Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

Comparison of Mixture and Multifluid Models for In-Nozzle Cavitation Prediction

[+] Author and Article Information
Michele Battistoni

Department of Industrial Engineering,
University of Perugia,
Perugia, 06125Italy
Visiting Researcher
Energy Systems Division,
Argonne National Laboratory,
Argonne, IL 60439
e-mail: michele.battistoni@unipg.it

Sibendu Som

Energy Systems Division,
Argonne National Laboratory,
Argonne, IL 60439
e-mail: ssom@anl.gov

Douglas E. Longman

Energy Systems Division,
Argonne National Laboratory,
Argonne, IL 60439
e-mail: dlongman@anl.gov

1Corresponding author.

Contributed by the Combustion and Fuels Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received December 3, 2013; final manuscript received December 16, 2013; published online February 4, 2014. Editor: David Wisler. The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States government purposes.

J. Eng. Gas Turbines Power 136(6), 061506 (Feb 04, 2014) (12 pages) Paper No: GTP-13-1436; doi: 10.1115/1.4026369 History: Received December 03, 2013; Revised December 16, 2013

Fuel injectors often feature cavitation because of large pressure gradients, which in some regions lead to extremely low pressures. The main objective of this work is to compare the prediction capabilities of two multiphase flow approaches for modeling cavitation in small nozzles, like those used in high-pressure diesel or gasoline fuel injectors. Numerical results are assessed against quantitative high resolution experimental data collected at Argonne National Laboratory using synchrotron X-ray radiography of a model nozzle. One numerical approach uses a homogeneous mixture model with the volume of fluid (VOF) method, in which phase change is modeled via the homogeneous relaxation model (HRM). The second approach is based on the multifluid nonhomogeneous model and uses the Rayleigh bubble-dynamics model to account for cavitation. Both models include three components, i.e., liquid, vapor, and air, and the flow is compressible. Quantitatively, the amount of void predicted by the multifluid model is in good agreement with measurements, while the mixture model overpredicts the values. Qualitatively, void regions look similar and compare well with the experimental measurements. Grid converged results have been achieved for the prediction of mass flow rate while grid-convergence for void fraction is still an open point. Simulation results indicate that most of the vapor is produced at the nozzle entrance. In addition, downstream along the centerline, void due to expansion of noncondensable gases has been identified. The paper also includes a discussion about the effect of turbulent pressure fluctuations on cavitation inception.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Andriotis, A., Gavaises, M., and Arcoumanis, C., 2008, “Vortex Flow and Cavitation in Diesel Injector Nozzles,” J. Fluid Mech., 610, pp. 195–215. [CrossRef]
Payri, F., Bermudez, V., Payri, R., and Salvador, F. J., 2004, “The Influence of Cavitation on the Internal Flow and the Spray Characteristics in Diesel Injection Nozzles,” Fuel, 83, pp. 419–431. [CrossRef]
Som, S., El-Hannouny, E. M., Longman, D. E., and Aggarwal, S. K., 2010, “Investigation of Nozzle Flow and Cavitation Characteristics in a Diesel Injector,” ASME J. Eng. Gas Turbines Power, 132(4), p. 042802. [CrossRef]
Som, S., Ramirez, A. I., Longman, D. E., and Aggarwal, S. K., 2011, “Effect of Nozzle Orifice Geometry on Spray, Combustion, and Emission Characteristics Under Diesel Engine Conditions,” Fuel, 90, pp. 1267–1276. [CrossRef]
Battistoni, M., and Grimaldi, C. N., 2012, “Numerical Analysis of Injector Flow and Spray Characteristics From Diesel Injectors Using Fossil and Biodiesel Fuels,” Appl. Energy, 97, pp. 656–666. [CrossRef]
Befrui, B., Corbinelli, G., Hoffmann, G., Andrews, R. J., and Sankhalpara, S. R., 2009 “Cavitation and Hydraulic Flip in the Outward-Opening GDi Injector Valve-Group,” SAE Technical Paper No. 2009-01-1483. [CrossRef]
Battistoni, M., and Grimaldi, C. N., 2010, “Analysis of Transient Cavitating Flows in Diesel Injectors Using Diesel and Biodiesel Fuels,” SAE Int. J. Fuels Lubr., 3(2), pp. 879–900. [CrossRef]
Battistoni, M., Grimaldi, C. N., and Mariani, F., 2012, “Coupled Simulation of Nozzle Flow and Spray Formation Using Diesel and Biodiesel for CI Engine Applications,” SAE Technical Paper No. 2012-01-1267. [CrossRef]
Arcoumanis, C., Gavaises, M., Flora, H., and Roth, H., 2001, “Visualisation of Cavitation in Diesel Engine Injectors,” Mec. Ind., 2, pp. 375–381.
Hayashi, T., Suzuki, M., and Ikemoto, M., 2012, “Visualization of Internal Flow and Spray Formation With Real Size Diesel Nozzle,” 12th Triennial International Conference on Liquid Atomization and Spray Systems, ICLASS 2012, Heidelberg, Germany, September 2–6, Contribution No. 1375.
Payri, R., Salvador, F. J., Gimeno, J., and Venegas, O., 2013, “Study of Cavitation Phenomenon Using Different Fuels in a Transparent Nozzle by Hydraulic Characterization and Visualization,” Exp. Therm. Fluid Sci., 44, pp. 235–244. [CrossRef]
Duke, D., Kastengren, A., Tilocco, F. Z., and Powell, C., 2013, “Synchrotron X-Ray Measurements of Cavitation,” 25th Annual Conference on Liquid Atomization and Spray Systems, ILASS-Americas, Pittsburgh, PA, May 5–8, Paper No. 8.
Bauer, D., Chaves, H., and Arcoumanis, C., 2012, “Measurements of Void Fraction Distribution in Cavitating Pipe Flow Using X-Ray CT,” Meas. Sci. Technol., 23, 055302. [CrossRef]
Kastengren, A. L., Tilocco, F. Z., Powell, C. F., Manin, J., Pickett, L. M., Payri, R., and Bazyn, T., 2012, “Engine Combustion Network (ECN): Measurements of Nozzle Geometry and Hydraulic Behavior,” Atom. Sprays, 22(12), pp. 1011–1052. [CrossRef]
Kastengren, A., Powell, C. F., Liu, Z., Fezzaa, K., and Wang, J., 2009, “High-Speed X-Ray Imaging of Diesel Injector Needle Motion,” ASME Internal Combustion Engine Division Spring Technical Conference, Milwaukee, WI, May 3–6, ASME Paper No. ICES2009-76032. [CrossRef]
Schmidt, D. P., and Corradini, M. L., 2001, “The Internal Flow of Diesel Fuel Injector Nozzles: A Review,” Int. J. Eng. Res., 2(1), pp. 1–22. [CrossRef]
Giannadakis, E., 2005, “Modelling of Cavitation in Automotive Fuel Injector Nozzles,” Ph.D. thesis, Imperial College, London.
Marcer, R., Le Cottier, P., Chaves, H., Argueyrolles, B., Habchi, C., and Barbeau, H., 2000, “A Validated Numerical Simulation of Diesel Injector Flow Using a VOF Method,” SAE Technical Paper No. 2000-01-2932. [CrossRef]
Alajbegovic, A., 1999, “Three-Dimensional Cavitation Calculations in Nozzles,” Second Annual Meeting of the Institute for Multifluid Science and Technology, Santa Barbara, CA, March 14–18, pp. 97–103.
Von Berg, E., Alajbegovic, A., Tatschl, R., Krüger, C., and Michels, U., 2001, “Multiphase Modeling of Diesel Sprays With the Eulerian/Eulerian Approach,” ILASS-Europe, Zurich, Switzerland, September 2–6.
Giannadakis, E., Gavaises, M., and Arcoumanis, C., 2008, “Modeling of Cavitation in Diesel Injector Nozzles,” J. Fluid Mech., 616, pp. 153–193. [CrossRef]
Giannadakis, E., Papoulias, D., Gavaises, M., Arcoumanis, C., Soteriou, C., and Tang, W., 2007, “Evaluation of the Predictive Capability of Diesel Nozzle Cavitation Models,” SAE Technical Paper No. 2007-01-0245. [CrossRef]
Schmidt, D. P., Gopalakrishnan, S., and Jasak, H., 2010, “Multi-Dimensional Simulation of Thermal Non-Equilibrium Channel Flow,” Int. J. Multiphase Flow, 36, pp. 284–292. [CrossRef]
Avva, R. K., Singhal, A., and Gibson, D. H., 1995, “An Enthalpy Based Model of Cavitation,” Proceedings of the ASME/JSME Fluids Engineering and Laser Anemometry Conference, Hilton Head, SC, August 13–18, Vol. 226, pp. 63–70.
Wallis, G. B., 1969, One-Dimensional Two-Phase Flow, McGraw-Hill, New York.
Winklhofer, E., Kull, E., Kelz, E., and Morozov, A., 2001, “Comprehensive Hydraulic and Flow Field Documentation in Model Throttle Experiments Under Cavitation Conditions,” ILASS-Europe, Zurich, Switzerland, September 2–6.
Richards, K. J., Senecal, P. K., and Pomraning, E., 2013, CONVERGE 2.1.0 Theory Manual, Convergent Science, Inc., Middleton, WI.
Senecal, P. K., Richards, K. J., Pomraning, E., Yang, T., Dai, M. Z., McDavid, R. M., Patterson, M. A., Hou, S., and Shethaji, T., 2007, “A New Parallel Cut-Cell Cartesian CFD Code for Rapid Grid Generation Applied to In-Cylinder Diesel Engine Simulations,” SAE Technical Paper No. 2007-01-0159. [CrossRef]
Zhao, H., Quan, S., Dai, M., Pomraning, E., Senecal, E., Xue, Q., Battistoni, M., and Som, S., 2013, “Validation of a Three-Dimensional Internal Nozzle Flow Model Including Automatic Mesh Generation and Cavitation Effects,” ASME 2013 Internal Combustion Engine Division Fall Technical Conference, Dearborn, MI, October 13–16, ASME Paper No. ICEF2013-19167.
Bilicki, Z., and Kestin, J., 1990, “Physical Aspects of the Relaxation Model in Two-Phase Flow,” Proc. R. Soc. London, Ser. A., 428, pp. 379–397. [CrossRef]
Plesset, M. S., and Prosperetti, A., 1977, “Bubble Dynamics and Cavitation,” Ann. Rev. Fluid Mech., 9, pp. 145–185. [CrossRef]
Downar-Zapolski, P., Bilicki, Z., Bolle, L., and Franco, J., 1996, “The Non-Equilibrium Relaxation Model for One-Dimensional Flashing Liquid Flow,” Int. J. Multiphase Flow, 22(3), pp. 473–483. [CrossRef]
Drew, D. A., and Passman, S. L., 1999, Theory of Multicomponent Fluids, Springer-Verlag, New York.
Kocamustafaogullari, G., and Ishii, M., 1995, “Foundation of the Interfacial Area Transport Equation and Its Closure Relations,” Int. J. Heat Mass Transfer, 38(3), pp. 481–493. [CrossRef]
Ishii, M., Sun, X., and Kim, S., 2003, “Modeling Strategy of the Source and Sink Terms in the Two-Group Interfacial Area Transport Equation,” Ann. Nucl. Energy, 30(13), pp. 1309–1331. [CrossRef]
Wang, D. M., and Greif, D., 2006, “Progress in Modeling Injector Cavitating Flows With a Multi-Fluid Method,” ASME Paper No. FEDSM2006-98501. [CrossRef]
Avl List GmbH, 2011 “AVL Fire v. 2011—Eulerian Multiphase,” Graz, Austria.
Lord Rayleigh, 1917 “VIII. On the Pressure Developed in a Liquid During the Collapse of a Spherical Cavity,” Philos. Mag., 34, pp. 94–98. [CrossRef]
Plesset, M. S., 1949 “The Dynamics of Cavitation Bubbles,” ASME J. Appl. Mech., 16, pp. 277–282.
Hinze, J. O., 1975, Turbulence, McGraw-Hill, New York.
Sato, Y., and Sekoguchi, K., 1975, “Liquid Velocity Distribution in Two-Phase Bubble Flow,” Int. J. Multiphase Flow, 2(1), pp. 79–95. [CrossRef]
Perry, R. H., and Green, D. W., 1997, Perry’s Chemicals Engineers’ Handbook, 7th ed., McGraw-Hill, New York.


Grahic Jump Location
Fig. 2

X-ray measurements of cavitation in a 500 μm polycarbonate nozzle, obtained via (a) radiographic imaging and (b) raster-scan microprobe radiography using a monochromatic synchrotron source at 8–10 keV. Images reproduced with permission from Duke et al. [12].

Grahic Jump Location
Fig. 1

Nozzle geometry tested by Duke et al. [12]

Grahic Jump Location
Fig. 4

Predicted void fraction integrated along the transverse direction using mixture and multifluid codes, compared to experimental data [12]. Dimensions are in millimeters. Flow is from bottom to top.

Grahic Jump Location
Fig. 3

Examples of grids generated in CONVERGE (a) and FIRE (b) with 150 μm base grid size and 9 μm minimum cell size

Grahic Jump Location
Fig. 6

Cell size effects on total void fraction αg along the channel

Grahic Jump Location
Fig. 5

Computed total volume fraction αg (vapor + air) along the channel axis evaluated in one cell layer thick slices, compared to the experimental data [12]

Grahic Jump Location
Fig. 7

Predicted velocity (a), pressure (b), volume fractions (c), (d), and (e), and mass fractions (f) and (g). Left column shows mixture model results, right column shows multifluid model results. Color scale range is shown above each row.

Grahic Jump Location
Fig. 9

Outlet pressure effects under equal CN value. Pressure profiles along the nozzle wall (a) and along the axis (b) are shown using the mixture model code.

Grahic Jump Location
Fig. 8

Pressure profiles along nozzle wall (a) and nozzle centerline (b)

Grahic Jump Location
Fig. 10

Outlet pressure effects under equal CN value. Predicted total volume fractions αg using the mixture model code. Dissolved air is set to the baseline value of 2 × 10−5 mass fraction (cf. Table 2).

Grahic Jump Location
Fig. 11

Effect of dissolved air mass fraction Y3 on total void fraction αg predicted along the channel using the mixture model code

Grahic Jump Location
Fig. 12

Effect of the dissolved air mass fraction Y3 on the vapor production and on the total void fraction patterns using the mixture model code. Left column shows vapor mass fraction Y2 and right column shows total void fraction αg. Color scale range is shown above each column.

Grahic Jump Location
Fig. 13

Effect of turbulent pressure fluctuations on total void fraction αg predicted along the channel using the multifluid model code

Grahic Jump Location
Fig. 14

Effect of turbulent pressure fluctuations on cavitation development using the multifluid model code



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In