ARL-TR-7873 ● NOV 2016

US Army Research Laboratory

Application of High Performance Computing 

for Simulations of N-Dodecane Jet Spray with 

Evaporation

by Louis Wonnell, Luis Bravo, and Anindya Ghoshal

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ARL-TR-7873 ● NOV 2016

US Army Research Laboratory

Application of High Performance Computing 

for Simulations of N-Dodecane Jet Spray with 

Evaporation

by Luis Bravo and Anindya Ghoshal

Vehicle Technology Directorate, ARL

Louis Wonnell

Oak Ridge Institute for Science and Education (ORISE), Oak Ridge, 

Tennessee

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4. TITLE AND SUBTITLE

Application of High Performance Computing for Simulations of N-Dodecane 

Jet Spray with Evaporation

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6. AUTHOR(S)

Louis Wonnell, Luis Bravo, and Anindya Ghoshal

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1120-1120-99

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US Army Research Laboratory

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Aberdeen Proving Ground, MD 21005-5066

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ARL-TR-7873

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

The problem of turbulent jet sprays of n-dodecane injected into a quiescent nitrogen gas chamber was investigated as a test 

case for the incorporation of a multiphysics Large-Eddy Simulation solver known as LESLIE into the US Army Research 

Laboratory’s High Performance Computing system. Preliminary simulations were performed on the Excalibur supercomputer 

to test the capability of the solver to simulate subcritical turbulent jet sprays. The solver was chosen for its ability to make use 

of alternative models that are capable of modeling multicomponent fluids such as n-dodecane. The long-term goal of this 

research is to incorporate these models into future simulations of turbulent jet sprays and develop a predictive theory for 

comparison to measurements in the laboratory of turbulent diesel sprays.

15. SUBJECT TERMS

high performance computing, fuel, spray, large eddy simulation, computational fluid dynamics

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Louis Wonnell

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Contents

List of Figures iv

List of Tables iv

Student Bio v

Acknowledgments vi

1. Summary 1

2. Introduction 1

3. Methods, Assumptions, and Procedures 3

4. Results and Discussion 6

5. Conclusion 9

6. References 10

List of Symbols, Abbreviations, and Acronyms 11

Distribution List 12
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iv

List of Figures

Fig. 1 Image of slice of mesh, showing relative uniformity of cell shapes......4

Fig. 2 Distribution of edge ratio in mesh .........................................................4

Fig. 3 Distribution of Jacobian value in mesh..................................................5

Fig. 4 Distribution of skewness in the mesh ....................................................5

Fig. 5 Distribution of stretch in the mesh.........................................................6

Fig. 6 Comparison of liquid length data between numerical and experimental 

data (IFPEN 2013). Consistent overestimation of liquid length in 

numerical results likely due to subcritical mixture assumption.............7

Fig. 7 Velocity slice comparison, T_chamb = 900 K, Left: r_parcel = 

0.5*r_initial, Right: r_parcel = 0.25*r_initial, t = 1 ms.........................7

Fig. 8 Temperature slice comparison, T_chamb = 900 K, Left: r_parcel = 

0.5*r_initial, Right: r_parcel = 0.25*r_initial, t = 1 ms.........................8

Fig. 9 Density slice comparison, T_chamb = 900 K, Left: r_parcel = 

0.5*r_initial, Right: r_parcel = 0.25*r_initial, t = 1 ms.........................8

Fig. 10 Liquid length (mm) measurements for T_chamb = 900 K for n_parc 

= 632 (r_parc = r_initial), 5 k (r_parc = 0.5*r_initial), and 32 k parcels 

(r_parc = 0.25*r_initial). Fluctuations decrease at 5 k parcels but pick 

back up with 32 k parcels.......................................................................9

List of Tables

Table 1 Initial values for fuel, chamber, and mesh. Parcel numbers were 

altered for parcel sensitivity simulations. ..............................................3
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v

Student Bio

Impact of High Performance Computing (HPC) Internship 

Program Research Experience

Prior to this summer’s internship, I held 2 Master’s degrees in Mechanical and 

Nuclear Engineering. I had focused on plasma physics at the University of 

California, San Diego, but the bulk of my research was in Computational Fluid 

Dynamics at North Carolina State University and Kansas State University. I was 

simulating turbulent incompressible and compressible flows, and the collaboration 

between my advisor and Dr Luis Bravo led to my internship at the US Army 

Research Laboratory (ARL). 

I did not know what to expect at ARL, having neither done a summer internship at 

a research laboratory, nor having any experience working with the Military. The 

staff and researchers all made me feel at home both in the lab and during social 

events. The tough stages of obtaining and processing paperwork were made easier 

by the assistance of every level of staff.

For the research, I expected to be challenged by the size and scope of a new 

industrial code, and my work with the LESLIE code clearly lived up to those 

expectations. The scope and size of modules available in LESLIE made clear what 

kinds of efforts went into typical industrial codes. Luckily, the process of installing 

and running the code went without major hurdles, due in large part to the help of 

the Georgia Institute of Technology staff.

The preliminary simulations I performed with turbulent jet sprays will likely 

continue as Dr Bravo and my advisor, Dr Chen, collaborate with our Morphing 

Continuum Theory at Kansas State University. We are looking to better predict 

turbulent physics within compressible flows, which require good predictions of the 

thermodynamics of the flow. Dr Chen gave a lecture regarding this topic at ARL 

recently; therefore, there does seem to be interest in working together in the future. 

I would be glad to work with Dr Bravo in the future, as he has been a window into 

the larger world of fluid physics research as it applies to the Military.
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vi

Acknowledgments

I would like to thank Dr Luis Bravo for being a most helpful mentor while I was at 

the US Army Research Laboratory (ARL) and for accepting me. I would like to 

thank Dr Chen for supporting my decision to apply for an internship at ARL and 

for supporting me at Kansas State University. I would like to thank Deborah 

Stowell for her help and assistance escorting us on base. Finally, I would like to 

thank my coworkers, and particularly my roommates, Kathryn Esham and Richard

Blocher. 
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1

1. Summary

The problem of turbulent jet sprays of n-dodecane injected into a quiescent nitrogen 

gas chamber was investigated as a test case for the incorporation of a multiphysics 

Large-Eddy Simulation solver known as LESLIE into the US Army Research 

Laboratory’s (ARL’s) High Performance Computing (HPC) system. Preliminary 

simulations were performed on the Excalibur supercomputer to test the capability 

of the solver to simulate subcritical turbulent jet sprays. The solver was chosen for 

its ability to make use of alternative models that are capable of modeling 

multicomponent fluids such as n-dodecane. The long-term goal of this research is 

to incorporate these models into future simulations of turbulent jet sprays and 

develop a predictive theory for comparison to measurements in the lab of turbulent 

diesel sprays.

The results obtained in this study were compared with experimental measurements 

of real turbulent jet sprays by the Institute Francais du Petrole Energies Noivelles

(IFPEN).

1 Visualizations of the contour plots in the domain were obtained using 

ParaView, showing the formation of individual eddies in temperature, density, and 

velocity contours. The lack of evaporation in the domain is demonstrated by the 

comparison with experimental data. Numerical results show a 3 mm increase in the 

drop of mean liquid length when compared with experiments obtained by IFPEN.1

2. Introduction

A critical component of maintaining performance and durability of a diesel engine 

involves the formation of a fuel-air mixture as a diesel jet spray mixes with a 

quiescent gas chamber. When the liquid fuel interacts with the quiescent gas, 

turbulent mixtures form and may even combust. Obtaining a better understanding 

of the flow characteristics of the mixture and combustion processes will help 

improve emissions and aid the military in choosing a single fuel that will reduce 

the payload for all of its diesel-powered vehicles, including unmanned aerial 

vehicles.

2

A consistent problem in conducting this research involves producing clear images 

and reliable data of the fuel-air mixture at each stage of its development at 

reasonable costs. New methods involving X-rays and ballistic imaging of the near 

field in a diesel spray and the use of medical imaging have observed the liquid core 

or near-nozzle behavior of spray-vapor mixtures.3,4 When the spray becomes 

optically dense, these X-ray techniques have been the only effective way of 

capturing 3-D, time-averaged images of the primary breakup region of optically 

dense sprays.4 Still, a full 4-D description of the optically dense regions of the 
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spray, with the spatio-temporal resolution required for a detailed analysis, has yet 

to be achieved.5

Therefore, to obtain better data for these fuel mixtures, the research community has 

looked to numerical solvers designed to incorporate turbulence models as well as 

thermodynamic equations to handle evaporation or combustion in the spray. 

Bharadwaj et al. performed Large-Eddy Simulations (LES) on nonevaporating 

sprays featuring large numbers of particles and they found good agreement with Xray experiments done by Argonne National Lab.6 The study demonstrated that LES 

could model 2-phase flows as well as track the effects of subgrid scales on turbulent 

kinetic energy. 

In the simulations of more complex fluid mixtures, however, current numerical 

results have relied on simpler thermodynamic equations of state designed for binary 

mixtures and flows where the liquid and vapor phases could easily be distinguished. 

Current problems in turbulent jet sprays involve multicomponent fluids, where the 

fuel-mixture is composed of several different compounds. Dahms and Ofelein

derived equations of state for multicomponent fluids based on Gradient Theory.7

The theory determined the significance of factors—such as surface tension, meanfree path, and the liquid-vapor interface—to the overall behavior of the mixture. 

Still, the complex model had the drawback of remaining computationally 

inefficient.7

The demand remains for a flexible multiphysics solver capable of simulating 

turbulent jet sprays composed of multicomponent fluids without incurring high 

computational costs. For this research, preliminary steps of obtaining this solver 

were performed. A multiphysics solver known as LESLIE was incorporated into 

the ARL HPC system. The solver relied on particle-based LES methods, and came 

equipped with several different turbulence and thermodynamics models. In 

particular, a real-fluids model known as the Peng-Robinson model will allow for 

more realistic modeling of these multicomponent fuels. For this research, the solver 

was tested for subcritical n-dodecane fuels injected into a quiescent chamber of 

100% nitrogen gas. Critical parameters were measured for chamber temperatures 

ranging from 700 to 1000 K and compared with experimental results. In addition, 

test simulations for numbers of particles and processors were performed to gauge 

how well the code performed when default parameters were altered. The basics of 

the LESLIE code and the test case parameters are briefly described in Section 3. 

Section 4 presents the comparison of numerical results to experimental results, and 

ParaView contour plots of density, velocity, and temperature of the jet spray. 

Section 5 summarizes the progress obtained with the code and the next steps 

involved in future simulations with LESLIE.
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3. Methods, Assumptions, and Procedures

The LESLIE solver comes equipped with finite volume and finite difference 

schemes of various orders. The simulations for this research made use of 

MacCormack’s Method, which combined the 2 approaches. Finite volume 

equations were solved to obtain solutions to the Euler equations, while the viscous 

fluxes were solved using a finite-difference approach. The Eulerian fluxes at the 

face were extrapolated from the cell-averaged values at the interior, while the 

viscous fluxes are determined from the grid. Governing equations, filtering 

processes, and turbulence model details for the LESLIE code are all specified in 

detail in the LESLIE manual.8

All of the simulations were performed in a rectangular prism of 10-mm width and 

height and a 100-mm length, with the material and mesh parameters listed in 

Table 1. A slice of the mesh is visible in Fig. 1, giving a sense of the relative 

uniformity of the mesh. Figure 2 shows a distribution of the edge ratios of the mesh. 

The edge ratios remained low for a large majority of the cells. Figures 3–5 indicate 

the Jacobian, Skew, and Stretch values for the mesh. Low orders of magnitude 

indicate relatively little alteration in the cells across the domain, with most of the 

deformation occurring near the nozzle.

Table 1 Initial values for fuel, chamber, and mesh. Parcel numbers were altered for parcel 

sensitivity simulations.

Parameter Value

v_inject 450 m/s

n_cells 4059072

n_points 4666368

n_blocks 384

Time step 4.00E-09 s

r_parcel 4.50E-05 m

n_parcels 632

r_nozzle 4.50E-05 m

m_rate .00233 kg/s

T_fuel 363 K

ρ_fuel 22.8 kg/m^3
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4

Fig. 1 Image of slice of mesh, showing relative uniformity of cell shapes

Fig. 2 Distribution of edge ratio in mesh
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5

Fig. 3 Distribution of Jacobian value in mesh

Fig. 4 Distribution of skewness in the mesh
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6

Fig. 5 Distribution of stretch in the mesh

For this simulation, the dodecane spray was assumed to be subcritical. Therefore, 

evaporation was not considered in the equations of state governing the 

thermodynamics. It was predicted, therefore, that the liquid penetration length 

would be overestimated in comparison with the experimental results. Parcel 

sensitivity studies were done with the radius of the injected parcels reduced by 2 in 

each simulation. The larger numbers of parcels would hopefully yield a higher 

resolution of the contour slice and reduce the fluctuations in the liquid length. 

4. Results and Discussion

The numerical data are summarized in Figs. 6 and 9. The predicted overestimation 

of the liquid length due to the lack of evaporation in the thermodynamic equations 

of state is clearly demonstrated in Fig. 6 for chamber temperatures of 800 to 

1000 K. The trend in evolution of the liquid length, however, is similar to the 

IFPEN results, so the effects of chamber temperature appear to be captured. Figure 

10, meanwhile, shows the liquid length behavior from the parcel sensitivity study. 

When the parcel radius was reduced to half of the original radius, the oscillations 

about the numerical mean decreased and the liquid length began to stabilize. After 

the parcel radius was reduced to a quarter of the original radius, however, the 

oscillations picked up again. A more detailed study would show whether this trend 
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7

would occur for all chamber temperatures and whether it is a sign of numerical 

instability. Figures 7–10 show a comparison of the contour slices for the half-sized 

and quarter-sized parcel simulations at 900 K at a time of 1 ms. Some of the diffuse 

spray appears to disappear for the quarter-sized parcel simulations, but the 

simulations do not appear to match each other in behavior regardless. It is possible 

that the spike in parcel number associated with the quarter-sized simulations 

allowed for spikes in the liquid ratio out by the edge of the spray. 

Fig. 6 Comparison of liquid length data between numerical and experimental data 

(IFPEN 2013). Consistent overestimation of liquid length in numerical results likely due to 

subcritical mixture assumption.

Fig. 7 Velocity slice comparison, T_chamb = 900 K, Left: r_parcel = 0.5*r_initial, Right: 

r_parcel = 0.25*r_initial, t = 1 ms
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Fig. 8 Temperature slice comparison, T_chamb = 900 K, Left: r_parcel = 0.5*r_initial, 

Right: r_parcel = 0.25*r_initial, t = 1 ms

Fig. 9 Density slice comparison, T_chamb = 900 K, Left: r_parcel = 0.5*r_initial, Right: 

r_parcel = 0.25*r_initial, t = 1 ms
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Fig. 10 Liquid length (mm) measurements for T_chamb = 900 K for n_parc = 632 (r_parc 

= r_initial), 5 k (r_parc = 0.5*r_initial), and 32 k parcels (r_parc = 0.25*r_initial). 

Fluctuations decrease at 5 k parcels but pick back up with 32 k parcels.

5. Conclusion

The preliminary results from the first few simulations of the LESLIE code do not 

yield surprising results. The trend in liquid penetration length with chamber 

temperature matches closely with experimental data, but overshoots the 

experiments likely due to the lack of evaporation. With the real fluids models 

currently built into the LESLIE code, future simulations should be able to determine 

whether other factors influence this disparity. The more interesting results come 

from the parcel sensitivity data, as the oscillations begin to emerge again with the 

quarter-sized parcels. Data for simulations with parcel sizes even smaller than 

quarter-sized parcels were not shown as these led to instabilities in the solver;

therefore, it appears that the code is highly sensitive to the number of parcels 

present. The results from the quarter-sized parcels, therefore, may deviate from 

physically reliable data. Still, preliminary simulations indicate that the LESLIE 

code is ready for future simulations to compare with more available experimental 

data as it arrives.
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6. References

1. Malbec L-M, Egúsquiza J, Bruneaux G, Meijer M. Characterization of a set of 

ECN spray A injectors: nozzle to nozzle variations and effect on spray 

characteristics. SAE International Journal of Engines no. 2013-24-0037.

2013;6:1642–1660.

2. Pagett M. Ultra endurance unmanned aerial vehicle heavy fuel engine 

program. ONR Code 352. [accessed 2016 Aug 12] http://www.onr.navy.mil/~

/media/Files/Fact-Sheets/35/UE-UAV-Heavy-Fuel-Engine.ashx.

3. Linne M, Paciaroni M, Hall T, Parker T. Ballistic imaging of the near field in 

a diesel spray. Experiments in Fluids. 2006;40(6):836–846.

4. Filippo C, Benson MJ, Sagues AL, Miller BH, Fahrig R, Eaton JK. Threedimensional mass fraction distribution of a spray measured by X-ray computed 

tomography. Journal of Engineering for Gas Turbines and Power. 136(5):

2014051508.

5. Bravo L, Ivey CB, Kim D, Bose ST. High fidelity simulation of atomization 

in diesel engine sprays. Proceedings of the Center for Turbulence Research 

(CTR) Summer Program; 2014.

6. Bharadwaj N, Rutland CJ, Chang S-M. Large eddy simulation modelling of 

spray-induced turbulence effects. International Journal of Engine Research.

2009;10(2):97–119.

7. Dahms RN, Oefelein JC. On the transition between two-phase and singlephase interface dynamics in multicomponent fluids at supercritical pressures.

Physics of Fluids. 1994-present; 2013;25(9):092103.

8. Georgia Tech Computational Combustion Lab. 2014. [accessed 2016 Aug 12].

http://www.ccl.gatech.edu/leslie.
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List of Symbols, Abbreviations, and Acronyms

3-/4-D 3-dimensional/4-dimensional

ARL US Army Research Laboratory

HPC High Performance Computing 

IFPEN Institute Francais du Petrole Energies Noivelles

K Kelvin

LES Large-Eddy Simulation
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