Research Objective: To develop and test a version of the 2-D PPM code for simulating transient supersonic flows about objects which move under the influence of the pressure forces exerted upon them by the surrounding flow.

Methodology: In this experimental computational approach, the surface of the moving sabot petals is represented on a uniform Cartesian grid as a series of zones, or cells, which are partially filled with impenetrable fluid. The problem is thus reduced to a two-fluid hydrodynamics problem, and in the process, the surfaces are made rough on a scale comparable to the grid spacing. A rigid object mask is accelerated by the flow and used to determine the new zone filling factors on each time step. Two grid resolutions were used in order to evaluate convergence of the results. The results were also discussed with several aerodynamics experts and with experts on sabot discard at ARL, Aberdeen. The simulations were restricted to 2-D in order to achieve interestingly high grid resolutions.

Accomplishments: Results for the two grid resolutions, the finer of which involved 5 million computational zones, compared quite well. In particular, the motion of the sabot petals was very nearly the same in both runs. Interesting features of this very dynamic flow could be traced to viscous effects. These features require a viscosity in order to develop, but the similarity of the two runs, in which effective viscosities differ by a factor of 8, indicates that the precise details of the viscosity do not affect these features significantly. A recirculating wedge of air was found to form and to extend to the projectile tip. The angle of this wedge of air was independent of the grid resolution, and hence of the size of the viscosity. The opening angle of this wedge of air, and hence the angle of the attached bow shock, appears to be determined by the back pressure set up by the choked air flow in the confined region between the opening sabot petals and the projectile. This phenomenon occurs early in the discard process even in 3-D, as a visit by the Minnesota team to ARL and discussions with experts there revealed. However, in 3-D this phase is very brief, since the back pressure is rapidly relieved as the air escapes between the opening sabot petals. In 2-D, the sabot "petals" are actually slabs, and no such relief of the back pressure is possible until the petals are fairly completely blown away.

Significance: The problem of sabot discard is a true Army "grand challenge." The importance of the problem and the novelty of this experimental approach, which greatly simplifies the treatment of complex projectile and sabot geometry, make this project worth pursuing. In this extremely transient process of sabot discard, it is difficult to see why the details of boundary layer structure should be important. Therefore a highly simplified treatment of these layers should be justified. The computational techniques tested here are applicable to a wide range of problems involving the interaction of supersonic gaseous streams and/or shock waves with movable objects or surfaces. Such problems are of importance to the D.o.E. in the context of weapons effects simulations.

Future Plans: 3-D simulations will be performed to verify that some features of these runs, which are unfamiliar to those involved in 3-D experiments, are strictly 2-D effects.

Vorticity and density in a Mach 4 sabot discard simulation