Numerical Modeling of Cylindrically Shaped Propellant Packages for the U.S. Army
Authors: Zimmerman Eric B. 
Published: November 2021

Abstract
The United States Army is in the process of developing the next generation of 155mm self propelled artillery through the Armament Systems Division of United Defense in Minneapolis, Minnesota. This next generation artillery system, called Crusader, is fully automated and can fire up to 10 rounds a minute at distances in excess of 40 km. The weapon system employs a new Modular Artillery Charge System (MACS). MACS consists of a low zone charge, the M231, and a high zone charge, the XM232. Both are rigid combustible cylinders filled with propellant and they are approximately 15 cm in diameter and length. The XM232 is filled with approximately 500 cylindrically shaped propellant grains. The grains are similar in size and shape to that of a typical foam ear plug issued to visitors to high noise areas. A two centimeter thick center core of the cylinder which runs the length of both charges is filled with granular explosive powder which is used to centrally ignite the charges. Between one and six of the 15 cm diameter cylinders are loaded into the gun barrel depending on the distance to the target.
It is the goal of this new program to have highly accurate first fire capability for maximum effectiveness on the battlefield. It is imperative to have an accurate prediction of the exit velocity of the artillery projectile at time of firing to achieve this goal. Actual firings of the new gun tube with the XM232 propellant canisters revealed that the exit velocity of the projectile was highly dependent on the temperature of the propellant prior to firing. (The velocity achieved by the M231 is relatively insensitive to temperature.) One avenue under review to provide the propellant temperature prior to firing is to physically measure it. This was easily accomplished in earlier artillery systems as the propellant was granular and stored in cloth sacks. The soldier simply inserted a thermometer through the cloth to obtain a bulk temperature of the propellant inside. The new XM232 does not allow this as the canister walls are impervious and even if a way was found to insert a thermometer into the canister — the obtained temperature would be questionable considering the jumbled nature of the small propellant cylinders inside. Additionally, Crusader’s high rate of fire and automated ammunition handling system does not permit the soldier to manually take the temperature of the charge.
During August 1998 a series of test firings of the new gun barrel were conducted with the XM232s. Selected XM232s were instrumented with thermocouples located at different locations within the cylinder as shown in figure 1. The MACS were then soaked for 24 hours at either 50C or −30C. The MACS were then placed on wooden racks in a large thermal chamber maintained at 20C. The temperatures of the thermocouples were then recorded over a period of time as they either warmed or cooled. With this transient experimental data in hand a numerical model could be developed to predict the temperature of the MACS under varying environmental conditions. It was desired to achieve a thermal model in the most simple manner as possible. Thus the first effort was to model the XM232 cylinders as a homogeneous material. If reasonable predictions of the XM232 temperature could be achieved in this mode — more complex efforts could be avoided.
Consultations with the propellant manufacturer in Radford, Virginia provided the basic thermal properties of the material. A thermal circuit was then created between the outer surface of the XM232 to the inner core. Thermal energy has to pass through the outer shell material and then through the numerous small propellant cylinders and air voids between them. The material was handled as a homogeneous material and the porous nature of the insides was ignored. It was understood that there would be some thermal stratification of the air inside as shown from the experimental data. But it was hoped that reasonable predictions could be accomplished without considering the bouancy of air trapped between the small cylinders. Series and parallel thermal circuits were developed with either the air and propellant in series or in parallel to get the range of thermal resistances between the two situations. It was expected that the actual thermal resistance would lie somewhere between the two situations. Initial efforts involved superimposing transient solutions to one dimensional problems (infinite cylinder and plane wall) to obtain the multidimensional solution to the short cylinder. While that method provided reasonable comparison to the experimental results after an initial two hour period — there was not a very good comparison prior to that time. The Fluent software package was then used with the ambient air temperature profile in the experiments and the initial temperatures of the XM232s to obtain the predicted three dimensional internal temperatures of the XM232. A three dimensional tetrahedral grid was created with approximately 74,000 nodes. Time steps of 100 seconds were applied for the first 20 minutes with longer time steps being applied as the gradients between the outer surface and the surrounding air decreased. The XM232s were cooled or warmed via natural convection from the surrounding ambient air. At the beginning of each time step the average surface temperature would be obtained from the Fluent software package and then the average convective heat transfer coefficient “h” between the outer surface and surrounding ambient air would be calculated usingreadily available correlations from standard heat transfer books.
Comparison of the experimental and numerical predictions at various locations within the XM232 for both the hot to ambient and cold to ambient were very good. The numerical predictions were a bit low on the upper half of the cylinder and a bit high on the lower half of the cylinder. This was expected as we did not consider buoyancy in this analysis. The experimentally measured temperature along the outer edge of the inner core tube matched up very well for both the hot and cold XM232 predictions. This was good news considering that the temperature at this location provided excellent correlation to the exit velocity of the projectile. The result of the above efforts was that a simple three dimension numerical model was developed to predict the temperature near the center of the XM232 for both a warming and cooling situation. The next use of the model is to predict the XM232 average temperature under a variety of transient ambient conditions. It is expected that these studies will facilitate higher first fire accuracy for the new Crusader Artillery System.