Numerical simulation of detonation re-initiation following Mach reflection S. She-Ming Lau-Chapdelaine Rohit Bhattacharjee Matei I. Radulescu 2012/10/26
Numerical simulation of detonation re-initiation following Mach reflection
Apr 18, 2015
Numerical simulation of detonation re-initiation following Mach reflection. She-Ming Lau-Chapdelaine's Graduate Seminar, October 2012. Department of Mechanical Engineering, University of Ottawa. All rights reserved.
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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
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