三维结冰表面上的水膜流动和结冰增长是结冰计算模型应考虑的核心内容，其中广泛应用的是Myers模型。Myers模型考虑了空气剪切力和空气压力对结冰表面水膜流动的影响，以及冰层、水膜和空气之间的导热与对流传热对结冰速率的影响。本文在使用Myers模型进行结冰预测时，发现Myers模型对霜冰转化为明冰的判断标准存在缺陷，会在结冰极限处产生不合理的冰角。因此对Myers模型的结冰类型判断标准进行了修改，对机翼表面的结冰过程进行了更加准确的模拟，并应用了有效的离散算法计算水膜流动和结冰增长过程。对比了二维NACA0012翼型的单步法、多步法计算结果和实验结果。明冰结冰温度较低时，本文计算结果与实验结果吻合很好，明冰结冰温度较高时，本文对上冰角的计算与实验结果有一定差距。本文提供了三维GLC-305后掠翼的结冰计算结果和实验结果的对比，冰角厚度的计算结果略小于实验结果，但整体趋势一致。
Calculating the flow of thin water film and the accretion of ice layer is important for predicting of aircraft icing. The Myers model takes into consideration the water flow driven by air shear and pressure, and the ice accretion rate influenced by heat conduction and convection among ice layer, water film and ambient air. When the Myers model is used to predict aircraft icing, undesired ice horn will occur as the model's criterion for determining the ice type is simple. To solve this problem, the criterion for ice type determination is revised, and an effective numerical method is presented to solve the equation for water flow and ice accretion. The single-step and multi-step computational results of the two-dimensional NACA0012 airfoil are presented and compared with the experimental results. For glaze ice accretion at lower temperature, the computational results agree well with the experimental results. For glaze ice accretion at higher temperature, the computational results of the upper ice horn are slightly different from the experimental results. The computational results of ice accretion on the three-dimensional GLC-305 airfoil are also presented and compared with the experimental results. The computational results of the ice horn thickness is slightly less than the experimental results, but the computational results of the overall ice accretion tendency agree well the experimental results.
[1] MINGIONE G, BRANDI V, ESPOSITO B. Ice accretion prediction on multi-element airfoils:AIAA-1997-0177[R]. Reston, VA:AIAA, 1997.
[2] POURYOUSSEFI S G, MIRZAEI M, NAZEMI M, et al. Experimental study of ice accretion effects on aerodynamic performance of an NACA23012 airfoil[J]. Chinese Journal of Aeronautics, 2016, 29(3):585-595.
[3] BROEREN A P. Aerodynamic simulation of runback ice accretion[J]. Journal of Aircraft, 2010, 47(3):924-939.
[4] MESSINGER B L. Equilibrium temperature of an unheated icing surface as a function of air speed[J]. Journal of the Aeronautical Sciences, 1953, 20:29-42.
[5] GHENAI C, KULKARNI S, LIN C X. Validation of LEWICE 2.2 icing software code:Comparison with LEWICE 2.0 and experimental data:AIAA-2005-1249[R]. Reston, VA:AIAA, 2005.
[6] HEDDE T, GUFFOND D. ONERA three-dimensional icing model[J]. AIAA Journal, 1995, 33(6):1038-1045.
[7] 易贤, 桂业伟, 朱国林. 飞机三维结冰模型及其数值求解方法[J]. 航空学报, 2010, 31(11):2152-2158. YI X, GUI Y W, ZHU G L. Numerical method of a three-dimensional ice accretion model of aircraft[J]. Acta Aeronautica et Astronautica Sinca, 2010, 31(11):2152-2158(in Chinese).
[8] 申晓斌, 林桂平, 卜雪琴, 等. 发动机进气道短舱前缘结冰三维模拟研究[J]. 航空学报, 2013, 34(3):517-524. SHEN X B, LIN G P, BU X Q, et al. Three-dimensional simulation research on ice shape at engine inlet nacelle front[J]. Acta Aeronautica et Astronautica Sinca, 2013, 34(3):517-524(in Chinese).
[9] CHEN X, ZHAO Q J. Numerical simulations for ice accretion on rotors using new three-dimensional icing model[J]. Journal of Aircraft, 2017, 54(4):1428-1442.
[10] BOURGAULT Y, BEAUGENDRE H, HABASHI W G. Development of a shallow-water icing model in FENSAP-ICE:AIAA-1999-0246[R]. Reston, VA:AIAA, 1999.
[11] MYERS T G, THOMPSON C P. Modeling the flow of water on aircraft in icing conditions[J]. AIAA Journal, 1998, 36(6):1010-1013.
[12] MYERS T G. Extension to the Messinger model for aircraft icing[J]. AIAA Journal, 2001, 39(2):211-218.
[13] MYERS T G, HAMMOND D W. Ice and water film growth from incoming supercooled droplets[J]. International Journal of Heat and Mass Transfer, 1999, 42:2233-2242.
[14] CAO Y H, HOU S. Extension to the Myers model for calculation of three-dimensional glaze icing[J]. Journal of Aircraft, 2016, 53(1):106-116.
[15] CAO Y H, HUANG J S. New method for direct numerical simulation of three-dimensional ice accretion[J]. Journal of Aircraft, 2015, 52(2):650-659.
[16] DANIEL M, SILVA D. Quasi-3D multi-step ice accretion simulation:AIAA-2012-0313[R]. Reston, VA:AIAA, 2012.
[17] VERDIN P G, THOMPSON C P. Automatic multi-stepping approach for ice predictions[R]. State College, PSU:The Pennsylvania State University, 2005.
[18] MYERS T G, CHARPIN J P F, CHAPMAN S J. The flow and solidification of a thin fluid film on an arbitrary three-dimensional surface[J]. Physics of Fluids, 2002, 14(8):2788-2803.
[19] MYERS T G, CHARPIN J P F, THOMPSON C P. Slowly accreting glaze ice due to supercooled water impacting on a cold surface[J]. Physics of Fluids, 2002, 14(1):240-256.
[20] WRIGHT W B, RUTKOWSKI A. Validation results for LEWICE 2.0:NASA CR-1999-208690[R]. Washington, D.C.:NASA, 1999.
[21] PAPADAKIS M, YEONG H W. Aerodynamic performance of a swept wing with ice accretions:AIAA-2003-0731[R]. Reston, VA:AIAA, 2003.
CJA