zbMATH — the first resource for mathematics

Quasi-molecular modeling of a single supercooled large droplet impact. (English) Zbl 1459.82307
Summary: A mesoscale model for droplet dynamics based on a quasi-molecular approach is proposed. It considers the interaction between quasi-molecules within a single liquid droplet, each quasi-molecule representing an agglomeration of a large number of actual water molecules. The goal is to improve the understanding of the dynamics of large droplet collisions over dry or wet surfaces at velocities typical of aeronautical applications. This detailed analysis will eventually be used to refine the macroscopic Eulerian description of the water impingement process by providing numerical correlations for splashing and bouncing phenomena relevant for in-flight icing applications. Based on the Equipartition Theorem, approaches for extracting macroscopic quantities such as temperature and transport coefficients from the quasi-molecular method are discussed. A proper choice of the free parameters of the model that leads to accurate values of the macroscopic properties is also addressed.
82D15 Statistical mechanics of liquids
Full Text: DOI
[1] Cooper, W. A.; Marwitz, J. D., Winter storms over the San Juan Mountains. Part III: seeding potential, J. Appl. Meteorol., 19, 942-949 (1980)
[2] Politovich, M. K., Aircraft icing caused by large supercooled droplets, J. Appl. Meteorol., 28, 856-868 (1989)
[3] Rioboo, R.; Tropea, C.; Marengo, M., Outcomes from a drop impact on solid surfaces, Atomization Sprays, 11, 155-165 (2001)
[5] Hirt, C. W.; Nichols, B. D., Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys., 39, 201-225 (1981) · Zbl 0462.76020
[6] Graham, P. J.; Farhangi, M. M.; Dolatabadi, A., Dynamics of droplet coalescence in response to increasing hydrophobicity, Phys. Fluids (1994-present), 24, Article 112105 pp. (2012)
[7] Osher, S.; Sethian, J. A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79, 12-49 (1988) · Zbl 0659.65132
[8] Eckhardt, W.; Heinecke, A., SuperMUC boosts the largest molecular dynamics simulation by 4X in Number of Particles, Innovatives Supercomput. Deutschland, 11, 19-21 (2013)
[9] Fang, H.; Bao, K.; Wei, J.; Zhang, H.; Wu, E.; Zheng, L., Simulations of droplet spreading and solidification using an improved SPH model, Numer. Heat Transfer, Part A: Appl., 55, 124-143 (2009)
[10] Tofighi, N.; Yildiz, M., Numerical simulation of single droplet dynamics in three-phase flows using ISPH, Comput. Math. Appl., 66, 525-536 (2013) · Zbl 1360.76216
[11] Jiang, T.; Ouyang, J.; Li, X.; Ren, J.; Wang, X., Numerical study of a single drop impact onto a liquid film up to the consequent formation of a crown, J. Appl. Mech. Tech. Phys., 54, 720-728 (2013) · Zbl 1297.76175
[12] Melean, Y.; Sigalotti, L. D.G.; Hasmy, A., On the SPH tensile instability in forming viscous liquid drops, Comput. Phys. Commun, 157, 191-200 (2004)
[13] Liu, M.; Liu, G., Smoothed particle hydrodynamics (SPH): an overview and recent developments, Arch. Comput. Methods Eng., 17, 25-76 (2010) · Zbl 1348.76117
[14] Greenspan, D., Quasimolecular Modelling (1991), World Scientific Pub Co Inc. · Zbl 0754.65006
[15] Abdollahi, V.; Habashi, W. G.; Fossati, M.; Baruzzi, G. S., Quasi-molecular modeling of supercooled large droplets dynamics for in-flight icing simulations, (5th AIAA Atmospheric and Space Environments Conference (2013))
[16] Greenspan, D., Computer studies in particle modelling of fluid phenomena, Math. Modell., 6, 273-294 (1985) · Zbl 0578.76005
[17] Greenspan, D., Quasi-molecular, particle modeling of crack generation and fracture, Comput. Struct., 22, 1055-1061 (1986) · Zbl 0577.73096
[18] Greenspan, D., Quasimolecular simulation of large liquid drops, J. Phys. D: Appl. Phys, 22, 1415 (1989)
[19] Greenspan, D., Supercomputer simulation of liquid drop formation on a solid surface, Int. J. Numer. Methods Fluids, 13, 895-906 (1991) · Zbl 0729.76616
[20] Korlie, M. S., Particle modeling of liquid drop formation on a solid surface in 3-D, Comput. Math. Appl., 33, 97-114 (1997) · Zbl 0900.76471
[21] Kulsri, S.; Jaroensutasinee, M.; Jaroensutasinee, K., Simulation of Water Droplet on Horizontally Smooth and Rough Surfaces Using Quasi-Molecular Modelling, 20 (2006), World Academy of Science, Engineering and Technology
[22] Sikdar, S., A Quasimolecular Simulation of Liquid Droplet Collision and Thin Film Dynamics (1994), Washington State University
[23] Sikdar, S.; Chung, J., A quasimolecular approach for discrete study of droplet collision, Int. J. Comput. Fluid Dyn., 8, 189-200 (1997) · Zbl 0895.76072
[24] Swope, W. C.; Andersen, H. C.; Berens, P. H.; Wilson, K. R., A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: application to small water clusters, J. Chem. Phys., 76, 637-649 (1982)
[25] Woodcock, L.-V., Isothermal molecular dynamics calculations for liquid salts, Chem. Phys. Lett, 10, 257-261 (1971)
[26] Helfand, E., Transport coefficients from dissipation in a canonical ensemble, Phys. Rev., 119, 1 (1960) · Zbl 0089.45103
[27] Verlet, L., Computer “experiments” on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules, Phys. Rev., 159, 98 (1967)
[29] Audet, C.; Dennis Jr., J. E., Mesh adaptive direct search algorithms for constrained optimization, SIAM J. Optim., 17, 188-217 (2006) · Zbl 1112.90078
[30] Brambilla, P.; Guardone, A., Automatic tracking of corona propagation in three-dimensional simulations of non-normal drop impact on a liquid film, Computing, 95, 415-424 (2013) · Zbl 1310.76013
[31] Guevara-Carrion, G.; Nieto-Draghi, C.; Vrabec, J.; Hasse, H., Prediction of transport properties by molecular simulation: methanol and ethanol and their mixture, J. Phys. Chem. B, 112, 16664-16674 (2008)
[32] Edelsbrunner, H.; Mücke, E. P., Three-dimensional alpha shapes, ACM Trans. Graphics (TOG), 13, 43-72 (1994) · Zbl 0806.68107
[34] Cossali, G.; Marengo, M.; Coghe, A.; Zhdanov, S., The role of time in single drop splash on thin film, Exp. Fluids, 36, 888-900 (2004)
[35] Xu, L.; Zhang, W. W.; Nagel, S. R., Drop splashing on a dry smooth surface, Phys. Rev. Lett, 94, Article 184505 pp. (2005)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.