Available online at www.sciencedirect.com

Proceedings of the Combustion Institute 37 (2019) 3303–3310 www.elsevier.com/locate/proci

Large-eddy simulations of transcritical injection and

auto-ignition using diffuse-interface method and

finite-rate chemistry

Peter C. Ma

a , ∗, Hao Wu

a , Thomas Jaravel b , Luis Bravo

c , Matthias Ihme

a , b

a Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, United States b Center for Turbulence Research, Stanford University, Stanford, CA 94305, United States

c Propulsion Division, Vehicle Technology Directorate, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD

21005, United States

Received 30 November 2017; accepted 20 May 2018 Available online 22 June 2018

Abstract

The need for improved engine efficiencies has motivated the development of high-pressure combustion

systems, in which operating conditions achieve and exceed critical conditions. Associated with these condi- tions are strong variations in thermo-transport properties as the fluid undergoes mixing and phase transition, and two-stage ignition with low-temperature combustion. Accurately simulating these physical phenomena at real-fluid environments remains a challenge. This study examines a diffuse-interface method for simulating the injection and ignition of n -dodecane at transcritical conditions. To this end, a compressible solver with

a real-fluid state equation and finite-rate chemistry is employed. Simulations of an ECN-relevant diesel-fuel injector are performed for both inert and reacting conditions. For the spray ignition, four specific operat- ing points (corresponding to ambient temperatures between 900 K and 1200 K) are investigated to examine effects of the real-fluid environment and low-temperature chemistry. Comparisons with available experimen- tal data demonstrate that the presented numerical method adequately captures the diesel fuel injection and

auto-ignition processes under transcritical conditions. © 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Diesel injection; Transcritical combustion; Auto-ignition; Diffuse-interface method; Finite-rate chemistry

∗ Corresponding author. E-mail address: peterma@stanford.edu (P.C. Ma).

https://doi.org/10.1016/j.proci.2018.05.063 1540-7489 © 2018 The Combustion Institute. Published by Elsev

1. Introduction

As propulsion systems continue to push

towards higher efficiencies, the demand for high- performance combustion devices operating at even-higher pressures has been steadily increas- ing. This trend concerns traditional applications,

ier Inc. All rights reserved.

3304 P.C. Ma et al. / Proceedings of the Combustion Institute 37 (2019) 3303–3310

Fig. 1. Ignition delay time at φ = 1 . 0 for n -dodecane at different conditions from homogeneous reactor sim- ulations. The blue curve separates the low- and high- temperature combustion regimes. Critical point, Widom

line, and compressibility factor contour for n -dodecane are also shown. Ambient conditions for LES calculations in this study are labeled by triangles. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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uch as diesel and gas turbine engines, as wells rocket motors and pressure-gain combustionystems [1,2] . In these environments, reactingows undergo exceedingly complex and inter-elated thermophysical processes, starting withompressible fuel injection, atomization, mixing,nd heating, leading to ignition and combustion,nd are often subject to pressure levels well abovehe thermodynamic critical state. In the contextf diesel engines, the compressed fluid is typically

njected at subcritical temperatures into a mixturehat undergoes a thermodynamic state transitionnto the supercritical regime. During this process,he fuel typically crosses the Widom line [3] , whichs depicted in Fig. 1 for n -dodecane. Mani et al.4] conducted high-speed long-distance microscopy

easurements of n -dodecane sprays and showedhat the interfacial behavior of fluids exhibitsroperties markedly different from classical two-hase breakup, including diminishing effectsrom surface tension and heat of vaporization.ahms et al. [5,6] presented a theoretical frame-ork that explains the conditions under which aulti-component fluid mixture transitions from

wo-phase breakup to single phase mixing in aanner consistent with experimental observations.

Traditionally, Lagrangian droplet methodsave been utilized assuming the presence of spray.lthough good agreement with experimental dataas reported, these models often involve careful

election of the breakup and evaporation modelslong with parameter tuning [7] . Recently, theranscritical nature of flows in a diesel injectionrocess has motivated several studies to utilize theiffuse-interface method [5] . In contrast to sharp

interface techniques, where interfaces are explicitlytracked or resolved in the computational do-main, this method artificially diffuses the interface.Oefelein et al. [8] presented an LES framework cou-pled with real-fluid thermodynamics and transportto show that for typical diesel conditions the dy-namics of the dense liquid jet mixing layer is domi-nated by real-fluid effects. Using similar numericaltechniques, Lacaze et al. [9] further analyzed the de-tails of the transient mixing and processes leadingto autoignition during diesel injection. Knud-sen et al. [10] employed a compressible Eulerianmodel to describe the liquid fuel injection processunder consideration of the internal nozzle flowand compressibility effects. Matheis and Hickel[11] developed a thermodynamic model wherephase separation is considered through vapor liq-uid equilibrium calculations in a fully-conservativediffuse-interface method. Ma et al. [12] developed aquasi-conservative scheme by extending a double-flux model with entropy-stability to enable therobust simulation of transcritical injection process.

For reacting sprays, Lagrangian droplet modelshave been used in conjunction with a gas-phasecombustion model, for which flamelet-basedmodels and transported probability density func-tion (TPDF) methods are typically employed.Simulations of multiple-injection realizationswere conducted by Pei et al. [13] using the TPDFmethod, showing that the first ignition was initiatedin a lean mixture and subsequently propagatedto the rich mixture. Using LES, coupled with aFlamelet Generated Manifold combustion model,Wehrfritz et al. [14] carried out an investigationto characterize the early flame development withrespect to temperature and formaldehyde at near-Spray A conditions. More recently, a coupledLES and Tabulated Flamelet Model with multiplerealizations was presented in [15] to study the flamestructure and ignition dynamics at low-temperaturecombustion (LTC) conditions in the range between750–1100 K. Significant differences in flame struc-ture were found at the low-temperature conditions(750 K), including the formation of formaldehydein lean regions from first-stage ignition. Using1D unsteady flamelet calculations with detailedchemistry, Dahms et al. [16] provided a conceptualmodel to describe the turbulent ignition processin high-pressure spray flames, demonstratingthe significance of turbulence-chemistry interac-tions under these conditions. The utilization of finite-rate chemistry with detailed chemical mech-anism is currently limited in multi-dimensionalsimulations for the study of diesel auto-ignitionprocess.

The objective of this study is to investigate dieselinjection and auto-ignition processes under real-istic engine conditions by combining a compress-ible real-fluid solver with diffuse-interface methodand finite-rate chemistry combustion model. The

P.C. Ma et al. / Proceedings of the Combustion Institute 37 (2019) 3303–3310 3305

governing equations are presented in Section 2 , fol-lowed by a discussion of thermo-transport mod-els and numerical methods employed. The flowconfiguration and numerical setup are discussed inSection 3 . Simulation results of both non-reactingand reacting cases are examined in Section 4 usingavailable experimental data and effects of turbu-lence and LTC on spray ignition are analyzed. Themanuscript finishes with conclusions in Section 5 .

2. Mathematical formulation

2.1. Governing equations

The governing equations for the diffuse-interface method are the Favre-filtered conserva-tion laws for mass, momentum, total energy, andspecies, taking the following form:

∂ t ̄ρ + ∇ · ( ̄ρ˜ u ) = 0 , (1a)

∂ t ( ̄ρ˜ u ) + ∇ · ( ̄ρ˜ u ̃ u + p̄ I ) = ∇ · τ̄v + t , (1b)

∂ t ( ̄ρ˜ e ) + ∇ · [ ̃ u ( ̄ρ˜ e + p̄ )] = ∇ · ( ̄τv + t ·˜ u ) − ∇ · q̄ v + t , (1c)

∂ t ( ̄ρ ˜ Y k ) + ∇ · ( ̄ρ˜ u ˜ Y k ) = −∇ · j̄ k, v + t +

¯̇ ω k , (1d)

where ρ is the density, u is the velocity vector, p isthe pressure, e is the specific total energy, τ is thestress tensor, q is the heat flux, and Y k , j k , and ˙ ω k

are the mass fraction, diffusion flux, and chemicalsource term for species k , and the species equationsare solved for k = 1 , . . . , N S − 1 where N S is thenumber of species. Subscripts v and t denote vis-cous and turbulent quantities, respectively.

The system is closed with a state equation,p̄ = f ( ̄ρ, ˜ T , ˜ Y ) , where T is the temperature andsubgrid-scale terms are neglected in the evaluationof the pressure. The effects of high-order terms inthe state equation for compressible solvers were in-vestigated by Ribert et al. [17] but the consider-ation of these effects is beyond the scope of thiswork. A Vreman subgrid-scale model [18] is used asturbulence closure. The subgrid-scale turbulence-chemistry interaction is accounted for by using thedynamic thickened-flame model [19] . The maxi-mum thickening factor is set to be 4 in this study.

2.2. Thermodynamic and transport properties

For computational efficiency and for accuratelyrepresenting properties near the critical point [20] ,the Peng–Robinson cubic state equation [21,22] isused in this study, taking the following form

p =

RT

v − b − a

v 2 + 2 bv − b 2 , (2)

where R is the gas constant, v is the specific vol- ume, and the coefficients a and b are dependent on temperature and composition to account for ef- fects of intermolecular forces [22] . Procedures for evaluating thermodynamic quantities such as in- ternal energy, specific heat capacity and partial en- thalpy using the Peng–Robinson state equation are described in detail in Ma et al. [12] . The dynamic viscosity and thermal conductivity are evaluated

using Chung’s method with high-pressure correc- tion [23] , and Takahashi’s high-pressure correction

[24] is used to evaluate binary diffusion coefficients.

2.3. Finite-rate chemistry

Chemical source terms in the species conserva- tion equations are defined to be the net produc- tion rates from all reactions which in the present work is modeled by finite-rate chemistry. For large- scale turbulent simulations, the reaction chemistry requires dimensional reduction such that the num- ber of transported scalars is maintained at a rea- sonable level. In the present study, a 33-species reduced mechanism for n -dodecane is used. This mechanism is reduced from a 54-species skeletal mechanism [25] by setting 21 species in QSS ap- proximation, which are identified using the level of importance criterion [26] . Linearized quasi-steady state approximation [27] (L-QSSA) is applied to

this selection of species. The concentrations of the quasi-steady state (QSS) species are determined by a sparse linear system. The system is solved ef- ficiently by separating the factorization from the construction of the elimination tree, of which the latter depends only on the mechanism-specific spar- sity pattern. The resulting mechanism is validated

through auto-ignition calculations at high-pressure conditions (see Supplementary Material).

2.4. Numerical methods

An unstructured finite-volume solver, CharLES

x , is employed in this study. In this solver, the convective fluxes are discretized using a sensor-based hybrid scheme [28] in which a high-order, non-dissipative scheme is combined

with a low-order scheme to describe interfaces and flow field discontinuities. A central scheme, which is 4th-order accurate on uniform meshes, is used along with a 2nd-order ENO scheme. A density sensor [12] is adopted in this study. Due to the large density gradients present at transcritical conditions, an entropy-stable flux correction technique [12] is used to ensure the physical realizability of the numerical solution

and to dampen non-linear instabilities in the numerical scheme. Due to strong non-linearities inherent in the real-fluid state equation, spurious pressure oscillations will be generated when a fully conservative scheme is used [12,29] . To eliminate the spurious pressure oscillations, an adaptive

3306 P.C. Ma et al. / Proceedings of the Combustion Institute 37 (2019) 3303–3310

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Fig. 2. Comparison of injection sequence between ex- periments and LES for the non-reacting case ( p ∞

=

6 . 0 MPa, T ∞

= 900 K). Experimental images are ob- tained using diffused back-illumination method with grayscale intensity threshold to indicate the liquid region [35,36] . Fuel mass fraction contours at the center-plane are shown from LES results with dense fluid region indi- cated by a mixture fraction value of 0.6. Spatial units in mm.

ouble-flux method [12,30,31] is extended to theranscritical regime. In this method, the effectivepecific heat ratio evaluated from the speed of ound is frozen both spatially and temporally for given cell when the fluxes at faces are evaluated,o that the thermodynamic system is equivalentlyransformed into a calorically perfect gas system. second-order Strang-splitting scheme [32] is

pplied to separate the convection, diffusion, andeaction operators. A strong stability preservingrd-order Runge–Kutta (SSP-RK3) scheme [33] issed for time integration of non-stiff operators.he reaction chemistry is integrated using a semi-

mplicit Rosenbrock–Krylov scheme [34] , which isth-order accurate in time and has linear cost withespect to the number of species.

. Case description

In this study, the Spray A configuration [7] isonsidered, representing a benchmark case of he Engine Combustion Network. The single-holeiesel injector is operated with pure n -dodecane at aail pressure of p rail = 150 MPa. Both non-reacting0% O 2 ) and reacting cases (15% O 2 ) are consid-red. Liquid n -dodecane fuel is injected at T inj =63 K through a nozzle with a nominal diameterf 90 μm into an ambient environment at a pres-ure of p ∞

= 6 . 0 MPa. An ambient temperaturef T ∞

= 900 K is considered for the non-reactingase and effects of LTC on the auto-ignition arexamined by performing simulations for a series of mbient temperatures (see Fig. 1 ). At these condi-ions, the liquid n -dodecane undergoes a transcriti-al injection process before auto-ignition, where theiquid fuel is heated and mixed with the ambientaseous environment.

A 3D cylindrical computational domain is usedn this study with a diameter of 40 mm and a lengthf 80 mm. The injector is not included in the com-utational domain and boundary conditions arerovided at the exit of the nozzle. A structuredesh with hexahedral elements is used. The mesh

s clustered in the region near the injector along thehear layers, and stretched in downstream and ra-ial directions. The minimum grid spacing is 4 μm,ith approximately 20 grid points across the injec-

or nozzle. The maximum grid spacing downstreams less than 50 μm. This grid resolution at locationshere ignition occurs is able to resolve the igni-

ion kernel length scale estimated by non-premixedame calculations. The total cell count of the mesh

s 8.7 millions. Fuel mass flux and temperature are prescribed

t the injector nozzle exit using the time-dependentate of injection as provided by the CMT virtual in-ection rate generator [7] , with default input param-ters recommended by ECN for the Spray A case. plug flow velocity profile is applied at the nozzle

xit without synthetic turbulence. Effects of inflow

turbulence are studied and the results are providedas Supplementary Material. The pressure is pre-scribed at 6.0 MPa at the outlet. Adiabatic bound-ary conditions are applied at all walls. All simu-lations are initialized with ambient conditions. ACFL number of unity is used during the simulationand a typical time step is about 0.6 ns. The simula-tions were performed using 2,560 Intel Xeon (E5-2698 v3) processors and 1 μs physical time couldbe completed in about half an hour for a reactingcase.

4. Results and discussion

4.1. Non-reacting case

Figure 2 shows a temporal sequence of the in-jection process comparing experimental measure-ments and current numerical simulations. It can beseen that the dense fuel jet remains stable in thevicinity of the injector nozzle, for x < 3 mm. Thejet starts to break up downstream of this region andinstabilities at the shear layer can be seen. Furtherdownstream, the fuel mixes with the ambient gasand large eddies are present. The spreading angleof the injected fuel is narrow in the near-injectorregion and broadens further downstream due tothe entrainment of ambient gas by turbulent mix-ing. The simulation results are qualitatively in goodagreement with the experimental images taken bythe diffused back-illumination method [35,36] interms of both fuel penetration and overall spread-ing rate. However, it can clearly be seen that themeasurements show a larger spreading angle near

P.C. Ma et al. / Proceedings of the Combustion Institute 37 (2019) 3303–3310 3307

Fig. 3. Liquid and vapor penetration lengths predicted by LES in comparison with measurements [37] for the non- reacting case ( p ∞

= 6 . 0 MPa, T ∞

= 900 K).

Fig. 4. Axial profile at center-line (top) and radial pro- files (bottom) of mean and rms values of mixture frac- tion in comparison with Rayleigh scattering measure- ments [39] for the non-reacting case ( p ∞

= 6 . 0 MPa, T ∞

= 900 K).

the injector. These results are comparable to thosereported in previous numerical studies [9–11] .

The liquid and vapor penetration lengths are ex-tracted from LES using a threshold value of 0.6and 0.01 for mixture fraction, respectively. Resultsup to 1 ms after injection are shown and comparedwith measurements in Fig. 3 . The experimental va-por and liquid penetration lengths determined fromSchlieren imaging and Mie scattering [7,37] are alsoshown for comparison. It can be seen that the va-por penetration agrees with measurements favor-ably. It was found that the utilization of the inflowboundary conditions with a time-dependent fuelmass flux is essential for the accurate prediction.Another simulation with a constant mass flux with-out the initial ramp-up yielded appreciably longerpenetration length, which is consistent with otherstudies [7] . The sensitivity of the criterion for thedetermination of the vapor penetration was stud-ied, confirming that the computed vapor penetra-tion length was insensitive to threshold values be-tween 0.005 and 0.1.

For the validation of the liquid penetrationlength, a threshold value of 0.6 is used for thefuel mass fraction, providing good agreement withmeasurements. However, this threshold value issomewhat arbitrary. The sensitivity of the liquidthreshold value was tested, and it was found thatfor mixture fraction values between 0.95 and 0.4,the predicted length varies between 5 mm and15 mm. It is also possible to conduct vapor liquidequilibrium calculations to identify the two-phaseregions using the simulation results. However, pre-vious studies by Ma et al. [31,38] showed that sincethe interface is artificially diffused by numericaldissipation, distinctly different phase separationbehaviors can be obtained merely because of thedifferent numerical schemes employed. Therefore,it is questionable to use these simulation results tostudy the potential phase separation behaviors. Itwas also pointed out in the experimental investiga-tions [35,36] that the measured liquid penetration

length is sensitive to measurement method, optical setup, threshold for determining liquid phase, and

the actual geometry of the injector. Indeed, the res- olution in either the simulation or the experiment is still not adequate to fully resolve the interfacial gradients near the injector nozzle.

The flow structure and mixing behavior of the injection process further downstream are com- pared with measurements of mixture fraction from

Rayleigh scattering [39] . The results are shown

in Fig. 4 . Multiple-injection experiments provide ensemble-averaged statistics. In the simulation, statistics of the steady period of injection are ob- tained by temporally averaging between 0.6 ms and

1.2 ms after the injection. As can be seen from

Fig. 4 , good agreement is obtained for both mean

and rms values of mixture fraction and the simula- tion results fall well within experimental uncertain- ties. These results along with the good agreement of the vapor penetration length, as presented in Fig. 3 , show that the current numerical method is capable of adequately predicting the turbulent mixing pro- cess between the fuel and surrounding environment downstream of the injector after the dense liquid

fuel is fully disintegrated.

4.2. Reacting case

Following the evaluation of the solver for the non-reacting case, we now turn our atten-

3308 P.C. Ma et al. / Proceedings of the Combustion Institute 37 (2019) 3303–3310

Fig. 5. Ignition delay time at different ambient temper- ature conditions predicted by LES compared with mea- surements [7] . Results from 0D homogeneous reactor cal- culations are shown by dashed lines for different equiva- lence ratio.

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Fig. 6. Comparison between CH 2 O mass fraction from

LES and false-color PLIF measurements [40,41] at sev- eral injection times at 900 K ambient temperature. Spatial units in mm.

Fig. 7. Comparison of OH mass fraction from LES and OH PLIF measurements [7,40] at two injection times at 900 K ambient temperature. Spatial units in mm.

Fig. 8. Temperature fields (left) and spatial distribution of species (right) at t ∗ = 2 . 0 for 900 K (top) and 1200 K

(bottom) ambient temperature conditions; real-fluid re- gions are enclosed by white contours; time is normalized by corresponding ignition delay times (given in Fig. 5 ). Spatial units in mm.

ion to the investigation of reacting conditions.igure 5 shows the ignition delay time at differentmbient temperature conditions, predicted by LESompared with measurements. Following the ECN-ecommendations [7] and criteria used by previoustudies [13,15] , the ignition delay time in LES isefined as the time when the maximum OH massraction reaches 14% of the value at quasi-steadytate of the flame. As can be seen from Fig. 5 , goodgreement is observed between LES and experi-ents, with about 10% maximum error from LES.ote that shorter ignition delay times were also

redicted by Yao et al. [25] where the same parentkeletal chemical mechanism was adopted. Previ-us work utilizing flamelet-based combustion mod-ls [14] also showed that the chemical mechanismas a significant effect on accurately predicting the

gnition delay time. Note that although the ignitionelay time for the cases with ambient temperaturesf 1000 K and 1100 K are shorter than that forhe 900 K case from homogeneous reactor calcula-ions due to LTC (see Figs. 1 and 5 ), the actual igni-ion delay time for the 3D injection process exhibits monotonic behavior with respect to the ambientemperature, demonstrating the significance of tur-ulent mixing and heat transfer between the fuel jetnd the ambient prior to the ignition.

Figures 6 and 7 show results for mass fractionsf CH 2 O and OH species along the center-plane ateveral injection times for the 900 K case in com-arison with PLIF measurements [40] . CH 2 O is

ormed initially at the radial periphery of the jet. Atater times, the maximum concentration of CH 2 Os observed in the center of the penetrating jet. Itan be seen from Fig. 6 that there is a good agree-ent between LES and measurements in terms of

hape, magnitude, and location of the formationf CH 2 O. The formation of OH is associated withhe subsequent consumption of CH 2 O [16] and theigh-temperature chemistry (HTC) correspondingo the main ignition process. High concentrationsf OH are found near the edges of the penetrat-

ng jet due to the relatively low scalar dissipationate and longer residence time in these regions [15] .

Good agreement between LES and experimentscan be observed in Fig. 7 , with a sharper represen-tation in the simulation results.

Figure 8 shows temperature fields and spatialdistributions of different species at both 900 Kand 1200 K ambient temperature conditions at thesame normalized time after ignition, representingthe quasi-steady state behavior. Here, the time isnormalized by the corresponding ignition delay

P.C. Ma et al. / Proceedings of the Combustion Institute 37 (2019) 3303–3310 3309

Fig. 9. Evolution of temperature, CH 2 O, and OH in mixture fraction space at 900 K (top) and 1200 K (bottom) ambient temperature conditions; time is normalized by corresponding ignition delay times (given in Fig. 5 ).

time computed from the simulations, which aregiven in Fig. 5 . The flame structure for these twocases are similar. After the fuel goes through theinjection and mixing process with the ambientenvironment, a cool-flame region is formed alongthe center of the jet, which is indicated by the highconcentration of CH 2 O. At the periphery of thejet, HTC takes place in the stoichiometric regionresulting in rapid heat release and formation of OH species.

The real-fluid region identified using the crite-rion with more than 5% deviation from unity com-pressibility factor is enclosed by white contours inFig. 8 . It can be seen that the real-fluid regions arelimited to the vicinity of the injector nozzle and areseparated from chemical reactions with relativelyhigh temperatures. If we approximate the time scalefor heating the liquid jet by the surrounding usingthe classical droplet evaporation model [42]

τevap =

ρl D

2 0 c p,g

8 k g ln [1 + c p,g (T ∞

− T s ) / �H v ] C conv , (3)

the ratio between evaporation time and ignition de-lay time varies between 20 and 8 for ambient tem-peratures between 900 K and 1200 K with dropletdiameter being half the nozzle diameter ( D 0 =45 μm). These results indicate minimal real-fluid ef-fects on ignition characteristics for conditions rele-vant to this study.

Mixture-fraction conditioned scatter data dur-ing the ignition sequence at both 900 K and 1200 Kare presented in Fig. 9 . It can be seen that CH 2 Ois initially formed at conditions near the stoichio-metric mixture, and diffuses into the fuel-rich re-gion at later times. This is consistent with the re-sults from 1D unsteady flamelet calculations byDahms et al. [16] . An increase in temperature byapproximately 200 K can be observed for the 900 Kcase at t ∗ = 0 . 5 , with a temperature peak occurring

at slightly fuel-rich conditions. This peak is not ev- ident for the other case, and can be attributed to

low-temperature ignition. After the ignition, CH 2 O

persists in mixture fraction space due to the pres- ence of the cool-flame region shown in Fig. 8 . The peak in CH 2 O occurs at mixture fraction condi- tions of approximately 0.15 for the case with 900 K

and slightly richer conditions with mixture frac- tion of 0.2 for the case with 1200 K. Following the early ignition phase, the temperature and species profiles during the second-stage ignition are simi- lar with peak temperature and OH mass fractions occurring at stoichiometric conditions and CH 2 O

present on the fuel-rich side. The importance of tur- bulence during this ignition phase is manifested by the broad distribution in composition space. This is further evidenced by the deviation of the corre- sponding ignition delay from the 0D homogeneous reactor (see Fig. 5 ).

5. Conclusions

In this study, a diffuse-interface method in

conjunction with a finite-rate chemistry model is presented for the modeling of diesel fuel injec- tion and auto-ignition processes under transcriti- cal conditions. Compressible multi-species conser- vation equations are solved with a Peng–Robinson

state equation and real-fluid transport properties. A finite-volume method with an entropy-stable scheme [12] is utilized to simulate real-fluid flows with strong nonlinearities.

LES-calculations are performed to simulate the ECN Spray A target configuration [7] for both inert and reacting conditions. Simulation re- sults are analyzed and compared with available experimental measurements. For the non-reacting case, flow fields of the injection sequence and pre-

3310 P.C. Ma et al. / Proceedings of the Combustion Institute 37 (2019) 3303–3310

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icted vapor penetration length are qualitativelyn good agreement with experimental results. Fourmbient temperature conditions are considered foreacting conditions. Good agreement of the igni-ion delay time is obtained from simulation resultst different ambient temperature conditions andhe for mation of inter mediate species is capturedy the simulations, indicating that the presented nu-erical framework adequately reproduces the cor-

esponding LTC and HTC ignition processes underigh-pressure conditions.

Observed differences in the flow-field behav-or near the injector require further investigationsoth numerically and experimentally. Effects of theubgrid-scale model on ignition delay time predic-ions will also be the subject of future work.

cknowledgments

Financial support by ARL under awardW911NF-16-2-0170 and NASA under awardNNX15AV04A is gratefully acknowledged. Thisork is supported in part by resources from DoDigh Performance Computing Modernizationrogram (HPCMP) FRONTIER Award at ARL

hrough project “Petascale High Fidelity Simula-ion of Atomization and Spray/Wall Interactionst Diesel Engine Conditions.” Simulations wereerformed on DoD Supercomputing platformExcalibur” Cray XC40.

upplementary material

Supplementary material associated with thisrticle can be found, in the online version, atoi: 10.1016/j.proci.2018.05.063 .

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