Special Issue Article

International J of Engine Research2019, Vol. 20(1) 58–68� IMechE 2018Article reuse guidelines:sagepub.com/journals-permissionsDOI: 10.1177/1468087418819546journals.sagepub.com/home/jer

Large eddy simulations of diesel-fuelinjection and auto-ignition attranscritical conditions

Matthias Ihme1 , Peter C Ma1 and Luis Bravo2

AbstractLarge eddy simulations of transcritical injection and auto-ignition of n-dodecane in a combustion chamber are per-formed. To this end, a diffuse-interface method is employed that solves the compressible multi-species conservationequations, and a cubic state equation together with real-fluid transport properties is employed to describe the transcriti-cal fluid state. The reaction chemistry is represented by a finite-rate chemistry model involving a 33-species reducedmechanism for n-dodecane. Compared to commonly employed two-phase approaches, the method presented in thiswork does not introduce tunable parameters for spray-breakup. Large eddy simulation calculations are performed byconsidering the Spray A single-hole injector at non-reacting and reacting conditions at a pressure of 60 bar and tempera-tures between 800 and 1200 K. Quantitative comparisons with measurements for liquid and vapor penetration lengthsare performed for non-reacting conditions, and sensitivity to threshold values on mixture fraction are examined. Theanalysis of reacting flow simulations focuses on comparisons of the instantaneous temperature and species fields for OHand CH2O at 800 and 900 K, respectively. Quantitative comparisons with measurements for ignition delay and lift-offheights as a function of ambient temperature are performed. To examine the transient ignition phase, comparisons ofradially integrated OH profiles obtained from the simulations with reported measurements for OH* are performed,showing good agreement. These results show that the large eddy simulation modeling framework adequately reproducesthe corresponding ignition processes, which are relevant to realistic diesel-fuel injection systems.

KeywordsDiesel engine, transcritical injection, auto-ignition, diffuse-interface method, finite-rate chemistry

Date received: 5 October 2018; accepted: 19 November 2018

Introduction

Achieving further improvements in thermal efficienciesof reciprocating engines requires the operation athigher pressures. At these conditions, the fluid under-goes complex thermophysical processes, involving com-pressible fuel injection, phase transition, mixing, andheating, followed by ignition and combustion. Theseprocesses are often subject to pressure conditionsexceeding the critical state. For diesel engines, the fuelis commonly injected at subcritical temperatures(T\Tc) into a mixture that undergoes a thermody-namic transition to a supercritical regime (see Figure 1for n-dodecane). During the transient injection process,the fuel mixture traverses the Widom line.1 This transi-tion is characterized by changes in the thermodynamicresponse functions.

Long-distance microscopy measurements performedby Manin et al.2 showed that the interfacial behavior ofn-dodecane spray exhibits properties markedly different

from classical two-phase breakup, including diminish-ing effects of surface tension and heat of vaporization.Dahms and colleagues3,4 employed linear gradient the-ory to describe conditions at which a multi-componentfluid mixture transitions from two-phase breakup tosingle-phase mixing in a manner consistent with experi-mental observations. Results from this theory suggestthat the transition to a supercritical state is a result ofthermal gradients within the interfacial region, therebybroadening the interface and reducing the molecularmean free path. The dynamics of the interfacial forces

1Department of Mechanical Engineering, Stanford University, Stanford,

CA, USA2U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen,

MD, USA

Corresponding author:

Matthias Ihme, Department of Mechanical Engineering, Stanford

University, 488 Escondido Mall, Building 500, Stanford, CA 94305, USA.

Email: mihme@stanford.edu

were shown to gradually decrease as the interfacebroadens once it enters the continuum regime.Poursadegh et al.5 performed experimental and theore-tical investigations to show that under typical operatingconditions, relevant to diesel engines, the time scale forthe heating of the liquid jet by its surrounding is muchshorter than the jet breakup time scale, explaining theturbulent mixing behavior observed in experiments.

Predicting high-pressure injection and combustionprocesses requires reliable simulation tools. Because ofthe transcritical characteristics of diesel-fuel injection,diffuse-interface methods have been considered.Compared to sharp interface methods in which theliquid–vapor interface is tracked or resolved, thesemethods artificially diffuse the interface. This is attrac-tive for transcritical flows where interfaces are not pres-ent. However, it remains an open research question asto whether interfacial flows or droplets exist under con-ditions relevant to real applications.6 Oefelein et al.7

developed a large eddy simulation (LES) method toconsider real-fluid thermodynamics and transport pro-cesses, showing that for typical diesel conditions thedynamics of the dense liquid jet core is dominated byreal-fluid effects. Their results show that the mixingpath in the thermodynamic state space does not crossthe liquid–vapor regime, suggesting that interfacialmixing remains locally supercritical. Lacaze et al.8 ana-lyzed the transient mixing and processes leading toauto-ignition during diesel injection. These resultsshowed that the large momentum ratio between thesupercritical fuel and the ambient gas causes significantpenetration of the jet and enhanced turbulent mixing.Furthermore, due to the local reduction in the speed ofsound by real-gas thermodynamics in conjunction withthe high injection velocity, regions of supersonic condi-tions occur in the mixing layer.

A compressible Eulerian formulation was employedby Knudsen et al.9 to model the liquid fuel injectionprocess under consideration of the internal nozzleflow. Matheis and Hickel10 used a conservativediffuse-interface method in which the phase separa-tion was considered through vapor–liquid equilibriumcalculations.

Two-phase reacting flow models have beenemployed by considering Lagrangian droplet methodsand the gas-phase chemistry is described through fla-melet models or transported probability density func-tion (TPDF) methods. Pei et al.11 utilized a TPDFmethod to simulate multi-injection realizations, show-ing that the first ignition is initiated in a lean mixtureand subsequently propagates to rich conditions.Wehrfritz et al.12 performed LES calculations with aflamelet generated manifold combustion model toinvestigate the early flame development at conditionssimilar to the Spray A operating point. They reportedmulti-stage ignition and observed formaldehyde forma-tion prior to ignition at the tip of the fuel-rich gas jet.More recently, a coupled LES with tabulated flameletmodel was employed by Kundu et al.13 to study theflame structure and ignition dynamics in the tempera-ture range between 750 and 1100K. Appreciable differ-ences in flame structure were found at low-temperatureconditions. Dahms et al.14 employed an unsteady fla-melet calculation with detailed chemistry to describethe turbulent ignition process in high-pressure sprayflames.

The objective of this study is to perform LES calcu-lations to investigate fuel injection and auto-ignition ina single-hole diesel-fuel injector. To this end, a diffuse-interface method in conjunction with a finite-rate com-bustion model is employed. The mathematical model,consisting of governing equations, transport model,and chemical mechanism, is described in the next sec-tion. The experimental configuration and computa-tional setup are then presented. This is followed bydiscussing simulation results and making comparisonswith experimental data to examine the performance ofthe developed numerical framework. The article finisheswith conclusions.

Mathematical model

Governing equations

The governing equations for the diffuse-interfacemethod are the Favre-filtered conservation laws formass, momentum, total energy, and species, taking thefollowing form

∂t�r+r � (�r~u)=0 ð1aÞ∂t(�reu)+r � (�reueu+ �pI)=r � tv+ t ð1bÞ∂t(�ree)+r � ½eu(�r~e+ �p)�=r � (tv+ t � eu)�r � qv+ t

ð1cÞ

∂t(�r eYk)+r � (�reu eYk)= �r � Jk, v+ t + �_vk ð1dÞ

Figure 1. Reduced temperature–pressure state space showingisocontours of ignition delay time for n-dodecane/air mixture atf = 1:0 from homogeneous reactor simulations. The criticalpoint and Widom line for n-dodecane are shown as white dotand lines, respectively. Ambient operating conditions consideredin this study are labeled by triangles.

Ihme et al. 59

where r is the density; u is the velocity vector; p is thepressure; e is the specific total energy; t is the stress ten-sor; q is the heat flux; and Yk, Jk, and _vk are the massfraction, diffusion flux, and chemical source term forspecies k, respectively. The species equations are solvedfor k=1, . . . ,N� 1 where N is the number of species.Subscripts v and t denote viscous and turbulent quanti-ties, respectively. The system is closed with a state equa-tion, p= p(r,T,Y).

Thermodynamic state description

To accurately represent properties near the criticalpoint,15 the Peng–Robinson cubic state equation16 isemployed in this work

p=RT

v� b� a

v2 +2bv� b2ð2Þ

where R is the gas constant, v is the specific volume,and the coefficients a and b, taking into considerationeffects of volume displacement and intermolecularforces, are dependent on temperature and composition,and are evaluated as

a=XNi=1

XNj=1

XiXjaij ð3aÞ

b=XNi=1

Xibi ð3bÞ

where Xi is the mole fraction of species i. In this work,the extended corresponding states principle and thepure fluid assumption for mixtures are adopted.17,18

Parameters aij and bi are evaluated using the recom-mended mixing rules by Harstad et al.19 Procedures forevaluating thermodynamic quantities such as internalenergy, specific heat capacity, and partial enthalpyusing the Peng–Robinson state equation are describedin detail in Ma et al.20,21

To describe the dynamic viscosity and thermal con-ductivity, the high-pressure correction by Chunget al.22,23 is employed. This method is known to pro-duce oscillations in viscosity for multi-species mixtureswhen both positive and negative acentric factors arepresent for individual species.24 To address this issue, amole-fraction-weighted viscosity that is evaluated fromthe viscosity of each individual species is employed.The binary diffusion coefficients are evaluated fromTakahashi’s25 high-pressure correction.

Chemical kinetics mechanism

Because of the high computational cost associatedwith the evaluation of detailed chemical mechanisms,the representation of the reaction chemistry in large-scale simulations requires dimensional reduction. Inthis work, a 33-species mechanism for n-dodecane/aircombustion is employed.26 This mechanism wasreduced from a 54-species skeletal mechanism.27

Zero-dimensional auto-ignition computations wereperformed at a pressure of p=60 bar, initial tempera-tures in the range of T=800� 1000 K, and equiva-lence ratio in the range of f=0:5� 2. The results aresampled to apply the level of importance criterion28

using the YARC reduction tool.29 From this, 21 spe-cies are identified to be suitable for quasi-steady-state(QSS) approximation. A comparison of the resultingskeletal mechanism with its parent mechanism is pro-vided in Figure 2. This comparison shows that theprediction of the ignition time is in good agreementwith the skeletal mechanism for the entire range oftemperature and equivalence ratio conditions.

The reduced mechanism is incorporated into theCFD solver using a Cantera library interface.30 Thislibrary allows for the run-time specification of QSS spe-cies and linearized quasi-steady-state approximation(L-QSSA)31 is applied to this selection of species. Thesparse linear system for L-QSSA is solved efficiently byseparating the construction of the elimination tree fromfactorization via Eigen.32

Numerical methods and boundary conditions

The unstructured finite-volume solver, CHARLESx, isemployed in this study. The convective fluxes are dis-cretized using the sensor-based hybrid scheme with theentropy-stable flux correction technique developed byMa et al.21 This scheme combines a central scheme witha second-order essentially non-oscillatory (ENO)scheme, and a density sensor is employed for adapta-tion. Due to strong non-linearities inherent in the real-fluid state equation, spurious pressure oscillations aregenerated when a fully conservative scheme is used. Toeliminate these pressure oscillations, an adaptivedouble-flux method20,21 is employed. A Strang-splittingscheme33 is applied to separate the convection,

Figure 2. Arrhenius plot of ignition delay for n-dodecane/airmixture comparing results from 54-species skeletal mechanism27

(black solid line) and 33-species reduced mechanism26 (reddashed line) for three equivalence ratios at p = 60 bar.

60 International J of Engine Research 20(1)

diffusion, and reaction operators. A strong stabilitypreserving third-order Runge-Kutta (SSP-RK3)scheme34 is used for the temporal integration of thenon-stiff operators. The stiff chemical source term isintegrated using a semi-implicit Rosenbrock-Krylov(ROK4E) scheme,35 which is fourth-order accurate intime and has linear cost complexity with respect to thenumber of species. The stability of the ROK4E schemeis achieved through the approximation of the Jacobianmatrix by its low-rank Krylov-subspace projection. Asfew as three right-hand-side evaluations are performedover four stages. Details about the development of theROK4E scheme can be found in Wu et al.36

The turbulent stresses are modeled using a Vreman37

sub-grid scale (SGS) model. The turbulence/chemistryinteraction is accounted for using the dynamicthickened-flame model,38 in which the maximum thick-ening factor is set to a value of 4 in this study.

The mass flux of the fuel and temperature areprescribed at the injector nozzle exit using the time-dependent rate of injection as provided by the CMTvirtual injection rate generator,39 with default inputparameters recommended by the engine combustionnetwork (ECN) for the Spray A case. A plug flow velo-city profile is prescribed at the nozzle exit without syn-thetic turbulence. A sensitivity analysis was performedto examine the effects of inflow turbulent and spraycharacteristics.26 These parametric investigationsshowed that turbulence has a negligible effect on thevapor penetration length and the liquid penetrationlength was found to decrease slightly with increasingturbulence intensity. The outlet pressure conditions arespecified at 60 bar. Adiabatic boundary conditions areapplied at the walls, and all simulations are initializedwith quiescent ambient conditions. The governingequations are time-advanced at a Courant–Friedrichs–Lewy (CFL) number of unity, corresponding to a typi-cal time step of 0.6 ns. All simulations are conductedup to 1.2ms after the injection. The simulations wereperformed on 2560 Intel Xeon (E5-2698 v3) processors,and one calculation (over 1.2ms) required approxi-mately 1:53 106 CPU-hours.

Experimental configuration andcomputational setup

Spray A configuration

This study considers the Spray A single-hole injectorconfiguration, representing an ECN benchmark case.39

The injector has a nominal diameter of 90mm and isoperated with pure n-dodecane fuel at a rail pressure ofprail = 1500 bar.

The conditions in the chamber considered in thisstudy are illustrated in the p-T diagram of Figure 1.Both non-reacting and reacting cases are studied andcorrespond to 0% and 15% ambient O2 compositions,respectively. Liquid n-dodecane fuel is injected at a sub-critical temperature of Tinj = 363 K into the chamber

at a pressure of p‘ =60 bar. An ambient temperatureof T‘ =900 K is considered for the non-reacting case(Spray A conditions) and effects of low-temperaturechemistry on the auto-ignition are examined byconsidering different ambient temperatures varyingbetween 800 and 1200K. At these conditions, the liquidn-dodecane undergoes a transcritical transition processbefore auto-ignition, during which the fuel is heatedand mixed with the ambient gaseous environment.

Computational setup

The computational domain is represented by a cylindri-cal geometry with a diameter of 40mm and a length of80mm. The domain is discretized by a structured meshwith hexahedral elements. The mesh is locally refinedin the shear-layer region near the injector and stretchedin downstream and radial directions. The minimumgrid spacing is 4mm near the injector exit, which resultsin approximately 20 grid points across the nozzle. Themaximum grid spacing downstream is less than 50mm.The mesh resolution was selected to resolve the ignitionkernel, which was estimated from one-dimensionalunsteady flamelet calculations.40 The total mesh size is8.7millions. Due to computational cost, a furthermesh-sensitivity analysis was not performed. The injec-tor geometry is not included in the simulations.Boundary conditions are provided at the exit of theinjector nozzle.

Results and discussion

Non-reacting conditions: fuel injection and mixing

The transcritical injection process is studied by consid-ering non-reacting flow conditions with ambient tem-perature of 900K. Results for liquid and vaporpenetration lengths are presented in Figures 3 and 4,showing the sensitivity of the threshold value for mix-ture fraction to predictions of the penetration length.The experimental vapor and liquid penetration lengthsdetermined from Schlieren imaging and Mie scatter-ing39,41 are also shown for comparison. Direct compari-sons with measurements show that the vaporpenetration length is nearly insensitive to the thresholdvalue, whereas stronger variations for the liquid pene-tration length are observed as shown in Figure 4.Specifically, it can be seen that for mixture fraction val-ues between 0.95 and 0.4, the predicted liquid penetra-tion length varies between 5 and 15mm. It was pointedout in the experimental investigations42,43 that the mea-sured liquid penetration length is sensitive to measure-ment method, optical setup, threshold for demarcatingthe liquid phase, and the actual geometry of the injec-tor. The resolution in either the simulation or theexperiment remains insufficient for fully resolving theinterfacial flow near the injector nozzle, if multi-phaseflows do exist under these conditions.

Ihme et al. 61

Radial profiles of the scalar mixing field at threeaxial locations downstream of the nozzle exit are com-pared to measurements from Rayleigh scattering44 inFigure 5 for three different axial locations (x=17.85,25, and 35mm). Multiple injections in the experimentsprovide ensemble-averaged statistics. In the simulation,statistics of the steady period of injection are obtainedby temporally averaging between 0.6 and 1.2ms afterthe start of the injection. As can be seen from Figure 5,there is overall good agreement for mean mixture frac-tion profiles at all three locations, while the simulationpredicts slightly higher RMS values compared to theexperimental data. These radial profiles together withthe transient results for liquid and vapor penetrationlengths, presented in Figures 3 and 4, show that thediffuse-interface LES-method is capable of predictingthe turbulent mixing process between fuel and sur-rounding environment downstream of the injector afterthe dense liquid fuel is fully disintegrated. In this con-text, it is noted that this LES formulation does notintroduce tunable model coefficients so that it isexpected to be applicable to other transcritical injectionconfigurations.

Reacting conditions: auto-ignition

We proceed by considering reacting conditions with thespecific goal of examining effects of temperature varia-tions on the low-temperature combustion. A directcomparison of transient simulation results for two dif-ferent ambient temperatures of 800K and 900K areshown in Figure 6. Temperature fields are presented atseveral injection times along with the CH2O and OHfields. Flow-field results for CH2O and OH are super-imposed to illustrate the spatial separation associatedwith the first-stage and second-stage ignition condi-tions. It can be seen from the temperature results that

the liquid fuel jet is heated by the surrounding hot envi-ronment after being injected into the combustion cham-ber and the occurrence of a first-stage ignition can beobserved at early ignition times (e.g. see temperaturefields at 600ms for 800K and 300ms for 900K), whichis associated with an incremental temperature changeand the formation of CH2O. The lower temperaturefor the case with 800K delays the ignition by a factorof two. After the second-stage ignition process (seeresults in Figure 6 after 600/300ms for 800/900K),high-temperature regions with temperatures in excessof 2000K can be seen downstream of the combustionchamber. It can also be seen that the ignition transitionextends over a shorter axial distance and wider radialregion compared to the case with higher ambienttemperature.

From the species results in Figure 6, it can be seenthat CH2O is formed initially at the radial periphery ofthe jet. At later times, the maximum concentration ofCH2O is observed in the center of the penetrating jet.The formation of OH is associated with the subsequentconsumption of CH2O

14 and the high-temperaturechemistry by the second-stage ignition. High concentra-tions of OH are found near the edges of the penetratingjet due to the relatively low scalar dissipation rate andlonger residence time in these regions.13

To assess the model performance in predicting inter-mediate species, we compare instantaneous mass frac-tion contours of CH2O and OH at the nominal ignitiondelay time for the condition of 900K. Measurementswere obtained from planar laser induced fluores-cence.39,45,46 It can be seen from Figure 7 that there is agood qualitative agreement between LES and measure-ments in terms of shape, magnitude, and location ofthe formation of CH2O. Similarly, acceptable agree-ment for OH is observed, with a sharper representationin the simulation results.

Figure 3. Vapor penetration length predicted by LES incomparison with measurements41 for the non-reacting case(p‘ = 60 bar, T‘ = 900 K).

Figure 4. Liquid penetration length predicted by LES incomparison with measurements41 for the non-reacting case(p‘ = 60 bar, T‘ = 900 K).

62 International J of Engine Research 20(1)

Figures 8 and 9 show comparisons of predictedand measured ignition delay and lift-off length for dif-ferent ambient temperature conditions. Following theECN-recommendation39 and criteria used in previousstudies,11 the ignition delay time in LES was definedas the time when the maximum OH mass fractionreaches 14% of the value at quasi-steady state condi-tions of the flame. The lift-off length is calculatedusing the line-of-sight OH mass fraction results bytime-averaging LES results between 0.8 and 1.2msduring the quasi-steady-state period. In Figures 8 and9, measurements from multiple experiments areshown with error bars indicating experimental varia-bility. As can be seen from Figures 8 and 9, goodagreement is observed for both the ignition delay timeand the lift-off length between LES and experiments.The LES method quantitatively captures this beha-vior with respect to variations in ambient tempera-ture. About 10% underprediction in ignition delaytime from the LES can be observed. This discrepancyis partially attributed to uncertainties in the chemicalmechanism and the mesh resolution. Shorter ignition

delay times were also predicted by Yao et al.27 wherethe same parent skeletal chemical mechanism wasadopted. Previous work utilizing flamelet-based com-bustion models12 showed that the chemical mechan-ism has a significant effect on the prediction of theignition delay. Further investigations are needed toexamine the sensitivity of the ignition process on thechemical mechanism and mesh resolution.

Note that although the ignition delay time for thecases with ambient temperatures between 1000K and1100K are shorter than those for the condition at900K from homogeneous reactor calculations, theobserved ignition delay time for the three-dimensionalinjection process exhibits a monotonic behavior withrespect to the ambient temperature, demonstrating thesignificance of turbulent mixing and the shift of theignition delay with respect to the stoichiometry duringthe ignition phase.47

We complement this analysis by examining the tran-sient ignition. Following the work by Maes et al.,46 wecompute so-called Ixt-plots by radially integrated planarfields of OH and CH2O

Figure 5. Radial profiles of mean and RMS mixture fraction in comparison with Rayleigh scattering measurements44 for thenon-reacting Spray-A condition (p‘ = 60 bar, T‘ = 900 K).

Ihme et al. 63

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64 International J of Engine Research 20(1)

Ixt, i =

ð eYi(x, y, t)dy with i= fOH,CH2Og ð4Þ

Figure 10 compared the results of computed OHintensities with OH* chemiluminescence measurementsperformed at Sandia National Laboratory. Operatingconditions presented in this figure correspond to theambient temperature of 900K. Due to computationalcost of the finite-rate simulation, LES calculations wereonly conducted until 1.2ms so that direct comparisonsare restricted to the ignition and early-stage combus-tion. The apparent streaks in the radially integratedintensity plots from the simulation results are due tothe transient ignition, with a slope proportional to theadvective velocity. The illustration of intensity plots forCH2O and OH from the simulation confirms that theformation and consumption of CH2O and OH are axi-ally separated with the formaldehyde formation loca-lized to the nozzle-near region, whereas the location ofthe peak-OH formation is shifted further downstream.

The computed OH-intensity during auto-ignition andearly-stage combustion is in good agreement with experi-mentally determined OH*-chemiluminescence data.Predictions for flame penetration, represented by theupper bound of the OH profiles, are comparable to themeasurements, indicating that the LES model capturesthe initial ignition phase. Further extensions of the simu-lation time are desirable to examine the combustionrecession and burn-out phase.

Conclusion

Large eddy simulations were performed to examine theinjection and auto-ignition of a diesel-fuel injector attranscritical conditions. A diffuse-interface method wasemployed and the ignition process was described usinga finite-rate chemistry model consisting of a 33-speciesreduced mechanism. LES calculations of the ECNsingle-hole Spray A configuration39 at non-reactingand reacting conditions were performed. Comparisons

Figure 7. Comparison of CH2O and OH mass fraction fields from PLIF measurements39,45,46 (top) and LES calculations (bottom) atthe time of nominal ignition delay for the condition of 900 K ambient temperature (Spray A conditions). Spatial units in mm.

Figure 8. LES predictions of ignition-delay time for differentambient temperature conditions and comparisons withmeasurements.39

Figure 9. LES predictions of lift-off length for different ambienttemperature conditions and comparisons with measurements.39

Ihme et al. 65

with experiments showed good agreement for predic-tions of the vapor penetration lengths, and a para-metric sensitivity analysis identified variations in theliquid penetration length with respect to threshold val-ues for the mixture fraction.

Reacting flow simulations considered five ambient tem-perature conditions, ranging between 800 and 1200K. Itwas found that the simulations accurately capture experi-mentally observed dependencies of the ignition delay andlift-off with respect to temperature. The spatio-temporalevolution of intermediate species was examined by com-paring radially integrated profiles of OH and CH2O frommeasurements and simulations, showing quantitativelygood agreement for ignition onset and early-stage com-bustion transition.

These results show that this LES method in conjunc-tion with a diffuse-interface method and finite-ratechemistry is able to capture complex injection and low-temperature ignition at transcritical conditions that arerelevant for diesel-fuel injectors.

Declaration of conflicting interests

The authors declared no potential conflicts of interestwith respect to the research, authorship, and/or publi-cation of this article.

Funding

The authors disclosed receipt of the following financialsupport for the research, authorship, and/or publica-tion of this article: Financial support by ARL underaward #W911NF-16-2-0170 and NASA under award#NNX15AV04A is gratefully acknowledged. This workis supported in part by resources from a DoD HighPerformance Computing Modernization Program(HPCMP) FRONTIER Award. This research usedresources of the National Energy Research ScientificComputing Center, a DOE Office of Science User

Facility supported by the Office of Science of the U.S.Department of Energy under Contract No. DE-AC02-05CH11231.

ORCID iD

Matthias Ihme https://orcid.org/0000-0002-4158-7050

References

1. Oschwald M, Smith JJ, Branam R, Hussong J, Schik A,

Chehroudi B and Talley D. Injection of fluids into super-

critical environments. Combust Sci Technol 2006; 178(1–3):

49–100.2. Manin J, Bardi M, Pickett LM, Dahms RN and Oefelein

JC. Microscopic investigation of the atomization and mixing

processes of diesel sprays injected into high pressure and

temperature environments. Fuel 2014; 134: 531–543.3. Dahms RN and Oefelein JC. On the transition between

two-phase and single-phase interface dynamics in multi-

component fluids at supercritical pressures. Phys Fluids

2013; 25(9): 092103.4. Dahms RN. Understanding the breakdown of classic

two-phase theory and spray atomization at engine-

relevant conditions. Phys Fluids 2016; 28(4): 042108.5. Poursadegh F, Lacey JS, Brear MJ and Gordon RL.

On the fuel spray transition to dense fluid mixing at

reciprocating engine conditions. Energ Fuel 2017; 31(6):

6445–6454.6. Yang V. Modeling of supercritical vaporization, mixing,

and combustion processes in liquid-fueled propulsion

systems. P Combust Inst 2000; 28(1): 925–942.7. Oefelein JC, Lacaze G, Dahms RN, Ruiz A and Misdar-

iis A. Effects of real-fluid thermodynamics on high-

pressure fuel injection processes. SAE Int J Engines 2014;

7: 1125–1136.8. Lacaze G, Misdariis A, Ruiz A and Oefelein JC. Analysis

of high-pressure diesel fuel injection processes using LES

with real-fluid thermodynamics and transport. P Com-

bust Inst 2015; 35(2): 1603–1611.9. Knudsen E, Doran EM, Mittal V, Meng J and Spurlock

W. Compressible Eulerian needle-to-target large eddy

Figure 10. Radially integrated intensity for CH2O and OH from LES calculations and comparisons against OH* chemiluminescencemeasurements performed at Sandia National Lab. Conditions correspond to 900 K ambient temperature (Spray A).Source: Figure on the right adapted from Maes et al.46

66 International J of Engine Research 20(1)

simulations of a diesel fuel injector. Proc. Combust Inst

2017; 36(2): 2459–2466.10. Matheis J and Hickel S. Multi-component vapor-liquid

equilibrium model for LES of high-pressure fuel injection

and application to ECN Spray A. Int J Multiphas Flow

2018; 99: 294–311.11. Pei Y, Som S, Pomraning E, Senecal PK, Skeen SA,

Manin J and Pickett LM. Large eddy simulation of a

reacting spray flame with multiple realizations under

compression ignition engine conditions. Combust Flame

2015; 162(12): 4442–4455.12. Wehrfritz A, Kaario O, Vuorinen V and Somers B. Large

eddy simulation of n-dodecane spray flames using flamelet

generated manifolds. Combust Flame 2016; 167: 113–131.13. Kundu P, Ameen MM and Som S. Importance of

turbulence-chemistry interactions at low temperature

engine conditions. Combust Flame 2017; 183: 283–298.14. Dahms RN, Paczko GA, Skeen SA and Pickett LM.

Understanding the ignition mechanism of high-pressure

spray flames. Proc. Combust Inst 2017; 36(2): 2615–2623.15. Miller RS, Harstad KG and Bellan J. Direct numerical

simulations of supercritical fluid mixing layers applied to

heptane–nitrogen. J Fluid Mech 2001; 436: 1–39.16. Peng DY and Robinson DB. A new two-constant equa-

tion of state. Ind Eng Chem Res 1976; 15(1): 59–64.17. Ely JF and Hanley HJM. Prediction of transport proper-

ties. 1. Viscosity of fluids and mixtures. Ind Eng Chem

Res 1981; 20(4): 323–332.18. Ely JF and Hanley HJM. Prediction of transport proper-

ties. 2. Thermal conductivity of pure fluids and mixtures.

Ind Eng Chem Res 1983; 22(1): 90–97.19. Harstad KG, Miller RS and Bellan J. Efficient high-

pressure state equations. AIChE J 1997; 43(6): 1605–1610.20. Ma PC, Bravo L and Ihme M. Supercritical and transcri-

tical real-fluid mixing in diesel engine applications. In:

Proc. Summer Program, Center for Turbulence Research,

Stanford University, 2014, pp.99–108.21. Ma PC, Lv Y and Ihme M. An entropy-stable hybrid

scheme for simulations of transcritical real-fluid flows. J

Comput Phys 2017; 340: 330–357.22. Chung TH, Lee LL and Starling KE. Applications of

kinetic gas theories and multiparameter correlation for

prediction of dilute gas viscosity and thermal conductiv-

ity. Ind Eng Chem Res 1984; 23(1): 8–13.23. Chung TH, Ajlan M, Lee LL and Starling KE. General-

ized multiparameter correlation for nonpolar and polar

fluid transport properties. Ind Eng Chem Res 1988; 27(4):

671–679.24. Hickey JP, Ma PC, Ihme M and Thakur SS. Large eddy

simulation of shear coaxial rocket injector: real fluid

effects. In: 49th AIAA/ASME/SAE/ASEE Joint Propul-

sion Conferences, San Jose, CA, 14–17 July 2013, AIAA

paper 2013-4071. Reston, VA: AIAA.25. Takahashi S. Preparation of a generalized chart for the

diffusion coefficients of gases at high pressures. J Chem

Eng Jpn 1975; 7(6): 417–420.26. Ma PC, Wu H, Jaravel T, Bravo L and Ihme M. Large-

eddy simulations of transcritical injection and auto-

ignition using diffuse-interface method and finite-rate

chemistry. Proc. Combust Inst. Epub ahead of print 22

June 2018. DOI: 10.1016/j.proci.2018.05.063.27. Yao T, Pei Y, Zhong BJ, Som S, Lu T and Luo KH. A

compact skeletal mechanism for n-dodecane with

optimized semi-global low-temperature chemistry for die-

sel engine simulations. Fuel 2017; 191: 339–349.28. Lovas T, Nilsson D and Mauss F. Automatic reduction

procedure for chemical mechanisms applied to premixed

methane/air flames. Proc. Combust Inst 2000; 28(2): 1809–

1815.29. Pepiot-Desjardins P and Pitsch H. An efficient error-

propagation-based reduction method for large chemical

kinetic mechanisms. Combust Flame 2008; 154(1): 67–81.30. Goodwin DG, Moffat HK and Speth RL. Cantera: an

object-oriented software toolkit for chemical kinetics,

thermodynamics, and transport processes, 2015, http://

www.cantera.org31. Lu T and Law CK. Systematic approach to obtain analy-

tic solutions of quasi steady state species in reduced

mechanisms. J Phys Chem A 2006; 110(49): 13202–13208.32. Guennebaud G and Jacob B. Eigen v3, 2010, http://

eigen.tuxfamily.org33. Strang G. On the construction and comparison of differ-

ence schemes. SIAM J Numer Anal 1968; 5(3): 506–517.34. Gottlieb S, Shu CW and Tadmor E. Strong stability-

preserving high-order time discretization methods. SIAM

Rev 2001; 43(1): 89–112.35. Tranquilli P and Sandu A. Rosenbrock-Krylov methods

for large systems of differential equations. SIAM J Sci

Comput 2014; 36(3): A1313–A1338.36. Wu H, Ma PC, Jaravel T and Ihme M. Pareto-efficient

combustion modeling for improved CO-emission predic-

tion in LES of a piloted turbulent dimethyl ether jet

flame. Proc. Combust Inst. Epub ahead of print 11 Sep-

tember 2018. DOI: 10.1016/j.proci.2018.08.010.37. Vreman AW. An eddy-viscosity subgrid-scale model for

turbulent shear flow: algebraic theory and applications.

Phys Fluids 2004; 16(10): 3670–3681.38. Colin O, Ducros F, Veynante D and Poinsot T. A thick-

ened flame model for large eddy simulations of turbu-

lent premixed combustion. Phys Fluids 2000; 12(7):

1843–1863.39. Pickett LM and Bruneaux G. Engine combustion net-

work, 2011, http://www.sandia.gov/ECN40. Ihme M and See YC. Prediction of autoignition in a lifted

methane/air flame using an unsteady flamelet/progress

variable model. Combust Flame 2010; 157: 1850–1862.41. Pickett LM, Kook S and Williams TC. Visualization of

diesel spray penetration, cool-flame, ignition, high-

temperature combustion, and soot formation using high-

speed imaging. SAE Int J Engines 2009; 2(1): 439–459.42. Pickett LM, Genzale CL, Manin J and Malbec L. Mea-

surement uncertainty of liquid penetration in evaporating

diesel sprays. In: 23rd Annual Conference on Liquid Ato-

mization and Spray Systems, Ventura, CA, 15–18 May

2011.43. Manin J, Bardi M and Pickett LM. Evaluation of the

liquid length via diffused back-illumination imaging in

vaporizing diesel sprays. In: Proceedings of the 8th Inter-

national Conference on Modeling and Diagnostics for

Advanced Engine Systems (COMODIA 2012), Fukuoka,

Japan, 23–26 July 2012, pp.665–673. Tokyo, Japan: The

Japan Society of Mechanical Engineers.44. Pickett LM, Manin J, Genzale CL, Siebers DL, Musculus

MPB and Idicheria CA. Relationship between diesel fuel

spray vapor penetration/dispersion and local fuel mixture

fraction. SAE Int J Engines 2011; 4(1): 764–799.

Ihme et al. 67

45. Skeen SA, Manin J and Pickett LM. Simultaneous for-maldehyde PLIF and high-speed Schlieren imaging forignition visualization in high-pressure spray flames. Proc.Combust Inst 2015; 35(3): 3167–3174.

46. Maes N, Meijer M, Dam N, Somers B, Toda HB, Bru-neaux G, et al. Characterization of Spray A flame struc-ture for parametric variations in ECN constant-volume

vessels using chemiluminescence and laser-induced fluor-

escence. Combust Flame 2016; 174: 138–151.47. Pei Y, Hawkes ER, Bolla M, Kook S, Goldin GM, Yang

Y, et al. An analysis of the structure of an n-dodecane

spray flame using TPDF modelling. Combust Flame

2016; 168: 420–435.

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