Numerical investigation of flame propagation in pulse detonation engine with variation of obstacle clearance

  • Noor AlamEmail author
  • K. K. Sharma
  • K. M. Pandey


The objective of present research work is to investigate the combustion flame acceleration and performance of pulse detonation engine (PDE). The PDE tube consisting of obstacles of varying gap with fixed blockage ratio is analyzed in the current study. The three-dimensional reactive Navier–Stokes equation along with realizable kε turbulence model is used to simulate the combustion phenomena of hydrogen–air mixture. The one-step irreversible chemical kinetics model analyzes detailed mechanism of exothermic reaction. The propagation of flame and deflagration-to-detonation transition (DDT) run-up length is based on normal propagating regime. As the gap between combustor inner surface and obstacle outer diameter increases, the propagating area near the combustor axis reduces. Therefore, loss of momentum of turbulence combustion particle and unburnt fuel particles (voids) are increased at the wake of obstacle due to the increase in gap (or reduction in obstacle outer diameter), which results reduction in detonation wave velocity and detonation total pressure. However, DDT flame run-up length increases with lower temperature along the axis of PDE combustor. The thrust force generated by PDE combustor also gets reduced as the obstacle diameter is reduced.


Combustion Hydrogen DDT Obstacle PDE 

List of symbols


Chapman Jouguet


Chapman Jouguet detonation speed


Diffusion coefficient


Number of moles of fuel


Specific enthalpy


Thermal conductivity


Symbol denoting species i


Number of chemical species in system




Heat flux


Universal gas constant


Source term




Velocity in i and j direction


Molar weight of fuel


Mass fraction of ith species

Greek symbols


Molar fraction

\(\nu_{\text{i,r}}^{{\prime }}\)

Stoichiometric coefficient for reactant i in reaction r

\(\nu_{\text{i,r}}^{{\prime \prime }}\)

Stoichiometric coefficient for product i in reaction r


Turbulent viscosity


Viscous stress tensor




Equivalent ratio of fuel and air



Computational fluid dynamics


Pulse detonation engine



The authors would like to express gratitude to the Department of Mechanical Engineering, NIT Silchar, Assam, India for providing CFD lab facilities, and also, thankful to TEQIP III for providing financial support to carry out the research work.


  1. 1.
    Dong H, Zan W, Hong T, Zhang X. Numerical simulation of deflagration to detonation transition in granular HMX explosives under thermal ignition. J Therm Anal Calorim. 2017;127:975–81.CrossRefGoogle Scholar
  2. 2.
    Liu HY, Qian XM, Du ZM. Thermal explosion model and calculation of sphere fireworks and crackers. J Therm Anal Calorim. 2012;110:1029–36.CrossRefGoogle Scholar
  3. 3.
    Tangirala VE, Dean AJ, Pinard PF, Varathrajan B. Investigations of cycle processes in a pulsed detonation engine operating on fuel–air mixtures. Proc Combust Inst. 2005;30:2817–24.CrossRefGoogle Scholar
  4. 4.
    Alam N, Sharma KK, Pandey KM. Numerical investigation of combustion phenomena in pulse detonation engine with different fuels. In: AIP Conference Proceedings. 2018.Google Scholar
  5. 5.
    Lee JH. Dynamic parameters of gaseous detonations. Ann Rev Fluid Mech. 1984;16:311–36.CrossRefGoogle Scholar
  6. 6.
    Kumar PP, Kim KS, Oh S, Choi JY. Numerical comparison of hydrogen–air reaction mechanisms for unsteady shock induced combustion applications. J Mech Sci Technol. 2015;29(3):893–8.CrossRefGoogle Scholar
  7. 7.
    Zhang G, Kim HD. Numerical simulation of shock wave and contact surface propagation in micro shock tubes. J Mech Sci Technol. 2015;29(4):1689–96.CrossRefGoogle Scholar
  8. 8.
    Liang D, Liu J, Xiao J, Xi J, Wang Y, Zhou J. Effect of metal additives on the composition and combustion characteristics of primary combustion products of B-based propellants. J Therm Anal Calorim. 2015;122:497–508.CrossRefGoogle Scholar
  9. 9.
    Heiser WH, Pratt DT. Thermodynamic cycle analysis of pulse detonation engines. J Propul Power. 2002;18(1):68–76.CrossRefGoogle Scholar
  10. 10.
    Goldmeer J, Tangirala VE, Dean AJ. System-level performance estimation of a pulse detonation based hybrid engine. J Eng Gas Turb Power. 2008;130(1):011201-1–8.CrossRefGoogle Scholar
  11. 11.
    Zheng K, Yu M, Zheng L, Wen X, Chu T, Wang L. Experimental study on premixed flame propagation of hydrogen/methane/air deflagration in closed ducts. Int J Hydrog Energy. 2017;42(8):5426–38.CrossRefGoogle Scholar
  12. 12.
    Kellenberger M, Ciccarelli G. Propagation mechanisms of supersonic combustion waves. Proc Combust Inst. 2015;35:2109–16.CrossRefGoogle Scholar
  13. 13.
    Lee JH, Moen IO. The mechanism of transition from deflagration to detonation in vapor cloud explosion. Prog Energy Combust Sci. 1980;6:359–89.CrossRefGoogle Scholar
  14. 14.
    Heidari A, Wen JX. Flame acceleration and transition from deflagration to detonation in hydrogen explosions. Int J Hydrog Energy. 2014;39:6184–200.CrossRefGoogle Scholar
  15. 15.
    Li J, Zhang P, Yuan L, Pan Z, Zhu Y. Flame propagation and detonation initiation distance of ethylene/oxygen in narrow gap. Appl Therm Eng. 2017;110:1274–82.CrossRefGoogle Scholar
  16. 16.
    Dzieminskaand E, Hayashi AK. Auto-ignition and DDT driven by shock wave–boundary layer interaction in oxyhydrogen mixture. Int J Hydrog Energy. 2013;38:4185–93.CrossRefGoogle Scholar
  17. 17.
    Gamezo VN, Ogawa T, Oran ES. Flame acceleration and DDT in channels with obstacles: effect of obstacle spacing. Combust Flame. 2008;155:302–15.CrossRefGoogle Scholar
  18. 18.
    Jie L, Longxi Z, Zhiwu W, Changxin P, Xinggu C. Thrust measurement method verification and analytical studies on a liquid-fueled pulse detonation engine. Chin J Aeronaut. 2014;27(3):497–504.CrossRefGoogle Scholar
  19. 19.
    Gaathaug AV, Vaagsaether K, Bjerketvedt D. Experimental and numerical investigation of DDT in hydrogen–air behind a single obstacle. Int J Hydrog Energy. 2012;37:17606–15.CrossRefGoogle Scholar
  20. 20.
    Gamezo VN, Ogawa T, Oran ES. Numerical simulations of flame propagation and DDT in obstructed channels filled with hydrogen–air mixture. Proc Combust Inst. 2007;31:2463–71.CrossRefGoogle Scholar
  21. 21.
    ANSYS. ANSYS fluent 14.0 theory guide. ANSYS Inc: Canonsburg; 2011. PA 15317.Google Scholar
  22. 22.
    Chapman S, Cowling TG. The mathematical theory of non-uniform gases. 3rd ed. Cambridge University Press: COMB; 1970.Google Scholar
  23. 23.
    Smirnov NN, Penyazkov OG, Sevrouk KL, Nikitin VF, Stamov LI, Tyurenkova VV. Detonation onset following shock wave focusing. Acta Astronaut. 2017;135:114–30.CrossRefGoogle Scholar
  24. 24.
    Gnani F, Zare-Behtash H, White C, Kontis K. Effect of back-pressure forcing on shock train structures in rectangular channels. Acta Astronaut. 2018;145:471–81.CrossRefGoogle Scholar
  25. 25.
    Alam N, Pandey KM, Sharma KK. Numerical investigation of combustion wave propagation in obstructed channel of pulse detonation engine using kerosene and butane fuels. J Appl Fluid Mech. 2019;12(3):883–90.CrossRefGoogle Scholar
  26. 26.
    Alam N, Sharma KK, Pandey KM. Combustion characteristics of hydrogen–air mixture in pulse detonation engines. J Mech Sci Technol. 2019;33(5):2451–7.CrossRefGoogle Scholar
  27. 27.
    Heywood JB. Internal combustion engine fundamentals. New York: McGraw-Hill; 1988.Google Scholar
  28. 28.
    Warnatz J, Maas U, Dibble RW. Combustion-physical and chemical fundamentals, modeling and simulations, experiments, pollutant formation. New York: Springer; 2001.Google Scholar
  29. 29.
    Hirschfelder JO, Gurtiss CF, Bird RB. Molecular theory of gases and liquids. J Am Chem Soc. 1955;77(7):2031–2.CrossRefGoogle Scholar
  30. 30.
    Kuhl AL, Leyer JC, Borisov AA, Sirignano WA. Dynamics of gaseous combustion. Reston: AIAA; 1991.Google Scholar
  31. 31.
    Wei H, Shang Y, Chen C, Gao D, Feng D. One dimensional numerical study on pressure wave–flame interaction and flame acceleration under engine-relevant conditions. Int J Hydrog Energy. 2015;40:4874–83.CrossRefGoogle Scholar
  32. 32.
    Anetor L, Osakue E, Odetunde C. Reduced mechanism approach of modeling premixed propane–air mixture using ANSYS fluent. Eng J. 2012;16(1):67–86.CrossRefGoogle Scholar
  33. 33.
    Choubey G, Pandey KM. Effect of different strut + wall injection techniques on the performance of two-strut scramjet combustor. Int J Hydrog Energy. 2017;42:13259–75.CrossRefGoogle Scholar
  34. 34.
    Choubey G, Pandey KM. Effect of parametric variation of strut layout and position on the performance of a typical two-strut based scramjet combustor. Int J Hydrog Energy. 2017;42:10485–500.CrossRefGoogle Scholar
  35. 35.
    Choubey G, Pandey KM. Investigation on the effects of operating variables on the performance of two-strut scramjet combustor. Int J Hydrog Energy. 2016;42:20753–70.CrossRefGoogle Scholar
  36. 36.
    Ezoji H, Shafaghat R, Jahanian O. Numerical simulation of dimethyl ether/natural gas blend fuel HCCI combustion to investigate the effects of operational parameters on combustion and emissions. J Therm Anal Calorim. 2019;135(3):1775–85.CrossRefGoogle Scholar
  37. 37.
    Choubey G, Pandey KM. Effect of different wall injection schemes on the flow-field of hydrogen fuelled strut-based scramjet combustor. Acta Astronaut. 2018;145:93–104.CrossRefGoogle Scholar
  38. 38.
    Phylippov YG, Dushin VR, Nikitin VF, Nerchenko VA, Korolkova NV, Guendugov VM. Fluid mechanics of pulse detonation thrusters. Acta Astronaut. 2012;76:115–26.CrossRefGoogle Scholar
  39. 39.
    Betelin VB, Nikitin VF, Altukhov DI, Dushin VR, Koo J. Supercomputer modeling of hydrogen combustion in rocket engines. Acta Astronaut. 2013;89:46–59.CrossRefGoogle Scholar
  40. 40.
    Smirnov NN, Betelin VB, Nikitin VF, Phylippov YG, Koo J. Detonation engine fed by acetylene–oxygen mixture. Acta Astronaut. 2014;104:134–46.CrossRefGoogle Scholar
  41. 41.
    Wintenberger E, Austin JM, Cooper M, Jackson S, Shepherd JE. An analytical model for the impulse of a single-cycle pulse detonation engine. 37th AIAA/ASME/SAE/ASEE joint propulsion conference and exhibit, Salt Lake City, UT, 2001.Google Scholar
  42. 42.
    Kailasanath K, Patnaik G, Li C. The flow field and performance of pulse detonation engines. Proc Combust Inst. 2002;29:2855–62.CrossRefGoogle Scholar
  43. 43.
    Card J, Rival D, Ciccarelli G. DDT in fuel–air mixtures at elevated temperatures and pressures. Shock Waves. 2005;14(3):167–73.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNational Institute of TechnologySilcharIndia

Personalised recommendations