. The radial dynamics of the tube after the passage of the shock wave is modeled using a thin-walled hoop stress approximation and the Cook-Johnson strain-rate dependent yield model. The passing shock wave and consequential pressure increase swells the tube, allowing the wall to act as a one-dimensional piston that generates an acoustic wave in the liquid explosive. Across an acoustic wave, the difference in pressure is proportional to the difference in wall speeds: This wave propagates at the sound speed c 0 of the fluid, and eventually meets the tamper and reflects back onto the inner tube, creating zones of different pressures as in Figure 2. In general, the motion of the tube wall will generate a new acoustic wave at each time step of the simulation. As such, we can express the total pressure as the instantaneous change in pressure felt by a differential segment of wall summed with the reflected pressure. This algorithm is described in detail by Szirti [1], and is used iteratively in the case of a three-body problem. Should an intermediate tamper exist between the pressurized tube and the outer tamper, the same algorithm may be applied at each time step. It first solves for the pressure on the outer surface of the pressurized tube and inner surface of the intermediate tamper, and then considers the latter as a pressurized tube generating its own acoustic waves and interacting with the tamper.
Sample results of the model showing the positions and radial velocities of the pressurize tube, the intermediate layer, and the outer tamper are presented in Figure 3 and Figure 4: A delayed response can be seen over the radial positions, owing to the slow outward propagation of the pressure in the innermost tube. Similarly, all three layers undergo similar velocity profiles, just with a delay between them. The timescale of this figure (10 μs) is representative of the timescale from passage of the precursor shock at a given section to the arrival of the detonation.

EXPERIMENTAL DESCRIPTION
The experiment test set-up was based on that of Szirti et al. [1], with the design modified to permit an intermediate layer of metal of various thicknesses to  be inserted into the explosive layer. The schematic of a typical charge is shown in Figure 5. The charge was instrumented with twisted pairs to give the detonation wave time of arrival and shock pins (Dynasen CA-1135) to monitor the arrival of the precursor shock wave in the gas. The explosive used for all experiments was nitromethane sensitized with 10% diethylenetriamine.
Each experiment consisted of a 12.7 mm outer diameter tube with 0.89 mm wall thickness with an effective length of 0.75 m that was pressurized with helium to 7 to 12 MPa initial pressure. Table 1 describes the radial geometry of the tampers and intermediate tampers (if used), as well as their initial fill pressures. Trials 1-3 did not use an itermediate tamper and varied the tamper thickness and diameter, which also results in a varying thickness of the layer

RESULTS
After the experiments were concluded, a standard detonation velocity of 6.73 km/s was determined by averaging the time of arrival and positions of all the twisted pairs. This value is greater than the detonation velocity at ambient conditions due to dynamic precompression from the expansion of the pump tube. As the detonation velocity in nitromethane is expected to be similar throughout the above charges, an average velocity was used to counter any experimental inaccuracy. This was then compared to the recorded average shock velocity of each charge, and the standoff distance was taken at 595 mm from the initiation point across all experiments. This value is presented in Table 2, along with predicted standoff distances from the model.
We note that at lower fill pressures (on the order of 7 MPa), standoff distances are not greatly affected by the presence of the intermediate tamper, as in trials 2-6. In contrast, at initial pressures between 10 and 12 MPa, charges with an intermediate tamper (trials 7-9) significantly outperformed those with just a thick layer of explosive (trial 1). Error between the model predictions and actual standoffs range between 5 and 45%. This can be accounted for in the simplicity of the one-dimensional model, which neglects the multidimensional aspects of the problem.

CONCLUSIONS
While the influence of intermediate tampers is questionable at lower fill pressures near 7 MPa, standoff distances noticeably improve at pressures greater than 10 MPa. Future work includes the testing of this implosion method for a single geometry across a range of initial fill pressures and the coupling of it to phased-detonation techniques [2].