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RAYLEIGH-TAYLOR INSTABILITY: MODELLING AND EFFECT ON COHERENT DEFLAGRATIONS
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm
J. Keenan, D. Makarov, V. MolkovPaper ID No: 146
INTERNATIONAL CONFERENCE ON HYDROGEN SAFETY
ICHS 2013PROGRESS IN SAFETY OF HYDROGEN TECHNOLOGIES AND INFRASTRUCTURE:
ENABLING THE TRANSITION TO ZERO CARBON ENERGY
9TH – 11TH SEPTEMBER, 2013, BRUSSELS, BELGIUM.
� Aim and objectives of research.
� Modelling approach.
� H2-air deflagration at FM Global large
scale deflagration chamber.
� Deflagration model results: ‘former’.
� Implementation of Rayleigh-Taylor
(RT) instability into model.
� Conclusions.
Presentation outline
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (1/21)
Hydrogen Safety Engineering (HSE):
� Application of scientific and engineering principles to
the protection of life, property and environment
from adverse effects of incidents/accidents involving
hydrogen.
HySAFER Centre at the University of Ulster:
� Understand and predict physical phenomena
associated with large scale hydrogen deflagration
scenarios.
� Using a Large Eddy Simulation modelling approach.
Introduction
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (2/21)
Aim and objectives
Aim of research:
� Further develop, improve and validate UU Very
Large Eddy Simulation (VLES/LES) deflagration
model against a broader range of experiments.
Objectives:
� Identify credible combustion enhancing
mechanism(s) not accounted for in the current
UU VLES/LES deflagration model.
� Implement identified mechanism(s) into model.
� Validate updated model against experiment(s).
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (3/21)
LES of deflagrationsFlamelets
10-3m 101m
Enclosures Bleve
103+m
� For large scale deflagrations majority of wrinkling is at sub-gridscale (SGS), “VLES” approach is implemented.
� For reacting flows the success of this approach requires a robustturbulent SGS combustion model (Pope, 2004).
� The successful implementation of the UU multi-phenomenadeflagration model depends on both unresolved and partiallyresolved phenomena.
� UU deflagration model employed using a User Defined Function(UDF) approach, dynamically loaded with ANSYS FLUENT.
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (4/21)
� Conservation of mass:
� Conservation of momentum:
� Conservation of energy:
UU LES model (1/2)
( ) 0~. =∂∂+
∂∂
jj
uxt
ρρ
( ) iijk
k
i
j
j
ieff
jiij
j
i gx
u
x
u
x
u
xx
puu
xt
u ρδµρρ +
∂∂−
∂∂
+∂∂
∂∂+
∂∂−=
∂∂+
∂∂ ~
3
2~~ ~~ ~
( ) ( )
eiji
i
i
j
j
ieff
j
m
eff
effm
jeff
peff
j
jj
j
Sx
u
x
u
x
u
x
Y
Sch
x
TC
x
x
pEu
xE
t
+
∂∂−
∂∂
+∂∂+
∂∂−−
∂∂
∂∂
=∂∂+
∂∂+
∂∂
∑ δµµµ
ρρ
3
2
Pr
.
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (5/21)
� Premixed flame front propagation, progress variable:
� Using gradient method for source term:
� ‘Former’ UU deflagration model is based on the interaction of fourmechanisms responsible for the increase of flame front surfacearea. Model is implemented using a modified version of Yakhot’sequation for turbulent flame propagation velocity.• Flow turbulence• Turbulence generated by the flame front itself, Ξk• Leading points (curvature radius & preferential diffusion), Ξlp• Fractal-like flame wrinkling, Ξf
UU LES model (2/2)
( ) ( ) c
jeff
eff
jj
j
Sx
c
Sc
µ
xcuρ
xcρ
t+
∂∂
∂∂=
∂∂+
∂∂ ~
~~~
~
)(cgradSS tuc
→= ρ
2)/exp(][ tflpKut SuSS ′⋅Ξ⋅Ξ⋅Ξ⋅=( )2exp tut SuSS ′⋅=
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (6/21)
Previous validations� Model has been successfully validated against:
• Large-scale hydrogen-air deflagrations in closed vessels with uniform and non-
uniform mixtures.
• Largest known unconfined experiments.
• 78.5m long tunnel.
� Application of the ‘former’ version of UU deflagration model, when compared to
FMG vented deflagration experiments, led to under-prediction of overpressures.
� FM Global modelling approach also did not initially replicate experimental
overpressures.
Bauwens et al., 3rd International Conference on Hydrogen Safety, Corsica, 2009
Central ign. / 2.7m2 vent Back wall ign. / 5.4m2 ventCentral ign. / 5.4m2 vent
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (7/21)
FM Global experiment
Bauwens et al., International Journal of Hydrogen Energy, 36, pp. 2329-2336, 2011
�FM Global large scale deflagration
chamber.
�Chamber dimensions:
4.6 m x 4.6 m x 3 m = 63.7 m3.
�Square vent: 2.7 m2 or 5.4 m2.
�Central or back wall ignition.
�18 % vol. hydrogen-air mixture.
�4 internal pressure transducers.
�Pressure data obtained from loc. P1.
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (8/21)
Former model results
Results from unmodified deflagration model:
Former UU model
Central Ignition
Vent = 2.7m2
Former UU model
Central Ignition
Vent = 5.4m2
Former UU model
Back Wall Ignition
Vent = 5.4m2
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (9/21)
� Rayleigh-Taylor (RT) instability identified as missing mechanism,
which would if implemented into UU LES deflagration model
increase flame front area.
� RT instability occurs at the interface between two fluids, subject
to acceleration in the direction from the lighter to the heavier.
� In a propagating flame:
• Unburned mixture – heavier fluid.
• Combustion products – lighter fluid.
� “Depending on the layout of the vent arrangement and the
point of ignition, RT instability may dominate all other
mechanisms that commonly are believed to be important in
governing pressure build-up” Solberg et al., Eighteenth Symposium (International) on Combustion, pp. 1607-1614, 1981
Rayleigh-Taylor instability
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (10/21)
Experimental observation
Growth of flame front turbulence investigated by Tsuruda & Hirano:
� Obstacle placed in path of flame inside combustion chamber.
� Acceleration induced just before flame front passed obstacle.
� Flame front became needle-like in structure.
� For this experimental setup acceleration induced mechanism - dominant over all mechanisms which
increase flame surface area.
Tsuruda and Hirano, Combustion Science and Technology, 51 (4-6), pp. 323-328, 1987
Time = 1.5 ms
Time = 1.25 ms
Time = 2 ms
Time = 1 ms
Time = 1.75 ms
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (11/21)
RT model (1/3)
Growth of perturbationRemoval of RT flame
wrinkling – ‘Sink’
Calculation of RT perturbation amplitude, hi,t:
Youngs, D. L., Physica 12D, Netherlands, 1985, pp. 32-44
� Acceleration: Calculated within each control volume, per timestep, in the direction
normal to the propagating flame front.
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (12/21)
( ) ( ) tSthh RTtittittiti ∆−Ξ⋅−∆⋅+= ∆− 11 ,,,,, αω
� Wavelength:
� Atwood number:
� Growth rate:
31
,,
2
,,
, 4
⋅⋅⋅=
titi
tiT
tiAtwAcc
νπλ
( )( ) tibtiu
tibtiu
tibtiu
tiAtw ,,,,
,,,,
,,,,
, , ρρρρρρ
>+−
=
ti
ti
titiAccAtw ,
,
,,
2 ⋅⋅=λπω
RT model (2/3)
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (13/21)
Source term, , generation and suppression of RT instability:td
d RTΞ
+
=
⋅
+
⋅
⋅==Ξ
2
2
2
22
,
2
,
2
,
2
,
2
,
2
,,
2
1
ti
ti
ti
ti
ti
titi
RT
hh
S
S
λ
λ
λπ
λλπ
( )( )1, −Ξ= RTti fhtd
hd
hd
d
td
d RTRT ×Ξ=Ξ
( ) ( )1,
2
2,,,,
2
,
2
,
,
, −Ξ⋅−⋅=
+
⋅=Ξ
RTtittiti
ti
ti
ti
tiRT Shtd
hd
h
hRT
hd
d αωλλ
�
�
Unsteady term Convection term Source term
RT model (3/3)
4C(1-C)
Weller et al., Flow, Turbulence and Combustion, 72, pp. 1-28, 2004
�Unsteady term: Accumulation of ΞΞΞΞRT in each CV.
�Convection term: Transport of ΞΞΞΞRT due to velocity field.
�Source term: Accounts for sources and sinks, which either
create or destroy ΞΞΞΞRT :
• SΞRT = (GrowthRT – SinkRT) x [4C(1-C)]
• Multiplier added to limit ΞΞΞΞRT growth outside the flame.
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (14/21)
( )RT
Sx
SUt i
RT
iti
RT
Ξ=∂Ξ∂⋅++
∂Ξ∂
,
( ) ( ) tSthh RTtittittiti ∆−Ξ⋅−∆⋅+= ∆− 11 ,,,,, αω
Growth of perturbation Removal of RT flame wrinkling – ‘Sink’
Model parametersRT model contains two user-defined parameters: kh & α
1. Initial amplitude of flame instability – kh:�To calculate initial RT amplitude inside CV ‘i’: h0,i,t = kh x λi
�Influence of RT limited to the area of the external deflagration:
• In the key area of interest, kh = 0.5.
• In all other locations, kh = 0.001.
2. Surface ‘Sink’ term – α:�Constant multiplier to increase or decrease removal rate.
�If term set to 1.0 – α has no influence on consumption rate.
�Following parametric analysis α set to 0.75.
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (15/21)
Former model result, central ignition, 5.4 m2 vent
Internal External
�‘Former’ model failed to
reproduce first distinct pressure
peak.
�This internal pressure peak is
caused by external deflagration.
�External pressure less than
internal pressure.
�To have influence, external
pressure should be at least
comparable to internal pressure
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (16/21)
Internal External
RT model result, central ignition, 5.4 m2 vent
�Intensification of external deflagration,
�Associated internal pressure peak reproduced.
�Partial vacuum following dissipation of external deflagration,
�Reduction of internal pressure following first pressure peak.
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (17/21)
‘Former’ model vs. RT model
Central ign. / 2.7m2 vent Back wall ign. / 5.4m2 ventCentral ign. / 5.4m2 vent
Former model results:
RT model results (in area of external deflagration, kh = 0.5):
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (18/21)
RT model result, in area of
external deflagration, kh = 0.5:
Inside Chamber Outside Chamber
kh α kh α
0.001 0.75 0.75 0.75
Inside Chamber Outside Chamber
kh α kh α
0.001 0.75 0.5 0.75
RT model result, central ignition, 2.7 m2 vent
RT model result, in area of
external deflagration, kh = 0.75:
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (19/21)
Comparison of result
Former UU model result
UU RT model result
Former FMG model result
FMG RT model result
Bauwens et al., 3rd ICHS, Corsica, 2009
Bauwens et al., IJHE, 36(3), pp. 2329-2336, 2011
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (20/21)
�Rayleigh-Taylor instability identified as credible combustion
enhancing mechanism for the considered experiments.
�Following introduction of RT instability model into UU LES
deflagration model, equation describing turbulent burning
velocity recast as:
�RT model implemented as an additional transport equation.
�In experimental scenarios investigated, introduction of RT model
led to improvement of simulation results.
�Two user defined parameters contained in RT model: kh & α:
• α set as a constant throughout the calculation domain.
• kh set to 0.5 & 0.75 in area of external deflagration.
( ) ( )2'exp tRTflpkut SuSS Ξ×Ξ×Ξ×Ξ×=
Conclusions
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (21/21)
Thank you for your attention
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm
�Rayleigh-Taylor instability identified as credible combustion
enhancing mechanism for the considered experiments.
�Following introduction of RT instability model into UU LES
deflagration model, equation describing turbulent burning
velocity recast as:
�RT model implemented as an additional transport equation.
�In experimental scenarios investigated, introduction of RT model
led to improvement of simulation results.
�Two user defined parameters contained in RT model: kh & α:
• α set as a constant throughout the calculation domain.
• kh set to 0.5 & 0.75 in area of external deflagration.
( ) ( )2'exp tRTflpkut SuSS Ξ×Ξ×Ξ×Ξ×=
Conclusions
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm (21/21)
Notes:
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm
• Conservation of mass
• Conservation of momentum
• Conservation of energy
LES model (1/3)
( ) 0~ =∂∂+
∂∂
jj
uρxt
ρ
( ) iijk
k
i
j
j
ieff
jii j
j
i gρδx
u
x
u
x
uµ
xx
p uuρ
xt
uρ +
−
++−=+
∂∂
∂∂
∂∂
∂∂
∂∂
∂∂
∂∂ ~
3
2~~~~
~
( ) ( )( )=+∂∂+
∂∂
pEux
Et j
j
~~~ ρρ
ccijk
k
i
j
j
ieffi
m j
m
eff
effm
jeff
peff
j
HSx
u
x
u
x
uu
x
Y
Sch
x
Tc
x⋅+
−
∂∂
+∂∂+
∂∂−−
∂∂
∂∂= ∑ δ
∂∂µ
µµ ~
3
2~~~
~~
~
Pr
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm
� Premixed flame front propagation (progress variable)
� Gradient method for the source term
� The SGS turbulent combustion model for LES is based on the interaction of four mechanisms responsible for increase the flame front surface area:� Flow turbulence � Turbulence generated by the flame front itself� Preferential diffusion of stretched flame� Fractal-like flame wrinkling
LES model (2/3)
~
)(cgradSS tuc
→= ρ
( ) ( ) c
jeff
eff
jj
j
Sx
c
Sc
µ
xcuρ
xcρ
t+
∂∂
∂∂=
∂∂+
∂∂ ~
~~~
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm
Existing UU turbulent burning velocity model
• Solves the conservation equations: mass, momentum and energy.
• Premixed flame front propagation, progress variable:
• Using gradient method for source term:
• Existing multi-phenomena turbulent burning velocity model for LES of
premixed combustion is defined by:
• Flow turbulence
• Turbulence generated by the flame front itself (TGFF)
• Preferential diffusion of stretched flame
• Fractal-like flame wrinkling
2)/exp(][ tflpKut SuSS ′⋅Ξ⋅Ξ⋅Ξ⋅=
( ) ( ) ~
)(,~
~~~ cgradSSSx
c
Sc
μ
xcuρ
xcρ
ttucc
jeff
eff
j
j
j
→=+
∂∂
∂∂=
∂∂+
∂∂ ρ
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm
• Renormalization group (RNG) theory is the basis of the
developed LES model
• Yakhot et al 1986, Su substituted with StSGS
• Renormalisation group (RNG) SGS turbulence viscous model
• In highly turbulent flows
2
exp
′=
t
SGStt S
uSS
Flow Turbulence
2
exp
′=
tut S
uSS
31
3
2
1001
−+=
µµµ
µµ effseff H
( ) ijijCVs SSV~~
2157.0231ρµ =
∂∂
+∂∂=
i
j
j
iij x
u
x
uS
2
1
( )3/1157.03
2
CV
tsgs
Vu
ρµ
=′seff µµ =
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm
• Karlovitz (1951)
• Upper limit of flame-induced turbulence:
• Upper limit for the flame-generated turbulence factor:
• Gostinstev et al 1989 reported transition from laminar to fully developed
turbulent regime at R0=1-1.2m for near Stoichiometric H2-air.
• Formula applied in the SGS for transient value of flame wrinkling factor:
3
)1( ui SEu
⋅−=′
3
)1(max −==Ξ i
u
tK
E
S
S
( ) ( )[ ]*/exp111 max RRKK −−⋅−Ξ⋅+=Ξ ψ
Turbulence Generated by the flame front itself
=<1ψDistance from ignition source=R Empirical coefficient
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm
Preferential diffusion
• Kuznetsov and Sabelnikov, 1990
• Turbulent flame speed is led by the reaction zone areas most protruded into the
unburnt mixture.
• Mixture composition locally altered by differences in diffusivities of fuel and
oxidiser.
• Within the leading point combustion zone:
φα 1=
5.0
=
f
ox
D
Dd
( )( ) 111 00
0 ≤⋅−⋅+⋅+
+= lp
stst
stlp
dCC
dC ααα
αα ,
( )1
110 ≥+
−+⋅+= lp
st
stlp
Cd
ddC ααα ,
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm
Fractal-like flame wrinkling
• Used to describe highly contorted, roughened curves and surfaces.
• The flame surface area of outward propagating turbulent flames will grow as
R2.RD-2, where D is the fractal dimension (2.11-2.35).
• The integral scale of the problem R is the outer cut-off.
• The inner cut-off is chosen as a laminar flame front thickness:
• The effect of changing temperature of unburned mixture and explosion
pressure on the inner cut-off:
kinematic viscosity
• To exclude a stage of quasi-laminar / transitional flame propagation after
ignition up to the critical radius R*: additional wrinkling coefficient due to
the fractals nature of turbulent premixed flame to be applied after R* is:
Lδε ≈
uL Sνδ = =ν
2−
⋅⋅=Ξ
D
Rf
R
R
εε*
*
1
35.2
1
05.2'' +
++
=uSSu
Duu
with (North &
Santavicca 1990)
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm
Leading point factor
� Using the formulation by Kuznetsov and Sabelnikov, Zimont and Lipatnikov determined the hydrogen concentration at the leading points and found corresponding values of burning velocities by linear interpolation of the experimental data provided by Karpov and Severin.
0.5
1.0
1.5
2.0
2.5
3.0
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80
Hydrogen mole fraction
X_l
p
ICHS 2013 Presentation – Tuesday 10th September, 3:20pm