Combustion mechanisms in detonation fronts Joe Shepherd, Caltech October 2004

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Combustion mechanisms in detonation frontsJoe
Shepherd, Caltech October 2004

• Progress report on work by
• Experiments Joanna Austin (UIUC), Florian
  Pintgen (CIT)
• Steady flame simulations Dan Lieberman (CIT),
  Sandeep Singh (Detroit Diesel)
• Transient flame simulations Marco Arienti
  (UTRC), Ralf Deiterding (CIT), Patrick Hung (CIT)
• Transient detonation simulations (Alexi Khokhlov,
  U Chicago)

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Detonation Tube Experiments

• 8 m long, 280 mm diameter
• cookie-cutter attached to the 150 mm square
  test section
• Initiation with an exploding wire and an
  acetylene-oxygen-driver

End plate soot foil
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Cellular Structure
R. Akbar 1997
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Themes

• Some experimental observations
• Speculations about combustion mechanisms
• The role of diffusive processes
• The classical theory of high-speed flames
• Transient processes at shear layers
• The turbulent flame
• Future studies

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Observations

• We observe a range of reaction front features
  which are strongly correlated with the
  sensitivity of the reaction rates to temperature
  variations.

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OH fluorescence images - irregular structure
5 mm
8 mm
Shot 1597, 2H2O2 8 N2, 20kPa
Shot 1604, 2H2O2 8 N2, 20kPa
2H2O2 9 N2, 20kPa, Image height 50mm
All 150x150mm testsection
Reference F. Pintgen, J. M. Austin, and J. E.
Shepherd, Detonation front structure Variety and
characterization, Confined Detonations and Pulse
Detonation Engines, pages 105-116. Torus Press,
Moscow, 2003.
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Highly Irregular MixturesN2O H2 mixtures
N2-diluted
10 mm
10 mm
10 mm
Shot 1607
Shot 1608
Shot 1609
H2 N2O 3 N2, 20 kPa, Cellsize 70mm
All 150x150mm testsection
Reference F. Pintgen, J. M. Austin, and J. E.
Shepherd, Detonation front structure Variety and
characterization, Confined Detonations and Pulse
Detonation Engines, pages 105-116. Torus Press,
Moscow, 2003.
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Highly Irregular MixturesN2O H2 mixtures
N2-diluted
Shot 1643, H2 N2O 2 N2, 20kPa, Cell size 42mm
50 mm
50 mm
50 mm
20 mm
Shot 1609, H2 N2O 3 N2
Shot 1656, H2 N2O 2 N2
Shot 1643, close up
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Instability driven turbulence
highly unstable (high Ea/RTS)
f1
unstable
stable
weakly unstable (low Ea/RTS)
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What are we learning?

• Front structure not universal
• Strong function of chemical system
• Characterize with reaction zone structure
• Activation energy
• Shape of reaction zone ti/tr
• Correlated with longitudinal instability
  threshold
• Range of scales increases with increasing
  activation energy
• For fuel-air mixtures
• 102-103 range of length scales
• High frequency temporal fluctuations
• Decoupling at end of reaction zone

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Explosive events following decoupling
4mm
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Turbulent detonations?

• Reaction zone appears to be dominated by
  fluctuations in leading shock velocity
• Consequence of highly unstable structure
• Leads to large fluctuations in species and energy
  release rate
• Transverse waves
• Consequence or cause of spatial variation of
  leading shock?
• May lead to explosive events following decoupling
• Diffusive processes may operate at very small
  scales but
• Smallest scales not resolved in experiments
• Suggests that turbulent detonations may be
  intrinsically different than turbulent
  deflagrations

Is this a new or an old regime of turbulent
combustion?
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Why?

• 1. Why is the reaction zone turbulent?
• Conjecture The mean flow is highly unstable to
  small perturbations. Numerous modes of transverse
  and longitudinal instability are present
  simultaneously. Nonlinear interactions of these
  modes creates a highly fluctuating environment
  within the reaction zone.

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What?

• 2. What is the nature of the turbulence?
• At least two possibilities
• Coherent quasi-periodic keystone structures
  created by hierarchy of transverse waves
• Incoherent random superposition of fluctuations
  in front velocity creates random fluctuations
  in OH thermicity. Transverse waves are acoustic
  mode of turbulence.

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How?

• 3. How is this different from classical
  turbulence?
• Speculations
• Fluctuations in temperature much more significant
  than fluctuations in velocity.
• Three dimensional shock geometry more significant
  than vorticity distribution.

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Possible Consequences

• 4. How does turbulence influence detonation
  propagation?
• Unknown but we speculate that
• Perturbations to reaction rate
• Increases mean reaction rate
• Decreases sensitivity to mean fluctuations
• Harder to quench detonation by diffraction or
  energy absorption

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Numerical Simulations

• Two-dimensional inviscid simulations with
  simplified reaction mechanism (1-step) but highly
  refined spatial discretization (A. Khokhlovs FTT
  method)
• Ea/RT chosen to match regular and irregular
  mixture thermochemical computations.

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Regular Instability, Ea/RT 6.5
Numerical
Experimental
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Irregular instability, Ea/RT 10
Experimental
Numerical
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Conclusions

• Two-dimensional simulations at CJ condition
  feasible even with simplified reaction mechanism.
• Cellular substructure, wrinkling of reaction
  front, localized explosions consistent with
  experimental observations.
• Purely chemical-gasdynamic explanation for
  inviscid turbulence

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However

• Computations are based on Euler model no
  diffusive processes. Is this what happens in
  nature?
• What happens at even higher values of Ea/RT?
• Most probable situations for diffusive transport
• Thin layers of unreacted material surrounded by
  products
• Shear layers between warm (shocked) reactants and
  hot products.
• Could conventional diffusive turbulent combustion
  be possible?

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Regimes for Conventional Diffusive Turbulent
Combustion
from N. Peters (2000) Turbulent Combustion
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Can we put some points on this plot?

• Are there regimes where laminar flames can exist
  in detonation fronts?
• What is the characteristic values of laminar
  flame speed in post-shock conditions?
• What are the range of length scales and
  fluctuation velocities in turbulent detonations?

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Classical analysis of diffusive transport in
high-speed combustion

• Numerical study of Clarkes one-dimensional fast
  flames
• Re-examining conclusions reached with asymptotics
  for realistic detailed chemistry.
• Examine key issue not addressed by Clarke When
  do diffusion flames cease to be well defined?

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One-Dimensional Fast Flame
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Postshock Conditions
Stoichiometric CH4-air mixtures at various shock
speeds
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Governing Equations
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Two Extremes
CJ-ZND
Adiabatic flame
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Magnitude of the terms in the energy balance
equation
v2m/s
v5.81m/s
tconv
tcond
tdiff
treac
tpress

tsum
v20m/s

v100m/s
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Fast flame study conclusions
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Existence of flames behind shocks
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Results of flame computations
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Summary of fast flame study
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Characterization of fronts
Coastlines
Distribution of lengths
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Scale-dependent fractal?
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Wrinkled laminar flamelet analysis
M r u A
M r SL AT
AT/A U/SL
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Conclusions

• Identified potential relevance of
  diffusion-controlled mechanisms in irregular
  detonation cellular structure
• Highly unstable reactive mixtures provide
  sufficient time-scale separation between thotcv
  and twarmcv in the decaying part of the
  detonation cell cycle.
• Molecular transport and thermal conduction can
  accelerate chemical kinetics in the time-scale of
  interest

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Transient ignition of flames at shear layers

• Motivated by OH PLIF observations and numerical
  simulations.
• Analog of classic Marble-Adamson problem for
  ignition behind flame holder

Warm reactants
Hot products
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The Marble-Adamson problem

• Chemical changes occur by a single reaction step
  
• Boundary layer scaling ?
• Diffusive term is of the same order as convective
  terms? ?
  ?

• Schvab-Zeldovich formulation
• Steady, low speed (isobaric) flow
• Binary diffusion coefficients of all species
  equal
• Unit Lewis number

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The Marble-Adamson problem
propagating laminar flame
cold combustibles ? u1
hot inerts ? u2
boundary layer

• But
• Warm not cold combustible stream close to
  reaction.
• Hot stream is not inert (role of radicals
  diffusion vs. thermal diffusion).

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Time scale competition

• Two streams
• hot, with temperature Th and adiabatic (c.v.)
  induction time thotcv
• warm, with temperature Tw and adiabatic (c.v.)
  induction time twarmcv
• Time to ignite a homogeneous mixture
• Time for a diffusive flame to developwhere
• Diffusive flame at shear layer if

• ? Look for large separation of thotcv and twarmcv

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Local triple point analysis

• Polar analysis for non-reactive gas.
• Flow is steady in the reference frame of the
  triple point.
• Constant track angle f from incident leading
  shock.
• Known shock speed D at the cell centerline.
• All waves are straight.

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Comparison of adiabatic ignition times
2H2-O2-7Ar P16.67kPa Miller Bowman
C2H4-3O2-8N2 P120kPa GRI-Mech 3.0
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Homogeneous mixing ignition at shear layer
idealizedcell
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Dependence from chemical mechanism

• 0-dimensional calculations at constant pressure
  usingthe CHEMKIN library Kee et al., 1989.

0.21 O2-0.79 N2
0.25 H2-0.75 N2
1100K
300K
Z kg
(1-Z) kg
1 atm
Mixture fraction Z
tHMI(Z)
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Time scales competition
C2H4-3O2-8N2 P120kPa GRI-Mech 3.0
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Flame development 1-D unsteady code

• AMROC provides access to adaptive data management
  as well as to detailed reaction mechanisms (via
  CHEMKIN).
• Operator splitting approach added subroutine to
  compute diffusive fluxes

• Species molecular diffusion, mixture thermal
  conductivity and thermal diffusion coefficients
  from TRANSPORT software package.
• Mixture averages using CHEMKIN gas-phase
  utilities.

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Test 1 H2-O2 premixed laminar flame

• Comparison with steady solution from PREMIX
  program.

2H2-O2-7Ar mixture at P11 atm
H2-O2 mechanism by Miller Bowman (1989)
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Test 2 H2-O2 non-premixed laminar flame
0.25 H2-0.75 N2 (300K) / 0.21 O2-0.79 N2 (1100K)
at P11 atm H2-O2 mechanism by
Kreutz Law (1996)
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Weakly and strongly unstable reactive mixtures
2H2-O2-8N2
2H2-O2-7Ar
Composition at 10 peak temperature in hot-stream
c.v. explosion. H2-O2 mechanism by Miller
Bowman (1989)
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Example I Diffusion flame at shear layer
2H2-O2-8N2
Composition hot stream at equilibrium ? or inert
? at 2213 K warm stream
unreacted at 1020 K ? twarmcv 1470 ms
? Estimated tHMI(0.95) 17. ms
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Example II Convective explosion at shear layer
2H2-O2-8N2
T at 23.6 ms
XOH at 23.6 ms
Composition hot stream at equilibrium ? or
inert ? at 2213 K warm
stream reactants at 1200 K ? twarmcv 19.8 ms
? Estimated tHMI(0.95) 8. ms
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Example III Energy vs. radical diffusion effects
2H2-O2-11N2
Composition hot stream at equilibrium ? or inert
? at 1427 K warm stream
reactants at 1000 K ? twarmcv 327 ms
? Estimated tHMI(0.95) 162 ms