To understand the phase transition effects of the droplet in an icing wind tunnel, a method based on the Euler theory is developed to simulate mass and heat transfer of coupling of momentum of gas-droplet mixed flows. Using this method, the droplet phase transition effects on the process of the droplet heat transfer are explored for the main test section configuration of a 3 m×2 m icing wind tunnel. Parametric studies are then conducted to evaluate the supercooling state of the droplet in the test section. Results show that the droplets experience firstly evaporation and then condensation in the configuration. The evaporation effects enhance the trend of decrease in the droplet temperature in the quasi-1D stage, and then make the droplet temperature close to the wet-bulb temperature. However, the condensation effects inhibit the trend of decrease in the droplet temperature in the 3D contraction stage, so that the temperature difference between droplet and gas in the test section is increased. As a result, the droplet phase transition has an effect on the supercooling state of the droplet in the test section. In addition, the increased initial relative humidity and test section velocity reduce the evaporation effects, but enhance the condensation effects. Therefore, the effects of relative humidity and test section velocity on the supercooling state of the droplet are enhanced. On the contrary, effects of both evaporation and condensation are reduced, as the initial sizes of the droplet increases. Therefore, the effect of the droplet size on the droplet supercooling is reduced. In typical test conditions, small droplets (the diameter is bigger than 40 μm and smaller than 100 μm) in the center of the test section deviate from the supercooling state (the temperature difference between droplet and gas is higher than 3℃) at the high velocity (the velocity is higher than 164 m/s).
[1] 杜雁霞, 李明, 桂业伟, 等. 飞机结冰热力学行为研究综述[J]. 航空学报, 2017, 38(2):520706. DU Y X,LI M, GUI Y W, et al. Review of thermodynamic behaviors in aircraft icing process[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(2):520706(in Chinese).
[2] 桂业伟, 周志宏, 李颖晖, 等. 关于飞机结冰的多重安全边界问题[J]. 航空学报, 2017, 38(2):520723. GUI Y W, ZHOU Z H, LI Y H, et al. Multiple safety boundaries protection on aircraft icing[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(2):520723(in Chinese).
[3] 易贤, 王斌, 李伟斌, 等. 飞机结冰冰形测量方法研究进展[J]. 航空学报, 2017, 38(2):520700. YI X, WANG B, LI W B, et al. Research progress on ice shape measurement approaches for aircraft icing[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(2):520700(in Chinese).
[4] RAGNI A, ESPOSITO B, MARRAZZO M, et al. Calibration of the CIRA IWT in the high speed configuration[C]//43th AIAA Aerospace Science Meeting and Exhibit. Reston, VA:AIAA, 2005.
[5] STEEN L E, IDE R F, van ZANTE J F, et al. NASA Glenn icing research tunnel:2014 and 2015 cloud calibration procedures and results:NASA/TM-2015-218758[R]. Washington, D. C.:NASA, 2015.
[6] WILLBANKS C E, SCHULZT R J. Analytical study of icing simulation for turbine engines in altitude test cells[J]. Journal of Aircraft, 1975, 12(12):960-967.
[7] MILLER D R, ADDY H E, IDE R F. A study of large droplet ice accretions in the nasa glenn irt at near-freezing conditions:NASA TM-1996-107142-REV1[R]. Washington, D. C.:NASA, 1996.
[8] BELLUCCI M, ESPOSITO B M, MARRAZZO M, et al. Calibration of the CIRA IWT in the low speed configuration[C]//45th AIAA Aerospace Science Meeting and Exhibit. Reston, VA:AIAA,2007.
[9] 易贤, 马洪林, 王开春, 等. 结冰风洞液滴运动及传质传热特性分析[J]. 四川大学学报, 2012, 44(2):132-135. YI X, MA H L, WANG K C, et al. Analysis of water droplet movement and heat/mass transfer in an icing wind tunnel[J]. Journal of Sichuan University, 2012, 44(2):132-135(in Chinese).
[10] 郭向东,王梓旭,李明,等.结冰风洞中液滴过冷特性数值研究[J].航空学报, 2018, 39(1):121254. GUO X D, WANG Z X, LI M, et al. Numerical study of droplet supercooling in an icing wind tunnel[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(1):121254(in Chinese).
[11] HILL P G. Condensation of water vapor during supersonic expansion in nozzles[J]. Journal of Fluid Mechanics, 1966, 25(3):593-620.
[12] CHENG W, LUO X S, van DONGEN M E H. On condensation-induced waves[J]. Journal of Fluid Mechanics, 2010, 651(1):145-164.
[13] 郭向东, 黄生洪, 吴颖川, 等. 氢燃料燃烧加热风洞中水蒸气相变效应的数值研究[J]. 推进技术, 2017, 38(4):932-941. GUO X D, HUANG S H, WU Y C, et al. Numerical evaluation of water vapor phase transition effects in a hydrogen-fueled combustion-heated wind tunnel[J]. Journal of Propulsion Technology, 2017, 38(4):932-941(in Chinese).
[14] CAO Y, LUO X S. Numerical study on Homogeneous condensation in a vortex[J]. Procedia Engineering, 2015, 126:607-611.
[15] LUO X S, WANG G, OLIVIER H. Parametric investigation of particle acceleration in high enthalpy conical nozzle flows for coating applications[J]. Shock Waves, 2008, 17(5):351-362.
[16] KERSEY J, LOTH E, LANKFORD D. Effects of Evaporating Droplets on Shock Waves[J]. AIAA Journal, 2010, 48(9):1975-1986.
[17] RUSSO E, KUERTEN J G M, van der Geld C W M, et al. Water droplet condensation and evaporation in turbulent channel flow[J]. Journal of Fluid Mechanics, 2014, 749:666-700.
[18] SAITO T. Numerical analysis of dusty-gas flows[J]. Journal of Computational Physics, 2002, 176(1):129-144.
[19] FUJITA A, KUROSE R, KOMORI S. Experimental study on effect of relative humidity on heat transfer of an evaporating water droplet in air flow[J]. International Journal of Heat and Mass Transfer, 2010, 36(3):244-247.
[20] MILLER R S, HARSTAD K, BELLAN J. Evaluation of equilibrium and non-equilibrium evaporation models for many-droplet gas-liquid flow simulations[J]. International Journal of Multiphase Flow, 1998, 24(6):1025-1055.
[21] HINDMARSH J P, RUSSEL A B, CHEN X D. Experimental and numerical analysis of the temperature transition of a suspended freezing water droplet[J]. International Journal of Heat and Mass Transfer, 2003, 46(7):1199-1213.
[22] COBER S, BERNSTEIN B, JECK R, et al. Data and analysis for the development of an engineering standard for supercooled large drop conditions:DOT/FAA/AR-09/10[R]. Washington, D. C.:FAA, 2009.
[23] KUROSE R, FUJITA A, KOMORI S. Effect of relative humidity on heat transfer across the surface of an evaporating water droplet in air flow[J]. Journal of Fluid Mechanics, 2009, 624:57-67.
[24] LUXFORD G. Experimental and modelling investigation of the deformation, drag and break-up of drizzle droplets subjected to strong aerodynamic forces in relation to SLD aircraft icing[D]. Bedfordshire:Cranfield University, 2005:5-7.