Thermo-mechanical analysis of double base propellant combustion in a barrel

doi:10.1016/j.applthermaleng.2016.04.062

Applied Thermal Engineering

Volume 102, 5 June 2016, Pages 1287-1299

https://doi.org/10.1016/j.applthermaleng.2016.04.062 Get rights and content

Highlights

•
Propellant grain size and initial temperature alter the interior ballistic parameters.
•
Numerical model of interior ballistics problem was validated experimentally.
•
Developed thermo-mechanical model can be used for small and large caliber weapons.
•
Heat transfer and stress analysis were done using numerical and analytical methods.
•
Thermal effects and stresses determined the barrel behavior for successive shots.

Abstract

Accurate determination of burning characteristics of the propellant and thermo-mechanical loads acting on the barrel supports better gun design and its tactical use. As the frequency of successive shots changes, burning rate of the gun propellant also changes and consequently the bullet velocity and internal pressure of the barrel changes as well. In this work, combustion characteristics of double base propellants with various grain sizes and initial temperatures were determined by performing a series of shooting tests and employing a thermo-mechanical model with ABAQUS® finite element code. Effects of various grain sizes (300–425, 425–500, 500–600, 600–710, 710–850 μm) and initial temperatures (−60, −20, 0, 20, and 60 °C) of double base propellants on internal pressure, bullet velocity and barrel heat transfer were investigated experimentally and computationally. Samples of propellants were tested in a shooting range by using a NATO standard small caliber barrel of 7.62 mm in diameter, and barrel internal pressure, bullet velocity and barrel surface temperatures were measured experimentally. The barrel experienced high thermal stresses during the shootings. Based on the comparisons between the simulations and the experiments, the finite element model was in agreement with the data within 90% accuracy.

Introduction

The analysis of propellant combustion and thermo-mechanical loading generated inside the barrel along with the projectile motion through the barrel is the subject matter of interior ballistics. Many physical and chemical approaches are employed to improve the interior ballistic performance of guns with consideration based on the relationship between the gas pressure and projectile velocity. Because of the high degree of nonlinearity of combustion and the variables basic to the problem such as chemical composition of the propellant, rate of reaction, ignition characteristics, grain geometry, grain size, charge weight and environmental factors solution of the interior ballistic problem is not simple [1]. The solution may be based on theoretical analysis, established empirical relationships, numerical methods and detailed experimentation.

Bullets that are used in a barrel with helical grooves receive their energy inside the barrel from a gun propellant and keep their projectile path without any external correction until reaching their targets. Gun propellants burn without any need for an oxidizer because they contain both fuel and oxidizer in their structures. Bullets in conventional weapon systems get their propulsion and spin energies while being inside the barrel and only from solid propellant fuels or gun powders. During shots, the barrel experiences high internal pressure and temperature. Because of the complexity of solid propellant combustion inside the barrel, computations are performed based on certain assumptions [2], [3], [4], [5], [6], [7]. Parameters such as temperature, compressibility and gas volume of combustion products are determined using the ideal gas law [1], [2], [3] and the assumption that the solid propellant is burned in a single step under atmospheric conditions [7]. Temperature and heat transfer coefficient as a function of pressure can be calculated using the internal conditions of the barrel which are modified according to atmospheric data [7].

Under different pressures, solid propellants show different combustion behaviors and burn rates. Burn rate increases with respect to increasing internal pressure and temperature. Thus, as propellant temperature increases, pressure at the end of combustion chamber increases and combustion duration decreases. It has been determined that the addition of high energy materials into composite modified double base (CMDB) propellants increases combustion pressure and burn rate. Burn rate is a strong function of burn surface area, grain shape and internal pressure [8], [9], [10], [11], [12], [13].

The heat transfer through the inner wall of the barrel and thermal stresses can be predicted using various approximations. Heat transfer occurring in large caliber weapons causes wear and failure on the barrel surface. In order to reduce the heating for successive shots, cooling of the barrel has been investigated by creating cooling channels at the joints of the two-part barrel. Thermal stresses and erosion on the inner wall of the barrel are important due to high thermal and pressure loads. Thermo-mechanical cracking and wear mechanisms for large caliber guns have been investigated in detail. Initial temperature and grain size of the solid propellant has an important effect on the ballistics performance and the barrel heating [14], [15], [16], [17], [18].

In this work, combustion characteristics of double base propellants (85% Nitrocellulose and 15% Nitroglycerine) with various grain sizes and initial temperatures were determined by performing a series of shooting tests and employing a thermo-mechanical model setup with ABAQUS® finite element code. Effects of various grain sizes (300–425, 425–500, 500–600, 600–710, 710–850 μm) and initial temperatures (−60, −20, 0, 20, and 60 °C) of double base propellants on internal pressure, bullet velocity and barrel heat transfer were investigated experimentally and computationally. Samples of propellants were tested in a shooting range by using a NATO standard small caliber barrel of 7.62 mm in diameter, and barrel internal pressure, bullet velocity and barrel surface temperatures were measured experimentally. The events that occur in the barrel during burning of the propellant are very complex and it is not easy to determine the ballistic parameters and the temperature/stress distribution along the barrel axis. It is not possible to measure the temperature distribution in the barrel experimentally where the temperature values are required to determine the thermal stress distribution in the barrel. So, the temperature distribution was tried to obtain numerically. FEA analysis is conducted to determine the distribution of temperature, stress and displacement under coupled thermal and mechanical loading. The developed numerical model was experimentally validated for the interior ballistics problem based on the propellant grain size at different conditioning temperatures. Outer surface temperature of the barrel was measured using thermocouples and compared to the model solution. In addition, inner wall temperature of the barrel was determined as a function of the shooting frequency using FEA. The developed model of this study can be used in other studies with the least experimental work to offer convenient solutions for various parametric studies.

Section snippets

Theoretical formulation

This study is based on an analysis of the impulsive gaseous mixture from the burning of a gun powder consisting of 85% Nitrocellulose and 15% Nitro-glycerin in a barrel. The chemical reaction is given in Eq. (1) [7]. $17 C_{24} H_{30} {({NO}_{2})}_{10} O_{20} + 3 C_{3} H_{5} {({NO}_{3})}_{3} \to 250 {CO}_{2} + 167 CO + 40 H_{2} O + 222.5 H_{2} + 89.5 N_{2} + 1000 cal / g$

Solid propellant fuels provide chemical energy, which is converted to kinetic energy for conventional bullets to spin and move along the weapon barrel. Thus, burn rate is one of the most important design

Experimental study

The shooting tests were conducted with double based 7.62 × 51 mm standard NATO ammunition. Ballistic tests were performed with a special test barrel. In the tests, magazines with a capacity of 10 cartridges were used. Bullets were 9.5 g and the solid propellant was 2.8 g. Double base propellants with various grain sizes (300–425, 425–500, 500–600, 600–710, 710–850 μm) and initial temperatures (−60, −20, 0, 20, and 60 °C) were employed in a series of shooting tests to determine the internal pressure,

Thermo-mechanical modeling

Combustion gases due to complex thermo-chemical reactions inside the barrel provide propulsion and spin energies to bullets. During these reactions, dynamic internal temperatures and pressures occur. The period of successive shots can be expressed in two stages as shooting and preparation. During the shooting period, the solid propellant starts burning, the bullet moves and reaches the tip of the barrel and these events take 1.34 ms. Preparation period includes the waiting time between two

Validation of numerical model using paired t-test

Paired t-test analysis based on the comparison of two different methods of measurements is employed to two sets of temperature measurements from the outer surface of the barrel. Using this analysis a confidence interval for the difference between the two temperature means based on the paired differences of numerical and experimental data is determined. The difference between the experimental and numerical temperature values is defined by $D_{j} = X_{j} - Y_{j} j = 1, 2, \dots, N$ where N is the total number of data to be

Results and discussion

The inner and outer wall temperatures of the barrel were analyzed three-dimensionally using the ABAQUS solver. The gas temperature distribution along the barrel, which was determined using the equations from Eq. (6) to Eq. (8), and the convection heat transfer coefficient calculated from Eq. (12) constituted the input data for coupled analysis in ABAQUS. Experimental measurements from temperature readings at the locations where thermocouples were installed on the outer wall of the barrel were

Conclusions

Variation of the grain size of the solid propellant as well as the initial temperature changes combustion characteristics which affect dynamic pressure and temperature. The interior ballistics parameters were comprehensively investigated employing experimental, numerical and analytical methods with a thermo-mechanical approach. A numerical model was developed and experimentally validated for the interior ballistics problem based on the propellant grain size at different conditioning

Acknowledgements

The authors wish to thank to the Ministry of Industry of Turkey and to Turkish Mechanical and Chemical Industries (MKE) for financial support and technical cooperation.

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Research PaperThermo-mechanical analysis of double base propellant combustion in a barrel

Highlights

Abstract

Introduction

Section snippets

Theoretical formulation

Experimental study

Thermo-mechanical modeling

Validation of numerical model using paired t-test

Results and discussion

Conclusions

Acknowledgements

Appl. Therm. Eng.

Fuel

Fuel

Mater. Sci. Eng. C

Appl. Math. Comput.

Appl. Therm. Eng.

Int. J. Therm. Sci.

Wear

Int. J. Therm. Sci.

Comput. Mater. Sci.

Int. J. Eng. Sci.

Ballistics Theory and Design of Guns and Ammunition

Research Paper
Thermo-mechanical analysis of double base propellant combustion in a barrel