Optimization of the Internal Ballistic Performance of Supercritical Nitrogen Ejection

This paper investigates a scheme of introducing TNT into a high-pressure chamber containing supercritical nitrogen as the working substance to enhance the utilization of the working substance and the mass of the ejection missile. Based on the S-R-K real gas state equation and the quasi-static pressure and temperature prediction model of TNT, the internal ballistic equations for supercritical nitrogen are established for a missile of 30000 kg, so as to demonstrate the scheme for ejecting a large mass missile and analyze its optimization. Meanwhile, the influence of the high-pressure chamber volume and TNT initiating time on internal ballistic performances is studied, respectively. Simulation results indicate that when the capacity of the high-pressure chamber decreases and the initiating time is delayed, the peak acceleration of the missile and its ejection velocity could be steadily lowered, but the utilization of nitrogen working substance increases. Moreover, the duration of high temperatures in the low-pressure chamber increases as the delay of the initiating time grows. These conclusions could be utilized as a reference for optimizing the design of ejectors.


Introduction
Ejection technology has been widely used in aerospace, especially in the field of missile launch.It can reduce the missile's own fuel consumption and increase its range.Except for electromagnetic launch, all the other methods rely on working substance to achieve ejection.At present, the relatively mature working substances are: gas, compressed air, liquid and so on [1].However, the gas-fired ejection system has disadvantages of serious ablative effect on the launcher, high thermal protection requirements, and poor concealment [2].Although the compressed gas ejection system has low operating temperature and good environmental adaptability [3], it has defects of complex equipment and small ejection load [4].Besides, the equipment of liquid ejection is so sophisticated that it will have a high failure rate [5].Therefore, it is urgent to find a more powerful working substance to solve these problems.
In the last four decades, supercritical fluid technology has flourished and it has been widely used in extraction [6], chromatographic analysis [7], power generation and hydrothermal synthesis [8].The variety of its applications stems from the dual nature of its physical properties, which can have both gas-like and liquid-like properties [9].Supercritical fluid as a working substance of ejection, on the one hand, can generate a high enough working pressure, which can be adapted to most of the ejection.On the other hand, its working temperature is low, which reduces the requirement for thermal protection.At the same time, it also has the advantages of high specific internal energy, clean, environmental protection, and low intensity of heat signal during launch.Therefore, supercritical fluid gradually enters the vision of researchers [1].In this paper, supercritical nitrogen, as a common engineering substance, is used to study the internal ballistic performances during ejection.
Yang et al. [10] considered the influence of real gas effects on the internal ballistic performances of missile and established a model based on the improved Virial state equation.They pointed out that high pressure would cause the physical properties of the working substance to deviate from the ideal gas, so using the real gas state equation is more accurate.Ren et al. [11] proposed a method to evaluate the aerodynamic performance of a high-pressure air ejection system by using the residual function to compensate for the uncertainty caused by the real gas effect.Li et al. [12] constructed the ejection equations by fitting the physical parameters through the National Institute of Standards and Technology (NIST) database.They simulated in the missile range of 1000 ~2000 kg and discussed the feasibility of supercritical fluid.Yao et al. [13] established the internal ballistic equations of inclined ejection, carried out a numerical simulation on the ejection mass of 500 kg, and discussed the influence of parameters such as the initial volume of the low-pressure chamber and the initial state of the high-pressure chamber on the internal ballistic performances.Zhao et al. [1] established a nozzle model and constructed a dynamics model based on the S-R-K real gas state equation.They pointed out that this system could meet the ejection index and this model is less sensitive to the time step.
In the above studies, the utilization of working substance is low, that is, there is too much remaining working substance at the end of ejection.This can cause problems such as large size of the high-pressure chamber, bulky ejection equipment, and waste of the working substance.In addition, there is little research on the ejection of objects over 2000 kg.To solve the problems of low utilization of working substance and small ejection missile, a novel optimization scheme of high-pressure chamber is proposed in this paper.TNT is placed in the high-pressure chamber, and the instantaneous high temperature and high pressure generated by the explosion can be used to further improve the energy of the working substance (supercritical nitrogen) in the high-pressure chamber and improve the utilization.

Geometry description
Figure 1 shows the structure of the ejection system, which is mainly composed of high-pressure chamber, nozzle, low-pressure chamber, push plate, missile and ejection canister.Nitrogen working substance and TNT are stored in the high-pressure chamber.When the nozzle is opened, owing to the large pressure difference between the high and low pressure chamber, the working substance enters the low-pressure chamber through the nozzle, increasing the pressure here.When the pressure is high enough, the missile is accelerated by the push plate and leaves the ejection canister.After the missile moves for a while, the TNT in the high-pressure chamber explodes, generating high temperature and high pressure, which increases the energy of nitrogen.In the process of missile ejection, the flow of working substance in the ejector is complicated.To simplify the model, the basic assumptions of the internal ballistic model constructed in this paper are as follows: ICMSOA-2023 Journal of Physics: Conference Series 2755 (2024) 012023 • The parameters of the high and low pressure chamber are distributed in space uniformly and only change with time.• The nitrogen flow in nozzle is regarded as one-dimensional isentropic flow, without the consideration of the influence of friction and shock wave.• The Mach number of nozzle throat is a constant value (Ma = 1.0).• The transient influence of the TNT explosion in the high-pressure chamber is ignored, while the effect of quasi-static pressure and temperature after the explosion is just considered.In addition, nitrogen can fully absorb the energy produced by the TNT explosion.• The heat exchange between ejection system and outside is not considered.

Thermodynamic model 2.2.1. S-R-K real gas state equation
In the supercritical state, thermodynamic properties appear clearly different from the traditional liquid or gas states [14].The physical properties of nitrogen will deviate from the ideal gas, so the ideal gas state equation is no longer applicable.Real gas effects need to be taken into account.In 1972, Soave et al. [15] improved the intermolecular force term based on the R-K equation [16], and proposed S-R-K state equation.It has good calculation accuracy for both non-polar and low-polar gases [17], because the S-R-K state equation has less correction coefficient.Therefore, this equation is adopted in this paper to calculate the thermodynamic parameters of supercritical nitrogen.
The S-R-K state equation is expressed as follows: where p and T are the pressure and temperature of the working substance respectively, g R is the specific gas constant, and v is the specific volume.Besides, a and b are the specific material coefficients, which values are: where Tc and Pc are the critical temperature and critical pressure of the working substance respectively.
In equation (1),   ,T   is the correction function which is related to the working substance temperature: where Tr is the comparison temperature: S is the correlation coefficient of material properties: where ω is the eccentric factor of the substance.

Thermodynamic parameters of supercritical nitrogen
The thermodynamic parameters of real gas are obtained by the deviation function method, that is, these parameters are regarded as consisting of ideal gas and deviation term: where  and i  are the thermodynamic parameters of real gas and ideal gas respectively.  is the deviation between the real value and the ideal value.
First, calculate the value of the deviation term.According to equation (1), the partial derivative relation among temperature, pressure and specific volume will be obtained by: The change in specific internal energy, du, is a function of temperature and specific volume: In equation (11), if the temperature is constant, the volume is integrated, and then: The specific internal energy only depends on temperature, when the specific volume is infinite.Therefore, the second term on the left of equation ( 12) is the ideal gas value.Combining equation ( 1), ( 7) and ( 9), the deviation term of specific internal energy can be obtained: The specific enthalpy and specific internal energy of the gas satisfy the following relation: 14) is expressed in the form of ideal value plus deviation term, and then: For the ideal gas, there is: The deviation term of specific enthalpy can be calculated from equation (14) to equation ( 16): According to Maxwell's expressions [18], the partial derivative of specific heat at constant volume with the specific volume could be expressed as: Keeping the temperature in equation ( 18) unchanged, and integrating the specific volume: When the specific volume is infinite, V c only depends on temperature.So the second term on the left of equation ( 19) is the ideal value.Combining with equation ( 7), the deviation term of specific heat at constant volume will be obtained by: The relationship between the specific heat at constant pressure and constant volume [19] is as follows: Expressing equation ( 21) in the form of an ideal value plus a deviation term.

   
For the ideal gases, there is: Combining equation ( 21) to equation ( 23), the deviation term of specific heat at constant pressure can be obtained: The ideal values of the thermodynamic parameters are calculated as polynomial functions of temperature.Passut et al. [20] gave formulas for these ideal values, as shown in Table 1.
Suitable factors are selected according to the actual temperature of the working substance.

Governing equation 2.3.1. High-pressure chamber
The change in the mass of the high-pressure chamber is: where m1 is the mass of the working substance in the high-pressure chamber.Qout is the flow out of the chamber, which is calculated as follow: C is the flow coefficient associated with the nozzle, At is the cross-sectional area of the nozzle throat.p1, ρ1 are the pressure of the chamber and the density of the working substance respectively.According to the law of conservation of energy, the energy equation of the high-pressure chamber can be written as: where u1, h1 are specific internal energy and specific enthalpy of the working substance respectively.

Low-pressure chamber
The change in the mass of the low-pressure chamber is: where m2 is the mass of the working substance in low-pressure chamber.Qin is the flow into the chamber, which is calculated as follow: The energy equation of the low-pressure chamber can be obtained from the law of conservation of energy: where u2 is specific internal energy of the working substance.p2, V2 are the pressure and volume of the chamber respectively.According to Newton's second law, the equation of missile motion is: where vm, mm are the velocity and mass of the missile respectively.S2 is the cross-sectional area of the chamber, pa is the external atmospheric pressure, and g is the gravitational acceleration.
Combining equation (1), equation (11) and the missile kinematic equation, the ballistic equations of supercritical nitrogen ejector can be obtained.

TNT explosion model 2.4.1. TNT quasi-static pressure prediction model
WeiBull et al. [22] conducted an experimental study on the explosion of TNT in a semi-closed container.The experiment shows that the quasi-static pressure of TNT is related to the ratio of the TNT mass to the volume of the container.Liu et al. [23] studied the explosion of CL-20 based composite explosive in a confined space.They obtained the variation of quasi-static pressure with the volume of confined space when the explosive sample is fixed.Zhang et al. [24] carried out an experimental study on TNT by using explosive tanks and chambers, and obtained the characteristics of TNT explosion.Based on the experimental data, they improved the existing quasi-static pressure formula to get an empirical formula with higher accuracy.Ferdgun et al. [25] derived the quasi-static pressure formula of TNT internal explosion based on the law of conservation of energy.According to the conservation of energy: where p0 is the initial pressure in the container, ps is the quasi-static pressure of the TNT, γ0 is the initial adiabatic index of the working substance, γ is the quasi-static adiabatic index of products, ρ0 is the initial density of the remaining working substance.E  and ρ are the density of the TNT and products respectively.V and E V are the volume of the container and TNT respectively.E  is the detonation heat of the TNT.By transforming equation (32), the following formula can be obtained: 1 1 According to the relation: The quasi-static pressure of the TNT can be obtained: where TNT m is the mass of TNT.

TNT quasi-static temperature prediction model.
Edri et al. [26] considered the reignition reaction after the explosion of TNT in the confined space, and derived the theoretical formula for the quasi-static temperature of the TNT based on the law of conservation of energy.Taking the final temperature state in constrained space as the target, Zhong et al. [27] gave the quasi-static temperature fitting curves of TNT with different dosage-to-volume ratios under two working conditions (considering whether the products will produce chemical reactions).It is difficult to oxidize the products of TNT in this oxygen-free environment, as the high-pressure chamber studied in this paper is supercritical nitrogen.Therefore, the influence of the chemical reaction of products can be ignored.According to the law of conservation of energy: where Q  is the increase in energy per unit mass of gas inside the container, 0 e and 0 T are the internal energy and the temperature of the gas at the initial moment respectively.cp is the heat capacity per unit mass weighted by the mass fraction λ of products and the gas, that is:

Validation of thermodynamic models
To determine the calculation accuracy of the S-R-K real gas state equation, the numerical results of thermal physical parameters are compared with the data of NIST [21].Six different pressure conditions {1, 5, 10, 15, 20, 25} (unit: MPa) are selected, and the temperature range is set as [120,600] (unit: K) for comparison.The results are shown in Figure 2.  It can be seen that the S-R-K state equation can effectively capture the dramatic changes of the physical parameters of nitrogen near the critical point.When the temperature is greater than 150 K, ρ, h and cp obtained by the simulation are in good agreement with the experimental data from NIST.In the temperature range below 140 K, there is a certain deviation between the simulation value of ρ and the NIST data.Under the condition of 5 MPa, ρ obtained by the simulation changes dramatically near 130 K, while in the corresponding NIST data under this pressure, ρ decreases significantly near 135K, resulting in a large deviation.In addition, the maximum error of cp appears in the condition of 1 MPa, which is 5.44%.
The S-R-K equation has high accuracy in the range of p > 1 MPa and T > 140 K.In the actual ejection process, 1 p is much larger than 3 MPa generally.Besides, to make the working substance has high initial energy, this paper adopts the method of heating the high-pressure chamber by Li et al. [12] and the initial temperature of the high-pressure chamber is set to 450 K. Therefore, in the above pressure and temperature ranges, the S-R-K real gas state equation can meet the requirements of the internal ballistic simulation.

Verification of ejection internal ballistic model
To verify the correctness of the above equations, this paper simulates the calculation conditions of Wen et al. [28].Due to the lack of the relevant experimental literature on supercritical nitrogen as the ejection working substance, it cannot be directly verify the results.Therefore, we choose to verify the correctness of this paper indirectly by proving the model with supercritical carbon dioxide as the working substance.The model uses a high-pressure chamber with the pressure of 15 MPa to eject a 1000 kg missile to 6 m.
The comparison between simulation and test is shown in Figure 3.It can be seen that the acceleration and displacement of the missile obtained from the simulation almost coincide with the test data, and the errors are small.Although the missile velocity has a certain deviation at the end of the ejection, the maximum deviation is only 6.97%, which is within the acceptable range.Therefore, the internal ballistic model adopted in this paper has high reliability.

Validation of TNT explosion prediction model
To verify the correctness of the quasi-static pressure and temperature equations for TNT.The results are compared with the experimental data of Zhang et al. [25], Wang et al. [29] and Xu et al. [30].The comparisons are shown in Table 3 and Table 4.It can be seen that the maximum deviation of the pressure is 11.16% and the average deviation is only 5.63%, while the maximum deviation of the temperature is 11.42% and the average is 10.56%.It is proved that the quasi-static pressure and temperature prediction model of TNT has high accuracy.

Comparison between without TNT and with TNT
Table 5 shows the parameters used for the simulation without the addition of TNT.To verify the feasibility of the proposed scheme, the missile mass is selected as 30,000 kg.For the high-pressure chamber with TNT added, the mass of the TNT is 4 kg and the initiating time (ti) is 0.3 s.The motion parameters taken during the calculation are as follows: the effective length of the ejection canister is 25 m, that is, the calculation stops when the displacement of the missile reaches 25 m, the minimum exit velocity ( , ) is 30 m/s, and the maximum overload ( , ) limit is 11 g.During ejection, nitrogen in the high and low pressure chamber may undergo complex phase transitions.If nitrogen changes from vapor phase to liquid phase or even solid phase, its work capacity will be greatly weakened, and cannot meet the needs of ejection.Therefore, it is necessary to analyze the phase change of nitrogen during ejection.Figure 4 shows the change of nitrogen phase states during ejection.It can be seen that nitrogen in the high-pressure chamber under both conditions undergoes a transition from the supercritical to the vapor.Nitrogen in the low-pressure chamber is always kept in the vapor phase.Hence, there is no vapor-liquid coexistence or vapor-liquid-solid (three-phase) coexistence, so the working capacity of nitrogen will not decline, which is favorable for ejection.Figure 5 and Figure 6 show the temperature and pressure of the high and low pressure chamber during the ejection respectively.As can be seen from Figure 5, for the case without TNT, T1 gradually decreases from 450 K to 273 K as the working substance flows out of the high-pressure chamber.T2 increases first and then decreases.The peak temperature is about 553 K.For adding TNT, the trend of T1 and T2 before 0.3 s is the same as that without TNT.After the TNT explosion, T1 rises rapidly to the quasi-static temperature of 436 K, and then gradually decreases to about 294 K.As T1 rises promptly after the explosion, T2 changes at the same time.At the end of the ejection, T2 is close to 283 K.It can be found that both T1 and T2 increase after adding TNT, but the peak temperature is lower than 450 K, and T2 decreases to 283 K at the end of the ejection.This is acceptable for the thermal protection of the missile and the launcher.As can be seen from Figure 6, 1 p decreases with the outflow of the working substance.For the condition of adding TNT, 1 p changes stepwise at 0.3 s, increasing by about 2.4 MPa, and then decreases gradually.In addition, the rate of 2 p decrease with the addition of TNT becomes slower, and from 0.3 s to the end of the ejection, the pressure is always higher than that under the condition without adding TNT, which is due to the TNT explosion increases the work capacity of nitrogen.
According to equation (31), 2 p will directly affect d a .Therefore, the scheme of adding TNT has an important impact on improving the internal ballistic performances of ejection.Figure 7 shows the comparison of the acceleration, velocity and displacement of the missile.Before 0.3 s, the motion trend is basically the same, where d a reaches its peak within 0.15 s, about 106.92 m/s 2 (10.9 g), and the exit velocity of the missile ( d v ) is more than 30 m/s.All of them meet the design requirements of the ejection.After the TNT explosion, d a decreases at a slower rate compared to the condition without TNT.At the end of the ejection, d v increases from 31.43 m/s (without TNT) to 33.34 m/s (add TNT), with an increase of 6.08%.It is easy to see that the scheme of adding TNT can effectively improve the performances.Meanwhile, the feasibility of this scheme for ejecting large mass missile is verified.
Table 6 shows the use of nitrogen in the high-pressure chamber.It can be seen that after optimization, the utilization increases from 68.43% (before) to 69.38% (after), with a small increase.The increased work capacity of nitrogen after adding TNT leads to a shorter ejection time, which makes more nitrogen still remain in the high-pressure chamber at the end of the ejection.This indicates that under the condition of adding TNT, if the original volume of the high-pressure chamber is still used, part of the nitrogen will not participate in the work, resulting in waste.Therefore, the utilization can be reduced by decreasing the volume of the high-pressure chamber.

The influence of the high-pressure chamber volume on performances
To study the influence of V1 on the internal ballistic performances, five conditions (2.4 m 3 , 2.2 m 3 , 2.0 m 3 , 1.8 m 3 , 1.6 m 3 ) are selected for analysis.This part of the simulation considers the addition of TNT and detonates at 0.3 s.
Figure 8 shows the acceleration, velocity and displacement of the missile under different V1. , d max a gradually decreases from 108.01 m/s 2 to 102.23 m/s 2 with the decreasing of the volume in Figure 8(a), and the rate is 5.35%.As V1 decreases from 2.4 m 3 to 1.8 m 3 , d v decreases from 34.33 m/s to 30.75 m/s in Figure 8(b).When V1 = 1.6 m 3 , d v = 28.99 m/s, which no longer satisfies the design requirements of missile ejection.Therefore, the following analysis is conducted only for other four conditions.In addition, as V1 decreases, the missile ejection time is gradually extended from 1.004 s to 1.086 s, which is an increase of 8.17%.Considering the actual ejection process, the impact caused by the increase in time can be ignored.Table 7 shows the utilization of nitrogen under different V1 conditions.As the volume grows, the utilization increased by 17.27% from 65.89% to 77.27%.This optimized scheme has a significant effect on reducing the size of the ejection device and improving the utilization of the working substance.

The influence of the initiating time on internal ballistic performances
After the explosion of TNT, the energy inside the high-pressure chamber will rise instantaneously, which will affect the thermodynamic state of the low-pressure chamber and the missile motion.Therefore, if ti is not reasonable, it may lead to ejection failure.For V1 = 1.8 m 3 , five differences ti (0.1 s, 0.2 s, 0.3 s, 0.4 s, 0.5 s) are selected for simulation analysis.Figure 9 shows the variation of the acceleration, velocity and displacement of the missile under different ti.As can be seen from Figure 9 a .The acceleration changes, but the change does not exceed the previous peak.From Figure 9(b), as ti is gradually delayed from 0.1 s to 0.5 s, d v gradually decreases from 32.21 m/s to 30.08 m/s.And as shown in Figure 9(c), the ejection time increases from 1.029 s to 1.074 s.Hence, as ti advances, d v becomes larger and the ejection time becomes shorter.However, if ti is too early, d a will exceed the maximum overload limit; if ti is too late, d v will be too slow to reach the predesigned value, resulting in ejection failure.
Table 8 shows the use of nitrogen in the high-pressure chamber under different ti.It can be seen that in the range of 0.1 s to 0.4 s, the utilization gradually increases with the delay of ti, and the maximum increase is 1.67%.When ti = 0.5 s, it is found that the utilization is lower than the previous condition.Therefore, the simulation is added for the condition of ti = 0.55 s, and the utilization is found to be further reduced.During the ejection, if the temperature is too high, it will have a negative impact on the thermal protection of the missile.As can be seen from Figure 10, T2 has the same peak value (550 K) under different ti.After the TNT detonation, T2 decreases slowly.In addition, with the delay of ti, the time of maintaining high temperature in the low-pressure chamber decreases.This reduces the thermal protection requirement of the missile and ejection canister.
According to the above analysis, it can be found that when the conditions of missile ejection are satisfied, the more delayed the ti has, the higher the utilization of the working substance has, and the shorter the duration of high temperature in the low-pressure chamber has.Therefore, it is more beneficial to the thermal protection of the missile.During the ejection, it can be seen that there is no vapor-liquid coexistence or vapor-liquid-solid (three-phase) coexistence.This indicates that the working capacity of nitrogen is not reduced by the phase change, which favors the ejection.

•
It is of great advantage to use the scheme of adding TNT to eject large mass missiles.Compared with the condition without TNT, the temperatures of both high and low pressure chambers increase within an acceptable range.The descending rate of both the low-pressure chamber pressure and missile acceleration decreases, and the missile exit velocity is increased by 6.08%.The ballistic performance is significantly improved.

•
As the high-pressure chamber volume decreases, the peak missile acceleration and the exit velocity decrease, while the utilization of the working substance increases.When the volume is equal to 1.8 m 3 , the missile motion parameters meet the design requirements, and the nitrogen utilization reaches the highest (77.27%), which increases by 17.27% compared with the initial operating condition.

•
The initiating time can have a significant effect on the thermodynamic state of the high and low pressure chamber and the missile motion.If it is too early, the peak acceleration limit will be exceeded.With the delay of the time, the missile exit velocity becomes smaller.However, the utilization of nitrogen increases in a range, and the duration of high temperature in the lowpressure chamber decreases.It is benefit for the thermal protection of missile and launcher.For the cases investigated, when the high-pressure chamber volume is 1.8 m 3 and the initiating time is 0.4 s, the utilization of nitrogen is the highest and the duration of high temperature is the shortest, which is the best operating condition.
heat capacity coefficients of the products and the gas respectively.λ is calculated by the following equation: of the gas.

Figure 2 .
Figure 2. Comparison between simulation values and NIST data of thermodynamic parameters of nitrogen.

Figure 3 .
Figure 3.Comparison of simulation results with those of Wen et al. [28].

Figure 4 .
Figure 4. Phase change trajectory of nitrogen during ejection.

Figure 5 .
Figure 5. Temperature change in the high and low pressure chambers.

Figure 6 .
Figure 6.Pressure change in the high and low pressure chambers.

Figure 7 .
Figure 7. Variation of the missile acceleration, velocity and displacement.

Figure 8 .
(a) Acceleration.(b) Velocity.(c) Displacement.The influence of the high-pressure chamber volume on the missile acceleration, velocity and displacement.

Figure 9 .
The influence of the TNT initiating time on the missile acceleration, velocity and displacement.
(a), when ti = 0.1 s, , d max a = 110.75m/s 2 (11.29 g).The result exceeds the maximum overload limit of the missile, while the remaining four conditions have the same peak acceleration.This is because the TNT detonates at the rising stage of d a , which further increases the acceleration rate, and increases , d max a .In the other working conditions, the detonation occurred in ICMSOA-2023 Journal of Physics: Conference Series 2755 (2024) 012023 IOP Publishing doi:10.1088/1742-6596/2755/1/01202313 the descending stage of d

Figure 10 .
Figure 10.The influence of the TNT initiating time on the low-pressure chamber temperature.
scheme of adding TNT in the high-pressure chamber is proposed, to improve the utilization of working substance and increase the mass of ejection missile.Based on the S-R-K real gas state equation and TNT quasi-static pressure and temperature prediction model, the influence of ICMSOA-2023 Journal of Physics: Conference Series 2755 (2024) 012023 IOP Publishing doi:10.1088/1742-6596/2755/1/01202314 the high-pressure chamber volume and the detonation time of TNT on the internal ballistic performances are studied respectively.Conclusions are summarized below: •

Table 3 .
Comparison of quasi-static pressure simulation and test results.

Table 4 .
Comparison of quasi-static temperature simulation and test results.

Table 5 .
Initial values of internal ballistic parameters.

Table 6 .
Usage of the nitrogen.

Table 7 .
Usage of the nitrogen.

Table 8 .
Usage of the nitrogen.