Shock-Initiated Ignition

Shock-initiated ignition for hydrogen mixtures of different concentrationsJosue Melguizo-Gavilanes, & Luc BauwensUniversity of Calgary

4th International Conference on Hydrogen SafetySan Francisco, CA USA September 12-14, 2011MotivationPossible use of hydrogen as a fuel for transportation.Hydrogen: burns without releasing CO2 + buoyant + detonates easily = ??? Hydrogen storage and handling remains an issue (i.e. risk of detonation)We need: Improved understanding of relevant scientific issues.ObjectivesRelevant Scientific Issues

Clarification of the physics of shock-initiated ignition and detonation waves.Study how chemical kinetics affect the ignition dynamics of combustible mixtures.Relationship with deflagration to detonation transition (DDT).Advance the understanding of the role played by chain-branching and its key features on DDT.BackgroundTwo modes of combustion: Deflagrations and Detonations.Deflagration: subsonic combustion waveDetonation: supersonic combustion wave (reacting shock wave). First experimental evidence of detonations in 1881 by Berthelot & Vieille and by Mallard & Le Chtelier.First theory in 1905 by Chapman and Jouguet, independently.BackgroundTwo means of initiating a detonation Direct Initiation & deflagration to detonation transition (DDT).

DDTOrdinary, relatively slow flame, accelerates and suddenly turns into a much destructive detonation wave.Difficult outstanding problem in combustion science.Most likely means of initiating a detonation in an accidental explosion.

The ProblemNumerical simulation of ignition behind a shock moving into combustible mixture.Ignition behind leading shock, evolution and appearance of a detonation Sequence of events identified in many DDT scenarios.Simulations Short & Dold (1996), Sharpe & Short (2004-2007), Sharpe & Maflahi (2006), Melguizo-Gavilanes et. al (2010) and others.Formulation: Governing equations & chemistryOne dimensional Eulers equations for reactive, inviscid, non-conducting flows

Three-steps: Initiation, branching and termination heat release associated with termination onlyFormulation: Initial and Boundary ConditionsLeft boundary: Fresh incoming combustible mixture

Conditions ahead of the shock given by:Right boundary: Inert/burnt mixture1=1 & 2=0 1=0 & 2=0 Formulation: ChallengesInitial conditions are singular at t=0, shock separates uniform supersonic flow of unburnt mixture from burnt/inert mixtureNon-existence of initial domain where chemistry takes place (shocked unburnt mixture) on spatial (x) grid

9Formulation: TransformationTransforming the problem from x and t as independent variables to and t yields a finite domain at t=0

Formulation: Initial ConditionsNormal GridTransformed grid

Normal gridFormulation: Initial ConditionsMs=0.7011, ps=s=Ts=1.0, us= ub=0, Tb=4.0

Plot of pressure at t=0

Plot of temperature at t=0

Formulation: Boundary ConditionsLeft Boundary Condition: Fresh incoming combustible mixture

Right Boundary Condition: Burnt/inert mixture

Domain Length: On left, < 0, smaller than the opposite of the speed of the shock. On right max greater than the local speed of sound.

1=1 & 2=0 1=0 & 2=0 Numerical SchemeShock Capturing SchemeEssentially Non-Oscillatory for space integration and Runge-Kutta for time integration (2nd Order Accurate)Flux limiting near shocksParallelized using MPI (Message Passing Interface)Proper implementation requires a careful derivation of the CFL conditionShort-time asymptotics is used to derive our initial conditionsResults: Hot Spot Formation

=1.4, TB=0.9, EB=8.0, TI=3.0, EI=20 and 102,400 grid pointsFigure 1: Hot spot formation for Q=2 at times t = 7.131, 7.727, 8.372, 8.714, and 9.071. Left: Pressure profiles. Right: Temperature profiles.

Results: Hot Spot Formation

=1.4, TB=0.9, EB=8.0, TI=3.0, EI=20 and 102,400 grid pointsFigure 2: Hot spot formation for Q=6 at times t = 7.131, 7.573, 7.727, 7.883, and 8.042. Left: Pressure profiles. Right: Temperature profiles.

Results: Hot Spot Formation

=1.4, TB=0.9, EB=8.0, TI=3.0, EI=20 and 102,400 grid pointsFigure 3: Hot spot formation for Q=8 at times t = 6.989, 7.276, 7.423, 7.573, and 7.727. Left: Pressure profiles. Right: Temperature profiles.

Results: Transition to Detonation

=1.4, TB=0.9, EB=8.0, TI=3.0, EI=20 and 102,400 grid pointsFigure 4: Transition to detonation for Q=2 at times t = 10.649, 11.538, 12.501, 13.545, 14.675, 15.901, 17.228 and 17.932. Left: Pressure profiles. Right: Temperature profiles.

Results: Transition to Detonation

=1.4, TB=0.9, EB=8.0, TI=3.0, EI=20 and 102,400 grid pointsFigure 5: Mass fraction profiles for Q=2 at times t = 10.649, 11.538, 12.501, 13.545, 14.675, 15.901, 17.228 and 17.932.

Results: Transition to Detonation

=1.4, TB=0.9, EB=8.0, TI=3.0, EI=20 and 102,400 grid pointsFigure 6: Transition to detonation for Q=6 at times t = 8.206, 8.372, 8.714, 9.071, 9.442, 10.230, 11.084, 12.009 and 13.012. Left: Pressure profiles. Right: Temperature profiles.

Results: Transition to Detonation

=1.4, TB=0.9, EB=8.0, TI=3.0, EI=20 and 102,400 grid pointsFigure 7: Mass fraction profiles for Q=6 at times t = 8.206, 8.372, 8.714, 9.071, 9.442, 10.230, 11.084, 12.009 and 13.012.

Results: Transition to Detonation

=1.4, TB=0.9, EB=8.0, TI=3.0, EI=20 and 102,400 grid pointsFigure 8: Transition to detonation for Q=8 at times t = 8.043, 8.372, 8.714, 9.442, 10.230, 11.084, and 12.009. Left: Pressure profiles. Right: Temperature profiles.

Results: Transition to Detonation

=1.4, TB=0.9, EB=8.0, TI=3.0, EI=20 and 102,400 grid pointsFigure 9: Mass fraction profiles for Q=8 at times t = 8.043, 8.372, 8.714, 9.442, 10.230, 11.084, and 12.009.

ConclusionsThe scenario of shock-induced ignition was analyzed using a three-step chain-branching kinetic scheme which attempts to model properly the key feature of hydrogen mixtures.

Results show that as the heat release is increased: -ignition takes place faster. -the location where the secondary shock forms, and a fully developed detonation appears occurs closer to the contact surface. -The pressure and temperature maxima for both stages of the process, hot spot formation, and transition to detonation, attain higher values.

For all cases simulated, except for Q = 2, transition to detonation took place before merging of the resulting structure with the leading shock.

ConclusionsThe approach proposed was shown to be effective to tackle the difficult problem of shock-induced ignition. The propagation of pressure and temperature disturbances, their steepening into a secondary shock, and subsequent transition to detonation was properly captured by our current framework.

AcknowledgementsWork supported by the Natural Science and Engineering Research Council of Canada and the H2Can Strategic Network

References[1] Sharpe, G.J. and Short, M. (2007) Ignition of thermally Sensitive Explosives between a Contact Surface and a Shock. Physics of Fluids, 19:126102.

[2] Short, M. and Quirk, J.J. (1997) On the non-linear stability and detonability limit of a detonation wave for a model three step chain-branching reaction, Journal of Fluid Mechanics, 339:89.

[3] Sharpe, G.J., Maflahi, N. (2006) Homogeneous explosion and shock initiation for a three-step chainbranching reaction model, J.Fluid Mech., 566:163.

[4] Clarke, J.F., Nikiforakis, N.N. (1999) Remarks on diffusionless combustion, Phil. Trans. R. Soc. Lond. A, 357:3605.

[5] Melguizo-Gavilanes, J., Rezaeyan, N., Lopez-Aoyagi, M. and Bauwens, L. (2010) Simulation of shock-initiated ignition, Shock Waves, 20:467.

[6] Bedard-Tremblay,L.,Melguizo-Gavilanes,J. and Bauwens, L. (2009) Detonation structure under chain-branching kinetics with small initiation rate, Proceedings of the Combustion Institute, 32:2339.

[7] Melguizo-Gavilanes, J., Rezaeyan, N., Tian, M. and Bauwens, L. (2010) Shock-induced ignition with single step Arrhenius kinetics, International Journal of Hydrogen Energy, 36:2374.