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Journal of Engineering for Gas Turbines and Power | Volume 130 | Issue 3 | Research Paper
Research Papers: Internal Combustion Engines

Reduction of Numerical Parameter Dependencies in Diesel Spray Models

[+] Author and Article Information
Neerav Abani, Achuth Munnannur, Rolf D. Reitz

Engine Research Center, University of Wisconsin-Madison, Madison, WI 53706

J. Eng. Gas Turbines Power 130(3), 032809 (Apr 02, 2008) (9 pages) doi:10.1115/1.2830867 History: Received October 30, 2007; Revised October 31, 2007; Published April 02, 2008
Article
References
Figures
Tables
Citing Articles

Numerical grid and time-step dependencies of discrete droplet Lagrangian spray models are identified. The two main sources of grid dependency are due to errors in predicting the droplet-gas relative velocity and errors in describing droplet-droplet collision and coalescence processes. For reducing grid dependency due to the relative velocity effects, a gas-jet theory is proposed and applied to model diesel sprays. For the time-step dependency, it is identified that the collision submodel results in drop size variation in the standard spray model. A proposed spray model based on the gas-jet theory is found to improve the time-step independency also along with the mesh independency. The use of both Eulerian (collision mesh) and Lagrangian (radius of influence) collision models along with the gas-jet theory is found to provide mesh-independent results.
Copyright © 2008 by American Society of Mechanical Engineers
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References

1
Amsden, A. A., 1997, “KIVA-3V: A Block Structured KIVA Program for Engines With Vertical or Canted Valves,” Los Alamos National Laboratory, Technical report No. LA-13313-MS.
2
O’Rourke, P. J., and Bracco, F. V., 1980, “Modeling Drop Interactions in Thick Sprays and a Comparison With Experiments,” "Proceedings of the IMechE Conference on Stratified Charge Automotive Engines", pp. 101–116.
3
O’Rourke, P. J., 1981, “Collective Drop Effects on Vaporizing Liquid Sprays,” Ph.D. Thesis, Princeton University.
4
Beale, J. C., and Reitz, R. D., 1999, Atomization Sprays, 9 , pp. 623–650.
5
Patterson, M. A., and Reitz, R. D., 1998, SAE Technical Paper No. 980131.
6
Abraham, J., 1997, “What Is Adequate Resolution in the Numerical Computation of Transient Jets,” SAE Paper No. 970051.
7
Post, S., Iyer, V., and Abraham, J., 2000, “A Study of the Near-Field Entrainment in Gas Jets and Sprays Under Diesel Conditions,” ASME J. Fluids Eng.  [CrossRef], 122 , pp. 385–395.
8
Aneja, R., and Abraham, J., 1998, “How Far Does the Liquid Penetrate in Diesel Engine: Computed Results Vs. Measurements?” Combust. Sci. Technol., 138 (1–6), pp. 233–255.
9
Schmidt, D. P., and Rutland, C. J., 2000, “A New Droplet Collision Algorithm,” J. Comput. Phys.  [CrossRef], 164 , pp. 62–80.
10
Schmidt, D. P., and Rutland, C. J., 2004, “Reducing Grid Dependency in Droplet Collision Modeling,” ASME J. Eng. Gas Turbines Power  [CrossRef], 126 , pp. 227–233.
11
Nordin, N., 2000, “Complex Chemistry Modeling of Diesel Spray Combustion,” Ph.D. thesis, Chalmers University of Technology.
12
Beard, P., Duclos, J. M., Habchi, C., Bruneaux, G., Mokaddem, K., and Baritaud, T., 2000, “Extension Application to High-Pressure Evaporating Diesel Sprays,” SAE Technical Paper No. 2000-01-1893.
13
Lippert, A. M., Chang, S., Are, S., and Schmidt, D. P., 2005, “Mesh Independence and Adaptive Mech Refinement for Advanced Engine Spray Simulations,” SAE Technical Paper No. 2005-01-0207.
14
Abraham, J., 1996, “Entrainment Characteristics of Transient Jets,” Numer. Heat Transfer, Part A  [CrossRef], 30 , pp. 347–364.
15
Schlichting, H., 1976, "Boundary Layer Theory", McGraw-Hill, New York.
16
Allen, M. R., and Tildesley, T. J., 1987, "Computer Simulation of Liquids", Oxford University Press, New York, p. 147.
17
Sundaram, S., and Collins, L. R., 1996, “Numerical Consideration in Simulating a Turbulent Suspension of Finite Volume Particles,” J. Comput. Phys.  [CrossRef], 124 , pp. 337–350.
18
Naber, J. D., and Siebers, D. L., 1996, “Effects of Gas Density and Vaporization on Penetration and Dispersion of Diesel Sprays,” SAE Technical Paper No. 960034.

Figures

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+Schematic of the new diesel spray model
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Schematic of the new diesel spray model
Figure 1

Schematic of the new diesel spray model

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+Standard KIVA: spray structure at t=3.0ms. ρamb=60.6kg∕m3.
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Standard KIVA: spray structure at t=3.0ms. ρamb=60.6kg∕m3.
Figure 2

Standard KIVA: spray structure at t=3.0ms. ρamb=60.6kg∕m3.

Grahic Jump Location
+Standard KIVA: spray-tip penetration. Experimental data from Ref. 18, ρamb=60.6kg∕m3.
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Standard KIVA: spray-tip penetration. Experimental data from Ref. 18, ρamb=60.6kg∕m3.
Figure 3

Standard KIVA: spray-tip penetration. Experimental data from Ref. 18, ρamb=60.6kg∕m3.

Grahic Jump Location
+Standard KIVA: overall SMD. ρamb=60.6kg∕m3.
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Standard KIVA: overall SMD. ρamb=60.6kg∕m3.
Figure 4

Standard KIVA: overall SMD. ρamb=60.6kg∕m3.

Grahic Jump Location
+Standard KIVA: total number of parcels. ρamb=60.6kg∕m3.
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Standard KIVA: total number of parcels. ρamb=60.6kg∕m3.
Figure 5

Standard KIVA: total number of parcels. ρamb=60.6kg∕m3.

Grahic Jump Location
+Coarse mesh illustration
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Coarse mesh illustration
Figure 6

Coarse mesh illustration

Grahic Jump Location
+Collision mesh sensitivity with improved spray model. CFD mesh size of 4×4mm2 and ρamb=60.6kg∕m3.
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Collision mesh sensitivity with improved spray model. CFD mesh size of 4×4mm2 and ρamb=60.6kg∕m3.
Figure 7

Collision mesh sensitivity with improved spray model. CFD mesh size of 4×4mm2 and ρamb=60.6kg∕m3.

Grahic Jump Location
+Total number of coalescences in the domain with increase in collision mesh size
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Total number of coalescences in the domain with increase in collision mesh size
Figure 8

Total number of coalescences in the domain with increase in collision mesh size

Grahic Jump Location
+Standard KIVA with collision mesh: spray-tip penetration. Experimental data from Ref. 18, ρamb=60.6kg∕m3.
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Standard KIVA with collision mesh: spray-tip penetration. Experimental data from Ref. 18, ρamb=60.6kg∕m3.
Figure 9

Standard KIVA with collision mesh: spray-tip penetration. Experimental data from Ref. 18, ρamb=60.6kg∕m3.

Grahic Jump Location
+Standard KIVA with collision mesh: overall SMD. ρamb=60.6kg∕m3.
View Large  |  Save Figure  |  Download Slide (.ppt)
Standard KIVA with collision mesh: overall SMD. ρamb=60.6kg∕m3.
Figure 10

Standard KIVA with collision mesh: overall SMD. ρamb=60.6kg∕m3.

Grahic Jump Location
+Standard KIVA: overall SMD with different time steps (4×4mm2 mesh)
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Standard KIVA: overall SMD with different time steps (4×4mm2 mesh)
Figure 19

Standard KIVA: overall SMD with different time steps (4×4mm2 mesh)

Grahic Jump Location
+Standard KIVA: total number of parcels with different time steps (4×42mm mesh)
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Standard KIVA: total number of parcels with different time steps (4×42mm mesh)
Figure 20

Standard KIVA: total number of parcels with different time steps (4×42mm mesh)

Grahic Jump Location
+Improved spray model: spray-tip penetration with different time steps (4×42mm mesh)
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Improved spray model: spray-tip penetration with different time steps (4×42mm mesh)
Figure 21

Improved spray model: spray-tip penetration with different time steps (4×42mm mesh)

Grahic Jump Location
+Improved spray model: overall SMD with different time steps (4×42mm mesh)
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Improved spray model: overall SMD with different time steps (4×42mm mesh)
Figure 22

Improved spray model: overall SMD with different time steps (4×42mm mesh)

Grahic Jump Location
+Improved spray model: total number of parcels with different time steps (4×4mm2 mesh)
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Improved spray model: total number of parcels with different time steps (4×4mm2 mesh)
Figure 23

Improved spray model: total number of parcels with different time steps (4×4mm2 mesh)

Grahic Jump Location
+Standard KIVA+collision mesh: total number of parcels. ρamb=60.6kg∕m3.
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Standard KIVA+collision mesh: total number of parcels. ρamb=60.6kg∕m3.
Figure 11

Standard KIVA+collision mesh: total number of parcels. ρamb=60.6kg∕m3.

Grahic Jump Location
+Improved model: spray structure at t=3.0ms
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Improved model: spray structure at t=3.0ms
Figure 12

Improved model: spray structure at t=3.0ms

Grahic Jump Location
+Improved model with different meshes: spray-tip penetration. Experimental data from Ref. 18, ρamb=60.6kg∕m3.
View Large  |  Save Figure  |  Download Slide (.ppt)
Improved model with different meshes: spray-tip penetration. Experimental data from Ref. 18, ρamb=60.6kg∕m3.
Figure 13

Improved model with different meshes: spray-tip penetration. Experimental data from Ref. 18, ρamb=60.6kg∕m3.

Grahic Jump Location
+Improved model with different meshes: overall SMD. ρamb=60.6kg∕m3.
View Large  |  Save Figure  |  Download Slide (.ppt)
Improved model with different meshes: overall SMD. ρamb=60.6kg∕m3.
Figure 14

Improved model with different meshes: overall SMD. ρamb=60.6kg∕m3.

Grahic Jump Location
+Improved model with different meshes: total number of parcels. ρamb=60.6kg∕m3.
View Large  |  Save Figure  |  Download Slide (.ppt)
Improved model with different meshes: total number of parcels. ρamb=60.6kg∕m3.
Figure 15

Improved model with different meshes: total number of parcels. ρamb=60.6kg∕m3.

Grahic Jump Location
+Improved model (ROI collision model) with different meshes: spray-tip penetration. ρamb=60.6kg∕m3.
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Improved model (ROI collision model) with different meshes: spray-tip penetration. ρamb=60.6kg∕m3.
Figure 16

Improved model (ROI collision model) with different meshes: spray-tip penetration. ρamb=60.6kg∕m3.

Grahic Jump Location
+Improved model with ROI collision model with different meshes: overall SMD. ρamb=60.6kg∕m3.
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Improved model with ROI collision model with different meshes: overall SMD. ρamb=60.6kg∕m3.
Figure 17

Improved model with ROI collision model with different meshes: overall SMD. ρamb=60.6kg∕m3.

Grahic Jump Location
+Standard KIVA: spray-tip penetration with different time steps (4×4mm2 mesh)
View Large  |  Save Figure  |  Download Slide (.ppt)
Standard KIVA: spray-tip penetration with different time steps (4×4mm2 mesh)
Figure 18

Standard KIVA: spray-tip penetration with different time steps (4×4mm2 mesh)

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