On this page there are two types of examples talked about; they are 2D and 3D examples.
We will cover 2D examples first then move into the 3D examples.
Below are some two-dimensional examples of the coupled simulation, where the gas phase and the solid phase are solved coupled with the boundary conditions along the propellant surface.
To the right is an example of a periodic sandwich (AP/binder/AP) propellant.
The Damkohler number on the right is four times larger than that on the left. Note that the speed of the regressing front is faster at the higher Damkohler number.
The periodic sandwich configuration is important for code development.
Below are two examples of the burning of AP/binder propellant.
The propellant, shown as gray circles, and the binder, shown as yellow circles, is bimodal (200 micron/80 micron). The averaged regression rate (averaged over space and time) is approximately 2 mm/sec.
The movies show the transient nature of the propellant as it burns, as well as the non-flat regression surface.
Rocfire was run on the ASCI Blue Pacific, a 1,464 node 4-CPU IBM/AIX hypercluster located at LLNL, with 432 nodes feature 2.5G SDRAM and 18G local disk. The remaining nodes have 1.5G SDRAM and 9G local disk. The Blue Pacific resource operates in a classified environment that supports the Stockpile Stewardship Program. Scalability and timing results, shown in the figure below, were obtained while the Blue Pacific was in dedicated mode on the weekend of June 15, 2001. The top subfigure plots the speedup factor (circles) as a function of the number of processors. The speedup factor is defined as $p t_1/t_p$, where $p$ is the number of processors, $t_1$ is the time to run the code for one time step on one processor, and $t_p$ is the time to run the code for one time step on $p$ processors. (On the Blue Pacific, which has 4 processors per node, the use of $t_4$ instead of $t_1$ is more appropriate.) In this plot the baseline grid was 100 grid points in each of the two directions tangential to the surface, and 40 points in the normal direction. As the number of processors increased, the number of grid points in each tangential direction was increased by $\sqrt{p}$. In this way the number of grid points per processor remain fixed. For comparison, scalability studies were also conducted on the Turing cluster, with results plotted using squares. The Turing cluster, located at UI, consists of 208 dual-processor machines ranging in architecture from 400MHzPII to 1GHzPIII's, each with 1G RAM. The Turing cluster was made possible by an Intel donation of Dell Computers. In both cases excellent speedup was observed. The bottom subfigure shows timing results (defined as the time per grid point per time step, in $\mu s$) for a fixed grid of 20 million grid points. In this case the grid was held fixed, while the number of processors increased. The speedup was again linear, except when going from 256 processors to 400 processors on the Blue Pacific.
Burning rate variations are shown in the figures below for Miller packs SD-III-88-3 (left most figure) and SD-III-88-17 (center figure), respectively. Also shown are the corresponding experimental burning rates of Miller. SD-III-88-3 consists of 55.79% (by weight) of a 20 micron AP cut and 31.58% of a 0.7 micron AP cut. SD-III-88-17 consists of 31.58% of a 90 micron AP cut and 55.79% of a 20 micron AP cut. The actual packing data used in the simulations are given in Table 4 (right most figure; $N_j$ is the number of particles of sphere $j$ with diameter $d_j$). For each run a grid of 80x80x40 was used; a grid study using 180x180x60 at one pressure gave an average burning rate that differed by only 2%, and so the coarser grid was deemed sufficient. Each pressure and pack combination ran on 25 processors and took about 4 wall clock hours to complete two periods of burn-through. While the calculations gave averaged burning rates somewhat lower than the experimental values for SD-III-88-3, in both cases the trends show good promise. We are currently in the process of improving our model and will report new results at a later date.
For the burning rate figures, the experimental results of Miller are shown as solid/square, while the computational results are shown as dash/circle.
Shown here is a three-dimensional model of AP/binder propellant combustion. The 3D burning propellant movie is about 49 Mbytes and can be viewed by clicking on the image. In order to make the movie the grid was very coarse (only 40x40x40 grid), and so there is some noise in the data.
T.L. Jackson (webmaster)
E-mail: tlj@csar.uiuc.edu
URL: www.csar.uiuc.edu/~tlj
Site Last Modified: February 1, 2003
