A Compressible Fluid Power Dynamic Model of a Liquid Propellant Powered Rifle

This paper presents a dynamic model of the interior ballistics of an experimental liquid propellant-powered rifle. The liquid propellant-powered rifle described utilizes a mixture of Hydroxyl Ammonium Nitrate (HAN) and hydrocarbon fuel to replace gunpowder typically used in such firearms. The motivation for such a development is to discard the need for a shell casing whereby carrying only propellant and bullets will reduce both the mass and volume per shot carried by the soldier. A first-principles dynamic model of the interior ballistics is derived as a compressible fluid power problem with the chemical liberation of heat within the chamber modeled via a condensed-phase reaction rate law. The model is used to predict the overall performance in terms of ballistic kinetic energy as well as draw design insight regarding the role of friction, chamber geometry, and the profile of chamber pressure with respect to time. Simulation results are presented as well as preliminary experimental results from a proof-of-concept device. 1.0 INTRODUCTION The motivation for this work is primarily to dispense of the brass shell casing that houses gunpowder in firearms such as the M16-A2 military rifle in order to lighten the ammunition load of foot soldiers. The proposed mechanism for achieving this is to replace the conventional solid propellant (gunpowder) with a liquid propellant that is a stable mixture of fuel (hydrocarbon fuel) and oxidizer (Hydroxyl Ammonium Nitrate). This paper outlines the potential advantages of this approach and formulates a dynamic model of the interior ballistics used to offer design insight and predictions regarding performance. Experimental results and observations are used to validate the model. A conventional rifle is shown in Figure 1. An impact primer ignites a mixture of sulfur, charcoal, and potassium nitrate or some similar mixture that is contained in a brass case. These solid pellets of propellant begin to burn rapidly, creating a highpressure gas that pushes the bullet down the barrel. A liquid propellant approach uses the same basic concept regarding the generation of a high-pressure gas to propel a bullet, yet allows a number of potential advantages. Among these are the following: 1) a reduction in the total mass carried per shot given that the brass casing is no longer necessary, 2) a reduction in the mass of propellant per shot given that the liquid propellant can be formulated to be more energy dense that the solid propellant, 3) the capacity to carry more rounds per clip given that only the bullets need to occupy the clip, 4) a weapon less prone to jamming given that no ejection port or mechanism is required, 5) the potential for variable selectable muzzle velocity (non-lethal to high-power) by injecting variable amounts of liquid propellant into the combustion chamber, and 6) safer logistics given the transport of non-explosive liquid containers. Figure 1: M16-A2 Rifle Previous work regarding liquid propellant powered weapons includes a broad research effort by the U.S. military to employ liquid propellants for large scale artillery guns. The Crusader or “Advanced Field Artillery System” (AFAS) was a large-scale artillery gun (Figure 2) that was to replace the solid propellant powered M109A6 Paladin howitzer and older M109A2/A3 howitzer in service since 1960. There were, however, numerous problems with its design and the program was cancelled in 2002. One of the largest problems with the Crusader was the rapid reaction rate of the propellants, if bulk loaded, would 1 Copyright © 2004 by ASME cause a pressure spike leading to catastrophic failure of the gun. The Crusader therefore employed a so-called regenerative system that would inject propellant into the chamber as the reaction preceded in order to slow the rate of pressure build-up. This requirement led to various design complications and a complex overall system. The Crusader program was cancelled in 2002. A mass based comparison of the proposed HAN/ethanol liquid propellant powered system reveals a significant advantage over a conventional M16A2 system. The most obvious way that the mass reduction will occur is through elimination of the shell casing due to the fact that the propellant can be injected directly into the chamber. The casing amounts to nearly half of the mass of a round of ammunition in the conventional M16A2 system. Mass savings are further enhanced when considering the high mass specific energy density of the liquid propellant over powder. Experimental firing data yields a maximum value of 2205 kJ of delivered kinetic projectile energy per kilogram of propellant, as compared to 1215 kJ/kg for powder in a conventional M16A2 weapon. As summarized in Table 1, this implies that the mass per round for an equal kinetic energy shot with the liquid propellant system is 42% of that for the conventional M16A2 system. M855/SS109 (M16A2) Mass Liquid Propellant System Mass Case 6.2 g Case N/A Bullet 4.0 g Bullet 4.0 g Powder 1.6 g Propellant 0.9 g Total 11.8 g Total 4.9 g Figure 2: Crusader As shown by the dynamic model presented here, the application of a liquid propellant powered weapon system on a smaller scale avoids the difficulties of over-pressurization and allows a simple bulk-loaded design. Smaller caliber weapons, such as the M16, are promising application domains given the appropriate scaling of the coupled chemical reaction rate dynamics and inertial dynamics of the projectile. Specifically, the inertia of the projectile is more appropriately matched such that the reaction rate dynamics of the bulk-loaded propellant is of an appropriate time scale to produce a pressure profile with peak pressures capable of being contained with conventional materials. Table 1: Mass-based comparison for equal muzzle velocity. A volumetric comparison also yields benefits with regard to the number of bullets that can be carried in a magazine (clip), as well as the reduced volume occupied by the propellant. Seven times the number of bullets can be placed in a magazine because of the elimination of the shell casings. Figure 3 shows a pictorial representation of this increase. Dispensing of the shell casings requires that the propellant must be housed somewhere in the weapon. Candidate locations for storage of the propellant include the hollow spaces in the handle or the stock, or both (see Figure 1). Based on experimental data, the volumetric energy density of the proposed system is 3.05 kJ/ml (projectile kinetic energy per milliliter of propellant) versus 1.04 kJ/ml for the conventional M16A2 system. This implies a volumetric requirement per shot of the proposed system that is 34% of that for the conventional system. 2.0 MERITS OF THE PROPOSED SYSTEM The most compelling motivation for looking into small-scale liquid propellant powered weapons is their distinct advantage over conventional propellant guns in ammunition mass that must be carried, volume occupied by the ammunition, and deliverable energy stored in the propellant. There has been a considerable amount of work done in studying the merits of various HAN-based liquid propellants for various applications. HAN has been stoichiometrically mixed with fuels such as methanol, ethanol, 1-propanol, 2-propanol, 1butanol, HEHN, and glycine. Various candidates have their advantages and disadvantages. Glycine, for example, has very safe propellant properties, however, its energy content is relatively low when compared with other fuels, and additionally is not very soluble in HAN. A HAN/methanol mix has much higher energy per unit mass, is a stable mixture, and is very soluble in HAN. However, methanol can be toxic if ingested or absorbed through the skin. A HAN/ethanol mixture has somewhat more energy than does HAN/methanol, is very soluble in HAN, is somewhat more stable than HAN/methanol, and is non-toxic. The comparisons, dynamic model, simulation results and experimental results presented in this paper are based on a stoichiometric mixture of 13 molar HAN and ethanol. Figure 3: Shows the number of shots capable of being stored in an M16 magazine with (left) and without (right) shell casings. 2 Copyright © 2004 by ASME Additional merits of the proposed system include: a weapon less prone to jamming given that no ejection port or ejection mechanism is required, the potential for variable selectable muzzle velocity (non-lethal to high-power) by injecting variable amounts of liquid propellant into the combustion chamber, and safer logistics given the transport of nonexplosive liquid containers. 3.0 DYNAMIC MODEL As shown in the model presented below, the reaction rate of HAN-based combustion reactions is proportional to the area of the barrel as well as the temperature of the reaction product gases. Simulations of a bulk-loaded system show that the inertia and length scales of an M16 result in reasonable and appropriate pressure profiles, and thereby support the notion of applying the liquid propellant concept to small-scale arms. The dynamics of the interior ballistics of the liquid propellant powered rifle can be cast as a lumped parameter model consisting of the motion dynamics of the bullet and remaining liquid propellant, the chemical combustion rate dynamics, and an energetically-based fluid power model relating the rates of change of pressure of the combustion gases to the work done by the gases. The literature contains various models and assumptions regarding the combustion of liquid propellants in guns. As was assumed in [1] and [2], it will be assumed here that the process results in a pocket of high-pressure combustion gases that forces the remaining quantity of propellant up against the bullet. This assumption results in a gas/liquid interface. The formation of such an interface, along with the assumption of an incompressible liquid propellant, allows the bulk representation of the slug of liquid propellant as a rigid body with variable mass. The combustion rate dynamics can then be expressed in terms of the area of the gas/liquid interface and the temperature at the interface surface. An energetic balance of a control volume drawn around the gas relates the enthalpy of the reaction, the pressure and temperature of the gas, and the work rate. Figure 4 shows a schematic of the process and the nomenclature used.