Advertisement

The Study of Gun Barrel’s Two-Dimensional Nonlinear Thermal Conduction

  • Guo-Tong FengEmail author
  • Ke-Dong Zhou
  • Ying-Qi Zhang
  • Lei He
  • Jun-Song Li
  • Jia Wang
Article
  • 4 Downloads

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.

Keywords

ADI Gun barrel Modeling Nonlinear heat conduction Numerical simulation Temperature field 

List of Symbols

\( T \)

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

Notes

References

  1. 1.
    I.A. Johnston, understanding and predicting gun barrel erosion, in ADA440938 (2005)Google Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    A. Hameed, M. Azavedo, P. Pitcher, Experimental investigation of a cook-off temperature in a hot barrel. Def. Technol. 10, 86–91 (2014)CrossRefGoogle Scholar
  4. 4.
    P.J. Conroy, Gun tube thermal management, in U.S. Army Ballistic Research Laboratory (1993), pp. 83–93Google Scholar
  5. 5.
    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. 331–342Google Scholar
  6. 6.
    K.C. Jane, Z. Ylee, Thermo elasticity of multilayered cylinders. J. Therm. Stress 22, 57–74 (1999)CrossRefGoogle Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    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. 223–31Google Scholar
  9. 9.
    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. 207–214Google Scholar
  10. 10.
    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. 371–379Google Scholar
  11. 11.
    L. Chen, L. Qian, X. Shi, Numerical heat transfer analysis of composite material barrel. J. Proj. Rocket. Missiles Guid. 25, 92–95 (2005)Google Scholar
  12. 12.
    X. Li, K. Zhou, The finite element analysis of axisymmetric unsteady heat conduction problem. J. North China Inst. Technol. 20, 14–20 (1999)Google Scholar
  13. 13.
    R.D. Hill, J.M. Conner, Transient heat transfer model of machine gun barrels. Mater. Manuf. Process. 27, 840–845 (2012)CrossRefGoogle Scholar
  14. 14.
    S. Yang, W. Tao, Heat Transfer (High Education Press, Beijing, 2006)Google Scholar
  15. 15.
    J. Lu, S. Yu, Heat Transfer of Weapons and Thermal Processes of Variable Gas (East China Engineering Institute Press, Nanjing, 1985)Google Scholar
  16. 16.
    M.N. Ozisk, Heat Conduction (Wiley, New York, 1990)Google Scholar
  17. 17.
    J. Lin, X. Ruan, B. Chen et al., Fluid Mechanics (Tsinghua University Press, Beijing, 2013)Google Scholar
  18. 18.
    Y. Li, Research on Temperature Measurement Technology and Application Based on Infrared Thermal Imager (Harbin Institute of Technology, Harbin, 2010)Google Scholar
  19. 19.
    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)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Guo-Tong Feng
    • 1
    Email author
  • Ke-Dong Zhou
    • 2
  • Ying-Qi Zhang
    • 2
  • Lei He
    • 2
  • Jun-Song Li
    • 3
  • Jia Wang
    • 3
  1. 1.Suzhou Institute of Industrial TechnologySuzhouChina
  2. 2.School of Mechanical EngineeringNUSTNanjingChina
  3. 3.No. 208 Research Institute of China Ordnance IndustriesBeijingChina

Personalised recommendations