Special Section Articles

A Eulerian Method for Water Droplet Impingement by Means of an Immersed Boundary Technique

[+] Author and Article Information
Francesco Capizzano

Senior Research Scientist
Fluid Dynamics Laboratory CIRA,
Italian Aerospace Research Center,
Capua (CE) 81043Italy
e-mail: f.capizzano@cira.it

Emiliano Iuliano

Senior Research Scientist
Fluid Dynamics Laboratory CIRA,
Italian Aerospace Research Center,
Capua (CE) 81043Italy
e-mail: e.iuliano@cira.it

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 23, 2013; final manuscript received October 23, 2013; published online February 28, 2014. Assoc. Editor: Elias Balaras.

J. Fluids Eng 136(4), 040906 (Feb 28, 2014) (8 pages) Paper No: FE-13-1044; doi: 10.1115/1.4025867 History: Received January 23, 2013; Revised October 23, 2013

The estimation of water droplet impingement is the first step toward a complete ice accretion assessment. Numerical approaches are usually implied to support the experimental testing and to provide fast responses when designing ice protection systems. Basically, two different numerical methodologies can be found in literature: Lagrangian and Eulerian. The present paper describes the design and development of a tool based on a Eulerian equation set solved on Cartesian meshes by using an immersed boundary (IB) technique. The tool aims at computing the evolution of a droplet cloud and the impingement characteristics onto the exposed surfaces of an aircraft. The robustness of the methodology and the accuracy of the approach are discussed. The method is applying to classical two- and three-dimensional test cases for which experimental data are available in literature. The results are compared with both experiments and body-fitted numerical solutions.

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Extice project website, June 2009, http://extice.cira.it/
Wright, W., 1995, Users Manual for the Improved NASA Lewis Ice Accretion Code LEWICE 1.6. CR 198355, NASA Glenn Research Center, Cleveland, OH.
Hedde, T., and Guffond, D., 1993, “Improvement of the ONERA 3-D Icing Code, Comparison With 3D Experimental Shapes,” AIAA Paper No. 93-0169.
Gent, R. W., 1990, “Trajice2—A Combined Water Droplet and Ice Accretion Prediction Code for Airfoils,” Royal Aerospace Establishment, Tech. Report No. TR90054, Farnborough, UK.
Mingione, G., and Brandi, V., 1998, “Ice Accretion Prediction on Multielement Airfoils,” J. Aircraft, 35(2), pp. 240–246. [CrossRef]
Crowe, C. T., 1982, “Review—Numerical Models for Dilute Gas-Particle Flows,” ASME J. Fluids Eng., 104, pp. 297–303. [CrossRef]
Durst, F., Milojevic, D., and Schonung, B., 1984, “Eulerian and Lagrangian Predictions of Particulate Two-Phase Flows: A Numerical Study,” Appl. Math. Model., 8, pp. 101–115. [CrossRef]
Di Giacinto, M., Sabetta, F., and Piva, R., 1982, “Two-Way Coupling Effects in Dilute Gas-Particle Flows,” ASME J. Fluids Eng., 104, pp. 304–312. [CrossRef]
Sabetta, F., Piva, R., and Di Giacinto, M., 1976, “Navier Stokes Flows With Suspended Particles: Mathematical Modelling and Numerical Simulation,” Theoretical and Applied Mechanics, Proceedings of the Fourteenth International Congress, Delft, The Netherlands, August 30–September 4, North-Holland Publishing Co., Amsterdam, The Netherlands, pp. 425–438.
Bourgault, Y., Habashi, W. G., Dompierre, J., and Baruzzi, G., 1999, “A Finite Element Method Study of Eulerian Droplets Impingement Models,” Int. J. Num. Meth. Fluids, 29, pp. 429–449. [CrossRef]
Morency, F., Beaugendre, H., and Habashi, W., 2003, “Fensap-Ice: A study of Effects of Ice Shapes on Droplets Impingement,” AIAA Paper No. 2003-1223.
Iuliano, E., Brandi, V., Mingione, G., de Nicola, C., and Tognaccini, R., 2006, “Water Impingement Prediction on Multi-Element Airfoils by Means of Eulerian and Lagrangian Approach With Viscous and Inviscid Air Flow,” 44th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper No. 2006-1270.
Capizzano, F., 2011, “Turbulent Wall Model for Immersed Boundary Methods,” AIAA J., 49(11), pp. 2367–2381. [CrossRef]
Fadlun, E. A., Verzicco, R., Orlandi, P., and Mohd-Yusof, J., 2000, “Combined Immersed-Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations,” J. Computat. Phys., 161, pp. 35–60. [CrossRef]
Tseng, Y. H., and Ferziger, J. H., 2003, “A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry,” J. Computat. Phys., 192, pp. 593–623. [CrossRef]
Yang, J., and Balaras, E., 2006, “An Embedded-Boundary Formulation for Large-Eddy Simulation of Turbulent Flows Interacting With Moving Boundaries,” J. Computat. Phys., 215, pp. 12–40. [CrossRef]
Iuliano, E., Mingione, G., Domenico, F. D., and de Nicola, C., 2010, “An Eulerian Approach to Three-Dimensional Droplet Impingement Simulation in Icing Environment,” AIAA Atmospheric and Space Environments Conference, Toronto, Ontario, Canada, AIAA Paper No. 2010-7677.
Crowe, C., Sommerfeld, M., and Tsuij, Y., 1998, Multiphase Flows With Droplets and Particles, CRC Press, Boca Raton, FL.
Schiller, L., and Naumann, A., 1933, “Uber die grundlegenden berechnungen bei der schwekraftaubereitung,” Zeitschrift des Vereines Deutscher Ingenieure, 77(12), pp. 318–320.
Hirsch, C., 1990, The Numerical Computation of Internal and External Flows, Vol. 1–2, John Wiley & Sons, Chichester, West Sussex, UK.
Capizzano, F., 2007, “A Compressible Flow Simulation System Based on Cartesian Grids With Anisotropic Refinements,” 45th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper No. 2007-1450.
Ham, F. E., Lien, F. S., and Strong, A., 2002, “A Cartesian Grid Method With Transient Anisotropic Adaptation,” J. Computat. Phys., 179, pp. 469–494. [CrossRef]
Mavriplis, D. J., 2003, “Revisiting the Least-Squares Procedure for Gradient Reconstruction on Unstructured Meshes,” NASA, NIA Report No. 2003-06.
Catalano, P., and Amato, M., 2003, “An Evaluation of RANS Turbulence Modeling for Aerodynamic Applications,” Aerosp. Sc. Tech., 7(7), pp. 493–590. [CrossRef]
Papadakis, M., Hung, K., Vu, G., Yeong, H. W., Bidwell, C., Breer, M., and Bencic, T., 2002, “Experimental Investigation of Water Droplet Impingement on Airfoils, Finite Wings and an S-Duct Engine Inlet,” NASA, Report No. Nasa–tm–2002-211700.
Bidwell, C., and Papadakis, M., 2005, “Collection Efficiency and Ice Accretion Characteristics of Two Full Scale and One 1/4 Scale Business Jet Horizontal Tails,” NASA, Report No. Nasa–tm–2005-213653.


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Fig. 1

Linearly exact interpolation stencil for an x-normal directed face

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Fig. 2

Immersed boundary model: direct BC imposition

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Fig. 5

NACA0012 airfoil: M∞ = 0.236, Re∞ = 6.56×106, and α = 14deg. Water collection efficiency. Present method on mesh L10 (solid) and body-conforming reference method (dashed).

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Fig. 4

NACA0012 airfoil: M∞ = 0.33, Re∞ = 5.10×106, and α = 4 deg. Present method on mesh L10 (solid) and mesh L9 (dashed-dotted), body-conforming reference method (dashed).

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Fig. 3

NACA0012 airfoil: L10 Cartesian mesh in grey scale by the particle-phase volume fraction

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Fig. 9

NACA64A008 tail: α = 6deg. Water collection efficiency. Present method (solid), body-conforming reference method (dashed), and experimental data (symbols).

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Fig. 8

NACA64A008 tail: α = 0deg. Water collection efficiency. Present method (solid) and body-conforming reference method (dashed).

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Fig. 7

NACA64A008 tail: α = 0deg. Section y/b = 0.75. Present method (solid), body-conforming reference method (dashed), and experimental data (symbols).

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Fig. 6

NACA64A008 tail: α = 0deg



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