Numerical simulation of detonation re-initiation following Mach reflection

Numerical simulation of detonation re-initiation following Mach reflection

S. She-Ming Lau-ChapdelaineRohit BhattacharjeeMatei I. Radulescu

2012/10/26

Combustion

● Channel filled with premixed gas

● Deflagration● Detonation

Detonation

● Supersonic combustion wave

● Shock wave heats mixture● Mixture reacts● Energy release propels shock wave

Detonation Applications

● Pulse detonation engine

Detonation Applications

● Rotating detonation engine

Detonation Application

● Dust/powder explosion

Lakeland Mills sawmill, Prince George, B.C., April 2012

Detonation Applications

● Nuclear safety - hydrogen explosions

Fukushima, 2011

Chernobyl, 1986

Detonation

● Supersonic combustion wave

● Shock wave heats mixture● Mixture reacts● Energy release propels shock wave

Detonation

● Zeldovich-von Neumann-Doring

Detonation structure

● ZND structure is unstable

Detonation structure

● ZND structure is unstable

plane of symmetry

Shock Reflection

Unburnt Gas

Detonation re-initiation

● Importance of rapid reactions mechanisms in detonations difficult to determine

● Rapid reaction mechanisms– 1) Transverse wave

– 2) Mach-stem

– 3) “Wall” jetting effect

– 4) Kelvin-Helmholtz

– 5) Richtmyer-Meshkov

1

2

34

5

Previous work

Teodorczyk, A., J.H.S. Lee, and R. Knystautas. 1991. Prog. Astronaut. and Aeronaut. 133:223–240.

Previous work

T. Obara, J. Sentanuhady, Y. Tsukada, S. Ohyagi, Reinitiation process of detonation wave behind a slit-plate, Shock Waves 18 (2) (2008) 117–127.

Previous work

R. Bhattacharjee, S.SM. Lau-Chapdelaine, G. Maines, L. Maley, M.I. Radulescu. Detonation re-initiation following the Mach reflection of a quenched detonation. Proceedings of the International Combustion Symposium, (2012).

Previous work

R. Bhattacharjee, S.SM. Lau-Chapdelaine, G. Maines, L. Maley, M.I. Radulescu. Detonation re-initiation following the Mach reflection of a quenched detonation. Proceedings of the International Combustion Symposium, (2012).

Objectives

● Model detonation re-initiation● Isolate re-ignition mechanisms● Gain insight from simulations● Predict detonation re-initiation

Numerical Model

● Reactive Euler equations

● 1-step Arrhenius chemistry

∂ρ

∂ t+

∂ρ u∂ x

+v∂ρ v∂ y

=0

ρu t

+

x(ρu2

+ p )+

y(ρ vu)=0

ρ v t

+

x(ρuv )+

y(ρv2

+ p)=0

t(E+ Q λ)+

x((E+ p+ Q λ)u)+

y((E+ p+ Q λ)v)=0

∂ λ∂ t

+u ∂λ∂ x

+v ∂ λ∂ y

=k (λ−1)eE a

RT

Numerical Model

● Reactive Euler model● 1-step Arrhenius reaction● Non-dimensionalized by half-reaction length

and initial conditions∂ λ∂ t

+u ∂λ∂ x

+v ∂ λ∂ y

=k (λ−1)eE a

RT

Pre-exponential Factor

Numerical Model

● Reactive Euler model● 1-step Arrhenius reaction● Non-dimensionalized● Calibrated for post-shock conditions (CH4 + 2O2)

λ

t+ u

λ

x+ v

λ

y=k (λ−1)e

Ea

RT 0

Activation Energy

Numerical Model: Chemistry (CH4 + 2O2)

τ ig∝eEa

RT

Numerical Model

● Reactive Euler model● 1-step Arrhenius reaction● Non-dimensionalized● Calibrated for post-shock conditions (CH4 + 2O2)

t(E+ Q λ)+

x((E+ P+ Q λ)u)+

y((E+ P+ Q λ)v )=0

Heat Release

Numerical Model

● Reactive Euler model● 1-step Arrhenius reaction● Non-dimensionalized by half-reaction length● Calibrated for post-shock conditions (CH4 + 2O2)

● Domain

– Base grid: 200x24– Adaptive grid refinement technique– Resolution: >32 points per induction length

γ=1.17 ;EaRT 0

=48.3 ;QRT 0

=60.5

Numerical Model: DomainP

ost

-ZN

DE

xtrapolate

Reflect

Reflect

Numerical Model

● Reactive Euler model● 1-step Arrhenius reaction● Non-dimensionalized by half-reaction length● Calibrated for post-shock conditions (CH4 + 2O2)

● Domain

– Base grid: 200x24– Adaptive grid refinement technique– Resolution: >32 points per induction length

● AMRITA CFD

γ=1.17 ;EaRT 0

=48.3 ;QRT 0

=60.5

Results: P0=5.5kPa

Results: P0=5.5kPa

Quenching

Results: P0=10.3kPa

Results: P0=10.3kPa

Hot-spot re-ignition

Results: P0=11.9kPa

Results: P0=11.9kPa

Detonation re-initiation

Results: P0=11.9kPa

Density

Reaction progress

Results: P0=12.5kPa

Experimental results from 11.9kPa

Detonation re-initiation

Results: P0=12.5kPa

Results: P0=17.6kPa

Results: P0=17.6kPa

Detonation transmission

Summary

P0 Experimental Simulation5.5kPa Quenched

10.3kPa Hot-spot ignition behind Mach stem

11.9kPa Detonation re-initiation along Mach stem & transverse wave

Detonation re-initiation along Mach stem

17.6kPa Detonation direct transmission

Summary

Detonation StructureExperiments

Detonation diffraction over obstacle

Numerical simulations

P0 Results

5.5kPa Quenched

10.3kPa Hot-spot

11.9kPa Re-initation

17.6kPa Transmission

Numerical modelof experiment

Reactive Euler

1-step Arrhenius

Post-shock calib.

>32 grid/induc.

Conclusions

● Adiabatic Mach compression appears to play an important role

● Wall jetting could be significant

● Transverse wave not recreated in simulations

● Experiments show rapid combustion in unburnt tongue, strong effect of wall jet

Acknowledgements

Alexander Graham Bell CGS