Numerical Simulation of two-Phase Flow Modling of Solid Propellant Combustion

Numerical Simulation of two-Phase Flow Modling of Solid Propellant Combustion

Mahmoud Rashad XaioBing Zhang

School of Energy and Power Engineering, Nanjing University of Science and Technology

Corresponding Author Email: 
mahmodmosa2004@yahoo.com; zhangxb680504@163.com
Page: 
111-118
|
DOI: 
https://doi.org/10.18280/ijht.320116
| |
Published: 
31 December 2014
| Citation

OPEN ACCESS

Abstract: 

Up to date munitions developments are the leading stimulus to go through realistic investigations for the complex phenomenon occurs during interior ballistic cycle. Fast and accurate model is required to assure firing safety and performance of the guided projectile. In this paper, based on two-fluid model approach; a reactive two-phase flow model for the combustion process of solid granular propellant is developed. The model includes the governing equations of mass, momentum and energy for both phases as well as the constitutive laws. An accurate second order numerical technique is utilized to solve the system of equations. Sod shock tube problem is utilized to test the ability of the used numerical algorithm in solving the initial boundary value problem for the system of equations with shock wave behavior. The results of the numerical method are compared to the exact solution of a test problem for verification. The moving control volume conservation method is used to handle the moving boundary as well as a self-adapting grid algorithm is used to expand the computational domain to deal with the projectile motion. Simulation results are validated with an experimental data for validation. The interior ballistics performance is closely predicted using the developed model and the numerical code.

1. Introduction
2. Theoretical Model
3. Numerical Approach
4. Results and Discussion
5. Conclusions
  References

[1] M. M.Rashad, X. B. Zhang, and H. Elsadek, Numerical Simulation of Interior Ballistics for Large Caliber Guided Projectile Naval Gun, $J$, of Eng. and Appl. Sci, vol. $60,$ pp. $201-220,2013$

[2] P. G. Baer, and J. M. Frankle, The Simulation of Interior Ballistic Performance of Guns by Digital Computer Program. BRL, USA ARDC, Ballistic Rescarch Laboratories, Aberdeen Proving Ground, MD, Report No. $1183,1962$.

[3] K. D. Fickie and J. A Grosh, Technique for Code Augmentation. US Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, BRL-MR-3622, 1987.

[4] W.R. Fredrick and S. R. Timothy, A Lumped-Parameter Interior Ballistic Computer Code Using the TTCP Model. BRL, USA ARDC, Ballistic Rescarch Laboratories, Aberdeen Proving Ground, MD, Report No. $3710,1988$

[5] Jin Zhi Ming, Interior ballistics in guns. Publishing Company, of Beijing Institute of Technology, Beijing, 2004

6. A. W. Horst, E. K. George, and P. S. Gough, New Directions in Multiphase Flow Interior Ballistic Modeling, BRL, USA ARDC, Ballistic Research Laboratories, Aberdeen Proving Ground, MD, Report No. $3102,1990$

[7] A.J. Budka and J.D. Knapton, Pressure Wave Generation in Gun Systems: A Survey. USA Ballistic Research Laboratories, Aberdeen Proving Ground MD, BRL-MR-2567, 1975.

[8]A. W. Horst, I. W. May, and E. V. Clarke, The Missing Link between Pressure Waves and Breech Blows, USA ARRADCOM, Ballistic Rescarch Laboratory, Aberdeen Proving Ground, MD, ARBRL-MR-02849, 1978.

[9]I.W. May, and A. W. Horst, Charge Design Considerations and Their Effect on Pressure Waves in Guns, USA ARRADCOM, Ballistic Research Laboratory, Aberdeen Proving Ground, MD, ARBRLTR- $02277,1980$

[10] P. S.Gough, and F. J. Zwarts, Modeling Heterogeneous Two-Phase Reacting Flow. $A I A A J,$ vol17, $1,$ pp. $17-$ $25,1979$

[11] M. R. Baer and J. W. Nunziato, A Two-Phase Mixture Theory for the Deflagration-to-Detonation Transition (DDT) in Reactive Granular Materials, Int. J. Multiphase Flow, vol. $12,$ pp. $861-889,1986$

[12] C. R. Woodley, S. Billett, C. Lowe, W.Speares, and E. Toro, The FHIBS Internal Ballistics Code, $22^{n d}$ International Sympasium on Ballistics, Vancouver, Canada, pp. $322-329,2005$

[13] R. Acharya and K. K. Kuo, Implementation of Approximate Riemann Solver to Two-Phase Flows in Mortar Systems, ASME J. Appl. Mech., vol. 77, pp. 401$410,2010$

[14] C. Cheng, X. b. Zhang, Modeling of Interior Ballistic Gas-Solid Flow Using a Coupled Computational Fluid Dynamics-Discrete Element Method, $J$, of Appl. Mech. vol. $80,3,$ pp. $403-425,2013$

[15] P. S. Gough, Initial Development of Core Module of Next Generation Interior Ballistic Model NGEN, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD., ARL-CR-234,1995.

[16] P. S. Gough, Formulation of a Next-Generation Interior Ballistic Code. Proceedings of the $28^{\text {th }}$ JANNAF Combustion Subcommittee Meeting, San Antonio, pp. $321-337,1991$

[17] M. J. Nusca and P. S. Gough, Numerical Model of Multiphase Flows Applied to Solid Propellant Combustion in Gun Systems,AIAA joint propulsion conference, vol. $98,$ pp. $1-18,1998$

[18] Y. X. Yuan and X. B. Zhang, Multiphase Hydrokinetic Foundation of High Temperature and High Pressure, Publishing Company of Harbin Institute of Technology, Harbin, China, 2005 .

[19] C. J. Ma and X. B. Zhang, Simulation of Contamination Prevention for Optical Window in Laser Ignition Systems of Large-Caliber Guns, ASME J. Appl. Mech., vol. $78,5,$ pp. $051014,2011$

[20] J. S. Jang, H.G.Sung, T. S. Roh, and D. W. Choi, Numerical Study on Properties of Interior Ballistics According to Solid Propellant Positions in Chamber, $26^{\text {th }}$ International Symposium on Ballistics, Miami, pp. $721-730,2011$

[21] J. D. Anderson, Computational fluid dynamics: The basics and applications, McGraw-Hill, New York, 1995

[22] G. A. Sod, A Survey of Several Finite Difference Methods for Systems of Nonlinear Hyperbolic 27 Conservation Laws, $J$, of Comput. Phys., vol. pp. $1-31,1978$

[23] S. G. Ahmed, A new algorithm for moving boundary problems subject to periodic boundary conditions, Int. J. of Numer. Meth. for Heat \& Fluid Flow, vol. 16 pp. $18-27,2006$

[24] I. Demirdzic, and M. PeriéFinite, volume method for prediction of fluid flow in arbitrarily shaped domains with moving boundaries, Int. J. Numer. Meth. Fluids, vol. $10,$ pp. $771-790,1990$

[25] A. Van Dam and P. A. Zegeling, A Robust Moving Mesh Finite Volume Method Applied to ID Hyperbolic Conservation Laws from Magnetohydrodynamics, $J$, of Comput. Phys., vol. $216,$ pp. $526-546,2006$

[26] K. Herman and S. Rajan, Flame Spreading and Combustion in Packed Beds of Propellant Grains, $A I A A$ vol. $75,$ pp. $1-11,1975$

[27] W. Yu and X. B. Zhang, Aerodynamic Analysis of Projectile in Gun System Firing Process, $A S M E J$. Appl. Mech., $,$ vol. $77,5,$ pp. $051406,2010$.

[28] C. Lowe, CFD Modeling of Solid Propellant Ignition. Ph.D. thesis, Cranfield University, Cranfield, 1996 .

[29] K.Alexander, and L.Yu, New Adaptive Artificial Viscosity Method for Hyperbolic Systems of Conservation, Laws. J. of Comput. Phys., vol 231, pp. $8114-8132,2012$

[30] Kawai, S., Lele, S.K.L ocalized Artificial Viscosity and Diffusivity Scheme for Capturing Discontinuities on Curvilinear and Anisotropic Meshes. Center for Turbulence Research Annual Research Briefs, 2007 .

[31] E. J. Caramana, M. J. Shashkov, and P. P. Whalen, Formulations of Artificial Viscosity for Multidimensional Shock Wave Computations, J. of Comput. Phys., vol. $144,$ pp. $70-97,1998$

[32] P. N. Stephan, and L. W. Michael, Three Dimensional Shuman filter, $J$. of Appl.Meteorology, vol.19, pp. 464$469,1980$ 33. A. Harten, G. Zwas, Switched Numerical Shuman Filters for Shock Calculations, $J$, of Eng. Math., vol. 6 , 1972

[34] R. Courant, K. O. Friedrichs and Lewy, On the Partial Difference Equations of Mathematical Physics, $I B M J$ of Research and Development, vol. 11, pp. 215-234, 1964

[35] E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: a Practical Introduction,3$^{\text {rd }}$ Edition, Springer Verlag, 2009 .

[36] Carlo Bartoli, Fast, Transient Heat Transfer Analysis at Gas-solid Interface, Int. J. Of Heat and Technology, vol. $26,$ pp. $27-32,2008$

[37] F. Askri, M. Ben Salah and S. Ben Nasrallah, Numerical Prediction of Coupled Conduction, Convection and Radiation Heat transfer, Int. J. Of Heat and Technology, vol. $27,$ pp. $79-86,2009$