cfd-large eddy simulation of vented deflagration

7/27/2019 CFD-Large Eddy Simulation of Vented Deflagration

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Large Eddy Simulation of Vented DeagrationPierre Quillatre,*,, Olivier Vermorel, Thierry Poinsot, and Philippe Ricoux

CERFACS, 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, FranceTOTAL S.A., Tour Coupole, 92078 Paris La Defense Cedex, France

ABSTRACT: In order to understand gas explosion phenomena in industrial buildings, a reduced-scale vented combustionchamber is investigated numerically. In this conguration, a ame is ignited in an initially quiescent ammable mixture andpropagates past solid obstacles, generating a strong pressure increase. The aim of this numerical study is twofold: The rstobjective is to show how large eddy simulation manages to reproduce the parameters of critical relevance for this multiscaleproblem, in particular the overpressure generated during the ame propagation. The second objective is to highlight that, even iflarge- to small-scale turbulence effects play a crucial role in the ame development and the resulting overpressure, it is alsoneeded to correctly account for thermo-diffusive scale phenomena.

INTRODUCTION

Accidents due to gas explosions in industrial buildings such asoffshore oil and gas producing platforms or oil storage facilitiesare a major safety issue. Although the primary objective is ofcourse to prevent them, being able to understand themechanisms which control them is a societal, economical,and physical challenge of prime importance.

A typical explosion scenario begins with an ignition of aquiescentammable mixture inside a conned or semiconnedarea. Then, the ame propagates and accelerates by interaction

with obstacles (process equipment, structures, piping, ...),generating a strong increase of pressure. This overpressure isthe parameter of critical interest for safety studies, since it can

induce the destruction of the facilities involved. In order tounderstand explosions in conned and semiconned areas,small- to medium-scale congurations of vented chambers areusually considered. Experimental15 and numerical68 studiesof explosion have extensively been performed in order to pointout the mechanisms involved in ame acceleration and pressureincrease generation. Effects of geometric features or fuel typeon this overpressure have also been studied.911 Thanks to thegrowing computational power, computational uid dynamics(CFD) appears as an interesting alternative to experiments,

which remain expensive and dangerous and bring limitedmaterial for diagnostic and understanding of explosions.Explosions are a typical multiscale and multiphysics problemfor which adapted numerical methods must be used. Up to

now, safety related studies of explosions for industry havemainly been carried out using unsteady Reynolds averagedNavierStokes (URANS) methods.12,13 However, the emer-gence of large eddy simulation (LES) on massively parallelcomputers has considerably improved the ability to preciselysimulate fully unsteady ows in complex geometries11,14 andappears as a promising tool for explosion studies.

The ultimate objective of this research is to develop LEStools for realistic explosion cases where the sizes will be of theorder of 10100 m and Reynolds numbers will be very large.To develop these LES tools and make sure that they cancapture all phases of the ame development, the strategy is to

begin with a smaller size experiment (0.25 m) installed at the

University of Sydney.9 In this kind of conguration, the ow islargely turbulent during most of the explosion. The largespectrum of turbulent scales present in this ow interacts withthe ame and must be properly reproduced in order toaccurately simulate the amepropagation in this environment.

As shown by Di Sarli et al.,1517 the predictive ability of LESstrongly relies on the model implemented to take into accountthe ameturbulence interaction. It is well-known that the roleplayed by the combustion submodel is dependent on both thegrid resolution used and the combustion regime experienced bythe propagating ame. However, the main aim of the presentpaper is to point out that, in LES, in addition to the importanceto account for large- to small-scale turbulent combustioneffects, it is also needed to correctly account for thermo-

diffusive scale phenomena. Reaching a correct reproduction ofall of these multiscale phenomena is the prerequisite in order toaccurately predict the global quantities of critical interest forsafety related studies, in particular the overpressure generatedin the chamber.

TEST CASE

The conguration studied in this work was set up at theUniversity of Sydney.9 It consists of a square cross sectionpremixed combustion chamber (25 cm 5 cm 5 cm) withsolid obstacles. The obstacles consist of three removableturbulence generating grids and one xed central obstacle, asshown in Figure1 (left). The bottom end of the chamber is

closed, and the top end is opened out to the atmosphere. Thevessel is initiallylled with a premixed mixture of air and fuel atatmospheric pressure and temperature. Three different fuels areavailable: CNG (88% CH4) at equivalence ratio = 1, LPG(95% C3H8) at = 1, and H2 at = 0.7. The explosion

Special Issue: Multiscale Structures and Systems in ProcessEngineering

Received: December 14, 2012Revised: February 12, 2013Accepted: February 13, 2013Published: February 13, 2013

Article

pubs.acs.org/IECR

2013 American Chemical Society 11414 dx.doi.org/10.1021/ie303452p|Ind. Eng. Chem. Res. 2013, 52, 1141411423
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scenario begins with an ignition of the quiescent premixedmixture at the closed end of the chamber. Ignition is followed

by a laminar propagation phase and then an interaction withsolid obstacles. When touching the obstacles, the initiallylaminar ame gets wrinkled and becomes a turbulent amepropagating at high speed. Additional details of the setup may

be found in Masri et al.9

As mentioned earlier, the turbulence generating grids can beadded or removed so that several congurations can be studied.

Three con

gurations are studied here, where the number ofgrids is progressively increased from one to three, locatedfarthest from the ignition point. Illustrations of the investigatedcongurations can be found in Figure 1 (right). Two majoraspects can therefore be studied using this experimentalconguration:

the inuence of the fuel on the overpressure the inuence of the geometric features on the ame

propagation and the resulting overpressure

NUMERICAL METHODS FOR EXPLOSIONPHENOMENA

Explosions are a multiphysics problem which requires one toaccount for chemical kinetics, uid ow, turbulence, wall

phenomena, and acoustics considering that all of thesephenomena, which occur over a large range of scales, arestrongly coupled. The numerical method must thus be able totake into account all of these scales. Explosions areconsequently a typical multiscale problem (Figure2). Chemical

reactions taking place in ames occur in very thin fronts,typically less than 100 m, and their kinetics is controlled bythermo and mass diffusive effects across these ame fronts. Thesmallest turbulent structures can reach less than 10 m, whilethe largest scales of the ow correspond to vortices with sizes ofthe order of the building size (10100 m).

In order to reproduce explosion phenomena, variousnumerical approaches are available to solve the compressiblereactive NavierStokes equations. These methods mainly differ

by the way turbulence is accounted for: Direct numerical simulation (DNS) is a bruteforce

approach: all turbulent scales are resolved in space and time.This method requires meshes with a cell size smaller than thesmallest turbulent scale which is the Kolmogorov scale. Forexplosion congurations, this would consequently lead tomeshes of several hundreds of billion points which is notaffordable with the current CPU power. This method is inpractice dedicated to academic congurations (e.g., homoge-neous isotropic turbulence), in very simple and smallcongurations.18

Currently, CFDcodes used for safety studies mainly relyon URANS methods.12 This is a statistic approach where onlyaveraged values are resolved, consequently considerablyreducing the CPU cost. However, all turbulent scales have to

be modeled, which can potentially lead to errors in theirprediction.

The emergence of large eddy simulation (LES) onmassively parallel computers has considerably improved theability to precisely simulate fully unsteady ows in complexgeometries.19,20 Indeed, the LES technique is a ltereredapproach which relies on a scale analysis of the turbulence:according to Kolmogorov,21 turbulence may be considered in afractal way where the smallest scale eddies energy can bededuced from the larger ones. The LES method relies on thisstatement: The energetic largest turbulent scales are explicitlycomputed on the mesh points, while the smallest are modeledfrom the resolved large scales. The overall model contributionin LES is thus reduced compared to (U)RANS methods whereall turbulent scales are modeled. If the cell size is small enough,the model contribution naturally tends to zero and LESdegenerates toward DNS. These properties allow a priori a

better description of turbulent ows even though it requires

more computational time. It is also worth noting that, byconstruction, LES is expected to be much less mesh dependentthan (U)RANS as far as the LES cutofflength falls inside theinertial range of the energy spectrum.

LES has already shown its ability to give more reliablepredictions than URANS in unsteady complex congurationssuch as piston engines19 or gas turbines20 which present manyanalogies with gas explosions in terms of turbulent combustionor connement.

The LES solver used in this study is the AVBP code.22,23

AVBP solves the unsteady compressible and reactive NavierStokes equations on unstructured grids. The present simu-lations are performed with a nite volume LaxWendroffconvective scheme.24 NavierStokes characteristic boundary

conditions (NSCBC)25 are used at the outlet of the plenumwhich is located at the open end of the chamber in order tomimic the atmosphere. The solid walls that represent theobstacles and the explosion chamber are adiabatic nonslip walls.

As it has been mentioned, effects smaller than the mesh sizehave to be modeled:

Sub-grid-scale turbulence is modeled by the WALEviscosity based model.26

When dealing with turbulent combustion congurations,another aspect of modeling is to be able to handle ame fronts

which are generally much thinner than the cell size. If the amestructure is not resolved, it cannot be computed. Forcombustion, no theory enables one to predict ame properties

Figure 1.Left: Explosion chamber conguration of Masri et al.9 Thevessel is orientated vertically in the experiment: the bottom end of thevessel is on the left of the gure and the top end on the right. Right:Classication of the studied congurations.

Figure 2.Multiscale aspect of explosion phenomena.

Industrial & Engineering Chemistry Research Article

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from large scales, since combustion is inherently controlled bymolecular processes. A method similar to LES for turbulenceconsequently cannot be applied. However, combustiontheory27 tells us how ame fronts can be thickened in space

by a factor and stillpropagate at the same speed. Here thethickened ame method28 (TFLES) allows one to make thesefronts large enough to be resolved on the mesh. Flameturbulence interaction at subgrid scale is reproduced bymultiplying the resolved reaction rate by an efficiency factor which models the loss of wrinkling due to amethickening. is dened from the formulation of Colin et al.28 as the ratioof sub-grid-scale ame front wrinkling between a non-thickened and a thickened ame:

=

( )

( )l0

l0

(1)

where l0 is the laminar ame thickness of the nonthickened

ame. The sub-grid-scale ame front wrinkling is dened as

= +

c Re

u

S

u

S1

2 ln(2)

3 [ 1],

ms t

1/ 2

l

0

l

0

l

0

(2)with (/l

0, u/Sl0) = 0.75 exp[1.2/[u/Sl

0]0.3](/l0)2/3,

thelter size,Reta Reynolds number based on an estimation ofthe turbulent integral length scale LT(LT= 5 10

3),= 0.3,andcms= 0.28. Note that this set of parameters has been keptconstant for all the simulations presented in this paper.

In the context of LES, due to their prohibitivecomputational cost, integration of detailed kinetics isimpossible. In our work, chemistry is modeled by reducedschemes.29 Thus, only the principal species and reactions areconsidered. Several one-step and two-step reduced schemeshave been developed for this work. Details on these schemesand their impact on the results are given in the section ResultsSensitivity to LES Submodels.

Ignition processes are very complex (energy transfer bylaser to gas, plasma formation, shock waves, ...) and theirmodeling is a task that extends far beyond the scope of thisstudy. In order to avoid this part of the modeling, calculationsare consequently initialized by a small sphere of burnt gases(radius 1 cm) at the ignition point which is sufficiently strongto initialize the combustion process without any transientphase.

LES simulations were carried out on meshes of 20 milliontetrahedra with a typical cell size of 0.5 mm in the chamber.This mesh density has been chosen in order to ensure that theame, even thickened, remains thinner than the distance

between the bars of the baffle plate.

RESULTS

The aim of this section is to check the ability of LES to simulateame propagation past repeated obstacles and capture thecritical physical quantity related to safety related studies, i.e., theoverpressure generated in the chamber. Besides the under-standing of explosion phenomena using LES results, a particularinterest is brought to the inuence of the fuel and of the

number of turbulence generating grids. Finally, the focus is onthe sensitivity of LES results to the submodels used toreproduce small-scale chemistry and thermo-diffusive effects.

Phenomenological Study. The primary objective of thissection is to understand the phenomena occurring in explosionsand to highlight the mechanisms responsible for the pressureincrease. Results from LES of Cong2 are investigated in orderto understand the typical ame behavior during the explosion.

Figure3 shows LES images of ame propagation comparedwith experiments. In the early stage of propagation, theame islaminar and develops with a hemispherical shape and then ittransitions to a ngershape when it approaches the walls, still

being laminar. This long laminar phase controls the ame shapeand strength just before it touches the obstacles. Finally, the

ame front hits the obstacles, generating strong turbulencewhich accelerates the ame. All phases of ame propagationobserved in experiments are qualitatively well reproduced byLES. With the time interval between two successive images

being kept constant between experiments and LES, thishighlights that the simulation correctly reproduces the amearrival time even though the fourth LES image shows a slightlyfaster ame acceleration than experiments.

As mentioned earlier, the explosion induces a large pressureincrease in the chamber which is the parameter of criticalinterest for safety related studies. Here we propose toinvestigate the mechanisms responsible for this increase usingthe LES results.

Although turbulent combustion ows are inherently

controlled by small-scale physics (chemistry processes,interaction with turbulence, diffusive effects, ...), pressureincrease in the chamber can be explained from a more globalpoint of view, considering quantities integrated in the wholechamber. As explained by Di Sarli et al.,8 the pressure increaseobserved in the chamber is due to the competition between twoopposite phenomena: the combustion rate and the venting rate.On the one hand, the burnt gases accumulated inside thechamber by combustion processes have a lower density thanthe fresh gases they replace and consequently take up a bigger

volume, inducing a pressure increase. On the other hand, gasesexhausting through the vent opening contribute to decrease thepressure. Working on a volume balance, a ne diagnostic has

Figure 3.Images ofame propagation in Cong2 using C3H8. Left: experimental video captured images (false colorized) extracted from Gubba etal.6 Right: LES images (colored by reaction rate). Time intervals between two successive images are kept constant between experiments and LES.




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been set up in order to understand and highlight themechanisms responsible for the pressure increase inside thechamber.

First, the venting rate V vent is simply dened as the volumeow exhausting from the chamber:

=V U SdS

vent noutlet (3)

whereSoutletis the section area of the chamber outlet and Unisthe velocity normal to this section.

Considering that the fresh gases (densityf) which have beenreplaced by burnt gases (densityb) took up a volume Vf= b/fVb, the combustion rate V combcan be written as the variationof the burnt gas volume minus the variation of the consumedfresh gases:

=

=

V

V

t

V

t

V

t(1 / )comb

b f bb f (4)

The variation of the burnt gas volume can be obtained from themass reaction rate of any combustion product, here H2O:

=

V

t Y

b H O

b H Ob

2

2 (5)

where YH2Ob is the H2O mass fraction in the burnt gases and

H2Ois the production rate of species H2O integrated over the

whole chamber.When V comb < V vent, the created volume is larger than the

volume exhausting the chamber and the pressure increases.When V comb < V vent, the trend is opposite and the pressuredecreases. Figure 4 (top) compares V comb and V vent to the

overpressure (bottom) extracted from the LES results. We cannotice the perfect match between the change of sign ofV comb V vent and V comb < V vent. Theseoscillations are reproduced in agreement with the frequencyobserved in experiments.

Numerical Accuracy. As mentioned previously, allsimulations were performed on the same mesh compound of20 million tetrahedra with a typical cell size of 0.5 mm insidethe chamber. An important point is to be able to estimate thequality of the results and especially to check if this resolution is

adequate or not.Arst indication is to measure the respective contribution of

the resolved and sub-grid-scale parts of the combustion rate.Figure5shows the contribution of the resolved part dened as

the ratio between the resolved part of the reaction rate resandthe total reaction rate tot when the ame interacts with thecentral obstacle:

=

=

1res

tot

sgs

tot (6)

with sgs being the sub-grid-scale reaction rate. These valuescan be related to the efficiency function by

= =

1

tot res sgs

(7)

In areas where the ame is almost laminar (near the closed

end of the chamber, before the second baffle plate), the amewrinkling is fully resolved on the grid points and thecontribution of the sub-grid-scale combustion model is ofcourse nearly 0%. On the other hand, in areas where the ameis fully turbulent, typically after the third grid, the resolved partof the combustion rate hardly reaches 25% of the totalcombustion rate. For the whole chamber and for Cong3studied here, the mean ratio is 55%. This highlights the greatimportance of the sub-grid-scale combustion model for thiskind of simulation, as it has been shown by Di Sarli et al.,15,16

even if the conditions are here very favorable to LES (well-rened mesh and relatively large laminar ame thicknesscompared to other fuels or other thermodynamic conditions).

Figure 4. Up: Comparison between combustion rate V comb andventing rate V vent as a function of time. Bottom: Overpressure inside

the chamber as a function of time.

Figure 5.Resolved amount of reaction rate . Equation6 - Cong3 -C3H8.




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Values of the efficiency function and thickening factor averaged over the ame front for the different simulationsperformed are listed in Table1. These values are calculated at

the time at which the ame wraps around the main centralobstacle, i.e., when the ame is fully turbulent. It means thatthese values are representative of the maximum values obtainedin the simulations. When going from CH4to C3H8and to H2,the global ame thickening factor increases as the laminar amethickness decreases. The efficiency factor increases as well whengoing from CH4to C3H8and to H2. Indeed, when the laminarame speed of the mixture increases, the ame propagation past

the obstacles generates more turbulent structures, which willinteract with the ame and makes it even quicker and morewrinkled. The subgrid contribution of the combustion rateconsequently becomes higher when going from CH4 to C3H8and to H2. Finally, as expected, when the number of grids isincreased, the turbulence level is increased and so is the globalefficiency factor.

A second way to characterize the quality of the LES is toquantify the amount of turbulent kinetic energy resolved.

According to Popes criterion,30 LES should resolve 80% of thetotal turbulent kinetic energy. The contribution of the resolvedpart of the turbulent kinetic energy, , can be expressed as

= = k

k

k

k1res

tot

sgs

tot (8)

where kres and ksgs are, respectively, the resolved part and thesub-grid-scale part of the total turbulent kinetic energyktot. Theresolved turbulent kinetic energykresis dened as

= + + k u u u1

2( )x y zres

2 2 2

(9)

where ux, uy, and uz are the velocity uctuations in eachdirection, expressed as

= u U Ui i i2 2

(10)

withUibeing the resolved instantaneous velocity in direction iand denoting time averaging. With the phenomenon studiedhere being transient, dening a time-averaging procedure to

extract uctuating values may be tricky. Here, following Di Sarliet al.,15 a 0.1 ms time interval has been chosen for timeaveraging. This enables one to minimize the variations of themean elds due to the transient nature of the phenomenon,

while the size of the data sample is kept sufficiently large to getmeaningful statistics.

The sub-grid-scale turbulentenergy has been estimated fromthe sub-grid-scale viscositysgs:

31

=

kC

1

( )sgs

m2 sgs

2

(11)

where the constantCmis dened asCm= [(2/3)1/2A]/(K0

2/3).The coefficient K0 = 1.4 corresponds to an innite inertial

spectrum for a homogeneous isotropic turbulence in theframework of Kolmogorovs hypothesis. The constant A isevaluated as A = 0.44 in the eddy-damped quasi-normalMarkovian (EDQNM) theory.32

Figure6 shows the contribution of the resolved part of theturbulent kinetic energy in the ame front zone. In the most

turbulent zones, after the turbulence generating grids, thecriterion is fullled with about 100% of the total kinetic energyresolved. Close to the walls, at the closed end of the chamber,

nearly 0% of the turbulent kinetic energy is resolved in theame. However, the amount of total kinetic energy in theseareas is lower than 0.1% of the total kinetic energy in turbulentareas, showing that the level of turbulence in these areas isextremely low and the ame quasi-laminar. This is corroborated

by the results previously shown in Figure 5. It can beconsequently concluded that Popes criterion is reasonablyfullled, especially in areas where turbulence is a phenomenonof critical interest.

LES Validation. The overpressure generated during theame propagation is extracted from a probe located at theclosed end of the chamber in both experiments and LES. Itshould be noted that, due to the experimental variability on thetiming between the different experimental realizations,experimental signals have been shifted in time in order toperform the averaging procedure and to extract mean signalsand statistical envelopes. Consequently, validation of LESresults will not be performed on a timing criteria but only onthe magnitude and the trend of overpressure signals.

Figure7 shows LES results relative to explosions performedwith C3H8 for Cong13 together with experimental meansignal and envelope of individual realizations. First, it can benoticed that LES is able to precisely reproduce the overpressuremagnitude for any of the three congurations, from one tothree turbulence generating grids. As mentioned earlier,postmaximum overpressure oscillations are correctly capturedas well. The inuence of the number of turbulence generatinggrids is also correctly reproduced: the ame is accelerated whenadding grids, and the resulting overpressure is consequently

higher. This is mainly due to a higher global level of t urbulencein the chamber, as already mentioned by Masri et al.9

Figure8shows the results relative to the fuel inuence forexplosions performed in Cong3. Although compressiblenatural gas (CNG) and liquied petroleum gas (LPG) wereused in experiments, these mixtures have been approximated bytheir main respective component in LES: CNG has beenreplaced by CH4 (88% of CNG volume) and LPG by C3H8(95% of LPG volume). Once again, LES is also able to predictcorrectly the generated overpressure. C3H8explosions generatehigher overpressures than CH4ones. As shown experimentally

by Masri et al.,9 H2, even at a lower equivalence ratio of=0.7, generates a much higher overpressure than C3H8and CH4.

Table 1. Averaged Values inside the Flame Front ofThickening and Efficiency Factors

thickening efficiency

Cong1 Cong2 Cong3 Cong1 Cong2 Cong3

CH4 5.9 1.78

C3H8 7.2 7.2 7.2 1.38 1.67 1.84

H2 21.5 1.94

Figure 6. Contribution of the resolved part of the turbulent kineticenergy in the ame front - Cong3 - C3H8.




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This can be mainly related to its higher laminar ame speedSL0,

as shown in Table2.

These rst results clearly show that LES seems anappropriate tool to deal with the multiscale physics of explosionphenomena. Its ability to predict the critical parameters relatedto building safety issues has been shown:

the maximum overpressure magnitude is correctlyestimated

postmaximum pressure oscillations are captured the inuence of the obstacles is reproduced the inuence of the fuel type is reproduced

RESULTS SENSITIVITY TO LES SUBMODELSAlthough a large part of the overpressure is due to the turbulentcharacter of the ame, it is highly inuenced by the initiallaminar propagation phase which controls the ame strengthand shape before it hits the obstacles. This laminar phase ismainly controlled by chemical and thermo-diffusive small-scale

effects. In the following, it is proposed to estimate the errorscommitted if rough submodels are used to reproduce theseeffects. Two issues in particular are investigated:

chemistry modeling transport modeling

Chemistry Modeling Inuence.As mentioned earlier, theintegration of detailed kinetics into turbulent ame simulationsis impossible due to their prohibitive computational cost.Indeed, typical detailedmechanisms for C3H8air combustionsuch as GRI-MECH 3.033 involve more than 50 species and350 reactions. Tabulated chemistry methods34 have demon-strated their great potential to replace detailed kinetics.35

However, these methods may become difficultto handle whendealing with complex industrial congurations29 and curvatureand strain effects (important in the laminar phase) cannot beincluded easily. Another alternative solution is to use reducedchemical schemes.29,36 In these methods, the number of speciesand reactions is reduced to the main ones with the minimumobjective to reproduce the laminar ame speed and theadiabatic ame temperature at least. Reduced mechanisms areemployed here for all calculations presented in this paper. Inthe results presented up to now, a two-step mechanism (Table3) has been used. This mechanism was built to reproduce thesame laminar ame speed and burnt gas temperature as detailedmechanisms at = 1, Patm, and Tatm (Table5). Although therange of validity of this two-step mechanism is restricted, it is

Figure 7. Comparison of overpressure signals between LES (plain)and experiments.9 Mean signal (dashed) and statistical envelope (graybackground) from 5 to 20 ms - C3H8- Cong1, 2, and 3.

Figure 8. Comparison of overpressure signals between LES (plain)and experiments.9 Mean signal (dashed) and statistical envelope (graybackground) from 0 to 15 ms - Cong3 - CH4, C3H8, and H2.

Table 2. Laminar Flame Speed for Different Fuels

fuel type CH4 at = 1 C3H8 at = 1 H2at = 0.7

SL0 (cm/s) atPatmandTatm 36.3 38.4 128

Table 3. Two-Step Reduced Mechanism for C3H8AirCombustiona

n reaction A(cm3/mols) Ea (cal/mol)

1 C3H8+ 3.5O2 3CO + 4H2O 1.33 1012 4.15 104

forward:nC3H8F = 0.55 and nO2

F = 0.9

2 CO + 0.5O2 CO2 4.5 1010 2.0 104

forward:nCOF = 1.0 and nO2

F = 0.5

reverse: nCO2F = 1.0

aCoefficients are related to the Arrhenius formulation of the reactionrate: q = Ae(Ea/RT)(Yk/Wk)

nk, where Eais the activation energy ofthe reaction and Wkand nk are, respectively, the molecular mass andreaction exponent for species k.




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adapted to this study, since the ammable mixture is initiallyperfectly premixed and pressure variations are too small tomodifyame properties. However, in order to reduce the CPUcost, one could try to reduce even more the chemistrymodeling to only one reaction: the fuel oxidation by O2(Table4). However, when removing the COCO2 equilibrium

reaction, it is well-known that the prediction of burnt gastemperature may become rough. Even though the one-stepmechanism has been built to give exactly the same laminarame speed as the two-step mechanism, it consequentlyoverestimates the burnt gas temperature (Table5).

Both C3H8air schemes have been tested on Cong3 withour LES solver. The resulting overpressures are compared tothe experimental data in Figure 9 (left) and the ame frontpositions (referred to as the position of the furthest ame frontpoint from the ignition point) obtained with the two differentkinetic mechanisms are shown in Figure9(right). When thetwo-step mechanism used up to now is replaced by the one-step mechanism, the ame is accelerated and the overpressureis increased. The ame propagation speedSdobtained with theone-step mechanism is considerably higher than the oneobtained with the two-step mechanism all along the amepropagation.Sd is about 10% higher during the initial laminarphase and also during the turbulent propagation phase. Bothpropagation regimes are thus impacted, resulting in a 26%sensitivity of the overpressure to the chemical modeling. This

result is directly related to the burnt gas temperatureoverestimation by the one-step mechanism. Since the fresh to

burnt gas density ration f/b is overestimated, the resultingame propagation speed is overestimated

=S Sd

f

bL0

(12)

and the generated overpressure as well. This shows thatthermodynamics ame properties have a strong impact onglobal explosion parameters and should be correctly repro-duced using an appropriate kinetic mechanism.

Transport Modeling Inuence. Knowing how fuelparticles diffuse inside the mixture is characterized by itsLewis number LeF. More generally, the Lewis number Lekofany species kcontrols the competition between thermal andmass diffusion effects: Lek = T/Dk, where T and Dk arerespectively the thermal and mass diffusivities. A commonsimplication when using reduced schemes in reactive CFDcodes is to set Lewis numbers Lek to one for all species,consequently neglecting the competition between thermal andmass diffusion but also neglecting preferential diffusion between

the diff

erent species.A second important consequence of this simplication is thatthe ame response to stretch is strongly modied. Indeed,

when the ame is stretched, it can be shown that theconsumption speed Sc (dened as the integral of the fuel

burning rate across the ame front27) is strongly impacted. Inthe limit of smallcurvature terms, the consumption speed may

be written as37,38

=

S

SL

S1c

L0 a

c

L0

(13)

where Lac is the Markstein length for the consumption speed

and = (1/S) dS/dt is the ame curvature with S being theame surface area.

This formulation is dependent on the Lewis number throughLa

c. Several expressions of Lac can be found in the literature.

Clavin and Joulin39 give

=

+L Le

T

T T

x

xx

1

2( 1)

ln(1 )d

T T T

ac

Ff

b f 0

( )/b f f

(14)

where Tb and Tf are, respectively, the burnt and fresh gastemperatures and is the unstretched ame thickness. Theparameter= (Tb Tf)Ta/Tb

2 measures the activation energy,with Tabeing the activation temperature.

Table 4. One-Step Reduced Mechanism for C3H8AirCombustion

n reactionA

(cm3/mols) Ea (cal/mol)

1 C3H8 + 5O2 3CO2 + 4H2O 3.09 1012 3.347 104

forward: nC3H8F = 0.569 and

nO2F = 1.097

Table 5. Chemistry Mechanism Properties

properties at= 1, Patm, and Tatm

laminar ame speedSL

0 (m/s)burnt gas temperature

Tad (K)

detailedmechanism (GRI-MECH33)

38.4 2275

reduced two-stepmechanism

38.4 2289

reduced one-stepmechanism

38.4 2400

Figure 9. Inuence of chemistry modeling. Left: Comparison of overpressure signals between LES and experiments.9 One-step mechanism LES(plain with triangles), two-step mechanism LES (plain with circles), experimental mean signal (dashed) and statistical envelope (gray background).Right: Flame front position for LES calculations. One-step mechanism LES (plain with triangles), two-step mechanism LES (plain with circles) -Cong3 - C3H8.




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Equations 13 and 14 show that the Lewis number has adirect inuence on the consumption speed when the ame isstretched. The consumption speed of a fuel with Le > 1 (suchas C3H8) will therefore be signicantly reduced for highcurvatures, as it is typically the case in the early times afterignition. On the other hand, assuming that Le= 1 will lead to azero value for the Markstein length and a ame speedindependent of stretch to rst order.

The burnt gas temperature Tb is also affected by stretch. Inthe presence of stretch, the burnt gas temperature can be

written as40

=

T T

T Le

D

S

( ) 11b ad

ad L02

(15)

whereDis a characteristic diffusivity. This shows that, for a fuelwith Le > 1, when the ame is stretched, the burnt gastemperature will be signicantly reduced with regard to itsadiabatic value Tad for an unstretched ame. The Le = 1assumption will lead to a burnt gas temperature independent ofstretch. Using the simplicationLe = 1 for a fuel whose actualLewis number is larger than 1 consequently leads to an

overestimation of the burnt gas temperature which as a mainconsequence overestimates the ame propagation speed, asexplained by eq12.

In the results presented up to now, a realistic transportmodel has been used in our calculations, i.e., a transportmechanism for which the response of the thickened ame tostretch is correctly reproduced. This can be easily done sincethe ame thickening is almost constant during the wholecomputation and may be known a priori. In order to investigatethe consequences of theLe= 1 simplication, another two-stepmechanism has been built (Table 6), replacing the transport

model (used in the two-step mechanism of Table 3) by asimplied transport for which the Lewis numbersLekhave beenset to 1 for all species. It should be noted that both mechanisms

have been built to give exactly the same laminar ame speedand burnt gas temperature at = 1, Patm, and Tatm.

These two mechanisms have been tested on Cong3. Theresulting overpressures are compared to the experimental datain Figure10(left), and the ame front positions obtained withthe two different transport models are shown in Figure 10(right). When the realistic transport model is replaced by thesimplied transport model, the ame is accelerated and theoverpressure is overestimated. The ame propagation speedobtained with the simplied transport mechanism is higherthan the one obtained with the realistic transport mechanism bya factor varying around 9% during the whole ame propagation.Both laminar and turbulent propagation phases are impacted. Itmeans that, even though the ow is largely turbulent duringmost parts of the explosion, molecular and thermal transportsare important and have a signicant impact on the results. Theconsequence is a 23% sensitivity of the overpressure to thetransport modeling.

This result is consistent with the conclusions which havebeen drawn from the theory: using the simplied transportmodel for C3H8air combustion accelerates the ame becausethe effects of curvature on ame speed and burnt gas

temperature are not captured. This overestimation of theame propagation speed considerably modies the amedynamics and raises signicantly the peak overpressure in thechamber. For CH4 (Le 1), further simulations have shownthat, in agreement with the theory, the impact of such amodication is almost zero (+0.05%). For H2, the opposite

behavior is observed; i.e., theame propagation is slowed downand the overpressure is underestimated (9%).

Although explosion processes are driven by turbulentcombustion, the generated overpressure has been shown to

be highly inuenced by the initial laminar phase. A correctreproduction of this phase is a prerequisite to be able toprecisely predict the overpressure increase inside the chamber.Even though thermodynamic and diffusive ame properties

take place at very small scale, these effects must be correctlyaccounted for. This can be done using appropriate kineticmechanisms and transport modeling.

CONCLUSION

The ability of LES to handle the multiscale problem of gasexplosion in a vented chamber has been shown. Explosioncharacteristic properties such as the maximum overpressureinside the chamber have been precisely reproduced. Geometricand fuel modication effects on the generated overpressurehave been correctly captured as well. LES enabled us to

Table 6. Two-Step Reduced Mechanism with SimpliedTransport for C3H8Air Combustion

n reaction A(cm3/mols) Ea (cal/mol)

1 C3H8 + 3.5O2 3CO + 4H2O 1.41 1012 4.15 104

forward:nC3H8F = 0.55 and nO2

F = 0.9

2 CO + 0.5O2 CO2 4.5 1010 2.0 104

forward:nCOF = 1.0 and nO2

F = 0.5

reverse:nCO2F = 1.0

Figure 10. Inuence of transport modeling. Left: Comparison of overpressure signals between LES and experiments.9 Simplied transportmechanism LES (plain with squares), realistic transport mechanism LES (plain with circles), experimental mean signal (dashed), and statisticalenvelope (gray background). Right: Flame front position for LES calculations. Simplied transport mechanism LES (plain with squares), realistictransport mechanism LES (plain with circles) - Cong3 - C3H8.




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perform a diagnostic of explosions in order to improveunderstanding of phenomena which drive them.

Even though LES seems a promising tool for explosionstudies with higher predictive capacities compared to URANS,it remains very dependent on the quality of its submodels andof the associated assumptions or simplications. In this work,the strong inuence of two LES submodels has beenhighlighted. This shows that, even though explosions are dueto turbulent combustion processes, proper kinetic and transportmodeling reproducing small-scale effects must be used in orderto reproduce the correct initial laminar propagation phase

which is crucial for the overpressure prediction.Since the nal objective of this work is to apply LES in real-

size industrial buildings, it is now intended to extend thevalidity of these results to higher scale congurations. Scaled-upsetups of the chamber studied in this paper are currently aboutto be studied experimentally and numerically to conrm theseresults.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]

The authors declare no competing nancial interest.

ACKNOWLEDGMENTS

This work was performed using HPC resources from GENCI-IDRIS. This work was supported by Total and ANRT underthe CIFRE-2010-597. The authors thank Professor A. Masri(University of Sydney) for providing experimental data.

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mailto:[email protected]:[email protected]


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