Real Gas Effect on Motion of Self-gravitating Cylindrical Detonation Waves

Abstract

The effect of real gas on the adiabatic propagation of strong cylindrical imploding detonation waves in the non-homogeneous medium having power varying density distribution. Ignoring the effect of overtaking disturbances the CCW solution has been obtained for the problem at the detonation waves are initially in Chapman-Jouguet state. The analytical expressions for the detonation velocity just behind the front along with other flow variables are derived. The expressions for the freely propagating velocity of detonation front are derived. Using the jump condition across the strong detonation front, the numerical values of the pressure and density across the front have been computed with the help of the software MATLAB. It is observed that the variation of flow parameters with convergence of detonation front is depend upon the change in Alfven Mach number, the parameters of realness of the gas and initial density distribution. Finally, it is found that change in parameter of realness of the medium plays an important role on the post flow variables. The effect of change in Alfven Mach number and density parameter is also discussed through graphs. The outcome of the present study is compared with the results for the case of ideal reacting gas.

Introduction

I. INTRODUCTION

On account of the importance of study of phenomenon of shock wave propagation in different branches of science and technology, several scientists have considered the problem experimentally and analytically. The motion of detonation waves in  different type of uniform and non-uniform of media having cylindrical and spherical symmetries. Welsh (1967), Nigmatulin (1967) and Teipel (1983) have consider the problem of detonation wave propagation into a uniform combustible ideal gas. Vishwakarma et al. (2018) have further studied the the problem of Nigmatulin (1967) for the case of magnetogasdynamics. In non-uniform atmosphere, Verma and Singh (1980), (1981) have explored the problem of detonation wave propagation of  Teipel (1983) study. The CCW theory[Chester (1954)Chisnell (1955)Whitham (1958)] have been used by Tyl and Wlodarczyk (1983) for analytical study of concentric detonation waves in gaseous reactive mixtures. Self-gravitation effect on the adiabatic motion of weak and strong shock having cylindrical and spherical symmetries having different type of initial density distribution  in pure and dusty real and ideal gases have been studied by Gangwar (2018), (2020), (2022). Recently Gangwar and Verma (2024)a, (2024)b have applied the well- known CCW method for the motion of strong detonation front in ideal gas under the effect of self-gravitation and rotation.

In this present paper,  the effect of realness of the reacting gaseous atmosphere have been analyzed by using the well-known CCW method  for the propagation of converging detonation waves having cylindrical symmetry under the effect of self-gravitation. The effect of the flow behind the detonation front have been neglecting in this study. It is assumed that the detonation front is travels with sonic speed relative to the burst gas, which determines the law of convergence and it is assumed as Chapman-Jouguet front. In the case of strong detonation wave propagation, the pressure and internal energy in the undisturbed gas have been neglected in comparison to their values in the disturbed fluid. The values of non-dimensional pressure, density and detonation velocity have been derived and computed numerically. The impact of realness of the medium have been depicted through figures. It is found that the the change in the parameter of realness of the gas have play significant roll on the variation of all flow variables.

Conclusion

In this study the CCW method for solving the phenomenon of detonation wave propagation in the real reacting gaseous medium have been used. The effect of the realness of the gas have been calculated and discussed through graphs. The post detonation flow variables behind the cylindrical detonation front under the self-gravitating gas with initial power decreasing density have been explored. Impact of the flow behind the shock front has been neglected in this study. It is concluded that the role of realness of the gas is very significant in the phenomenon because it affects the variation of detonation velocity, the pressure across the detonation front, and the density across the front with the convergence of shock front.

References

[1] Chester, W. 1954. The diffraction and reflection of shock waves. Quarterly Journal of Mechanics and Applied Mathematics, 7(1), 57–82. [2] Chisnell, R. F. 1955. The normal motion of a shock wave through a non-uniform one-dimensional medium. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 232(1190), 350–370. [3] Gangwar, P. K. 2018. Behavior of dusty real gas on adiabatic propagation of cylindrical imploding strong shock waves. AIP Conference Proceedings, 1953, 130024. [4] Gangwar, P. K. 2020. Entropy production on dusty shock propagation in presence of overtaking disturbances. AIP Conference Proceedings, 2220, 120008. [5] Gangwar, P. K. 2022. Effect of solid dust particles on the motion of cylindrical strong imploding shock wave in self-gravitating real gas. 2451, 020077. [6] Gangwar, P. K., and Verma, R. 2024a. Imploding Detonation Waves in Self-gravitating Ideal Gas. International Journal Of Scientific Research In Engineering & Technology, 4(1), 45–49. [7] Gangwar, P. K., and Verma, R. 2024b. Strong Converging Detonation Waves in Rotating Ideal Gas. International Journal of Advanced Research in Basic Engineering Sciences and Technology (IJARBEST) , 10(3), 1–9. [8] Li, H., and Ben-Dor, G. 1998. A Modified CCW Theory for Detonation Waves. Combustion and Flame, 113(1–2), 1–12. [9] Li, H., Ben-Dor, G., and Grönig, H. 1997. Analytical study of the oblique reflection of detonation waves. AIAA Journal, 35(11), 1712–1720. [10] Nigmatulin, R. I. 1967. Converging cylindrical and spherical detonation waves. Journal of Applied Mathematics and Mechanics, 31(1), 171–177. [11] Teipel, I. 1983. Detonation waves in pipes with variable cross-section. Acta Mechanica, 47(3–4), 185–191. [12] Tyl, J., and Wlodarczyk, E. 1983. Thermodynamic characteristics of the detonation products of octogen. Journal of Technical Physics, 24(2), 139–146. [13] Verma, B. G., and Singh, J. B. 1980. Magnetogasdynamic converging spherical detonation waves. Astrophysics and Space Science, 72(1), 133–142. [14] Verma, B. G., and Singh, J. B. 1981. Imploding detonation waves. Defence Science Journal, 31, 1–6. [15] Vishwakarma, J. P., Nath, G., and Srivastava, R. K. 2018. Self-similar solution for cylindrical shock waves in a weakly conducting dusty gas. Ain Shams Engineering Journal, 9(4), 1717–1730. [16] Welsh, R. L. 1967. Imploding shocks and detonations. Journal of Fluid Mechanics, 29(1), 61-79. [17] Whitham, G. B. 1958. On the propagation of shock waves through regions of non-uniform area or flow. Journal of Fluid Mechanics, 4(4), 337–360. [18] Yadav, R. P. 1992. Effect of overtaking disturbances on the propagation of strong cylindrical shock in a rotating gas. Modelling, Measurement and Control B, 46(4), 1–11. [19] Yadav, R. P., and Gangwar, P. K. 2003. Theoretical study of propagation of spherical converging shock waves in self-gravitating gas. Modelling, Measurement and Control B, 72(6), 39–54.

Copyright

Copyright © 2024 Pushpender Kumar Gangwar, Rajesh Kumar Verma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.