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Energy Systems Division

Fuel Spray Modeling

Developing improved tools for diesel engine simulations that account for in-nozzle flow effects

In a diesel engine, liquid fuel is injected into the combustion chamber near the end of the compression stroke. Following injection, the fuel undergoes atomization and vaporization processes, followed by fuel-air mixing, ignition and combustion processes. It is well known that the primary breakup of the fuel influences downstream processes such as mixing, ignition combustion, etc.

Primary fuel atomization is induced by aerodynamics in the near-nozzle region, as well as cavitation and turbulence from the injector nozzle. The breakup models that are currently used in diesel engine simulations generally consider aerodynamically induced breakup using the Kelvin-Helmholtz (KH) instability model, but do not account for in-nozzle flow effects.

Argonne transportation engineers, in collaboration with the University of Illinois at Chicago, have developed and incorporated the Kelvin-Helmholtz-Aerodynamics Cavitation Turbulence (KH-ACT) model into CONVERGE code. This improved primary breakup model considers cavitation and turbulence effects along with aerodynamically induced breakup.

Primary Breakup Model

As shown in Figure 1, length and time scales are calculated:

  • Cavitation induced breakup: Based on bubble collapse and burst times
  • Turbulence induced breakup : Based on k-ε model
  • Aerodynamically induced breakup: KH and Rayleigh Taylor (RT) instability
  • Dominant ratio of length/time scale causes breakup
  • Extensive model validation against X-ray data (link to APS work) at Argonne

The spray simulations using the KH-ACT model are coupled with inner nozzle flow computations. As shown in Figure 2, this presents a novel tool that captures the influence of in-nozzle flow and fuel properties on spray, combustion and emission processes.

Spray Validation Against X-ray Data

The X-ray radiography data provides near-nozzle fuel distribution which is probably impossible to obtain with any other technique. This near-nozzle data is used for validation of the KH-ACT primary breakup model. Simulations with KH model are also presented for comparison purposes. The projected density plots from data are Gaussian in nature, both near the nozzle (0.3mm) and far afield (7mm). Simulations capture the Gaussian mass distributions from X-ray data well. Spray mass in the core (peak of the Gaussian curve)  and dispersion (tail of the plot) are accurately captured by only the KH-ACT model. The KH model under-predicts spray dispersion and consequently, overpredicts spray mass in the core (see Figure 3a and Figure 3b).

The KH-ACT primary breakup model has been extensively validated against other X-ray radiography data from Argonne’s Advance Photon Source and optical data from other national laboratories.

Collaborators in this work include University of Illinois at Chicago, Caterpillar, Inc. and Convergent Science, Inc.

Grid-Convergent Spray Modeling Approach

Historically, Lagrangian droplet models have been extensively used to simulate internal combustion engine sprays due to their relative ease of implementation and low simulation times. Although these models are widely used, many researchers have reported a strong dependency of spray characteristics on grid size. This large grid size dependency makes it difficult for modelers to know ahead of time what cell size to utilize. As a result, it is unknown if errors in engine simulation results are caused by input uncertainties, deficiencies in sub-models, or simply because the spray was under-resolved.

Argonne transportation engineers, in collaboration with Convergent Science, Inc., have developed a computational methodology that results in grid-convergent behavior. Specifically, the following items are critical to grid-convergence:

  1. Adaptive mesh resolution
  2. Fully-implicit momentum coupling
  3. Improved liquid gas coupling
  4. Increasing the number of injected spray parcels
  5. Inject parcels in a radius instead of point source

Figure 4 shows liquid penetration as a function of time for measurements and predictions using seven mesh resolutions (plotted as per the minimum grid sizes). It is clear from this comparison that coarse grids (i.e., 1.0 and 2.0 mm) significantly under-predict penetration in the early stages of injection and do not capture the correct behavior of penetration as a function of time. As the mesh is refined to 0.5 mm, the slope of the liquid penetration reduces, similar to the experimental behavior. At a cell size of 0.25 mm, reasonable grid convergence is achieved with only small changes occurring with further refinement. Finally, the penetration curves for cell sizes of 0.0625 mm and 0.03125 mm are virtually identical. In addition to grid convergence, excellent agreement with the experimental measurements is achieved for cell sizes of 0.25 mm and smaller.

Figure 5 presents the influence of grid size on the temperature, OH mass fraction, and equivalence ratio contours for the reacting spray cases at an ambient oxygen concentration of 21%. The field of view in these images is 85 mm x 25 mm in the axial and radial directions, respectively. Due to the axi-symmetric nature of the spray and combustion processes, images are presented on a cut-plane through the center of the fuel jet. The flame structure in terms of temperature, OH mass fraction and equivalence ratio is distinctly different between the 1 mm case and the other grid sizes. The flame is observed to propagate further upstream and the flame length is also longer for the 1 mm case. This represents higher reactivity which is not surprising since the ignition delay was observed to be lower for this case . In general, the flame length is seen to decrease with decreasing cell size. The contour plots of 0.25 mm and 0.125 mm cases look quite similar, further demonstrating grid convergence.


This work is supported by the U.S. Department of Energy’s Vehicle Technologies Office under Gurpreet Singh.

Selected Publications

  1. P.K. Senecal, E. Pomraning, K.J. Richards, S. Som, Grid-Convergent Spray Models for Internal combustion engine CFD simulations,” ICEF2012-92043, ASME Internal Combustion Engine Division Fall Technical Conference, Vancouver, Canada, September 2012.
  2. S. Som, D.E. Longman, G. D’Errico, T. Lucchini, Comparison and standardization of numerical approaches for the prediction of non-reacting and reacting diesel sprays,” SAE Paper No. 2012-01-1263, SAE 2012 World Congress, Detroit, April 2012.
  3. S. Som, S.K. Aggarwal, Effect of Primary breakup modeling on spray and combustion characteristics of compression ignition engines,” Combustion and Flame 157: 1179-1193, 2010.
  4. S. Som, A.I. Ramirez, S.K. Aggarwal, A.L. Kastengren, E. El-Hannouny, D.E. Longman, C.F. Powell, P.K. Senecal, Development and Validation of a Primary breakup model for Diesel Engine Applications,” 2009-01-0838, SAE 2009 World Congress, Detroit, April 2009.
  5. A.I. Ramirez, S. Som, S.K. Aggarwal, A.L. Kastengren, E. El-Hannouny, D.E. Longman, C.F. Powell, Quantitative X-Ray Measurements of High-Pressure Fuel Sprays from a Production Heavy Duty Diesel Injector,” Experiments in Fluids 47: 119-134, 2009.
  6. S. Som, S.K. Aggarwal, Assessment of Atomization models for Diesel Engine Simulations,” Atomization and Sprays 19(9): 885-903, 2009.
  7. A.I. Ramirez, S. Som, S.K. Aggarwal, A.L. Kastengren, E. El-Hannouny, D.E. Longman, C.F. Powell, Characterizing Spray Behavior Differences between Common Rail and Unit Injection Systems Using X-Ray Radiography,” 2009-01-0846, SAE 2009 World Congress, Detroit, April 2009.