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Center for Turbulence Research Annual Research Briefs 2016 181 Toward direct numerical simulation of multicomponent fuel spray auto-ignition By L. Esclapez, P. Govindaraju AND M. Ihme 1. Motivation and objectives Many industrial combustion devices, such as aeronautical gas turbines or internal com- bustion engines, use liquid hydrocarbon fuels due to their high energy density and ease of storage. The combustion efficiency, pollutant formation and engine operability are then closely related to the efficiency of the fuel/oxidizer mixing (Lefebvre 1998). In multiphase flows, the latter is controlled by the droplet size distribution resulting from the primary and secondary atomizations, the droplet dispersion by interactions with the surrounding gas flow and the evaporation rate (S´ anchez et al. 2015). All three processes depend upon the physical properties of the fuel, i.e., its composition. Realistic fuels are composed of dozens of compounds and little is known about the details of their distribution as it varies significantly depending on the time of year and the refining process (Edwards 2002). To overcome this difficulty, the common methodology is to design with only a handful of representative species a surrogate that emulates the behavior of the real fuel (Dagaut & Cathonnet 2006). The set of target properties to be matched ( e.g., density, molecular weight, H/C ratio, ignition delay time, flame propagation) and the selection of represen- tative species have been the topic of recent discussions (Honnet et al. 2009; Dooley et al. 2012). However, these studies focused on the gas-phase behavior, whereas the complexity of the surrogate design arises from the strong interactions between the liquid and the gas phases. Among the established target properties constraining the surrogate formulation is the Derived Cetane Number (DCN) (Dooley et al. 2012), which is measured through a stan- dardized procedure (ASTM International 2015). The DCN characterizes the ignition delay time of the real fuel in prescribed operating conditions, but the measurement pro- cedure does not provide details about the local conditions that favored the onset of ignition (e.g., local gas temperature and equivalence ratio, droplet size). Indeed, very little is known about the effect of the interaction between the droplet dynamic and evap- oration, and the chemical kinetics in the experimental device. Using 1D and 0D domains for the liquid and gas phases respectively, Stagni et al. (2016) recently showed that a wide range of ignition delay times can be observed in DCN conditions depending on the local mixture, droplet size and equivalence ratio, and that preferential evaporation has a direct effect on the ignition delay time. However, the effect of gas-phase dynamics was not accounted for in this study and is the focus of the present work. Direct numerical simulation (DNS) has been used over the past fifteen years to study droplet dispersion and evaporation in turbulent flows (Squires & Eaton 1991; Mashayek 1998; Reveillon & Demoulin 2007). More recently, several DNS studies have focused on two-phase flow combustion, studying ignition (Wang & Rutland 2007; Neophytou et al. 2010; Borghesi et al. 2013) or flame structure and stabilization (Reveillon & Vervisch 2005; Luo et al. 2011; Vi´ e et al. 2015). However, all these studies employed a single- component fuel because it strongly reduces the complexity and cost of the chemistry
Transcript
Page 1: Center for Turbulence Research Annual Research Briefs 2016 ...web.stanford.edu/group/ihmegroup/cgi-bin/MatthiasI...the coupling with the group contribution module (Govindaraju & Ihme

Center for Turbulence ResearchAnnual Research Briefs 2016

181

Toward direct numerical simulation ofmulticomponent fuel spray auto-ignition

By L. Esclapez, P. Govindaraju AND M. Ihme

1. Motivation and objectives

Many industrial combustion devices, such as aeronautical gas turbines or internal com-bustion engines, use liquid hydrocarbon fuels due to their high energy density and ease ofstorage. The combustion efficiency, pollutant formation and engine operability are thenclosely related to the efficiency of the fuel/oxidizer mixing (Lefebvre 1998). In multiphaseflows, the latter is controlled by the droplet size distribution resulting from the primaryand secondary atomizations, the droplet dispersion by interactions with the surroundinggas flow and the evaporation rate (Sanchez et al. 2015). All three processes depend uponthe physical properties of the fuel, i.e., its composition. Realistic fuels are composed ofdozens of compounds and little is known about the details of their distribution as it variessignificantly depending on the time of year and the refining process (Edwards 2002). Toovercome this difficulty, the common methodology is to design with only a handful ofrepresentative species a surrogate that emulates the behavior of the real fuel (Dagaut &Cathonnet 2006). The set of target properties to be matched ( e.g., density, molecularweight, H/C ratio, ignition delay time, flame propagation) and the selection of represen-tative species have been the topic of recent discussions (Honnet et al. 2009; Dooley et al.2012). However, these studies focused on the gas-phase behavior, whereas the complexityof the surrogate design arises from the strong interactions between the liquid and the gasphases.

Among the established target properties constraining the surrogate formulation is theDerived Cetane Number (DCN) (Dooley et al. 2012), which is measured through a stan-dardized procedure (ASTM International 2015). The DCN characterizes the ignitiondelay time of the real fuel in prescribed operating conditions, but the measurement pro-cedure does not provide details about the local conditions that favored the onset ofignition (e.g., local gas temperature and equivalence ratio, droplet size). Indeed, verylittle is known about the effect of the interaction between the droplet dynamic and evap-oration, and the chemical kinetics in the experimental device. Using 1D and 0D domainsfor the liquid and gas phases respectively, Stagni et al. (2016) recently showed that awide range of ignition delay times can be observed in DCN conditions depending on thelocal mixture, droplet size and equivalence ratio, and that preferential evaporation hasa direct effect on the ignition delay time. However, the effect of gas-phase dynamics wasnot accounted for in this study and is the focus of the present work.

Direct numerical simulation (DNS) has been used over the past fifteen years to studydroplet dispersion and evaporation in turbulent flows (Squires & Eaton 1991; Mashayek1998; Reveillon & Demoulin 2007). More recently, several DNS studies have focused ontwo-phase flow combustion, studying ignition (Wang & Rutland 2007; Neophytou et al.2010; Borghesi et al. 2013) or flame structure and stabilization (Reveillon & Vervisch2005; Luo et al. 2011; Vie et al. 2015). However, all these studies employed a single-component fuel because it strongly reduces the complexity and cost of the chemistry

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182 Esclapez, Govindaraju & Ihme

description. Le Clercq & Bellan (2004) performed DNS of multicomponent fuels in amixing layer and indicated an increase in evaporation time when replacing the multi-component fuel by a single-component fuel. Recently, Kitano et al. (2014) used DNSto compare the evaporation and auto-ignition of single-component, bi-component andtri-component surrogates of Jet-A fuel in a quiescent environment. Their results indicatethat the dynamic of ignition is controlled by the change in compound volatility.

The objective of the present report is to continue the work of Stagni et al. (2016) byincluding the multidimensional gas-phase effect using DNS of evaporating multicompo-nent fuel spray in DCN conditions. Section 2 provides the mathematical formulation,followed by a validation of the discrete multicomponents method implemented in theDNS solver. The numerical setup and the Jet-A2 surrogate are presented in Section 3.Section 4 analyzes the DNS results in light of the auto-ignition delay times obtained froma detailed mechanism at various fuel compositions.

2. Mathematical formulation

This section introduces the equations required for evaluating properties in the gas andliquid phases. A brief discussion presents the additional complexities introduced by themulticomponent evaporation as compared to single-component fuels.

2.1. Gas-phase equations

Simulations are performed with the low-Mach-number DNS solver 3DA (Vie et al. 2015),where the conservation equations for mass, momentum, species and energy can be writtenas

∂ρ

∂t+∂ρui∂xi

= Sm, (2.1)

∂ρui∂t

+∂ρuiuj∂xi

= − ∂p

∂xi+∂σij∂xj

+ Sui, (2.2)

∂ρYk∂t

+∂ρuiYk∂xi

= − ∂

∂xj

(ρDk

Wk

W

∂Xk

∂xj

)+ ωk + Smδk{f}, (2.3)

∂ρT

∂t+∂ρuiT

∂xi= − ∂

∂xj

cp

∂T

∂xj

)+

λ

cp2

∂T

∂xj

∂cp∂xj

+ ωT + ST , (2.4)

where ρ is the gas density, ui is the gas velocity, p is the pressure, T is the gas temperatureand Yk and Xk are the species mass and molar fraction, respectively. Sm, Sui and ST arethe source terms due to droplet evaporation, drag and heat transfer, respectively. δk{f}is the Kronecker delta function equal to 1 if k belongs to the liquid species ensemble {f}and zero otherwise. σij is the viscous stress tensor, and Wk and W denote the molecularweight of species k and its mixture-averaged value, respectively. Dk is the diffusivity ofspecies k, ωk is the reaction source term of species k, λ is the thermal conductivity, cp is

the mixture-averaged heat capacity and ωT = −∑Ns

k=1 hkωk/cp is the heat release rate.

2.2. Liquid-phase equations

The dispersed phase is described with a Lagrangian point-particle method (Miller et al.1998). In contrast with the continuous thermodynamic (CT) approach used by Le Clercq& Bellan (2004), a discrete multicomponent liquid description is used, in which the

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DNS of multicomponent spray 183

governing equations for each droplet are

dxd,idt

= ud,i, (2.5)

dud,idt

=f1

τd[ui@d − ud,i], (2.6)

dmd,k

dt= mev,k, (2.7)

dTddt

=Nucpf2

3PrcLτd(T@d − Td) +

∑k∈{f} mev,kLv,k

mdcL, (2.8)

where xd,i and ud,i are the droplet position and velocity component, respectively. τd isthe droplet relaxation time given by τd = ρld

2/18µg, with ρl as the liquid density, dits diameter and µg the gas dynamic viscosity. ui@d designates the gas velocity at thedroplet position. md,k is the mass of species k. Td is the droplet temperature, T@d is thegas temperature at the droplet position, and Nu and Pr are the Nusselt number andPrandtl number, respectively. Lv,k is the latent heat of vaporization of species k, md isthe droplet mass and cL is the averaged liquid heat capacity.

In order to evaluate the effect of preferential evaporation on the gas composition andauto-ignition delay time, multiple formulations exist in the literature and are based onthe choices for two properties, namely i) effective Schmidt number and ii) surface compo-sition. The Schmidt number is assumed to be that of the mixture in the high-diffusivitylimit. Alternatively, the evaporation rate can be computed using individual diffusivities,which is the case for low evaporation rates. For surface compositions, two particular limitsexist and correspond to the usage of either the initial or the current droplet compositionas that of the surface. Law (Law & Sirignano 1977) suggests that droplet compositioncan be uniform due to rapid internal mixing and not because of high diffusion coeffi-cients. The composition at the surface, in that case, is representative of the droplet,while the individual diffusion coefficients retain their identity. This model provides simi-lar results even when the mixture Schmidt numbers are used for fuels, as the diffusivitiesof the species involved are similar. In the current work, two particular formulations of theevaporation rate, mev,k, corresponding to the distillation and diffusion limits (Sirignano1999), are evaluated. These two limits arise from the competition of the internal diffu-sion/convection processes with the evaporation and are quantified by the Peclet number.For slowly evaporating droplets (distillation limit, small droplet Peclet number), theinternal transport of species in the droplet is faster than the evaporation rate so thatcompounds evaporate sequentially according to their volatility. On the contrary, for fast-evaporating droplets (diffusion limit, large droplet Peclet number), the evaporation rateis faster than the internal transport rate and all compounds tend to evaporate simulta-neously, as the evaporation rate of volatile components is limited by their diffusion rateto the droplet surface. The evaporation rate of species k is given by

mev,k,dil = −Shkmd

3Sckτdln(1 +BM,k), (2.9)

mev,k,dif = −Shmd

3Scτdln(1 +BM )Yl,k, (2.10)

for distillation and diffusion limits, respectively. Shk and Sck are the Sherwood numberand Schmidt number of species k, respectively; Sh and Sc are their mixture-averaged

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184 Esclapez, Govindaraju & Ihme

counterparts, respectively. BM,k is the mass transfer number of species k evaluated,following Wang et al. (2013). BM is the mass transfer number

BM =

∑k∈{f} Ysat,k −

∑k∈{f} Yk

1−∑k∈{f} Ysat,k

. (2.11)

The non-dimensional numbers in Eqs. (2.8)-(2.10) are evaluated in reference conditionsusing the one-third rule and mixture rules for viscosity, thermal-conductivity and speciesdiffusivity.

The coupling terms with the gas-phase equations are obtained by integration over alldroplets in the control volume ∆V , yielding

Sm = −

∑k∈{f}

mevap,k

, (2.12)

Sui = −

∑k∈{f}

mevap,kud,i

, (2.13)

ST = − 1

cp

cLmddTddt

+∑k∈{f}

mevap,k(cp,kTd + Lv,k)

, (2.14)

where {·} = 1/∆V∑d∈∆V .

The fuel thermodynamic and transport properties are obtained from a recent imple-mentation of the group contribution method (Govindaraju & Ihme 2016). This methodallows investigators to compute the critical properties and the acentric factors of eachcompound as a linear combination of its functional group. The physical properties arethen corrected to account for pressure and temperature dependence using Peng-Robinsonequation-of-state for density, Thodos correlation for latent heat of vaporization, Lee-Kesler correlation for saturated vapor pressure and the UNIFAC approach for the speciesactivity.

2.3. Multicomponent evaporation validation

In order to validate the implementation of the above equations in the DNS solver andthe coupling with the group contribution module (Govindaraju & Ihme 2016), the binarymixture droplet evaporation cases studied by Daif et al. (1999) are reproduced. Thebinary mixture is composed of heptane and decane, and the operating conditions of thetwo cases considered here are listed in Table 1. The experimental apparatus is operatedat ambient pressure and the droplets are suspended in a stream of heated air. In thesimulation, droplets are maintained static in the computational domain by setting theright-hand side of Eq. (2.6) to zero. Due to the low temperature difference between thetwo phases, the Peclet number is small, so that only the results obtained in the distillationlimit (Eq. (2.9)) are presented.

Figure 1(a) shows the comparison of the temporal evolution of the squared dropletradius extracted from the DNS against experimental measurements, and Figure 1(b)presents the droplet surface temperature evolution (note that experimental data for Case2 are not available). The simulation reproduces well the change in evaporation rateassociated with the depletion of the most volatile compound (heptane) in the droplet.This is characteristic of the distillation limit. The droplet surface temperature is over-

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DNS of multicomponent spray 185

Heptane Decane r0 Td,0 Tg ug

[%] [%] [mm] [K] [K] [m/s]

Case 1 74 26 0.667 294 348 3.10Case 2 63.5 36.5 0.521 292 341 3.36

Table 1. Operating conditions of Daif et al. (1999) for the two test cases.

0.5

0.4

0.3

0.2

0.1

0.0

r l2 [m

m2 ]

20151050

Time [s]

Expe Daïf - Case 1 Expe Daïf - Case 2 DNS - Case 1 DNS - Case 2

350

340

330

320

310

300

290

Liqu

id t

empe

ratu

re [

K]

20151050

Time [s]

Expe Daïf - Case 1 DNS - Case 1

(a) (b)

350

340

330

320

310

300

290

Liqu

id t

empe

ratu

re [

K]

20151050

Time [s]

Expe Daïf - Case 1 DNS - Case 1

350

340

330

320

310

300

290

Liqu

id t

empe

ratu

re [

K]

20151050

Time [s]

Expe Daïf - Case 1 DNS - Case 1

r l2

Figure 1. (a) Squared droplet radius temporal evolution. (b) Droplet surface temperatureevolution.

estimated. The present simplified model performs very well compared to more complexand expensive multicomponent evaporation models (Torres et al. 2003).

3. Computational parameters

The chosen configuration is a droplet slab in decaying homogeneous turbulence usedin previous studies of auto-ignition (Borghesi et al. 2013). The computational domainconsists of a cubic box of length L = 12.0 mm discretized using 256 grid points in eachdirection, corresponding to a grid resolution ∆x = 46.9µm. Periodic boundary conditionsare applied in all directions. The operating conditions match the DCN experimental testfacility: Tg,0 = 833 K and P = 22.1 atm.

The turbulent velocity is initialized using a Passot-Pouquet energy spectrum withan integral length scale L11 = L/6. The initial turbulent velocity fluctuation u′0 is setto a value of 0.5 m/s, which corresponds to a Kolmogorov length scale ηk = 57µm.Monodispersed fuel droplets are initially distributed in a central layer of thickness L/3as depicted in Figure 2. Two values of equivalence ratio in the droplet-laden region areused, φl,0 = 1.0 and φl,0 = 2.0; and three initial droplet diameters are investigated: d0 =10, 20 and 30 µm. This droplet size range ensures d0 < ∆x < ηk, and the correspondingStokes number relative to the Kolmogorov time scale is Stk = τd/τk = 0.12, 0.48 and1.07 for d0 = 10, 20 and 30 µm, respectively. In order to mimic the dynamic of the liquidinjection in the experimental device, the droplets have no initial velocity.

This work focuses on the conventional Jet-A POSF 4658 fuel surrogate proposedby Dooley et al. (2012). The recommended second-generation fuel surrogate is com-posed of n-dodecane (40.4%), iso-octane (29.5%), 1,3,5-trimethylbenzene (7.3%) and n-propylbenzene (22.8%) (in molar fraction). This mixture was found to match the molec-

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186 Esclapez, Govindaraju & Ihme

x

z

yL/3 2L/3

Figure 2. Schematic of the computational domain.

ular weight, H/C ratio, threshold sooting index and DCN of the Jet-A POSF 4658 fuel.Due to the prohibitive cost of including the detailed kinetic mechanism necessary toreproduce the ignition kinetics of all four compounds, the chemical kinetics is not in-cluded in the DNS. Instead, the auto-ignition delay τAI is computed a-priori for theentire gas mixture composition space of the four species composing the surrogate. Thesecalculations are performed with the skeletal mechanism derived by Stagni et al. (2016).

Figure 3(a) shows the ignition delay time of the vaporized surrogate mixture in functionof the equivalence ratio (at Tg,0 = 833 K) and in function of the initial gas temperature(at φ = 2.0). At Tg,0 = 833 K, a minimum τAI is observed around φMR ∼ 2.0, referred toas the most reactive equivalence ratio (Mastorakos 2009). At φMR, τAI is found to have anegative temperature coefficient region, which was found to affect the spray ignition delayin Stagni et al. (2016). The Karlovitz number based on the Kolmogorov time scale andthe ignition time scale at φMR is Ka = τAI/τk = 1.26. Due to preferential evaporation,the fuel mixture composition can vary from the initial surrogate composition. In order toshow the effect of composition on the ignition delay time, Figure 3(b) displays a three-component map of ignition delay time. For the sake of clarity, 1,3,5-trimethylbenzene andn-propylbenzene (the two aromatics) are combined, since they are the two less abundantspecies and their ignition delay times are very close. The vertices of the triangle representthe pure compounds, while the edges represent binary mixtures. The n-dodecane is foundto be the fastest igniting compound. Note that the preferential evaporation effect on theignition delay arises from the fact that the ignition delay time is mainly driven by then-dodecane mass fraction but it is the less volatile species.

An overview of the simulations parameters, along with the main characteristics ofeach case, is presented in Table 2. Note that the evaporation time τev is the dropletlifetime, evaluated through a 0D evaporation calculation at DCN conditions in a quiescentenvironment.

4. Results

Figure 4 shows instantaneous snapshots of the flow in a central cut-plane during τ =1.25τη, where τη denotes the Kolmogorov time scale for Case C. The velocity field is foundto be marginally affected by the droplets, with drag force and added mass inducing only

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DNS of multicomponent spray 187

(a) (b)

2

46

0.0012

46

0.012

46

0.1

Auto

-igni

tion

dela

y tim

e [m

s]

2.752.251.751.250.750.25Eq. ratio [-]

11001000900800700600Initial gas temperature [-]

Tg,0 = 833 K Eq. ratio = 2.0

Aromatics I-C8H18

NC12H16

0.0005

0.02

0.001

0.01

⌧ AI

[s]

Tg,0

Figure 3. (a) Auto-ignition delay time in function of the equivalence ratio (bottom scale) andthe initial gas temperature (top scale) for the second-generation surrogate of Dooley et al. (2012)at 22.1 atm. (b) Ternary mixture ignition delay map in DCN conditions at φ = 2.0.

d0 φl,0 Stk Td,0 τev τev/τAI mev,k

[µm] [-] [-] [K] [ms] [-]

Case A 10.0 2.0 0.12 300 0.4 0.39 Eq. (2.9)Case B 20.0 2.0 0.48 300 2.1 2.08 Eq. (2.9)Case C 30.0 2.0 1.07 300 4.2 4.16 Eq. (2.9)Case D 20.0 2.0 0.48 300 2.1 2.08 Eq. (2.10)Case E 20.0 1.0 0.48 300 2.1 2.08 Eq. (2.9)

Table 2. Spray properties used in the DNS.

local disturbance in the initial turbulent field. On the contrary, due to the low initialtemperature of the droplets, the gas temperature in the two-phase slab rapidly dropsaround the droplet locations and continues to drop as droplets start evaporating. Bothmolecular diffusion and droplet dispersion induce a progressive homogenization of thetemperature in the droplet-laden region. The mass fraction of iso-octane, the most volatilecompound, is shown on the bottom row. Although the global equivalence ratio in theslab is φl,0 = 2.0, the fast evaporation, compared to the molecular diffusion, results instrong mixture heterogeneities with a local equivalence ratio up to φ = 13.5. In all cases,the evaporation time is found to be smaller than the value presented in Table 2 due tothe beneficial effect of slip velocity on the evaporation rate.

For multicomponent fuels, the local equivalence ratio in the DNS is evaluated using

φ = sYfuelYO2

, (4.1)

where Yfuel =∑k∈{f} Yk and s is the mass stoichiometric ratio of the local fuel mixture.

s is computed from

s =∑k∈{f}

Xfuel,kνO2,kWO2

Wfuel, (4.2)

where Xfuel,k is the mole fraction of species k in the fuel, νO2,k is the stoichiometric

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188 Esclapez, Govindaraju & Ihme

0.0

1.9

0.0

0.06733

833

Velo

city

[m/s

]Te

mpe

ratu

re [K

]Y

[-]

t/⌧k = 0.0 t/⌧k = 0.24 t/⌧k = 0.56 t/⌧k = 0.98 t/⌧k = 1.25

I-C8H

18

Figure 4. Velocity magnitude (top row), temperature (middle row) and iso-octane massfraction (bottom row) at five instants during the evaporation process for Case C.

coefficient of O2 in its global reaction with species k and Wfuel is the mean molecularweight of the fuel.

In order to evaluate the effect of preferential evaporation on the ignition behavior,scatterplots of local fuel mixture composition are overlaid on the ternary ignition delaymap presented in Figure 3(b). Note that only the locations where φ > 0.5 are shown.The ignition delay time of the prevaporized surrogate composition at the most reactivemixture fraction, τAI(φMR), is used as a reference time scale for ignition. Figure 5 presentsresults at four instants for Case A–D. In the diffusion limit (Case D), the evaporationrate of each compound is proportional to its liquid mass fraction, which remains constantthrough the evaporation process. Then, there is no preferential evaporation (single pointmaterialized by the cross in the ternary map), which eventually leads to a high n-dodecanemass fraction and a small ignition delay time. This is consistent with the results of Stagniet al. (2016). For all the other cases, the composition is found to be scattered along theevaporation trajectory. This scatter is due to the variation of evaporation rate inducedby the change in slip velocity: droplets initially far from equilibrium evaporate faster.The dispersion is found to be more pronounced for larger droplets due to the largerdroplet relaxation time. At the beginning, iso-octane is the most abundant species inthe gas phase due to its higher volatility. As time proceeds, the gaseous mass fraction ofn-dodecane increases since it becomes the major compound in the liquid phase.

For small droplets, the evaporation time is smaller than the ignition delay time, sothat the compositional heterogeneities due to preferential evaporation are dissipated bythe molecular diffusion, before the ignition time is reached. In this case, the ignitiontime is also delayed by the cooling effect of the evaporation that further separates theevaporation and ignition time scales.

For intermediate droplets, the maximum composition dispersion is reached aroundthe ignition time τAI . Locally, the mass fraction of n-dodecane can reach higher valuesthan the initial composition in the liquid phase. As a result, the local ignition delay

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DNS of multicomponent spray 189

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

Case A Case B Case C Case D

0.0005 0.02

0.001 0.01

⌧AI [s]

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

t/⌧ A

I=

0.30

t/⌧ A

I=

0.53

t/⌧ A

I=

1.09

t/⌧ev

=0.8

t/⌧ev

=1.3

t/⌧ev

=2.9

t/⌧ev

=0.55

t/⌧ev

=0.25

t/⌧ev

=0.15

t/⌧ev

=0.55

t/⌧ev

=0.25

t/⌧ev

=0.15

t/⌧ev

=0.08

t/⌧ev

=0.12

t/⌧ev

=0.27

N-C12H26

I-C8H18Aromatics

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

t/⌧ A

I=

1.91

t/⌧ev

=4.8

t/⌧ev

=0.91

t/⌧ev

=0.91

t/⌧ev

=0.46

1.0

0.8

0.6

0.4

0.2

0.0-0.4 -0.2 0.0 0.2 0.4

Figure 5. Scatterplots of gas mixture composition extracted from the DNS overlaid on theternary ignition delay time map in DCN conditions and φ = 2 at four instants (rows) for CaseA–D (columns). The cross in all plots indicates the initial surrogate composition.

time can be smaller than the value inferred from the initial surrogate composition, thusfaster than the diffusion limit in Case D. This fact was not observed in Stagni et al.(2016) since the 0D description of the gas phase did not allow the droplet surroundingsto be renewed as the droplet was dispersed. The results for Case E are very similar toCase B, demonstrating that droplets interact very little. The main difference arises fromthe equivalence ratio distribution in the droplet-laden slab, which is found to peak, att = τAI , around φ = 0.6 for those for Case B and around φ = 0.15 in Case E. However,note that the maximum equivalence ratio is found to be similar in both cases and thuscould lead to similar auto-ignition delay timing, but in more ignition locations for thericher cases (Borghesi et al. 2013).

For the largest droplets, the compositional dispersion is even more pronounced dueto both the strong inertia of the droplets, which induces a slip velocity, and the largetemporal separation between the sequential evaporation of all the compounds. As a con-sequence, the mass fraction of n-dodecane can reach almost one at the vicinity of droplets

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190 Esclapez, Govindaraju & Ihme

near the end of evaporation. However, the evaporation time is much larger than the igni-tion delay of the surrogate, so that at τAI , most iso-octane has started evaporating andits ignition delay time is much larger than that of the surrogate mixture. Ignition is thendelayed due to the lack of n-dodecane as compared to the diffusion limit case.

5. Conclusions and future work

The evaporation of multicomponent droplets in homogeneous isotropic decaying tur-bulence is studied in DCN conditions. The analysis focuses on the effect of preferentialevaporation on the gas mixture composition and its potential consequences on the auto-ignition delay time. The extent of the deviation of gas composition from the initialsurrogate composition is found to depend on the droplet size due to the inertia of thedroplets and the lifetime of the droplets. Three classes of droplets are investigated.

For small droplets, with a lifetime shorter than the ignition delay (of the surrogatefuel mixture), the preferential evaporation has only a marginal effect on ignition sincethe gas mixture is homogenized by species transport before the onset of ignition.

For intermediate droplets, with a lifetime of the order of the ignition delay time, thecomposition dispersion is maximum around the ignition time, leading to a large scatterof the local auto-ignition delay values. The preferential evaporation is expected to havean effect on the ignition. This is consistent with the observation of Stagni et al. (2016)in 0D, but the present analysis also reveals that the proportion of the most reactivecompound can be locally higher than its value in the initial surrogate fuel composition.

For large droplets, whose lifetime is much longer than that of the ignition delay time,preferential evaporation effects are strong, with a large scattering of the fuel composition.However, dispersion occurs after the ignition delay time and ignition is controlled by theignition delay time of the more volatile species.

The next step is to investigate the direct coupling between the evaporation and chem-ical processes in the DNS. As a first step, an ignition progress variable based on theLivengood-Wu index will be added to the simulation to evaluate the ignition time ata limited computational cost, and eventual work can directly include a skeletal chem-ical mechanism in the calculations, which will enable a finer study of the preferentialevaporation effect on auto-ignition.

Acknowledgments

This work was funded by the US Federal Aviation Administration (FAA) Office ofEnvironment and Energy as a part of the ASCENT Project National Jet Fuel Com-bustion Program under FAA Award #13-C-AJFE-SU-005. The first author gratefullyacknowledges financial support from Safran.

REFERENCES

Astm international 2015 Standard test method for determination of ignition delayand Derived Cetane Number (DCN) of diesel fuel oils by combustion in a constantvolume chamber , ASTM standard D6890-15a.

Borghesi, G., Mastorakos, E. & Cant, R. S. 2013 Complex chemistry DNS ofn-heptane spray autoignition at high pressure and intermediate temperature condi-tions. Combust. Flame 160, 1254–1275.

Page 11: Center for Turbulence Research Annual Research Briefs 2016 ...web.stanford.edu/group/ihmegroup/cgi-bin/MatthiasI...the coupling with the group contribution module (Govindaraju & Ihme

DNS of multicomponent spray 191

Dagaut, P. & Cathonnet, M. 2006 The ignition, oxidation, and combustion ofkerosene: A review of experimental and kinetic modeling. Prog. Energy Comb. Sci.32, 48–92.

Daif, A., Bouaziz, M., Chesneau, X. & Cherif, A. A. 1999 Comparison of mul-ticomponent fuel droplet vaporization experiments in forced convection with theSirignano model. Exp. Therm. Fluid Sci. 18, 282–290.

Dooley, S., Won, S. H., Heyne, J., Farouk, T. I., Ju, Y., Dryer, F. L., Kumar,K., Hui, X., Sung, C.-J., Wang, H. et al. 2012 The experimental evaluation of amethodology for surrogate fuel formulation to emulate gas phase combustion kineticphenomena. Combust. Flame 159, 1444–1466.

Edwards, T. 2002 ’Kerosene’ fuels for aerospace propulsion—composition and proper-ties. AIAA Paper 2002-3874.

Govindaraju, P. B. & Ihme, M. 2016 Group contribution method for multicomponentevaporation with application to transportation fuels. Int. J. Heat Mass Tran. 102,833–845.

Honnet, S., Seshadri, K., Niemann, U. & Peters, N. 2009 A surrogate fuel forkerosene. Proc. Combust. Inst. 32, 485–492.

Kitano, T., Nishio, J., Kurose, R. & Komori, S. 2014 Evaporation and combustionof multicomponent fuel droplets. Fuel 136, 219–225.

Law, C. & Sirignano, W. 1977 Unsteady droplet combustion with droplet heating—ii:Conduction limit. Combust. Flame 28, 175–186.

Le Clercq, P. & Bellan, J. 2004 Direct numerical simulation of a transitional tempo-ral mixing layer laden with multicomponent-fuel evaporating drops using continuousthermodynamics. Phys. Fluids 16, 1884–1907.

Lefebvre, A. H. 1998 Gas turbine combustion. CRC Press.

Luo, K., Pitsch, H., Pai, M. & Desjardins, O. 2011 Direct numerical simulationsand analysis of three-dimensional n-heptane spray flames in a model swirl combustor.Proc. Combust. Inst. 33, 2143–2152.

Mashayek, F. 1998 Droplet–turbulence interactions in low-Mach-number homogeneousshear two-phase flows. J. Fluid Mech. 367, 163–203.

Mastorakos, E. 2009 Ignition of turbulent non-premixed flames. Prog. Energy Comb.Sci. 35 (1), 57–97.

Miller, R. S., Harstad, K. & Bellan, J. 1998 Evaluation of equilibrium and non-equilibrium evaporation models for many-droplet gas-liquid flow simulations. Int. J.Multiphas. Flow 24, 1025–1055.

Neophytou, A., Mastorakos, E. & Cant, R. 2010 DNS of spark ignition and edgeflame propagation in turbulent droplet-laden mixing layers. Combust. Flame 157,1071–1086.

Reveillon, J. & Demoulin, F.-X. 2007 Effects of the preferential segregation ofdroplets on evaporation and turbulent mixing. J. Fluid Mech. 583, 273–302.

Reveillon, J. & Vervisch, L. 2005 Analysis of weakly turbulent dilute-spray flamesand spray combustion regimes. J. Fluid Mech. 537, 317–347.

Sanchez, A. L., Urzay, J. & Linan, A. 2015 The role of separation of scales in thedescription of spray combustion. Proc. Combust. Inst. 35, 1549–1577.

Sirignano, W. A. 1999 Fluid Dynamics and Transport of Droplets and Sprays. Cam-bridge University Press.

Page 12: Center for Turbulence Research Annual Research Briefs 2016 ...web.stanford.edu/group/ihmegroup/cgi-bin/MatthiasI...the coupling with the group contribution module (Govindaraju & Ihme

192 Esclapez, Govindaraju & Ihme

Squires, K. D. & Eaton, J. K. 1991 Preferential concentration of particles by turbu-lence. Phys. Fluids 3, 1169–1178.

Stagni, A., Esclapez, L., Govindaraju, P., Cuoci, A., Faravelli, T. & Ihme,M. 2016 The role of preferential evaporation on the ignition of multicomponent fuelsin a homogeneous spray/air mixture. Proc. Combust. Inst. 36, 1–9.

Torres, D., O’rourke, P. & Amsden, A. 2003 Efficient multicomponent fuel algo-rithm. Combust. Theor. Model. 7, 67–86.

Vie, A., Franzelli, B., Gao, Y., Lu, T., Wang, H. & Ihme, M. 2015 Analysis ofsegregation and bifurcation in turbulent spray flames: A 3D counterflow configura-tion. Proc. Combust. Inst. 35, 1675–1683.

Wang, C., Dean, A. M., Zhu, H. & Kee, R. J. 2013 The effects of multicomponentfuel droplet evaporation on the kinetics of strained opposed-flow diffusion flames.Combust. Flame 160, 265–275.

Wang, Y. & Rutland, C. 2007 Direct numerical simulation of ignition in turbulentn-heptane liquid-fuel spray jets. Combust. Flame 149, 353–365.


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