Specificity of Burning of Porous Combustible Material Used as Cartridge Case

Abstract

The combustible cartridge case has become an integral part of many modern weapons systems. The energetic and burning characteristics of the combustible case can have a significant impact on shot parameters. This paper describes Closed Vessel Tests (CVTs) performed on combustible cartridge case material and presents a method of determining the physical burning law and the linear burning rate of the tested material. The method was verified on the basis of the results of CVT of the felted combustible cartridge case material of a 120 mm tank round. It is shown that, in the case of porous combustible materials, the standard methods of determining the burning rate fail. The porosity of combustible materials greatly increases the burning surface and heat feedback from the burning zone to the unburned structure. These effects significantly increase the burning rate of porous materials. The results of analysis show the strong dependence of the burning rate on pressure. The results of this study can be applied in the modeling of gun propellant systems that contain combustible case elements.

1. Introduction

The use of combustible cartridge cases in the production of ammunition dates back to World War II. Combustible cartridge cases are widely used in both small arms and artillery ammunition [1,2]. The elimination of metal cartridge cases has many advantages especially in artillery weapons, including no problems related to cartridge case removal from the combat vehicle after the shot, reduction in the amount of propellant gases inside the vehicle, and less weight of ammunition. The combustible case increases the mass of the gases produced as a result of its combustion. This has an impact on the parameters of the shot, such as the pressure in the barrel (space behind the projectile) and the velocity of the projectile. Therefore, simulations of the phenomenon of the shot, the so-called solution to the Internal Ballistic Main Problem (IBMP) [3,4,5,6,7], require input data, such as the energetic and ballistic characteristics of the combustible case material.

The equation of gas generation and the burning rate’s dependence on pressure are among the most important ballistic relationships from the point of view of solving the IBMP. The standard methods of experimental determination of the burning rate described in the monograph [4] and in the standardization document [8] are based on the geometric law of burning. According to this law, the gun propellant (as a solid material) burns in parallel layers on the outer surface. Analyses of the properties of combustible cartridge materials fabricated by various methods, such as by foaming, felt-moulding, winding, or impregnation of resin in the felted combustible components, show its porous internal structure [9,10,11].

The porosity of combustible materials greatly increases the burning surface and heat feedback from the burning zone to the unburned structure. These effects significantly increase the burning rate of porous materials. The results of investigations of the combustion of porous materials show that the burning process is different from that of traditional propellants, and the burning rate of porous propellants is much higher [12,13,14,15,16,17,18,19,20]. As previous methods for determining the burning rate have not taken into account the internal porous structure of the combustible case material, they failed and have led to significant errors in the ballistic calculations.

In this paper, a method of determining the physical burning law and linear burning rate of felted combustible case material is presented. The method was verified on the basis of the results of pyrostatic tests (CVT) of combustible cartridge case material of a 120 mm tank round. The findings may be applicable to define the ballistic characteristics of other combustible case types.

2. Materials and Method

The combustible specimens (samples) prepared from the combustible cartridge case of a 120 mm tank round, shown in Figure 1, were used in the experiments. The mean percentage composition of the tested material is as follows: nitrocellulose 47.5%, cellulose 27.5%, binder 12.5%, stabilizer 1%, and other 11.5%. The geometrical characteristics of the samples of the tested material are presented in

Table 1. Dimensions of samples of the tested material.

Parameter	Value
Sample shape	slab
Width (mm)	10
Length (mm)	20
Web thickness (mm)	3.3

.

Experimental investigations of the combustible material were based on a closed vessel with a capacity of 146.5 cm³. The gases pressure value was measured by using an AVL (nowadays HPI, Austria) 8QP 10,000 piezoelectric transducer, the signal of which was amplified by a TA-3/D amplifier and recorded on a Keithley DAS-50 12-bit analog-to-digital converter at 1 MHz frequency. The tests were performed for the tested material mass: 14.65 and 29.30 g. Therefore, the loading density values were ∆ = 100 and 200 kg/m³, respectively. The mass of the black powder igniter was adjusted to ensure that the nominal value of the ignition pressure p_ign = 3.0 MPa was the same in all tests. Pressure courses recorded in these experiments are presented in Figure 2. The maximum systematic error of the pressure measurement system was 1.1%.

The energetic parameters of the tested material, needed for the ballistic calculations, were established by using the Noble–Abel [3,4] equation of state:

$$p_m-p_{ign}=\frac{f{m}_p}{V_0-\mathsf{\eta }{m}_p}=\frac{f\Delta }{1-\mathsf{\eta }\Delta }$$

(1)

where p_m—the maximum pressure of gases, f—the force, m_p—the mass of tested material, V₀—the capacity (volume) of the closed vessel, η—the covolume, and Δ—the loading density (Δ = m_p/V₀).

The calculated values of f and η are given in

Table 2. Estimated equation of state parameters for the tested material.

Parameter	Uncorrected Heat Losses	Corrected Heat Losses
f (MJ/kg)	0.4914	0.5166
η (dm3/kg)	1.742	1.615

. Furthermore, using the methodology of heat losses correction described in [21], the corrected values f and η were obtained. The calculations performed showed that the values of the parameters without and with heat losses were very similar. This proves low heat losses, which may be limited by the large number of solid particles in the combustion products that cover the internal surface of the combustion chamber (Figure 3).

The process of gas generation can be described by Equation (2), widely used in computer codes for the simulation of the internal ballistics of guns [3,4]. Equation (2) relates the relative burned mass z of the propellant charge and the relative burning surface ϕ, the burning rate r, the initial volume V₀, and the initial surface area S₀ of the sample:

$$\frac{dz}{dt}=\frac{S_0}{V_0}\varphi \left(z\right)r\left(p\right)$$

(2)

The equation of gas generation is based on the following assumptions constituting the geometric law of burning:

-

All propellant grains are ignited simultaneously over the entire surface;

-

Propellant grains burn on the outer surface in parallel layers, which means that the burning process is superficial;

-

The burning rate is only a function of the gases’ pressure and initial temperature of the propellant grains.

Due to the porous structure of the combustible cartridge case material, the combustion surface is much larger than that resulting from the dimensions of the grains of the tested material and cannot be determined using geometrical relationships. For the reason mentioned above, the use of Equation (2) may lead to significant errors in ballistic calculations of shot parameters. Moreover, the assessment of the combustion rate r(p) using the method described in STANAG 4115, based on the geometric law, does not give correct results. Graphs of the dependence of the combustion rate on the pressure (Figure 4) determined by the method described in STANAG 4115 do not allow the coefficients of the burning law r(p) to be determined. Different burning rates are obtained for different loading densities Δ; therefore it is not possible to approximate these results.

An alternative to Equation (2) is the use of the physical burning law in the form:

$$\frac{dz}{dt}=G\left(z\right)p^{\alpha }$$

(3)

The function G(z), introduced in [22], is a generalization of the function Γ(z) introduced in [4] for the linear dependence of the burning rate on pressure. Function G(z) is used for the general power dependence of the burning rate on pressure. The application of the equation of gas generation in form (3) requires the determination of the function G(z) and the value of the exponent α.

Based on the Noble–Abel (1) equation of state, the values of the relative burned mass z of the propellant and its pressure derivative dz/dp are calculated:

$$z=\frac{p_s\left(\frac{1}{\Delta }-\frac{1}{\mathsf{\rho }}\right)}{f+p_s\left(\mathsf{\eta }-\frac{1}{\mathsf{\rho }}\right)}$$

(4)

$$\frac{dz}{dp}=\frac{f\left(\frac{1}{\Delta }-\frac{1}{\mathsf{\rho }}\right)}{{\left(f+p_s\left(\mathsf{\eta }-\frac{1}{\mathsf{\rho }}\right)\right)}^2}$$

(5)

where p_s = p − p_ign, and ρ—density of the tested material.

The time derivative of the relative burned mass of the propellant z is calculated:

$$\frac{dz}{dt}=\frac{dz}{dp}\frac{dp}{dt}$$

(6)

From Equation (3), we obtain:

$${\log }_{10}\left(\frac{dz}{dt}\right)={\log }_{10}G\left(z\right)+\alpha {\log }_{10}p$$

(7)

Using the calculated values of dz/dt and experimental values of p, we obtain for z = 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, and 0.8 a linear relation between the log₁₀(dz/dt) and log₁₀(p) values. The slope determines the value of α; thus, the α values for each value of z are determined, and the average value is calculated. Then, the values of the function G(z) are calculated:

$$G\left(z\right)=\frac{dz}{dt}\frac{1}{p^{\alpha }}$$

(8)

The calculated values of α and G(z) can be used in ballistic calculations. We do not need to know the dependence of the burning rate on pressure r(p) in Equation (2). However, we can define this dependence. Assuming the burning rate equation by Vieille’s law:

$$r=\mathsf{\beta }{p}^{\alpha }$$

(9)

and using the determined value of α, we need to estimate the coefficient β value.

We can calculate the value of β making use of the relationship on the linear burning rate:

$$r=\frac{d{e}_b}{dt}$$

(10)

where e_b—burned layer of sample.

Comparing Equations (9) and (10) and taking into account the function G(z) (8), we come to the following equation:

$$d{e}_b=\mathsf{\beta }\frac{1}{G\left(z\right)}dz$$

(11)

Integrating both sides, we can determine the β value:

$$\mathsf{\beta }={\displaystyle \underset{e_{b1}}{\overset{e_{b2}}{\int }}d{e}_b}/{\displaystyle \underset{z_1}{\overset{z_2}{\int }}\frac{1}{G\left(z\right)}dz}$$

(12)

where values e_b1 and e_b2 correspond to values z₁ and z₂.

3. Results and Discussion

Figure 5 presents the calculated log₁₀(dz/dt) values as a function of the log₁₀(p) and z values. Lines represent linear approximations. Points along a given line correspond to different values of Δ. The slopes of the approximating lines are very similar and, consequently, are the values of α corresponding to them. These are shown in Figure 6 for pressure ranges corresponding to the ranges of the plots in Figure 5. For the range of z [0.2, 0.8], the differences between α values are relatively low. The mean value of α for z = 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, and 0.8 is equal to 1.90 ± 0.03. The scatter of α values, assessed for the 0.95 confidence level, forms 1.6% of the mean α value.

The high value of the exponent α proves that the combustion rate of the combustible case material strongly depends on the pressure of the gases. A typical value of exponent α for propellants is close to one.

After determining the α value, the function G(z) can be determined based on Equation (8).

Figure 7 and Figure 8 present plots of the function G(z). As can be seen from the calculations, the function G(z) decreases over the entire combustion period, especially in the initial phase. In order to better illustrate the decline in the G function in the further combustion phase, it is shown in the limited range of z (Figure 8). For the initial combustion period, in the range of z = 0–0.2, there are some disturbances in the G(z) curves, which are expressed in increased values of the function G. This is also observed with other propellants (Figure 9). Such an effect has been already indicated in [4]. It may be caused by an initial heating of grains (samples) of the tested material before the ignition.

For comparison in Figure 9 and Figure 10, the function G(z) for traditional propellants was added.

The function G(z) is proportional to the burning surface area. If the grains of the material burn on their surface, the burning surface area will change slowly. In Figure 9 and Figure 10, the function G(z) for propellant 13N24 and JA-2, respectively, is presented. The plots of the G(z) function for the tested porous material prove that the burning surface diminishes very fast. This means that the burning process of the material is closer to the volumetric combustion than to the superficial burning.

The values of the calculated function G(z) are close to each other for the relative burned mass z > 0.2. For the initial period of combustion, there are large differences in G(z) values for the two loading densities. The reason for these differences can be considered. Twice the large mass of the tested material means twice the large total surface of the grains. Thus, two times more energy is needed for the ignition. This may cause a difference in the degree of ignition. The higher degree of ignition means a higher rate of gas production for a lower mass of the material. The second possible reason is connected with preheating of the material before its ignition. If the same igniter is used, this effect is stronger at lower loading density (Δ = 100 kg/m³). This causes a rise in the burning rate and consequently higher values of the function G(z).

For the above reasons, it is proposed to approximate the experimental function G(z) in the range z > 0.2 and use the approximation function in the entire range of z. An approximation of the function G(z) is presented by the red line in Figure 11. It corresponds to the following approximation function:

$$G_a\left(z\right)=-0.56z^3+1.55z^2-1.54z+0.55$$

(13)

This approximation can be used in the interior ballistic calculations.

For the validation of the physical burning law (3) with the determined function G(z) represented by Equation (13), the pressure courses as a function of time were evaluated and are presented in Figure 12 and Figure 13. The pressure values are calculated from the equation of state [4], assuming p_ign = 2 MPa.

$$p\left(z\right)=p_{ign}+\frac{f\Delta z}{1-\frac{\Delta }{\mathsf{\rho }}\left(1-z\right)-\mathsf{\eta }\Delta z}$$

(14)

The good agreement between the experimental and the calculated pressure for two loading densities confirms the physical correctness of the determined Equation (3) and its practical usefulness.

In the next step, we can calculate the β coefficient based on Equation (12). It was assumed that z₁ = 0.2 and z₂ = 0.9. The values e_b1 and e_b2 correspond to these values z₁ and z₂. Due to the omission of the initial part (z < 0.2) of the function G(z), the influences of the ignition phase of the tested material and the kind of igniter are eliminated. On the other hand, limiting the range to z ≤ 0.9 allows us to eliminate the phase of the prolonged pressure rise to the maximum value (Figure 2), probably caused by the slow burning of cellulose fibers. The calculated value of the β coefficient is equal to 8.92 × 10⁻⁵ m/s⁻¹ MPa^−α. Using the determined values of the coefficient β and the exponent α, a comparison of the burning rates of the tested material and the propellant JA-2 [24,25] used in 120 mm tank ammunition with combustible case material has been made. It is presented in Figure 14.

The burning rate of the combustible cartridge case material is much higher than the burning rate of the propellant JA-2. Due to the strong dependence of the combustion rate on the pressure, the difference in the burning rate of the combustible material and the propellant increases with the rising pressure. Such a relation of the burning rates is desirable, because the web thickness of the combustible case is much higher than the web thickness of the propellant (3.3 mm vs. 1.8 mm). Due to the higher burning rate, the combustible case is burnt out at approximately the same time as the propellant charge.

4. Conclusions

• The applied method of analysis of CVT results enables us to determine the characteristics of the combustion process of combustible case materials. The standard methods of the analysis fail in this case.
• The results obtained proved the strong dependence of the burning rate on pressure. The exponent value in the burning law is 1.9 and it is about twice as large as the exponent value for typical propellants.
• Due to the porous structure of the combustible case material, the geometric model of burning and Equation (2) cannot be used to determine the burning rate r(p) according to the method described in STANAG 4115. The process of combustion of the material is close to volumetric.
• The burning rate of the tested combustible case material is high enough to cause complete burning out of the case during the shot.