超音速燃燒衝壓引擎已經發展了數十年，使用之燃料由氣態燃料轉為液態燃料，而液態燃料之使用增加了流場之複雜性，因須考慮液態燃料之霧化效果、蒸發過程以及燃燒延遲之影響。而為了延長駐焰時間以及增加燃燒效率，在燃燒室添加了支架以及凹槽等駐焰機構，此舉更增加了實驗量測之困難，因此本文將使用CFD計算流體力學軟體ANSYS FLUENT進行具凹槽以及支架之超音速燃燒流場數值模擬計算，紊流模式採用SST k-ω，使用層流有限速率燃燒模式。針對具凹槽以及支架外型之燃燒室進行模擬分析，首先進行不同L/D值之凹槽進行分析，發現在L/D=2.6、3.6以及4.6比較後，值4.6所呈現之燃燒效率最好，顯示出不同L/D值之凹槽會呈現不同燃燒效率。其次進行不同燃料流率之分析，在流率4.6g/s、6.2g/s以及8g/s比較後，其流率4.6g/s所呈現之燃燒效率最好，因在其有限之燃燒室長度內，所能燃燒之燃料流率有限，且較大之燃料流率也會因導致較長燃燒點火延遲，影響燃燒效率。最後更改其注射位置，其結果與原始結果相差不多，推測由於燃料流率較小，所導致燃燒效率呈現相當一致，未來可考慮注入不同燃料流率以觀察其流場變化。

This study uses the CFD software ANSYS FLUENT to simulate supersonic combustion flow with flame-holding mechanism, such as cavity and strut. The SST k-ω turbulence model has been adopted, and the laminar finite-rate reaction model has been employed to analyze supersonic reaction flow. Results show that among all analyzed values of L/D (i.e., 2.6, 3.6, and 4.6), L/D=4.6 has the best combustion efficiency. Different L/D values are shown to induce different combustion efficiencies. This study also analyzes different fuel flow rates. After comparing different flow rates (i.e., 4.6, 6.2, and 8 g/s), we have determined that the flow rate 4.6 g/s presents the best combustion efficiency. The results are close to the original results even after changing the injection position. Given that the fuel flow rate is the same, the combustion efficiency is consistent. Future studies may consider different fuel flow rates to observe the effect of flow field on combustion efficiency.

[1] Lewis, M. J., “Significance of Fuel Selection for Hypersonic Vehicle Range, ”Journal of Propulsion and Power, Vol. 17, No. 6, 2001.
[2] Waltrup, P. J., “Upper Bounds on the Flight Speed of Hydrocarbon-Fuels Scramjet Power-Vehicles,” Journal of Propulsion and Power, Vol. 17, No. 6, 2001.
[3] Tetlow, M. R. and Doolan, C. J.,“Comparison of Hydrogen and Hydocarbon-Fueled Scramjet Engines for Orbital Insertion,” Journal of Spacrcraft and Rockets, Vol. 44, No. 2, 2007.
[4] Powell, A., Edwards, J. T. , Norris, R.B., Numbers, K.E., and Pearce, J.A., “Development of Hydrocarbon-Fueled Scramjet Engines: The Hypersonic Technology (HyTech) Program,” Journal of Propulsion and Power, Vol. 17,No.6, pp.1170-1176, 2001.
[5] Ali, M., Fujiwara, T., Leblanc, J. E., “Influence of Main Flow Inlet Configuration on Mixing and Flameholding in Transverse Injection into Supersonic Airstream,” International Journal of Engineering Science, Vol. 38, 1161-1180, 2000.
[6] Ali, M., Sadrul Islam, A. K. M. and Ahmed, S., “Mixing and Flameholding with Air Inlet Configuration in Scramjet Combustor,” International Journal of Heat and Mass Transfer, Vol. 31, No. 8, 1187-1198, 2004.
[7] Ali, M. and Sadrul Islam, A. K. M., “Study on Main Flow and Fuel Injector Configurations for Scramjet Applications,” International Journal of Heat and Mass Transfer Vol. 49, 3634-3644, 2006.
[8] Orth, R. C. and Funk, J. A., “An Experimental and Comparative Study of Jet Penetration in Supersonic Flow,” J. SPACECRAFT, Vol. 4, No. 9, 1967.
[9] Yu, G., Li, J. G., Zhao, J. R., Yue, L. J., Chang, X. Y. and Sung, C. J., “An Experimental Study of Kerosene Combustion in a Supersonic Model Combustor Using Effervescent Atomization,” Proceedings of the Combustion Institute, Vol. 30, 2859-2866, 2005.
[10] Yu, G., Li, J. G., Yang, S. R., Yue, L. J., Zhang, X. Y., Huang, Y. and Sung, C. J., “Investigation of Liquid Hydrocarbon Combustion in Supersonic Flow Using Effervescent Atomization,”AIAA Paper 2002-4279.
[11] Qian, L. J.,Lin, J. Z. and Xiong, H. B., “Simulation of Droplet-gas Flow in the Effervescent Atomization Spray with an Impinging Plate,” Chinese Journal of Chemical Engineering, Vol. 17, No. 1, 8-19, 2009.
[12] Lin, K. C., Kirkendall, K. A., Kennedy, P. J. and Jackson, T. A., “Spray Structure of Aerated Liquid Fuel Jets in Supersonic Crossflows,” AIAA Paper 1999-2374.
[13] Yue, L. J. and Yu, G., “Studies on Spray Characteristics of Barbotaged Atomizer,” Journal of Propulsion Technology, Vol. 24, No. 4, 2003.
[14] Wang, L., Zhang, C. L., Wei, B. X. and Xu, X., “Experimental Investigation of Kerosene Supersonic Combustion Test Using Aerated Liquid Injectors,” Journal of Aerospace Power, Vol. 24, No. 2, 2009.
[15] Im, K. S., Lin, K. C. and Lai, M. C., “Spray Atomization of Liquid Jet in Supersonic Cross Flows,” AIAA Paper 2005- 732.
[16] Wang, J. F., Liu, C. and Wu, Y. Z., “Numerical Simulation of Spray Atomization in Supersonic Flows,” Modern Physics Letters B, Vol. 24, No. 13, 1299-1302, 2010.
[17] Liu, J. and Xu, X.“Numerical simulation of atomization of liquid jet in supersonic crossflow,” Journal of Beijing University of Aeronautics and Astronautics, Vol. 36, No. 10, 2010.
[18] Yue, L. J. and Yu, G., “Numerical Simulation of Kerosene Spray in Supersonic Cross Flow,” Journal of Propulsion Technology, Vol, 25, No. 1, 2004.
[19] Wu, P. K., Kirkendall, K. A., Fuller, R. P. and Nejad, A., “Breakup Processes of Liquid Jets in Subsonic Crossflows,” Journal of Propulsion and Power, Vol. 13, No. 1, 1997.
[20] Fan, X. J., Yu, G., Li, J. G. Zhang, X. Y. and Sung, C. J., “Investigation of Vaporized Kerosene Injection and Combustion in a Supersonic Model Combustor,” Journal of Propulsion and Power, Vol. 22, No. 1, 2006.
[21] Tam, C. J., Susan, C. S. Lin, K. C. Gruber, M. and Jackson, T., “Gaseous and Liquid Injection into High-Speed Crossflows,” 43rd AIAA Aerospace Sciences Meeting and Exhibit, 2005-0301.
[22] Pandey, K. M., and Sivasakthivel T., “Recent Advances in Scramjet Fuel Injection - A Review,” International Journal of Chemical Engineering and Applications, Vol. 1, No. 4, December 2010.
[23] Ben-Yakar, A. , Hanson, R. K., “Experimental Investigation of Flame-Holding Capability of a Transverse Hydrogen Jet in Supersonic Cross-Flow,” Proceedings of the Twenty-Seventh International Symposium on Combustion, Combustion Inst. , Pittsburgh PA, pp. 2173–2180, 1998.
[24] Chenault, C., F. and Beran, P. S., “K-ε and Reynolds Stress Turbulence Model Comparisons for Two-Dimensional Injection Flows,” AIAA Journal, Vol. 36, No. 8, 1988.
[25] Chenault, C., F., Beran, P. S. and Bowersox, R. D. W., “Numerical Investigation of Supersonic Injection Using a Reynolds-Stress Turbulence Model,” AIAA Journal, Vol. 37, No. 10, 1999.
[26] Menter, F. R., “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA Journal, Vol. 32, No. 8, 1598-1605, 1994.
[27] Liu, O. Z., Cai, Y. H., Hu, Y. L., Liu, J. H. and Ling, W. H., “The Turbulence Models for Numerical Analysis of Liquid Kerosene Supersonic Combustion,” Acta Aerodynamica Sinica, Vol. 25, No. 3, 362-367, 2007.
[28] Li, J. G., Yu, G., Zhang, Y., Li, Y. and Qiang, D. X., “Experimental Studies on Self-Ignition of Hydrogen/Air Supersonic Combustion,” Journal of Propulsion and Power, Vol. 13, No. 4, 1997.
[29] Liu, O. Z., Hu, Y. Z., Cai, Y. H., Liu, J. H. and Ling, W. H., “Overview of Flameholders of Cavities in Supersonic Combustion,” Journal of Propulsion Technology, Vol. 24, No. 3, 2003.
[30] Ben-Yakar, A. and Hanson, R. K., “Cavity Flame-Holders for Ignition and Flame Stabilization in Scramjets: An Overview,” Journal of Propulsion and Power, Vol. 17, No. 4, 2001.
[31] Gruber, M. R., Bauerle, R. A., Mathur, T. and Hsu, K. Y., “Fundamental Studies of Cavity-Based Flameholder Concepts for Supersonic Combustors,” Journal of Propulsion and Power, Vol. 17, No.1, 2001.
[32] Wang, H. B., Wang, Z. G., Sun, M. B. and Qin, N., “Combustion Characteristics in Supersonic Combustion with Hydrogen Injection Upstream of Cavity Flameholder,” Proceedings of the Combustion Institute, Vol. 34, 2073-2082, 2012.
[33] Rasmussen, C. C., Driscoll, J. F., Hsu, K. Y. Donbar, J. M., Gruber, M. R. and Carter, C. C., “Stability Limits of Cavity-Stabilized Flames in Supersonic Flow,” Proceedings of the Combustion Institute, Vol. 30, 2825-2833, 2005.
[34] Neely, A. J., Riley, C., Boyce, R. R., Mudford, N. R., Houwing, A. F. P. and Gruber, M. R., “Hydrocarbon and Hydrogen-Fuelled Scramjet Cavity Flameholder Performance at High Flight Mach Numbers,”12th AIAA International Space Planes and Hypersonic Systems and Technologies, 2003-6989.
[35] 鄭瑞圻, “使用液態碳氫燃料之超音速燃燒流場模擬分析,” 成功大學航空太空工程學系碩士論文, 2013.
[36] Yu, G., Li, J. G., Chang, X. Y., Chen, L. H. and Sung, C. J., “Fuel Injection and Flame Stabilization in a Liquid-Kerosene-Fueled Supersonic Combustor,” Journal of Propulsion and Power, Vol. 19, No. 5, 2003.
[37] Chakraborty, D., “Numerical Simulation of Liquid Fueled SCRAMJET Combustor Flow Fields,” International Journal of Hypersonics, Vol. 1, No. 1 13-29, 2010.
[38] Tomioka, S., Murakami, A., Kudo, K., and Mitani, T., “Combustion Tests of a Staged Supersonic Combustor with a Strut”, Journal of Propulsion and Power, Vol. 17, No. 2, March-April 2001.
[39] Tomioka, S., Murakami, A., Kudo, K., and Mitani, T., “Effect of Injection Configuration on Performance of a Staged Supersonic Combustor”, Journal of Propulsion and Power, Vol. 19, NO. 5, September-October 2003.
[40] Gruber, M. R., Carter, C. D., Montes, D. R., Haubelt, L. C., King, P. I. and Hsu, K. Y., “Experimental Stusies of Pylon-Aided Fuel Injection into a Supersonic Crossflow,” Journal of Propulsion and Power, Vol. 24, No. 3, 2008.
[41] Tam, C. J., Hsu, K. Y., Gruber, M. R. and Raffoul, C. N., “Aerodynamic Performance of an Injector Strut for a Round Scramjet Combustor,”43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2007-5403.
[42] Hsu, K. Y., Carter, C. D., Gruber, M. R. and Tam, C. J., “Mixing Study of Strut Injectors in Supersonic Flows,” 45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2009-5226.
[43] Freeborn, A. B., King, P. I. and Gruber, M. R., “Swept-Leading-Edge Pylon Effects on a Scramjet Pylon-Cavity Flameholder Flowfield,” Journal of Propulsion and Power, Vol. 25, No. 3, 2009.
[44] Grady, N. R., Pitz, R. W., Carter, C. D., Hsu, K. Y., Ghodke, C. and Menon, S., “Supersonic Flow over a Ramped-Wall Cavity Flame Holder with an Upstream Strut,” Journal of Propulsion and Power, Vol. 28, No. 5, 2012.
[45] 吳政毅, “使用碳氫燃料之含凹槽超音速燃燒流場數值模擬分析,” 成功大學航空太空工程學系碩士論文, 2013.
[46] Iannetti, A. C. and Moder, J. P., “Comparing Spray Characteristics from Reynolds Averaged Navier-Stokes (RANS) National Combustion Code (NCC) Calculations Against Experimental Data for a Turbulent Reacting Flow,” AIAA Paper, 2010-578.
[47] ANSYS FLUENT, “ANSYS FLUENT 14.0 Theory Guide,”ANSYS Inc, 2011.
[48] Ranz, W. E. and Marshall, W. R., Jr., “Evaporation from drops, Part II,” Chemical Engineering Progress (CEP) magazine, vol. 48, pp. 173-180, 1952.
[49] Reitz, R. D., “Mechanisms of Atomization Processes in High-Pressure Vaporizing Sprays,” Atomization and Spray Technology, Vol. 3, pp. 309–337, 1987.
[50] Liu, A. B., Mather, D. and Reitz, R. D.,“Modeling the effects of drop drag and breakup on fuel sprays,” SAE, 1993.
[51] Barth, T. J. and Jespersen, D., “The design and application of upwind schemes on unstructured meshes,”Technical Report AIAA-89-0366. AIAA 27th Aerospace Sciences Meeting, Reno, Nevada, 1989.