One aspect of Rocfire requires a description of how the AP particles are packed. It is known that the size and distribution of the AP particles within the heterogeneous solid propellant affects its combustion. Early attempts at three-dimensional calculations used a lattice propellant, a regular bimodal array of spheres, but some of the surfaces created were physically unrealistic. Thus, an algorithm that generates random propellant morphologies, the way in which the particles are packed, was developed.

This packing algorithm is now called 'Rocpack'. The basic ingredients of Rocpack are (1) the AP and Al particles are treated as spheres, (2) the spheres can have various sizes, with the size distribution defined by experimental data, and (3) the algorithm uses a concurrent packing strategy.

The concurrent method differs from a sequentail method (where each sphere is placed inside the cube one at a time, most likely via a Monte-Carlo method, with special care so as not to have any two spheres lie inside one anther) in that all spheres are placed randomly within a periodic cube with an assigned random velocity, but with zero initial radius. As time evolves the spheres grow linearly in time and move in the direction as dictated by their velocities. When two spheres collide, they are repelled using classical collision dynamics. The algorithm stops when either a desired packing fraction (defined as the ratio of the total sphere volume to total cube volume) is achieved, or when the pack becomes jammed.

The packing algorithm is one of the most significant breakthroughs since the inception of the center, and without it multi-dimensional flame calculations are not possible.

Below are two examples generated by the packing algorithm.

The first example generated by Rocpack shows a packing model realization of SD-I-88-13 using data from R.R. Miller ("Effects of particle size on reduced smoke propellant ballistics." AIAA Paper 82-1096, June 1982).

The data consists of three cuts; an 18% by weight of 24 micron Aluminum (shown as red spheres), a 40% by weight of 20 micron AP (blue spheres), and a 30% by weight of 6 micron AP (copper spheres). Note that within each cut all spheres have the same diameter. The interstitial space is binder. The periodic cube is outlined in white.

The packing movie is about 11 Mbytes and can be viewed by clicking on the image. As the movie plays note that the spheres have random initial positions with zero radius, and as time evolves, the spheres grow and move colliding and bouncing off each other until the spheres are jammed tight and no further movement is possible. The movie shows the dynamic nature of the packing algorithm.

Real propellants are not, however, composed of single-size spheres within each cut. Generally there is a wide range of sizes within each cut. Thus, Rocpack was modified to allow for experimental particle size distributions within each experimentally defined cut. An example is shown at the right.

This is another Miller pack (cited above) called SD-III-88-24 consisting of 31.58% by weight of a 200 micron AP cut (red spheres), 42.11% of a 50 micron AP cut (blue spheres), and 13.68% of a 20 micron AP cut (yellow spheres); there is a total of 10,000 particles. Each cut contains a wide range of particle sizes, and in constructing the movie we have used data supplied by the Thiokol Corporation. The packing density achieved by the algorithm is 0.7698, which differs insignificantly from the true value of 0.766.

The 3D packing movie is about 11 Mbytes and can be viewed by clicking on the image. Again the movie shows the dynamical nature of the packing algorithm.

Recent improvements include the parallelization of Rocpack using OpenMP and MPI so as to simulate millions of AP particles. In the near future we plan to show packs generated with a large number of spheres. For more information about Rocpack, see references 10 and 11.

T.L. Jackson (webmaster)
E-mail: tlj@csar.uiuc.edu
URL: www.csar.uiuc.edu/~tlj

Site Last Modified: February 1, 2003