Abstract
In order to improve the life of gun barrel influenced by periodic transient thermal shock during firing, it is necessary to establish the heat conduction model of gun barrel to study the temperature field and its variation rule. Therefore, a mathematical model of two-dimensional nonlinear heat conduction is established. The governing equations and boundary conditions are linearized by Kirchhoff’s variation, and the finite difference equations of internal nodes and boundary nodes are derived using energy balance method and alternating difference implicit scheme. Based on the numerical results of the classics interior ballistic, temperature distribution of some 12.7 mm machine gun barrel during 120 successive firing rounds under the firing specification of the GJB3484-98 is calculated numerically. The temperature field of the external surface of the barrel is tested and the variation law of the temperature field is obtained. Comparison with experimental results shows good agreement with the simulation. The research results provided scientific basic for the studies of new barrel materials and coatings.
Similar content being viewed by others
Abbreviations
- \( T \) :
-
Temperature of gun barrel
- \( \lambda \) :
-
Thermal conductivity of the barrel material
- \( \lambda_{0} \) :
-
Thermal conductivity of the barrel at the temperature of 0 °C
- β :
-
Coefficient
- t :
-
Time
- r :
-
Distance between the node in the barrel and the barrel axis line
- \( \rho \) :
-
Density of barrel material
- \( c \) :
-
Specific heat of barrel material
- \( T_{\text{a}} \) :
-
Ambient temperature
- \( f(r) \) :
-
Barrel’s temperature distribution along radial direction caused by fired projectiles
- \( r_{0} \) :
-
Internal radius of barrel
- \( r_{N} \) :
-
External radius of barrel
- \( T_{\text{g}} \) :
-
Temperature of propellant gas in barrel
- \( h_{\text{g}} \) :
-
Composite heat transfer coefficient between propellant gas and gun barrel
- \( h_{\text{a}} \) :
-
Composite heat transfer coefficient between ambient temperature and gun barrel
- \( h_{\text{e}} \) :
-
Radiation heat transfer coefficient
- \( v_{\text{g}} \) :
-
Velocity of propellant gas
- \( \rho_{\text{g}} \) :
-
Density of propellant gas
- \( d \) :
-
Caliber of gun barrel
- \( \lambda_{\text{g}} \) :
-
Thermal conductivity of propellant gas
- \( C_{\text{Pg}} \) :
-
Specific heat capacity at constant pressure of propellant gas
- \( \mu_{\text{g}} \) :
-
Dynamic viscosity of propellant gas
- \( \varepsilon_{\text{g}} \) :
-
Radiation rate of propellant gas
- \( \varepsilon_{\text{F}}^{\prime } \) :
-
Effective radiation rate of gun barrel
- \( T_{\text{r}} \) :
-
Temperature of barrel’s internal bore
- \( T_{0} \) :
-
Temperature of gun barrel’s internal bore
- \( T_{\text{R}} \) :
-
Temperature of barrel’s external surface
- \( \lambda_{\text{a}} \) :
-
Thermal conductivity of air
- \( \nu_{\text{a}} \) :
-
Kinematic viscosity of air
- \( \alpha_{\text{V}} \) :
-
Volume expansion coefficient
- \( C_{\text{P}} \) :
-
Specific heat capacity at constant pressure of air
- \( \mu_{\text{a}} \) :
-
Dynamic viscosity of air
- \( C_{1} ,\;n_{1} \) :
-
Corresponding coefficients with Grashof number
- D :
-
External diameter of gun barrel
- \( \varepsilon_{\text{a}} \) :
-
Radiation rate of air
- U :
-
No physical meaning, used to linearize the governing equations, corresponding to T
- \( \alpha \) :
-
Thermal diffusivity of barrel material
- \( \Delta {\text{t}} \) :
-
Time step
- \( \Delta {\text{r}} \) :
-
Radial step
- \( \Delta {\text{r}} \) :
-
Axial step
- i :
-
x-directional unit node
- j :
-
r-directional unit node
- n :
-
t-directional unit node
References
I.A. Johnston, understanding and predicting gun barrel erosion, in ADA440938 (2005)
S. Sopok, C. Rickard, S. Dunn, Thermal chemical mechanical gun bore erosion of advanced artillery part two: modeling and prediction. Wear 258, 671–683 (2005)
A. Hameed, M. Azavedo, P. Pitcher, Experimental investigation of a cook-off temperature in a hot barrel. Def. Technol. 10, 86–91 (2014)
P.J. Conroy, Gun tube thermal management, in U.S. Army Ballistic Research Laboratory (1993), pp. 83–93
K. Csaba, M.W. Coleman, J.F. Polk, On the use of pleat pipes for the thermal management of rapid fire, large caliber gun breeches, in Proceedings of 14th International Symposium on Ballistics (1993), pp. 331–342
K.C. Jane, Z. Ylee, Thermo elasticity of multilayered cylinders. J. Therm. Stress 22, 57–74 (1999)
G.A. Pflegl, Bore Erosion and heat transfer measurement in 20 and 60 mm-caliber compared with predictions of model calculations, in Proceedings of the 8th U.S. Army Symposium on Gun Dynamics (1997)
M. Mayseless, Computation of boundary layers and calculation of parietal heat flux during a shot in a gun barrel, comparison with the experiment for the 45 mm CTA gun, in Proceedings of 15th International Symposium on Ballistics (1995), pp. 223–31
D. Boisson, R. Coyzac, G. Legreat, Study of the gas discharge and the heat exchanges occurring in a gun barrel after the projective leaves the barrel-validation for the 30 mm gun, in Proceedings of 18th International Symposium on Ballistics (1999), pp. 207–214
D. Boisson, 1D and 2D Thermal Modeling of the Heating and Cooling of Gun Barrel during a Burst, in Proceedings of 14th International Symposium on Ballistics (1993), pp. 371–379
L. Chen, L. Qian, X. Shi, Numerical heat transfer analysis of composite material barrel. J. Proj. Rocket. Missiles Guid. 25, 92–95 (2005)
X. Li, K. Zhou, The finite element analysis of axisymmetric unsteady heat conduction problem. J. North China Inst. Technol. 20, 14–20 (1999)
R.D. Hill, J.M. Conner, Transient heat transfer model of machine gun barrels. Mater. Manuf. Process. 27, 840–845 (2012)
S. Yang, W. Tao, Heat Transfer (High Education Press, Beijing, 2006)
J. Lu, S. Yu, Heat Transfer of Weapons and Thermal Processes of Variable Gas (East China Engineering Institute Press, Nanjing, 1985)
M.N. Ozisk, Heat Conduction (Wiley, New York, 1990)
J. Lin, X. Ruan, B. Chen et al., Fluid Mechanics (Tsinghua University Press, Beijing, 2013)
Y. Li, Research on Temperature Measurement Technology and Application Based on Infrared Thermal Imager (Harbin Institute of Technology, Harbin, 2010)
D. Wu, The extrapolation method of temperature and heat flow on the chamber surface and the computation of temperature field. J. East China Inst. Technol 34, 201–218 (1985)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Feng, GT., Zhou, KD., Zhang, YQ. et al. The Study of Gun Barrel’s Two-Dimensional Nonlinear Thermal Conduction. Int J Thermophys 40, 37 (2019). https://doi.org/10.1007/s10765-019-2502-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10765-019-2502-8