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30th April 2010
Friday, April 30, 2010

30th April 2010
Non-premixed ﬂame extinction
phenomena: analytical and
numerical investigations

30th April 2010
Non-premixed ﬂame extinction
phenomena: analytical and
numerical investigations
Praveen Narayanan
Department of Fire Protection Engineering
University of Maryland, College Park, MD-20740
Sponsors: DOE Ofﬁce of Science (INCITE - Innovative and Novel Computational Impact on Theory and
Experiment - Program); and National Science Foundation (CBET)

Scholastic background

✤ PhD: Mechanical/Fire Protection Engineering
• University of Maryland, College Park (2005-present)
• Thesis topic: Direct Numerical Simulations of non-premixed ﬂame extinction phenomena
• Advisers/collaborators: Dr. Arnaud Trouvé (UMD), Dr. Howard Baum (UMD), Dr. Hong
Im (UMich), Paul Arias (UMich)

✤ PhD: Mechanical/Fire Protection Engineering
• University of Maryland, College Park (2005-present)
• Thesis topic: Direct Numerical Simulations of non-premixed ﬂame extinction phenomena
• Advisers/collaborators: Dr. Arnaud Trouvé (UMD), Dr. Howard Baum (UMD), Dr. Hong
Im (UMich), Paul Arias (UMich)
✤ Batchelor and Master of Technology: Chemical Engineering
• Indian Institute of Technology Madras, Chennai, India (2000-2005)
• Masters thesis: Implementation of high order compact schemes for incompressible ﬂows

Research overview
✤ ‘Flame extinction` phenomena in non-premixed ﬂames
• Background and motivation
• Phenomenological description
• Premise, hypothesis
• Problems investigated
• Solution approaches and results
✤ Future HPC research in ﬁre/combustion phenomena

Background and motivation

✤ What is a diffusion flame?
• Diffusion flames
(or non-premixed flames): fuel and
oxidizer initially unmixed
✦ Examples: fires, diesel engines
Fuel
Flame
Air
Diffusion flames

Diffusion flame extinction
✤ Combustion science
• Impacts performance of non-premixed combustion
systems
• Determines turbulent flame structure and levels of
pollutant emission (NOx, soot, CO)
✤ Engine applications: extinction caused by high
turbulence intensities in diesel engines
(momentum driven, large Reynolds number flows
Diesel engine

✤ Fire applications
• Extinction caused by air vitiation
in underventilated compartment
ﬁres
• Forest ﬁres, oil spills
• Sprinkler systems
✦ Extinction caused by inert gaseous
agents or water spray suppression
systems
pool fire
sprinklers

smoke
Air
Fuel
Air Extinction
Flame surface
(Sunderland et al)
✤ What is flame extinction?
• A ‘hole` in flame: mixing without chemical reaction
• Examples: suppressing (or extinguishing) fires from water spray,
blowing out candle

Phenomenology

Fuel side Oxidizer side
Flame
Flame
Flame

✤ Types of ﬂame extinction phenomena
Flame
Flame
Flame

• Aerodynamic quenching: flame weakening due to
flow-induced perturbations (insufficient
residence time-blowing out a candle)
Flame
Flame
Flame

• Thermal quenching: ﬂame weakening due to heat
losses (wall cooling, thermal radiation,
evaporative cooling in suppression systems)
Flame
Flame
Flame

• Thermal quenching: flame weakening due to heat
losses (wall cooling, thermal radiation,
evaporative cooling in suppression systems)
• Quenching by dilution: insufficient fuel/oxidizer
concentration (air vitiation in under-ventilated
fires)
Flame
Flame
Flame

Types of ﬂame extinction
phenomena
✤ Aerodynamic quenching
• Blowout at large stretch rates (also known
as kinetic extinction)
• Extinction criterion
✤ Sources
• Linan, 1974, “Acta Astronautica”
• Williams, 1975, “Combustion theory”
• Carrier, Fendell & Marble, 1975, “SIAM
Journal of Applied Mathematics”

Types of ﬂame extinction
phenomena
✤ Thermal quenching:
• Radiative extinction (large radiation heat losses)
• Extinction due to evaporative cooling
• Extinction criterion
• Sources
✦ Sohrab, Liñan & Williams (1982) “Combustion Science and Technology”
✦ Chao, Law & T’ien (1992), “Combustion and Flame”
✦ T’ien (1986), “Combustion and ﬂame”

The premise: ‘uniﬁed’ extinction
criterion

Questions

Questions
✤ Whether extinction can be described in phenomenological terms with a
consistent mathematical model for cases with

Questions
• Stretch (due to turbulence)

Questions
• Radiative heat losses (soot, CO2, H2O, other gases)

Questions
• Evaporative cooling (suppression from water droplets)

Questions
• A combination of the above

Questions
• A combination of the above
✤ What kind of diagnostics may be developed to qualify (or quantify)
extinction?

The extinction ‘criterion’
✤ The Damköhler number
✤ Code supplies both quantities
✤ Need to test if hypothesis holds

Mixing

Mixing
Chemistry

What is new about this work?

✤ Extinction studies with stretch -widely studied (Linan-1974)

✤ Extinction studies with heat losses (primarily, radiation)

• Some theoretical developments by T’ien, Law, Chao, Liu

✤ Current study

✤ Current study
• Rigorous treatment of non-adiabatic environments (soot, radiation, water spray)

✤ Current study
• Theoretical developments validated with high quality numerical datasets

✤ Current study
• Questions asked about soot leakage and connection with radiative extinction

✤ Current study
• Questions asked about soot leakage and connection with radiative extinction
• Treatment of radiation absorption (with possible extension to optically thick media)

Pulications
✤ Radiation driven flame weakening effects in sooting turbulent flames (2008),
Narayanan & Trouvé, ”Proceedings of the combustion institute”
✤ Effects of soot addition on extinction limits of luminous laminar counterflow
flames, Narayanan, Baum & Trouvé (Accepted, Combustion symposium, 2010)
✤ Extinction of Nonpremixed Ethylene-Air flames by water spray, Arias, Im,
Narayanan & Trouvé (Accepted, Combustion symposium, 2010)
✤ Mixture fraction and state relationships in diffusion flames interacting with an
evaporating water spray, Narayanan, Trouvé, Arias & Im (in preparation, presented
at the US Combustion meeting, Ann Arbor, 2009)
✤ Constructing extinction maps for diffusion flames predicated by radiation emission
in sooting turbulent flames, Narayanan, Lecoustre & Trouvé (in preparation,
presented at the International Seminar on Fire and Explosions Hazards, Leeds, 2010)

Tools/approach

Tools/approach
✤ Direct numerical simulations to generate datasets
• Massively parallel Combustion solver S3D
• NERSC machines (Franklin,Hopper)

Tools/approach
✤ Mathematical modeling
• Canonical problems solved using singular perturbation techniques

Tools/approach
✤ Mathematical modeling
• Canonical problems solved using singular perturbation techniques
✤ Model validation and analysis

Numerical approach

Numerical approach
✤ Use Direct numerical simulations (DNS)

Numerical approach
✤ Leverage DOE sponsored SciDac collaboration solver S3D
• Collaborators: Sandia Ntl. Laboratories (J. J. Chen), University of Michigan (H. G. Im)

Numerical approach
✤ Leverage DOE sponsored SciDac collaboration solver S3D
• Collaborators: Sandia Ntl. Laboratories (J. J. Chen), University of Michigan (H. G. Im)
✤ DNS solver S3D
✓ Navier-stokes solver; fully compressible flow formulation
✓ Higher-order methods: 8th order finite difference; 4th order Runge Kutta time
✓ Characteristic based boundary conditions (NSCBC)
✓ Structured cartesian grids
✓ Parallel, MPI based (excellent scalability)
✓ Flame modeling: detailed fuel-air chemistry (CHEMKIN compatible); simplified soot formation model;
thermal radiation model (Discrete Ordinate/Discrete Transfer Method); Lagrangian particle model to
describe dilute liquid sprays

Flame modeling

Single step chemistry
✤ Ethylene-air chemistry model (Westbrook & Dryer, 1981)
✤ Used for simpliﬁed extinction model (in asymptotic analysis and
numerical validation with DNS)
€
˙ωF = BRR (
ρYF
MF
)ν F
(
ρYO2
MF
)νO
exp(−
Ta
T
)

Detailed Chemistry
✤ Used for more detailed calculations with water spray
✤ Reduced chemical kinetic mechanism (Lu & Law, 2009, Progress in
Energy and Combustion Science)
• Based on detailed chemistry mechanism for ethylene-air combustion (70 species,
463 elementary reactions, Wang et al., 2000, Proceedings of the Combustion Institute)
• Reduced chemistry mechanism using: the method of directed relations graphs
(DRG): sensitivity analysis; quasi steady-state assumption for fast reacting
radicals
• 19 species, 15 semi-global reactions

Soot formation model
✤ Phenomenological, two equation model (Moss et al., Lindstedt et al.)
✤ Soot formation process included into phenomenology
• nucleation, surface growth, coagulation, oxidation

Lagrangian spray model
✤ Adapted from ‘Wang
and Rutland‘ (2007),
Combustion and
Flame
✤ Spherical,
monodisperse droplets
✤ ‘Particle in cell’
✤ Dilute liquid phase
assumption
✤ Lagrangian-Eulerian
coupling
Position
Mass
Momentum
Energy
Lagrangian droplet
equations
Droplet source terms in
Eulerian gas equations
Mass
Momentum
Energy

Thermal radiation model
✤ Non-scattering, gray gas assumption; Discrete Transfer Method
(Lockwood & Shah, 1981)
✤ Solve radiative transfer equation
• Mean absorption coefﬁcient (ap,i)

Problems investigated

✤ Turbulent sooting/radiating wall ﬂames

• Radiative weakening and extinction ﬁrst come to light in turbulent simulation

✤ Laminar counterﬂow sooting/radiating ﬂames

• Attempts in understanding radiative extinction through asymptotic analysis and
numerical simulations

✤ Turbulent counterﬂow ﬂames weakened by water spray

✤ Turbulent counterﬂow ﬂames weakened by water spray
• More complex problem with detailed chemistry, explored via numerical
simulations and application of asymptotic model developed

Turbulent sooting flames
✤ Simplified turbulent configuration
✓ Two dimensional (8 x 4 cm2); grid size: 1216 x 375 (uniform x stretched); prescribed inflow
turbulent fluctuations (u’ = 1-2.5 m/s, Lt = 1.7 mm)
Air
Fuel
Solid Wall
2.5-5 m/s Δy ≈ 50 µm
Δx ≈ 66 µm

✤ Observations
• radiative cooling region is not
thin
• soot region is not thin
• weak flame events correlated
with soot mass leakage across
the flame
radiation cooling rate
soot mass fraction extinction
extinction
✤ Analysis of flame structure (case, Tw=300 K, with soot/radiation,
Csoot= 7000 m-1 K-1)

✤ Analysis of ﬂame structure (case, Tw=300 K, with soot/radiation,
Csoot= 7000 m-1 K-1)
weak spots
weak flame events occur at low values of
flame stretch (slow mixing limit)

Radiative extinction under
external soot loading

Overview
✤ Explore connection between flame extinction and soot leakage
• Relevance in radiating/sooting environments
✓ Poolfires
• Connection with smoking candle flames
Cold Soot
Hot Soot

Problem formulation
✤ ‘Asymptotic’ ﬂame structure with soot loading
• External soot loading to simulate multi-dimensional ﬂame structure in a one-
dimensional framework
• Soot loading from air side
Fuel
Air Air
Flame
Soot region
Flame
Sootinjection

Problem formulation
✤ Approach: setup counterflow flame with radiative heat loss
• Analytical setup (transform to one-dimensional scalar fields)
• Numerical setup (DNS) for validation (two dimensional counterflow flame)
✤ Outputs: Flame structure (flame variables such as temperature,
mixing rate, radiation cooling rate)
✤ Effect of soot loading on extinction properties
• how are the limits changed with radiation heat loss?

‘Activation Energy Asymptotics’
✤ Convert governing equations into one-dimensional coordinates using
Howarth transformation for variable density
✤ Constant specific heat, single step Arrhenius Chemistry
✤ Conventional solution using singular perturbation: split domain into
• Outer radiating zone-to obtain radiation corrected outer temperatures
✓ Full treatment-both emission and absorption handled (radiation transport equation solved)
• Inner reacting zone -complete flame structure and extinction conditions
✓ Solve using two point BVP solver
• Patch outer and inner solutions to obtain complete flame structure
• Solve for soot field using completed flame structure with BVP solver (but do not have
benefit of asymptotic expansions here!)
Outer
Outer
Inner

Governing equations
Only contributes near thin reaction zone (inner region)
Zero far from reaction zone (outer region)
Fuel
(Ethylene)
Outer layer
(radiatively active)
Thin ﬂame (inner layer)
Oxidizer
(air)

Outer solutions
✤ Solve for leading order solutions “far” from flame
Algorithm
✓Solve on either side of flame using
Green’s functions
✓Get temperature at flame location
✓Solve Inner equation
✓Obtain complete solution
Howarth
Transform

Inner solutions
✤ Solve for inner solutions by ‘zooming in’ at ﬂame zone
✤
Transform
Outer
Outer
Inner

Inner solutions
✤ Solve for inner solutions by ‘zooming in’ at ﬂame zone
✤
Transform
Outer
Outer
Inner
Reduced Damköhler number

What is the effect of radiation in
all this?
✤ Radiation free flame: (outer)
temperature is the adiabatic flame
temperature
✤ With radiation: (outer) temperature is
lowered!
✤ Effects of radiation felt when
• Large amounts of soot
• Small strain
✤ Radiation corrected flame temperature
feeds into inner equation
Radiation correction to give new
“Burke-Schumann” temperature
Text
Solve RTE

all this?
temperature
lowered!
• Small strain
Radiation
Text
Solve RTE

all this?
temperature
lowered!
• Small strain
Radiation
Strain
Text
Solve RTE

On radiative emission and
absorption
✤ Emission: local function of temperature
✤ Absorption: non-local convolution
integral
• Depends on optical thickness of surroundings
• Can develop asymptotic measures for
radiating regimes (‘thick’ (Szoke, LLNL),
‘thin’ (the optically thin assumption),
‘intermediate’)
• Possibilities of regime based approximations
(thick and thin somewhat amenable to
analytical solutions (!?), intermediate needs
computation)
Radiation
source term
Optically thin
Optically thick

Laminar counterflow flames
✤ Reference counterflow
flame
• Flamelet perspective: study
flame structure as a function
of flame stretch ranging
from ultra-low to ultra-high
values
• No soot injection
Flame

✤ Reference counterflow
flame
• Flamelet perspective: study
flame structure as a function
of flame stretch ranging
from ultra-low to ultra-high
values
• No soot injection
kinetic
extinction
limit
radiation
extinction
limit
DNS
AEA

✤ Reference counterflow flame
• Flamelet perspective: study flame structure as a function of flame
stretch ranging from ultra-low to ultra-high values

✤ Extinction values correspond to critical value of Damköhler number

✤ Extinction values correspond to critical value of Damköhler number
adiabatic
soot-free
with
soot
with external
soot loading
approximate
critical value
Extinction
Flammable

‘Flammability maps’
✤ Extinction limits
• Flammability maps with mixing rate and ﬂame temperature as coordinates
Extinction
Flammable
Engine
extinction event
Fire
extinction event

Analysis of turbulent flame data
✤ Extinction limits
• Flammability maps with mixing rate and flame temperature as coordinates
Extinction
representative conditions of
flame weakest spots in DNS
•Apparently, the flame’s weakest
spots are not actually ‘quenched’
•Soot leakage events may have more
to do with cessation of soot
oxidation chemistry than radiative
extinction
soot mass fraction extinction

Conclusions on sooting ﬂames

✤
Activation energy asymptotics and DNS have been used to make fundamental
observations on non-adiabatic turbulent sooting diffusion ﬂames

✤
✤
Two extinction limits are encountered
• Kinetic extinction (at high stretch)
• Radiative extinction (at low stretch)

✤
✤
✤
Extinction occurs at a single critical value of the ‘reduced’ Damköhler number
equalling unity
• Can construct maps to gauge extinction propensity of ﬂames

✤
✤
✤
Extinction occurs at a single critical value of the ‘reduced’ Damköhler number
equalling unity
• Can construct maps to gauge extinction propensity of ﬂames
✤
Turbulent ﬂame data indicate that soot leakage events are not necessarily radiative
extinction events. Further investigation of soot oxidation chemistry is warranted

DNS of turbulent spray ﬂames

Turbulent spray flames
✤ Counterflow laminar/turbulent
diffusion flames with water spray
injection
• Two dimensional, domain size (1 cm x 2
cm), 480 k grid points (400 procs on
Franklin)
✓ Detailed chemistry
✓ Strain rate of 440 s-1 (extinction: 1300 s-1)
✓ Turbulence injection at inlet (u’/U=0.85,
L11=0.5 cm)
1 cm
Δx = 16 µm
Δy= 25 µm
✓ Droplet diameter: 10 μm, mist
regime
✓ Injection at local gas velocity

Unexplored areas
✤ Extinction and soot leakage
• If soot leakage precedes radiative extinction, can one come up with a description based
on soot chemistry
✓ ‘Damköhler’ number criterion for cessation of soot oxidation chemistry
• Could have ramifications in smoking fires
✓ Strongly radiating, but not quenched
✤ Development of approximations in thick media (and thin) and its application
to radiating solvers
• Envisage cost reduction if only ‘intermediate’ regions need to be computed
✤ How do we incorporate chemistry effects in complex flames?

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