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Atomization and Sprays
IF: 1.737 5-Year IF: 1.518 SJR: 0.814 SNIP: 1.18 CiteScore™: 2.2

ISSN Print: 1044-5110
ISSN Online: 1936-2684

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Atomization and Sprays

DOI: 10.1615/AtomizSpr.2020032620
pages 239-266


Aqeel Ahmed
CORIA-UMR 6614—Normandie University, CNRS-University and INSA of Rouen, 76800 Saint Etienne du Rouvray, France
G. Tretola
Department of Mechanical Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, UK
Salvador Navarro-Martinez
Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, UK
K. Vogiatzaki
Advanced Engineering Centre, University of Brighton, Brighton, BN2 4AT, UK
B. Duret
CORIA-UMR 6614, Normandie University, CNRS-University and INSA of Rouen, Avenue de l'Université BP 12, Saint-Étienne-du-Rouvray 76800, France
Julien Reveillon
CORIA-UMR 6614 – Normandie Université, CNRS-Université et INSA de Rouen, Campus Universitaire du Madrillet, 76800 Saint Etienne du Rouvray, France
Francois-Xavier Demoulin
CORIA-UMR 6614 – Normandie Université, CNRS-Université et INSA de Rouen, Campus Universitaire du Madrillet, 76800 Saint Etienne du Rouvray, France


Correct prediction of the spray in automotive and aerospace engines remains a challenging task. In this work we present a numerical framework to characterize the spray, using both the large scale quantities, like mean liquid volume fractions, as well as small scale structures or liquid droplets. In the limit of high Reynolds and Weber number, the drop size is expected to be much smaller than can be resolved using first principles on a given mesh, thus a subgrid formulation is used to characterize the drop size. Using liquid gas interface surface density we have compared a standard formulation as well as a probability density function-based formulation. Using large eddy simulation we compared against the experimental database hosted by the engine combustion network for a single hole injector. Sauter mean diameter is predicted well using our formulation; at the same time use of the probability density function brings additional information regarding drop size distribution.


  1. Almeida, Y.P., Large Eddy Simulation of Supersonic Combustion Using a Probability Density Function method, PhD, Imperial College, London, UK, 2019.

  2. Andreini, A., Bianchini, C., Puggelli, S., and Demoulin, F., Development of a Turbulent Liquid Flux Model for Eulerian-Eulerian Multiphase Flow Simulations, Int. J. Multiphase Flow, vol. 81, pp. 88-103,2016.

  3. Anez, J., Ahmed, A., Hecht, N., Duret, B., Reveillon, J., and Demoulin, F., Eulerian-Lagrangian Spray Atomization Model Coupled with Interface Capturing Method for Diesel Injectors, Int. J. Multiphase Flow, vol. 113, pp. 325-342,2019.

  4. Anez, J., Canu, R., Duret, B., Reveillon, J., and Demoulin, F.X., Turbulent Statistical Transition from Euler to Lagrange Using Droplet Velocity PDF, ICLASS 2018-14th Triennial Int. Conf. on Liquid Atomization and Spray Systems, Chicago, IL, 2018.

  5. Arienti, M. and Sussman, M., A Numerical Study of the Thermal Transient in High-Pressure Diesel Injection, Int. J. Multiphase Flow, vol. 88, pp. 205-221,2017.

  6. Ashgriz, N., Handbook of Atomization and Sprays: Theory and Applications, New York, NY: Springer Science & Business Media, 2011.

  7. Battistoni, M., Magnotti, G.M., Genzale, C.L., Arienti, M., Matusik, K.E., Duke, D.J., Giraldo, J., Ilavsky, J., Kastengren, A.L., Powell, C.F., and Marti-Aldaravi, P., Experimental and Computational Investigation of Subcritical Near-Nozzle Spray Structure and Primary Atomization in the Engine Combustion Network Spray D, SAEInt. J. Fuels Lubr., vol. 11, no. 4, pp. 337-352,2018.

  8. Bravo, L., Kim, D., Ham, F., and Su, S., Computational Study of Atomization and Fuel Drop Size Distributions in High-Speed Primary Breakup, Atomization Sprays, vol. 28, no. 4, pp. 321-344,2018.

  9. Canu, R., Puggelli, S., Essadki, M., Duret, B., Menard, T., Massot, M., Reveillon, J., and Demoulin, F.X., Where Does the Droplet Size Distribution Come from?, Int. J. Multiphase Flow, vol. 107, pp. 230-245, 2018.

  10. Chesnel, J., Reveillon, J., Demoulin, F.X., and Menard, T., Subgrid Analysis of Liquid Jet Atomization, Atomization Sprays, vol. 21, no. 1, pp. 41-67,2011a.

  11. Chesnel, J., Reveillon, J., Menard, T., and Demoulin, F.X., Large Eddy Simulation of Liquid Jet Atomization, Atomization Sprays, vol. 21, no. 9, pp. 711-736,2011b.

  12. De Villiers, E., The Potential of Large Eddy Simulation for the Modeling of Wall Bounded Flows, PhD, Imperial College, London, UK, 2006.

  13. Demoulin, F.X., Reveillon, J., Duret, B., Bouali, Z., Desjonqueres, P., and Menard, T., Toward Using Direct Numerical Simulation to Improve Primary Break-Up Modeling, Atomization Sprays, vol. 23, no. 11, pp. 957-980,2013.

  14. Desantes, J.M., Salvador, F. J., Lopez, J.J., and De La Morena, J., Study of Mass and Momentum Transfer in Diesel Sprays based on X-Ray Mass Distribution Measurements and on a Theoretical Derivation, Exper. Fluids, vol. 50, no. 2, pp. 233-246,2011.

  15. Deshpande, S.S., Anumolu, L., and Trujillo, M.F., Evaluating the Performance of the Two-Phase Flow Solver InterFoam, Comput. Sci. Discovery, vol. 5, no. 1, p. 014016,2012.

  16. Dopazo, C., Probability Density Function Approach for a Turbulent Axisymmetric Heated Jet Centerline Evolution, Phys. Fluids, vol. 18, no. 4, p. 397,1975.

  17. Dopazo, C. and O'Brien, E.E., Functional Formulation of Nonisothermal Turbulent Reactive Flows, Phys. Fluids, vol. 17, no. 11, p. 1968,1974.

  18. Duret, B., Reveillon, J., Menard, T., and Demoulin, F.X., Improving Primary Atomization Modeling through DNS of Two-Phase Flows, Int. J. Multiphase Flow, vol. 55, pp. 130-137,2013.

  19. ECN, Engine Combustion Network website, accessed January 21, 2020, from https://ecn. sandia. gov/rad675/.

  20. ECN-LVF, Engine Combustion Network website-Near-Nozzle Mixture Derived from X-Ray Radiography, accessed January 21,2020 from,2020.

  21. Fedkiw, R.P., Aslam, T., Merriman, B., and Osher, S., A Non-Oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method), J. Comput. Phys, vol. 152, no. 2, pp. 457-492,1999.

  22. Gao, F. and O'Brien, E., A Large Eddy Simulation Scheme for Turbulent Reacting Flows, Phys. Fluids A, vol. 5, pp. 1282-1284,1993.

  23. Haworth, D., Progress in Probability Density Function Methods for Turbulent Reacting Flows, Prog. En-ergy Combust. Sci., vol. 36, no. 2, pp. 168-259,2010.

  24. Haworth, D.C. and Pope, S.B., A Generalized Langevin Model for Turbulent Flows, Phys. Fluids, vol. 29, no. 2, p. 387,1986.

  25. Hecht, N., Simulation aux Grandes Echelles des Ecoulements Liquide-Gaz: Application a l'Atomisation, PhD, University of Rouen, France, 2014.

  26. Hirt, C.W. and Nichols, B.D., Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comput. Phys, vol. 39, no. 1, pp. 201-225,1981.

  27. Jaberi, F.A., Colucci, P.J., James, S., Givi, P., and Pope, S.B., Filtered Mass Density Function for Large-Eddy Simulation of Turbulent Reacting Flows, J. FluidMech., vol. 401, pp. 85-121,1999.

  28. Jones, W.P. and Navarro-Martinez, S., Large Eddy Simulation of Autoignition with a Subgrid Probability Density Function Method, Combust. Flame, vol. 150, no. 3, pp. 170-187,2007.

  29. Kastengren, A., Ilavsky, J., Viera, J.P., Payri, R., Duke, D.J., Swantek, A., Tilocco, F.Z., Sovis, N., and Powell, C.F., Measurements of Droplet Size in Shear-Driven Atomization Using Ultra-Small Angle X- Ray Scattering, Int. J. Multiphase Flow, vol. 92, pp. 131-139,2017.

  30. Klimenko, A.Y. and Bilger, R.W., Conditional Moment Closure for Turbulent Combustion, Prog. Energy Combust. Sci, vol. 25, no. 6, pp. 595-687,1999.

  31. Kloeden, P.E. and Platen, E., Numerical Solution of Stochastic Differential Equations, English ed., New York, NY: Springer-Verlag, 1992.

  32. Lacaze, G., Misdariis, A., Ruiz, A., and Oefelein, J.C., Analysis of High-Pressure Diesel Fuel Injection Processes Using LES with Real-Fluid Thermodynamics and Transport, Proc. Combust. Inst., vol. 35, no. 2, pp. 1603-1611,2015.

  33. Larocque, J., Vincent, S., Lacanette, D., Lubin, P., and Caltagirone, J.P., Parametric Study of LES Subgrid Terms in a Turbulent Phase Separation Flow, Int. J. Heat Fluid Flow, vol. 31, no. 4, pp. 536-544, 2010.

  34. Lebas, R., Menard, T., Beau, P.A., Berlemont, A., and Demoulin, F.X., Numerical Simulation of Primary Break-Up and Atomization: DNS and Modelling Study, Int. J. Multiphase Flow, vol. 35, no. 3, pp. 247-260, 2009.

  35. Lindstedt, R., Louloudi, S., and Vaos, E., Joint Scalar Probability Density Function Modeling of Pollutant Formation in Piloted Turbulent Jet Diffusion Flames with Comprehensive Chemistry, Proc. Combust. Inst., vol. 28, no. 1,pp. 149-156,2000.

  36. Magnotti, G.M. and Genzale, C.L., Recent Progress in Primary Atomization Model Development for Diesel Engine Simulations, Two-Phase Flow for Automotive and Power Generation Sectors, K. Saha, A. Kumar Agarwal, K. Ghosh, and S. Som, Eds., Singapore: Springer Singapore, pp. 63-107,2019.

  37. Marle, C.M., On Macroscopic Equation Governing Multiphase Flow with Diffusion and Chemical Reactions in Porous Media, Int. J. Eng. Sci., vol. 20, no. 5, pp. 643-662,1982.

  38. Masri, A.R., Cao, R., Pope, S.B., and Goldin, G.M., PDF Calculations of Turbulent Lifted Flames of H2/N2 Fuel Issuing into a Vitiated Co-Flow, Combust. Theory Model., vol. 8, no. 1, pp. 1-22,2004.

  39. Mustata, R., Valifio, L., Jimenez, C., Jones, W., and Bondi, S., A Probability Density Function Eulerian Monte Carlo Field Method for Large Eddy Simulations: Application to a Turbulent Piloted Methane/Air Diffusion Flame (SandiaD), Combust. Flame, vol. 145,no. 1,pp. 88-104,2006.

  40. Navarro-Martinez, S., Large Eddy Simulation of Spray Atomization with a Probability Density Function Method, Int. J. Multiphase Flow, vol. 63, pp. 11-22,2014.

  41. Petrova, N., Turbulence-Chemistry Interaction Models for Numerical Simulation of Aeronautical Propulsion Systems, PhD, Ecole Polytechnique X, 2015.

  42. Pickett, L.M., Introducing the Engine Combustion Network, Multidimensional Engine Modeling User's Group, pp. 1-6, 2007.

  43. Pope, S.B., A Monte Carlo Method for the PDF Equations of Turbulent Reactive Flow, Combust. Sci. Tech., vol. 25, pp. 159-174,1981.

  44. Pope, S.B., PDF Methods for Turbulent Reactive Flows, Progress in Energy and Combustion Science, vol. 11, no. 2, pp. 119-192,1985.

  45. Roy, S., LES and DNS of Multiphase Flows in Industrial Devices: Application of High-Performance Computing, Singapore: Springer, pp. 223-247,2019.

  46. Sabel'nikov, V. and Soulard, O., Rapidly Decorrelating Velocity-Field Model as a Tool for Solving One-Point Fokker-Planck Equations for Probability Density Functions of Turbulent Reactive Scalars, Phys. Rev. E, vol. 72, p. 016301,2005.

  47. Salvador, F.J., Romero, J.V., Rosello, M.D., and Jaramillo, D., Numerical Simulation of Primary Atomization in Diesel Spray at Low Injection Pressure, J. Comput. Appl. Math., vol. 291, pp. 94-102,2016.

  48. Shinjo, J., Recent Advances in Computational Modeling of Primary Atomization of Liquid Fuel Sprays, Energies, vol. 11, no. 11, p. 2971,2018.?.

  49. Spalding, D.B., A Single Formula for the "Law of the Wall", J. Appl. Mech., vol. 28, no. 3, p. 455,1961.

  50. Sussman, M., A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow, J. Comput. Phys., vol. 114, no. 1,pp. 146-159,1994.

  51. Taylor, G.I., The Instability of Liquid Surfaces when Accelerated in a Direction Perpendicular to Their Planes. I, Proc. Royal Soc. London Ser. A. Math. Phys. Sci, vol. 201, no. 1065, pp. 192-196,1950.

  52. Valmo, L., A Field Monte Carlo Formulation for Calculating the Probability Density Function of a Single Scalar in a Turbulent Flow, Flow, Turbul. Combust., vol. 60, pp. 157-172,1998.

  53. Vallet, A. and Borghi, R., Modelisation Eulerienne de l'Atomisation d'un Jet Liquide, C. R. Acad. Sci., Paris, Ser. IIb, vol. 327, pp. 1015-1020,1999.

  54. Vallet, A., Burluka, A.A., and Borghi, R., Development of a Eulerian Model for the "Atomization" of a Liquid Jet, Atomization Sprays, vol. 11, no. 6, p. 24,2001.

  55. Villermaux, E., Fragmentation, Ann. Rev. Fluid Mech, vol. 39, no. 1, pp. 419-446,2007.

  56. Vincent, S., Larocque, J., Lacanette, D., Toutant, A., Lubin, P., and Sagaut, P., Numerical Simulation of Phase Separation and A Priori Two-Phase LES Filtering, Computers Fluids, vol. 37, no. 7, pp. 898-906, 2008.

  57. Weller, H.G., A New Approach to VOF-Based Interface Capturing Methods for Incompressible and Compressible Flow, OpenCFD Ltd., Report TR/HGW/04, 2008.

  58. Xu, J. and Pope, S., Assessment of Numerical Accuracy of PDF/Monte Carlo Methods for Turbulent Reacting Flows, J. Comput. Phys, vol. 152, no. 1, pp. 192-230,1999.

  59. Zalesak, S.T., Fully Multidimensional Flux-Corrected Transport Algorithms for Fluids, J. Comput. Phys., vol. 31, no. 3, pp. 335-362,1979.

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