This article contains Section 2.3 (Theoretical Calculations) of the "Dissertation on the Study of Insensitive Highly Energetic Materials" as part of the Doctoral requirements for Theodore S. Sumrall at The University of Tokyo, March of 1998. Theodore S. Sumrall was awarded a Doctorate Degree from the Department of Chemical Systems Engineering in April of 1998 as a result of his research, development testing and dissertation presentation.

2.3 Theoretical Calculations

Prior to any small scale mixing, a theoretical evaluation of a proposed composition, (from safety, performance and cost standpoints) permitted the elimination of a large number of ingredient candidates.

A number of thermochemical computer codes were evaluated to determine which codes would be considered the most accurate for this research project. Additionally, other considerations (such as cost and proposed raw material availability) were taken into consideration. Also, the predicted rheological characteristics of the proposed composition were calculated, based upon past experiences with these materials, and a geometric analysis code. A code was written for the purpose of permitting maximum solids packing so that appropriate particle sizes would be chosen for the purpose of achieving maximum density and minimum viscosity. The upper viscosity limit goal was 2kP as measured by the Brookfield viscometer. This value was required to meet the goal of TNT processing equipment compatibility (Objective #4). TNT processing equipment has very low shear capability and therefore, a very thin composition was required in order to meet these processing goals.

A number of thermochemical codes were evaluated to determine which codes would be considered the most accurate for this research project. At the time that this research was underway, the most reliable codes were the NASA/Lewis [4,5,6] burn code and the TIGER [7] detonation code. A burn code as well as a detonation code were chosen for this effort, because in an aluminized composition both detonation and deflagration reactions occur. First, a detonation occurs through the composition where in the molecular explosive (i.e. TNT, RDX, etc.) detonates. The detonation reaction heats and disperses the other non-molecular explosive ingredients (i.e. Al and AP). The effect is essentially an artificial "fuel/air" explosive where the Al is the fuel and the AP provides the oxygen to burn the Al powder. Within the blast zone, little atmospheric oxygen is present, because the blast wave pushes the air away from the reaction site. However, due to the presence of oxygen generated by AP, there is sufficient oxygen available for the super-heated aluminum powder to react and undergo a rapid deflagration or explosion. This imparts tremendous heaving properties to the explosive and results in greater rock breakage.

First the NASA/Lewis code was employed to determine the Theoretical Maximum Density (TMD) for the formulation. The input information required to run the NASA/Lewis code are: empirical formula; densities; ingredient heats of formation; and weight percentages of each ingredient. The first NASA/Lewis run is calculated at a pressure of 1000 psi. Additional information of interest from the NASA/Lewis program is a value known as the Impulse Density or ID. The ID is the product of the specific impulse (Isp) and the density. The data of primary interest from NASA/Lewis is a factor known as "Impulse Density" (ID). Impulse density is calculated by multiplying the composition’s Specific Impulse (Isp) by the density. The specific impulse a measure of force per unit weight of explosive consumed in a burn reaction (since the post detonation reaction is essentially a burning reaction) and is a measure of the theoretical efficiency of the explosive’s blast potential. ID is therefore the product of Isp times density. The ID therefore is a relative measurement of the theoretical blast impulse potential of an explosive. While calculation of the ID at pressures predicted by the TIGER code would have been more realistic, the NASA/Lewis code was not capable of consistently generating ID values at pressures representative of a detonation. However, relative rankings were possible even at the lower pressures.

Once the overall formulation TMD is determined, then this is input into the TIGER code. Information needed to run the TIGER code is essentially the same as for the NASA/Lewis code. Once the TIGER output is obtained, then the detonation pressures and velocities (along with the ID from NASA/Lewis) are input into a three dimensional statistical optimization program (called MATLAB [8]) to optimize performance as a function of ingredient content (within processing limitations).

The overall process for these theoretical calculations is detailed in Figure 2.3-1. After conducting theoretical calculations, the literature was reviewed once again to help ensure that initial theoretical calculations were within realistic parameters.

A number of theoretical calculations were conducted to determine the effect on performance (Detonation Velocity, Detonation Pressure, Impulse Density) when the HTPB non-oxygenated binder was replaced with an oxygenated binder as well as the effects of replacing the nitramine (RDX) with a perchlorate salt (AP). The baseline for this study was TP-H8299. Additionally, the effect on aluminum addition to these performance characteristics was also calculated.

Figure 2.3-2 shows the predicted improvement anticipated in the detonation velocity of TP-H8299 as HTPB based binder is replaced with a PEG based binder at various levels of RDX (replacing AP). An approximately 5% performance improvement is anticipated by virtue of binder replacement alone.

Figure 2.3-3 shows the predicted change in detonation velocity as RDX is replaced with AP for both HTPB and PEG based versions of TP-H8299 at various concentrations of aluminum. While at lower levels of aluminum concentration, the replacement of RDX with AP appears to have a negative effect on detonation velocity, as aluminum concentration increases, this gap narrows. Indeed, it was later calculated that 20% aluminum is about the ideal concentration. Also of note, as aluminum concentration increases, detonation pressure decreases.

Figure 2.3-4 shows the predicted change in detonation pressure as RDX is replaced with AP for both HTPB and PEG based versions of TP-H8299 at various concentrations of aluminum. Again, at lower concentrations of aluminum, the replacement of RDX with AP appears to have a negative effect on detonation pressure until a concentration of approximately 20% aluminum is reached where the points converge.

Figure 2.3-5 shows the predicted improvement in Impulse Density as a function of aluminum content, binder type and AP/RDX Ratio. Generally, as aluminum concentration increases, Impulse Density increases. Of major note is that the composition containing a 50/50 ratio of AP and RDX (with a PEG binder and at a level of 20% aluminum) had the highest ID of all other compositions, including the baseline.

These theoretical calculations substantiated the belief that replacement of the non-oxygenated binder with an oxygenated version would improve performance.

Additionally, the belief that replacement of RDX with AP could be accomplished while actually improving performance.