超音速燃燒衝壓引擎為新一代的推進系統，其特色為氣流在燃燒室內維持於超音速狀態，與一般衝壓引擎相比，燃燒室內部的流場現象更為複雜，且液態碳氫燃料注入燃燒室後，需要在極短時間內經過破碎、霧化、蒸發、與空氣混和等過程，才能燃燒以產生所需之推力。在計算流體力學中，噴霧破碎模式即用於模擬此一連續過程中液態燃料的破碎行為和噴霧現象。由於此過程的發生時間非常短暫，在超音速燃燒衝壓引擎的運作上卻極為關鍵，因此一適用的噴霧破碎模式可以準確地預測噴霧破碎現象，並有助於取得更精確的流場資訊，對於燃燒效率的提升以及燃燒室的設計都有重要的影響。近年以液態燃料注入超音速流場的數值模擬研究中，幾乎都是使用K-H/R-T破碎模式對噴霧現象進行模擬。因此，本研究首先分析計算流體力學軟體ANSYS FLUENT中的K-H/R-T破碎模式的計算原理和模式參數；並使用K-H/R-T破碎模式模擬液態煤油注入超音速流場的流場現象，研究其噴霧表現和液氣交互作用機制；接著對其五個模式參數進行參數分析，探討各模式參數對於噴霧之穿透高度和消散長度的影響。結果顯示，K-H與R-T兩破碎模式對於液滴顆粒大小和噴霧高度造成明顯影響的區域略有不同。K-H模式的兩個模式參數— B_0 和 B_1 —的影響範圍為完整噴霧區域；R-T模式的兩個模式參數— C_RT 和 C_τ —的影響範圍為噴霧中後段區域。與穿透高度相比，各模式參數對於消散長度的影響效果較為明顯，參數值的範圍也較廣。在五個模式參數中， B_0 和 B_1 對液滴顆粒大小和噴霧消散長度的影響最為顯著。最後，本研究將數值模擬結果與實驗量測結果作比較，提出一組與實驗結果接近的K-H/R-T破碎模式參數。

A numerical simulation of liquid kerosene injection into a supersonic combustor flow field by the computational fluid dynamics software ANSYS FLUENT was performed. The research on the effects of five model constants in K-H/R-T breakup model on the simulation results of spray, the penetration height and the dissipation distance, was presented. The turbulence effects were accounted for by the SST k- turbulence model. The five model constants in K-H/R-T breakup model are B_0, B_1, C_RT, C_τ, and C_L. B_0 and B_1 are the breakup radius constant and the breakup time constant of the K-H model respectively. C_RT and C_τ are the breakup radius constant and the breakup time constant of the R-T model, and C_L is Levich constant, which is the constant of proportionality of the liquid core length. The results showed that the influences of all model constants on the penetration height are limited if the constant values exceed certain ranges while the effects of each constant on the dissipation distance are more evident, and the ranges of the constant values are more extensive. The analysis also revealed that the constants of the K-H model, B_0 and B_1, could affect the entire spray area, however, the constants of the R-T model, C_RT and C_τ, would mainly dominate the rear part of spray. Furthermore, the droplet size and the dissipation distance show greater sensitivity to B_0 and B_1 among the five model constants. Comparison with experimental data is made in term of the penetration height and the dissipation distance with the aim of obtaining a set of appropriate model constant values. The simulation results of the set of model constants showed good agreement with the experimental results.

【1】 Manna, P., Behera, R., and Chakraborty, D., 2008,“Liquid-Fueled Strut-Based Scramjet Combustor Design: a Computational Fluid Dynamics Approach,”Journal of Propulsion and Power, Vol.24, No.2, pp.274-281.
【2】 Lewis, M. J., 2001,“Significance of Fuel Selection for Hypersonic Vehicle Range,”Journal of Propulsion and Power, Vol.17, No.6, pp.1214-1221.
【3】 Tetlow, M. R., and Doolan, C. J., 2007,“Comparison of Hydrogen and Hydrocarbon-Fueled Scramjet Engine for Orbital Insertion,”Journal of Spacecraft and Rockets, Vol.44, No.2, pp.365-373.
【4】 Powell, O. A., Edwards, J. T., Norris, R. B., Numbers, K. E., and Pearce, J. A., 2001,“Development of Hydrocarbon-Fueled Scramjet Engines: The Hypersonic Technology Program,”Journal of Propulsion and Power, Vol.17, No.6, pp.1170-1176.
【5】 Yue, L. J., and Yu, G., 2003,“Studies on Spray Characteristics of Barbotaged Atomizer,”Journal of propulsion technology, Vol.24, No.4, pp.348-352.
【6】 Yu, G., Li, J. G., Yang, S. R., Yue, L. J., and Zhang, X. Y., 2002,“Investigation of Liquid Hydrocarbon Combustion in Supersonic Flow Using Effervescent Atomization,”38th AIAA Joint Propulsion Conference and Exhibit, AIAA2002-4279.
 
【7】 Lin, K. C., Kirkendall, K. A., Kennedy, P. J., and Jackson, T. A., 1999,“Spray Structures of Aerated Liquid Fuel Jets in Supersonic Crossflows,”35th AIAA Joint Propulsion Conference and Exhibit, AIAA1999-2374.
【8】 Im, K. S., Lin, K. C., and Lai, M. C., 2005,“Spray Atomization of Liquid Jet in Supersonic Cross Flows,”43rd AIAA Aerospace Sciences Meeting and Exhibit, AIAA2005-732.
【9】 劉靜, 徐旭, 2010,“超音速橫向氣流中燃料霧化的數值模擬,”北京航空航天大學學報, Vol.36, No.10.
【10】 Yang, D. C., Zhu, W. B., Chen, H., Guo, J. X., and Liu, J. W., 2014,“Model the Secondary Breakup of a Liquid Jet in Supersonic Cross Flows,”Journal of Harbin Engineering University, Vol.35, No.1, pp.62-68.
【11】 Liu, O. Z., Cai, Y. H., Hu, Y. L., Liu, J. H., and Ling, W. H., 2007,“The Turbulence Models for Numerical Analysis of Liquid Kerosene Supersonic Combustion,”Acta Aerodynamica Sinica, Vol.25, pp.362-367.
【12】 Chenault, C. F., and Beran, P. S., 1998,“k- and Reynolds Stress Turbulence Model Comparisons for Two-Dimensional Injection Flows,”AIAA Journal, Vol. 36, pp.1401-1412.
【13】 Menter, F. R., 1994,“Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,”AIAA Journal, Vol.32, pp.1598-1605.
【14】 宋緯倫, 2010,“不同紊流模式對超音速流場數值模擬結果之影響,”國立成功大學航空太空工程學系碩士論文.
【15】 Aso, S., Okuyama, S., Kawai, M., and Ando, Y., 1991,“Experimental Study on Mixing Phenomena in Supersonic Flows with Slot Injection,”29th Aerospace Sciences Meeting, AIAA1991-16.
【16】 楊凡毅, 2016,“液態噴注於超音速流場之細部流場數值模擬分析,”國立成功大學航空太空工程學系碩士論文.
【17】 郭建嘉, 2017,“凹槽機構對液態燃料噴注之超音速燃燒流場影響之數值模擬分析,”國立成功大學航空太空工程學系碩士論文.
【18】 陳家禾, 2018, “凹槽機構之幾何參數對於超音速流場影響之數值模擬分析,” 國立成功大學航空太空工程學系碩士論文.
【19】 Balasubramanyam, M.S., Chen, C.P., 2008,“Modeling liquid jet breakup in high speed cross-flow with finite-conductivity evaporation,” International Journal of Heat and Mass Transfer, Vol. 51, pp.3896-3905
【20】 Im, K. S., Lin, K. C., Lai, M. C., and Chon, M. S., 2011,“Breakup Modeling of a Liquid Jet in Cross Flow,” International Journal of Automotive Technology, Vol. 12, pp.489-496.
【21】 Reinecke, W. G. and Waldman, G. D., 1970,“A Study of Drop Breakup Behind Strong Shocks with Applications to Flight,”AVCO Report AVSD-0110-70-RR.
【22】 Pilch, M. and Erdman, C. A., 1987,“Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop, ” Int. J. Multiphase Flow, Vol.13 , pp.741-757.
【23】 Zhu, L., Qi, Y.Y., Liu, W.L., Xu. B.J., Ge. J.R., Xuan, X.C., Jen, T.C., 2016, “Numerical investigation of scale effect of various injection diameters on interaction in cold kerosene-fueled supersonic flow,” Acta Astronautica, Vol. 129, pp.111-120
【24】 Li, P., Wang, Z., Sun, M., Wang, H., 2017,“Numerical simulation of the gas-liquid interaction of a liquid jet in supersonic crossflow,” Acta Astronautica, Vol. 134, pp.333-344
【25】 Liu, W.L., Zhu, L., Qi, Y.Y., Ge, J.R., Luo, F., Zou, H.R., Wei, M., Jen, T.C. 2017, “Effects of injection pressure variation on mixing in a cold supersonic combustor with kerosene fuel,” Acta Astronautica, Vol.139, pp. 67-76
【26】 Zhu, L., Luo, F. , Qi, Y.Y. , Wei, M. , Ge, J.R. , Liu, W.L. , Li, G.L., Jen, T.C., 2018, “Effects of spray angle variation on mixing in a cold supersonic combustor with kerosene fuel,” Acta Astronautica, Vol.144, pp.1-11
【27】 Fan, X.F., Wang, J.F., Zhao, F.M., Li, J.W. and Yang, T.P., 2018, “Eulerian-Lagrangian method for liquid jet atomization in supersonic crossflow using statistical injection model,” Advances in Mechanical Engineering, Vol. 10, No. 2, pp.1-13
【28】 沈雅蓁, 2015, “側向雙垂直噴注於超音速空氣流場之霧化混合探討,” 成功大學航空太空工程學系碩士論文.
【29】 何仲軒, 2017, “側向雙垂直噴注於超音速空氣流場之交互作用探討,” 成功大學航空太空工程學系碩士論文.
【30】 朱冠霖, 2015,“液態噴流注入超音速流場之數值模擬分析,” 成功大學航空太空工程學系碩士論文.
【31】 ANSYS FLUENT, 2013,“Ansys Fluent 15.0 Theory Guide,”ANSYS Inc.
【32】 Ranz, W. E., and Marshall, W. R., Jr., 1952,“Evaporation from Drops, Part II,”Chemical Engineering Progress Magazine, Vol.48, pp.173-180.