At present, the study only discusses the icing law between supercooling 0—20K, which is half of the icing range of flight. To solve this problem, a diffusive interface phase field method which is suitable for large supercooling simulation of crystal is adopted, and anisotropy and thermal disturbance are considered. The characteristics of growth speed, morphology and tip radius in the supercooling range of 20—40K are quite concerned. The analysis of ice growth law shows its slope is significantly higher than the existing data of 0—20K. This is due to the increase of the tip’s curvature, which has a rapid decrease of thermal diffusion length, and promotes the thermal diffusion, and the increasing of curvature leading to the dynamic supercooling. Both of them lead to the increase of ice growth rate with supercooling. Using the ice growth law obtained to analyze the runback icing in aircraft, it is found that the ice runback distance is sensitive to the liquid water content (LWC) when the supercooling is larger than 20K and the LWC is large. Under this condition, the abnormal icing characteristics of fast growth and severe runback may occur simultaneously.
［1］Council Aviation Safety. GE791 Occurrence investigation report, in-flight icing encounter and crash into the sea transasia airways flight 791, ATR72-200, B-22708, 17 kilometers southwest of Makung City, Penghu Islands, Taiwan, China, December 21, 2002［R］. ASC-AOR-05-04-001, Taipei: Council Aviation Safety.
［2］AKHURST R J. Aircraft accident report: In-flight icing encounter and loss of control, simmons airlines, DBA American Eagle Flight 4184, Avions de Transport Regional (Atr) Model 72-212, N401AM, Roselawn, Indiana, October 31, 1994［J］. Journal of Clinical Investigation, 2002, 109(12): 1533-1536.
［3］ZHANG C, LIU H. Effect of drop size on the impact thermodynamics for supercooled large droplet in aircraft icing［J］. Physics of Fluids, 2016, 28(6): 062107.
［4］KONG W L, LIU H. Development and theoretical analysis of an aircraft supercooled icing model［J］. Journal of Aircraft, 2014, 51(3): 975-986.
［5］BLACKMORE R Z, MAKKONEN L, LOZOWSKI E P. A new model of spongy icing from first principles［J］. Journal of Geophysical Research Atmospheres, 2002, 107(D21): 4563.
［6］LOZOWSKI E, OLESKIW M, BLACKMORE R, et al. Spongy icing revisited: Measurements of ice accretion liquid fraction in two icing tunnels［C］∥43rd AIAA Aerospace Sciences Meeting and Exhibit. Reno: AIAA, 2005: 658.
［7］KONG W L, LIU H. A theory on the icing evolution of supercooled water near solid substrate［J］. International Journal of Heat & Mass Transfer, 2015, 91: 1217-1236.
［8］TIRMIZI S H, GILL W N. Effect of natural convection on growth velocity and morphology of dendritic ice crystals［J］. Journal of Crystal Growth, 1987, 85(3): 488-502.
［9］SHIBKOV A A, GOLOVIN Y I, ZHELTOV M A, et al. Morphology diagram of nonequilibrium patterns of ice crystals growing in supercooled water［J］. Physica A Statistical Mechanics & Its Applications, 2003, 319(81): 65-79.
［10］SCHREMB M, TROPEA C. Solidification of supercooled water in the vicinity of a solid wall［J］. Physical Review E, 2016, 94(5): 052804.
［11］IVANTSOV G P. Temperature field around a spheroidal, cylindrical and acicular crystal growing in a supercooled melt［C］∥Dynamics of Curved Fronts. New York: Academic Press, Inc, 1988: 243-245.
［12］GLICKSMAN M E, SCHAEFER R J, AYERS J D. Dendritic growth-A test of theory［J］. Metallurgical Transactions A, 1976, 7(11): 1747-1759.
［13］KARMA A, RAPPEL W J. Quantitative phase-field modeling of dendritic growth in two and three dimensions［J］. Physical Review E Statistical Physics Plasmas Fluids & Related Interdisciplinary Topics, 1998, 57(4): 4323-4349.
［14］KARMA A, RAPPEL W J. Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics［J］. Physical Review E Statistical Physics Plasmas Fluids & Related Interdisciplinary Topics, 1996, 53(4): R3017.
［15］OHNO M. Quantitative phase-field modeling of nonisothermal solidification in dilute multicomponent alloys with arbitrary diffusivities［J］. Physical Review E, 2012, 86(1): 051603.
［16］XING H, DUAN P P, DONG X L, et al. Phase-field modeling of growth pattern selections in three-dimensional channels［J］. Philosophical Magazine, 2015, 95(11): 1184-1200.
［17］XING H, ZHANG L M, SONG K K, et al. Effect of interface anisotropy on growth direction of tilted dendritic arrays in directional solidification of alloys: Insights from phase-field simulations［J］. International Journal of Heat & Mass Transfer, 2017, 104: 607-614.
［18］XING H, DONG X L, WU H J, et al. Degenerate seaweed to tilted dendrite transition and their growth dynamics in directional solidification of non-axially orientated crystals: A phase-field study［EB/OL］. (2016-06-23) ［2017-08-17］. http:∥www.nature.com/scientificreports.
［19］DEMANGE G, ZAPOLSKY H, PATTE R, et al. A phase field model for snow crystal growth in three dimensions［J］. NPJ Computational Materials, 2017(3): 1.
［20］NAKAYA U, ISONOSUKE. Preliminary experiments on the artificial production of snow crystals［J］. Journal of the Faculty of Science, 1938, 2(1): 1-11.
［21］KARMA A, RAPPEL W J. Phase-field model of dendritic sidebranching with thermal noise［J］. Physical Review E Statistical Physics Plasmas Fluids & Related Interdisciplinary Topics, 1999, 60(4): 3614-3625.
［22］LIBBRECHT K G. Physical dynamics of ice crystal growth［J］. Annual Review of Materials Research, 2017, 47: 271-295.
［23］SHIBKOV A A, ZHELTOV M A, KOROLEV A A, et al. Crossover from diffusion-limited to kinetics-limited growth of ice crystals［J］. Journal of Crystal Growth, 2005, 285(1): 215-227.
［24］吕勇军. 声悬浮和自由落体条件下深过冷与快速凝固研究［D］. 西安: 西北工业大学材料学院, 2002.
L Yongjun. Rapid solidification of undercooled water and alloy during acoustic levitation and free fall［D］. Xi’an: School of Materials Science and Engineering, Northwestern Polytechnical University, 2002.
［25］段培培, 邢辉, 陈志, 等. 镁基合金自由枝晶生长的相场模拟研究［J］. 物理学报, 2015, 64(6): 60201-1-60201-9.
DUAN Peipei, XING Hui, CHEN Zhi, et al. Phase-field modeling of free dendritic growth of magnesium based alloy［J］. Acta Physica Sinica, 2015, 64(6): 60201-1-60201-9.
［26］LANGER J S, MLLER-KRUMBHAAR J. Stability effects in dendritic crystal growth［J］. Journal of Crystal Growth, 1977, 42: 11-14.
［27］HILLIG W B, TURNBULL D. Theory of crystal growth in undercooled pure liquids［J］. Journal of Chemical Physics, 1956, 24(4): 914.
［28］GLICKSMAN M E, LUPULESCU A O. Dendritic crystal growth in pure materials［J］. Journal of Crystal Growth, 2004, 264(4): 541-549.
［29］LIPTON J, GLICKSMAN M E, KURZ W. Dendritic growth into undercooled alloy metals［J］. Materials Science & Engineering, 1984, 65(1): 57-63.
［30］BEAUGENDRE H, MORENCY F, HABASHI W G. FENSAP-ICE’s three-dimensional in-flight ice accretion module: ICE3D［J］. Journal of Aircraft, 2003, 40(2): 239-247.
［31］MYERS T G, CHARPIN J P F. A mathematical model for atmospheric ice accretion and water flow on a cold surface［J］. International Journal of Heat & Mass Transfer, 2004, 47(25): 5483-5500.
