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Solid Propellant Cases

This set of cases was performed on the isolated solid propellant, unbound and free to move. There were two models of the solid: an open-ended cylinder (Figure 1), and an identical cylinder with a slit along its main axis (Figure 2). Each case was run for 1600 time steps of size 1.0e-5 seconds.

The first case was the introduction of the pressure profile equally to all points on the solid surface. Then a pressure wave travelling parallel to the main axis was introduced in addition to the profile. For both cases, the results were nearly identical. Both the solid and slitted models compressed, decreasing in size as the pressure increased. For the slitted propellant, the slit flexed opened as the propellant size decreased. Figure 3 shows this phenomenon when the pressure is near its peak at 500 MPa (time step 1200).
Figure 1 Figure 2 Figure 3

Next, the pressure profile was introduced with a 5% pressure difference between inner and outer walls, where the pressure was increased linearly in the radial direction. This was done for the case of greater inner pressure and greater outer pressure. The results were expected; the greater inner pressure models enlarged where the greater outer pressure decreased in size. Figures 4 and 5 show the greater inner and outer pressure, respectively, at the 1200 time step for the solid propellant; figures 6 and 7 show the slitted propellant at time steps 400 and 200, respectively (Fig. 4 is shown 2/3 size; Fig. 6 is shown 1/4 size). The slitted propellant was flexed open by the greater inner pressure, and closed shut by the greater outer pressure. These cases were also run with a 1% pressure difference. The 1% run still had dramatic effects.
Figure 4 Figure 5 Figure 6 Figure 7

The pressure wave was then sent along the propellant with its pressure greater on the inner wall surface. In the case of the normal propellant, no significant difference from the original pressure wave run was observed. The slitted propellant, on the other hand, opened as the greater inner pressure profile case did, but did so more gradually, opening completely by time step 1000 as opposed to time step 400 in the earlier case.

In order to gain an understanding of the role of the slit surfaces, a run was done with no pressure applied to these surfaces. The result was a collapsing of the sides, closing the slit. This result was expected, for there was no longer a balance of inner and outer surface forces.

The pressure information was then made to propagate, as a function of time, along the length of the propellant. As the pressure higher on one end than the other, the solid propellant moves from the unbalanced force in the direction of lesser pressure. Its slit closed. No other notable differences were observed.

Next, several cases were run with a pressure wave travelling tangentially around the propellant. First, the wave was sent around with its inner and outer pressure equivalent. Second, the wave was sent around with its inner pressure set 5% greater than the outer pressure of the wave. Last, the outer pressure was set 5% greater than the inner wave pressure. The outcome was almost identical to the original pressure profile cases for the solid and slitted propellant.