The PHERMEX radiographic facility has been used to study the interaction of shocks with cylindrical aluminum rods, V notches, and cylindrical voids in water. The experimental results are compared with two-dimensional numerical PIC (particle-in-cell) computations. Agreement between computation and experiment was within the resolution of the methods.
The authors gratefully acknowledge the assistance and contributions of S R Orr and G N White, Jr, of T-5, F H Harlow of T-3, W C Davis of GMX-8, and R K London of MX-l11 of the Los Alamos Scientific Laboratory.
The interaction of a shock wave with a cylindrical aluminum rod, a V PHERMEX [1] radiographic facility of GMX-11. The cylindrical void has also been studied using the framing cameras of GMX-8. These systems were further studied numerically using the PIC technique for solving the two-dimensional hydrodynamics. Although the resolution available to the PIC technique from present computers is not detailed enough for many purposes, this is the only method available to describe the fluid flow of greatly distorted multicomponent systems. Therefore the experimental results should be useful in evaluating future numerical hydrodynamic schemes for treating similar complex flow problems.
The particle-in-cell method for solving two-dimensional hydrodynamic problems has been described by its originator, F H Harlow of T-3, and his co-workers [2]. The particular version of his method that we used has been described by Mader [3] [4] [5].
The explosive-Plexiglas driving system was approximated as a constant-velocity piston whose velocity was adjusted to give the experimentally observed unperturbed position of the shock as it interacted with the density discontinuity. The equation of state parameters for water and aluminum were identical to those described in reference [6]. The cell size was 0.078125 cm for the cylindrical void and aluminum rod computations and 0.03125 cm for the V notch computations. The resolution of the computations was, at best, ± 0.05 cm.
The PHERMEX [1] radiographic facility was used by Taylor and Venable to study the interaction of a shock with the density discontinuities in water. A sketch of the experimental setup is shown in Fig. 1.
The shocks were generated by a 4 × 4 × 8in.-long block of Composition B × 4-in. Plexiglas box with 1/4-in.-thick sides and bottom and 1/16-in. -thick front and back walls, placed on top of the pad of explosive. The density discontinuities were aligned in the box so that the axis of the radiographic beam was identical with the longitudinal axis of the discontinuity. This arrangement permitted maximum radiographic resolution which was approximately ± 0.1 μsec and ±0.02 cm without time smear or μ0.05 cm with time smear for a 0.5-cm/μsec shock velocity.
The x-ray pulse was produced by a burst of 20-MeV electrons impinging upon a. 3-mm-diameter tungsten target resulting in radiation intensities up to 0.4 roentgen at the Plexiglas box, which was positioned approximately 3 meters from the target. The x-ray film was placed approximately 0.75 meters behind the box in a protective aluminum case.
The shock wave was plane for purposes of comparison with the computed model. Figure 7 shows the results of shots using an 8 × 8 × 8-in. pad of explosive to obtain a more nearly plane shock wave. The interactions with a cylindrical void of shocks produced by the 8 × 8-in. and the 4 × 4-in. driver were essentially the same. We conclude that the curvature of the wave does not have an important effect on the results.
The experimental shock wave was not flat-topped, and became attenuated as it ran through the water. The following measurements of the shock velocity of the front were made using pins.
| Distance from Plexiglas-Water Interface to Shock Front (cm) | Time (μsec) | Average Incremental Shock Velocity (cm/μsec) | Average Pressure(kbars) |
|---|---|---|---|
| 1.985 | 3.20 | 0.62 | 184 |
| 2.993 | 4.90 | 0.59 | 161 |
| 3.995 | 6.72 | 0.55 | 135 |
| Time after Shock Arrived at Plexigas-Water Interface | ||||||||
|---|---|---|---|---|---|---|---|---|
| 4.9 μsec | 6.0 μsec | 8.1 μsec | 9.5 μsec | |||||
| Exp | Comp | Exp | Comp | Exp | Comp | Exp | Comp | |
| Axial thickness (height) of A1 rod (cm) | 1.89 | 1.88 | 1.67 | 1.69 | 1.70 | 1.70 | 1.60 | 1.55 |
| Radial thickness (width) of A1 rod (cm) | 2.00 | 2.00 | 2.10 | 2.05 | 2.20 | 2.20 | 2.30 | 2.25 |
| Axial tdistance of shock wave above top of A1 rod (cm) | - | - | - | - | 0.45 | 0.45 | 0.70 | 0.75 |
| Maximum radial distance of reflected shock wave from axis of A1 rod (cm) | 1.20 | 1.23 | 1.90 | 1.80 | 3.20 | 3.30 | 3.90 | 5.80 |
The experimentally observed interaction of a shock with an aluminum rod in water is well described by the computations as is shown in Table I and in Fig. 2 and Fig. 3.
| Time After Shock Arrived at Apex of V Notch | ||||
|---|---|---|---|---|
| 1.5 μsec | 2.5 μsec | |||
| Exp | Comp | Exp | Comp | |
| Distance of jet peak above initial apex of V notch (cm) | 0.90 | 0.89 | 1.45 | 1.47 |
| Distance of lowest part of jet above initial apex of V notch (cm) | 0.70 | 0.72 | 1.10 | 1.12 |
The experimentally observed interaction of a shock with a V notch in water also appears to be well described by the computations as is shown in Table II and in Fig. 4 and Fig. 5. Density variations observed in the jet region are qualitatively reproduced by the computations; however, a quantitative comparison is not possible because of the lack of detail of the computations. It is interesting to note the large differences between the radiographs of a shock interacting with a V notch in water and those of a shock interacting with a V notch in aluminum [1]. The V notch in aluminum shows greater density gradients because of complicated spalling and elastic behavior of the aluminum. A fluid computation such as that used in this report, since it does not include spalling or elastic effects, yields similar results for water and aluminum V notches. While the computations appear to reproduce the water V notch radiographic results, they are completely inadequate to describe the aluminum V notch.
| Time After Shock Arrived at Plexiglas-Water Interface | ||||||||
|---|---|---|---|---|---|---|---|---|
| 4.9 μsec | 5.9 μsec | 7.6 μsec | ||||||
| Exp | Comp | Exp | Comp | Exp | Comp | |||
| Distance of jet at axis above initial bottom of void (cm) | 0.70 | 0.69 | 1.30 | 1.31 | 2.40 | 2.50 | ||
Finally, the experimentally observed interactions of a shock with a cylindrical void both in water and in polyethylene are shown in Fig. 6 and Fig. 7. The computed interaction of a shock with a cylindrical void in water is shown in Fig. 8. The experimental radiographs and the coputations agree well except near the time of closure of the void. The agreement is good both when the void is approximately half-closed and after the shock has traveled about half of the void diameter above the top of the void. Between these positions the computations correctly predict the position of the jet at the axis, as shown in Table III, but the water appears to move faster than was predicted above the equator of the void between the outer rim and the axis. Additional evidence of the position of this region is shown in Fig. 9. Framing camera pictures of the closure of a 1-cm-radius void in polyethylene with a shot geometry identical to that of the PHERMEX shots were taken by J Travis and W Morton.
Figure 10 shows the void profile from the computations, the framing camera, and PHERMEX, when the hole is approximately 5/6 closed at the axis. The difference between the PHERMEX and framing camera pictures is probably caused by the low density region between the outer rim of the void and the high density region at the axis; the framing camera positions are not density-dependent as are the PHERMEX results. The computations closely reproduce the density gradients of the PHERMEX radiograph. The computations and framing camera pictures agree well except that the outer rim is closing faster in the computations. This difference is within the resolution of the computations and of the shock curvature and attenuation effects present in the experimental results.
Agreement between the dynamic radiographs and the numerical PIC computations of the interaction of a shock with an aluminum rod and with a V notch in water was obtained within the error of approximately ±0.05 cm or ±5% of the initial density discontinuity radius or height in the experimental and numerical resolution of the interfaces and shock positions. The radiographs and the computations of the interaction of a shock with a cylindrical void in water agree well except near the time of closure of the void. The agreement between the framing camera pictures and the computations is satisfactory.
The experimental results should be useful for evaluating future numerical hydrodynamic schemes.
1. Venable, D, PHERMEX, Physics Today, 17, No 12, (1964).
2. Harlow, F H, The Particle-in-Cell Computing Method for Fluid Dynamics, in Methods in Computational Physics, Vol. 3, and Amsden, A A, The Particle-in-Cell Method for the Calculation of the Dynamics of Compressible Fluids, LASL, LA-3466, 1966.
3. Mader, Charles L, The Two-Dimensional Hydrodyamic Hot Spot, Los Alamos Scientific Laboratory Report LA-3077, 1964.
4. Mader, Charles L, The Two-Dimensional Hydrodynamic Hot Spot, Vol. II, L LA-3235, 1964.
5. Mader, Charles L, Initiation of Detonation by the Interaction of Shocks with Density Discontinuities, Phys. Fluids 8, 1811 (1965).
6. Mader, Charles L, The Two-Dimensional Hydrodynamic Hot Spot, Vol. III, LA-4350, 1966