臺灣博碩士論文加值系統

本文採用商用軟體ESI CFD來研究超音速流通過F-16機翼釋放飛彈高度變化數值模擬，在卡式座標系統下求解6-DOF剛體運動方程式和三維非穩態Euler方程式，使用重疊型網格(Chimera Grid)系統，讓不同區塊流場網格資料分別計算，而重疊區的格點訊息相互運算。將機翼流場與彈體流場結合，分析6-DOF剛體運動方程式取得計算結果，將彈體重心、速度、翻滾角度、角速度計算結果與實驗值進行比對，計算結果趨勢相近，再來使用不同高度的條件，進行機翼釋放彈體數值模擬。機翼分別在1000公尺、6000公尺、11600公尺處釋放彈體，探討機翼分離彈體的軌跡。隨著高度增加並施加8G推力釋放飛彈時，X軸方向，向前偏移量會逐漸增加；Y軸方向，向翼尖偏移量最小值逐漸變大；Z軸方向下位移量逐漸減少。

In this thesis, the commercial software ESI CFD FASTRAN is used to study the supersonic flows over a missile released from F-16 wing with altitude variation and 8G thrust. Three-dimensional unsteady Euler equations and six degree of freedom (6-DOF) rigid body motion equations are solved in the Cartesian coordinate. The Chimera grid system is used and the information of multiple blocks is calculated separately. Grid communication among multiple blocks is automatically implemented to obtain calculated results by coupling flow fields between a store and a wing and 6-DOF rigid-body motion equation. To evaluate the accuracy of the present calculation, the calculated store instantaneous trajectory of center of gravity of store, velocity, angles of roll and angular rate are compared with those of experimental data. The results are in good agreement with the experimental data. Store separation at 1000m, 6000m and 11600m is employed to investigate the trajectory of a store. In addition, the 8G thrust is added to analyze the physical variation of the store. As the altitude increases and an 8G thrust is applied when releasing the missile, the forward displacement in the X-axis gradually increases; in the Y-axis, the minimum wingtip displacement gradually increases; in the Z-axis, the downward displacement gradually decreases.

摘要....i
Abstract........ii
誌謝....iii
目錄....iv
表目錄....vi
圖目錄....vii
符號說明....ix
第一章 前言........1
1.1 研究動機........1
1.2 研究目的........1
1.3 參考文獻........2
第二章 分析........10
2.1 物理模式........10
2.2 流場守恆方程式........11
2.2.1 非運動架構的流場守恆方程式....11
2.2.2 可移動/變形控制體積的流場守恆方程式....12
2.3 運動方程式....13
2.4 Chimera解法....14
2.5 空間數值方法....15
2.6 時間數值方法....16
2.6.1 區集對角(Block Diagonal)隱式解法....16
2.6.2 Jacobi疊代隱式解法....16
第三章 數值方法及驗證........17
3.1 研究方法........17
3.2 網格系統配置....17
3.3 機翼釋放單顆彈體結果驗證........18
3.3.1機翼幾何形狀........18
3.3.2派龍幾何形狀........18
3.3.3彈體幾何形狀........19
3.3.4機翼、派龍與彈體網格格點配置....19
3.3.5程式測試與結果驗證....20
第四章 三維流場彈體分離結果與參數探討........22
4.1 概論........22
4.2 F-16機翼幾何形狀........22
4.3 機翼、派龍與彈體網格格點配置....23
4.4 流場參數設置....23
4.4.1穩態系統參數設置....23
4.4.2暫態系統參數設置....24
4.5 改變機翼釋放彈體流場探討........24
4.6 F-16機翼改變高度釋放彈體流場探討........29
4.7 F-16機翼改變高度施加8G推力釋放飛彈流場探討........33
第五章 結論........40
參考文獻....84
Extended Abstract........89

[1]Taylor, R. T., and Alford, W.,“A Wind Tunnel Investigation of the Carry Loads and Mutual Interference Effects of 1/40 Scale Models of the X-15 and B-52 Airplanes in Combination,” NASA TM X-184, 1959.
[2]Lijewski, E. L., and Suhs, N. E.,“Time-Accurate Computational Fluid Dynamics Approach to Transonic Store Separation Trajectory Prediction,” Journal of Aircraft, Vol. 31, No. 4, pp. 886-891, July-Aug 1994.
[3]Paresh Parikh., Shahyar Pirzadeh., and Neal Frink, T., “Unstructured Grid Solutions to a Wing/Pylon/Store Configuration,” Journal of Aircraft, Vol. 31, No. 6, pp. 1291-1296, November-December 1994.
[4]NathanC. P., Davy M. B., and Raymond, C. M.,“Multiple-Body Trajectory Calculation Using the Beggar Code,” Journal of Aircraft, Vol. 36, No. 5, pp. 802-808, September-October 1999.
[5]Ching, K. T.,“Grid Survey Approach to Store Separation Trajectory Prediction,” Journal of Aircraft, Vol. 37, No. 4, pp. 736-738, 2000.
[6]Wang, Z. J., and Parthasarathy, V., “A Fully Automated Chimera Methodology for Multiple Moving Body Problems,” Int . J . Numer . Meth . Fluids, pp. 919-938, 2000.
[7]Nathan, C., Prewitt, D., Belk, M., and Wei, S.,“Parallel Computing of Overset Grids for Aerodynamic Problems with Moving Objects,”J. Progress in Aerospace Sciences, 36, pp. 117–172, 2000.
[8]Anandhanarayanan, K.“Development of Three-Dimensional Grid-free Solver and Its Applicationns to Multi-Body Aerospace Vehicles,” Defence Science Journal, Vol. 60, No. 6, pp. 653-662, November 2010.
[9]Anandhanarayanan, K. “Grid-Free Kinetic Upwind Solver on Chimera Cloud of Points,” West-East High Speed Flow Field Conference, 19-22, November 2007.
[10]Bandu, N. P., Tartabini , Brett, R. S.“Ascent , Stage Separation and Glideback Performance of a Partially Reusable Small Launch Vehicle,” AIAA-2004-0876, pp. 1-16, October 2004.
[11]Dimitri, E., Bigarella, V., Luiz, J., Azevedo, F., and Scalabrin, L. C., “Centered and Upwind Multigrid Turbulent Flow Simulations of Launch Vehicle Configurations,” Journal of Spacecraft and Rockets, Vol. 44, No. 1, pp. 52-65, January-February 2007.
[12]ESI group CFD portal , Unsteady Simulation of a Tank Dropping from a Wing , 2007. http://www.esi-cfd.com/component/option,com_rapidrecipe/page, viewrecipe/recipe_id , 61/ Itemid ,2006.
[13]Liu, J. L.,“Trajectory Analyses of External Store Separation by Using the Euler Equations,” Journal of Aircraft, Vol. 40, No. 1, pp. 206-208, 2003.
[14]Dimitri, E., Bigarella, V., Luiz, J., and Azevedo, F., “Numerical Study of Turbulent Flows over Launch Vehicle Configuration,” Journal of Spacecraft and Rockets, Vol. 42, No. 2, pp. 266-277, March-April 2005.
[15]Liu, X., and Fu, S.,“Numerical Simulation of Compressible Separated Turbulent Flow Over Inclined Slender Body,” Journal of Spacecraft and Rockets, Vol. 42, No. 3, pp. 572-575, May-June 2005.
[16]Eugene, K., Jang, H. K., and Hyuk, P., “Prediction of Ballistic Separation Effect by Direct Calculation of Incremental Coefficients,” Journal of Aircraft, Vol. 47, No. 2, pp. 630-637, March-April 2010.
[17]Young, M. J. , Young, S. K., Jae, W. L., and Jun, S. P.,“Effect of C.G. and Control Surface Area on Supersonic Separation of an Air-launching Rocket from the Mother Plane,”Aerospace Science and Technology, pp. 19-25, 2010.
[18]Murman, S. M., Aftosmis, M. J., Berger M. J., “Simulations of Store Separation from an F/A-18 with a Cartesian Method,” Journal of Aircraft, Vol. 41, No. 4, July-August 2004.
[19]Malmuth, N. D.,“Theoretical Aerodynamics in Today's Real World : Opportunities and Challenges,” AIAA Journal, Vol. 44, No. 7, pp. 1377-1392, July 2006.
[20]Elias, E. P., and Spyridon D. K.,“CFD Transonic Store Separation Trajectory Predictions with Comparison to Wind Tunnel Investigations,” International Journal of Engineering, Vol. 3, Issue. 6, pp. 538 - 553, January, 2010.
[21]Yang, S. Y., Line, C. C., and Liao, W. T., “Numerical Study of Parametric Effects for Transonic Flows around a Store with Fins Released from a Wing,” Journal of Aeronautics, Astronautics and Aviation, Series B, Vol. 44, No. 2, 2012, pp. 99-108.
[22]楊世英 , 廖偉廷 , 連振傑 “紊流通過機翼釋放具鰭片彈體之數值探討,” 中國機械工程學會第二十九屆全國學術研討會,” 論文編號:A02-1246, Dec 2012.
[23]Mohagna J. Pandya., Neal T. Frink., and Ralph W. Noack., “Progress Toward Overset-Grid Moving Body Capability for USM3D Unstructured Flow Solver,” 17th AIAA Computational Fluid Dynamics Conference, AIAA 2005-5118, 6 – 9 June 2005.
[24]Zhang, L., Chang, X., Duan, X., Zhao, Z., and He, X., “Applications of Dynamic Hybrid Grid Method for Three-Dimensional Moving/Deforming Boundary Problems,” Computers & Fluids, Volume 62, pp. 45-63, 15 June 2012.
[25]Mahmood, T., Aizud, M. N., Zahir, S., “Aerodynamic Effects of the Store Release on the Roll Attitude of a Wing Configuration in Transonic Flight,” Proceedings of International Bhurban Conference on Applied Sciences & Technology, pp. 12-15, 10 - 13 January 2011.
[26]Tahir Mahmood, Nadeem Aizud, and Salimuddin Zahir, “CFD Simulations of the Store Separation and its Effect on the Attitude of the Parent Vehicle,” Proceedings of 2012 9th International Bhurban Conference on Applied Sciences & Technology (IBCAST), pp. 198-202, 9 - 12 January 2012.
[27]Roy Koomullil, Gary Cheng, Bharat Soni, Ralph Noack, Nathan Prewitt, “Moving-Body Simulations using Overset Framework with Rigid Body Dynamics,” Mathematics and Computers in Simulation, Volume 78, Issues 5–6, pp.618-626, September 2008.
[28]Anandhanarayanan, K., Arora Konark, Shah Vaibhav, Krishnamurthy, R., and Chakraborty Debasis, “Separation Dynamics of Air-to-Air Missile Using a Grid-Free Euler Solver,” Journal of Aircraft, Vol. 50, No. 3, pp. 725-731, May-June 2013.
[29]Di, Y. C., Gao, Ge., Xu, Jing Lei., Shao, Xing Chen., Yang, Qing “Time-Accurate Simulation of the Aircraft External Store Separation,” Applied Mechanics and Materials, Vol. 444-445, pp. 854-859, 2014.
[30]Rubin, T., “Development of a Store Trajectory Simulation Code CTSAERO Using the MGAERO Flow Solver,” 53rd Israel Annual Conference on Aerospace Sciences, Vol. 1, pp. 184-194, 6 - 7 March, 2013.
[31]Jafari M, Toloei A., Ghasemlu S., and Parhizkar H, “Simulation of Store Separation Using Low-cost CFD with Dynamic Meshing,” International Journal of Engineering, Transactions, B: Applications, Vol. 27, No. 5, pp. 775-784, 2014.
[32]Xi, K., and Yan, C., “CFD Trajectory Predictions of Three-Store Ripple Release Using Chimera Method,” Applied Mechanics and Materials, Vol. 513-517 , pp. 4490-4493, 2014.
[33]Konark Arora, Vaibhav Shah , K. Anandhanarayanan, R. Krishnamurthy, and Debasis Chakraborty, “Defence Science Journal,” Vol. 63, No. 3, May 2013, pp. 242-248,2013.
[34]劉邦毅，2016，“機翼釋放飛彈流場參數探討”，虎尾科技大學，碩士論文。
[35]Directory of U.S. Military Rockets and Missiles，民國105年12月，取自：http://www.designation-systems.net/dusrm/index.html
[36]Alaa A. Osman , Amgad M. Bayoumy , Osama E. Abdellatif , Essam E. Khallil, “Numerical Analysis of an External Store Separation from an Airplane,” AIAA Modeling and Simulation Technologies Conference, January 2016-2143
doi:10.2514/6.2016-2143.
[37]G. J. M. Loupy , G. N. Barakos and N. J. Taylor, “Store Release Trajectory Variability from Weapon Bays Using Scale-adaptive Simulations.,” AIAA Journal, Vol. 56 , No. 2 , pp.752-764 , February 2018.
doi:10.2514/1.J056485
[38]H. Özgür DEMİR , B. Tuğcan SELİMHOCAOĞLU., “CFD Applications in Store Separation,”North Atlantic Treaty Organization Science and Technolocy Organization. , ” May 2018.
doi: 10.14339 / STO-EN-SCI-277-2018
[39]V. Raghavender and R. Kannan ., “Computational Aerodynamic Analysis on Store Separation from Aircraft using Pylon,” International Journal of Engineering Science Invention., Vol. 1 , pp. 27-31 , 2014. Issn:2319-6734
[40]Görkem Demir , Nafiz Alemdaroğlu., “ Computational Fluid Dynamics Modelling of Store Separation for Transonic Generic Store,” 48th AIAA AVIATION Fluid Dynamics Conference, 25-29 June 2018.
doi:10.2514/6.2018-3860
[41]M. Sheharyar , E. Uddin , Z. Ali1, Q. Zaheer and A. Mubashar, “Simulation of a Standard Store Separated from Generic Wing, ” Journal of Applied Fluid Mechanics, Vol. 11, No. 6, pp. 1579-1589, 2018.
[42]A. Shikhar Jaiswal ,C. K. Niranjanan , Keshav Malagi , V. Ramesh and S. M. Deshpande , “Grid Method Based Store Separation Suite Using Paranam Mesh Free Solver,” Journal of Aerospace Sciences and Technologies, Vol. 71, No. 2, pp. 214-218, May 2019.
doi:10.5281/zenodo.3355155
[43]Gong, J., Wang, F., “Simulation of the Store Separation from Internal Weapons Bay Using M_SST DES Mode, ” Journal of Physics: Conf. Series, Vol. 1215 , pp. 1-9 , May 2019.
doi:10.1088/1742-6596/1215/1/012001
[44]Hak Mizrahi , Daniella E. Raveh , “Wing Elasticity Effects on Store Separation,” Journal of Aircraft, Vol. 56 , No. 3 , pp. 1231-1249 , May 2019.
doi:10.2514/1.C035204
[45]詹元合，“超音速流通過機翼釋放飛彈流場高度效應數值分析” 國立虎尾科技大學，碩士論文，民國110年。
[46]Aleksander Olejnik, Adam Dziubiński and Łukasz Kiszkowiak, “Separation Safety Analysis Using CFD Simulation and Remeshing,” Journal of Aerospace Science and Technology, Volume 106, Article 106190, November 2020.
doi: 10.1016/j.ast.2020.106190
[47]R. R. Heim., “CFD Wing/Pylon/Finned Store Mutual Interference Wind Tunnel Experiment,” AEDC-TSR-91-P4, 1991
[48]Z. Toor, T.I. Khan, O. Khan, Bilal Mufti and J. Masud, “Comparative Analysis of Store Release Trajectory Using Numerical and Experimental Techniques,” AIAA Scitech 2019 Forum, 7-11 January 2019.
doi: 10.2514/6.2019-0846
[49]William D. Gothard and Kenneth O. Granlund, “Store Separation Trajectory Clusters from Machine Learning,” Journal of Aircraft, Vol. 59, No. 1, January–February 2022.
doi:/10.2514/1.C036261
[50]Josh B. Doyle, Justin Paul and James DeSpirito, “Results of the Missile and Projectile Aeroprediction Discussion Group Case Study,” AIAA Scitech 2020 Forum, 6-10 January 2020.
doi:10.2514/6.2020-1992
[51]Berkay Y. YILDIRIM, Gorkem DEMIR and Onurhan AYHAN, “Computational Fluid Dynamics Modeling of a Mortar Bomb Separation from a FixedWing Aircraft,” AIAA Scitech 2020 Forum, 6-10 January 2020.
doi: 10.2514/6.2020-1995
[52]Vinod Singh Rao, Valerio Viti and Juan Abanto, “CFD Simulations of Super Hypersonic Missiles Validation Sensitivity Analysis and Improved Design,” AIAA Scitech 2020 Forum, 6-10 January 2020.
doi: 10.2514/6.2020-2123
[53]M. A. SHILO, “Six Degree of Freedom Flight Dynamic Model of a MK-82 Store,” Australia Defence Science and Technology Organization Aeronautical Research Laboratory, January 1994.
[54]J. P. Christopher and W. E. Carleton, “Captive-Trajectory Store-Separation System of The AEDC-PWT 4-FOOT Transonic Tunnel,” ARO, Inc. ,September 1968.
[55]Oscar G. Puentes and Timothy T. Takahashi, “Wingtip Treatments for Transonic Wing Planforms,” AIAA SCITECH 2024 Forum, 8-12 January 2024.
doi: 10.2514/6.2024-0001
[56]Alexander Brown and Donald L. Kunz, “Shock Migration on an Oscillating Straked Delta Wing Using an Unsteady Euler Solver,” AIAA SCITECH 2023 Forum, 23-27 January 2023.
doi: 10.2514/6.2023-1192
[57]Navdeep Pandey, Rohit Tembhare, Nisha Singh and Aniruddha Sinha, “Domain-Decomposed Reduced-Order Modelling of Steady Aerodynamics for 2D Store Separation Analysis,” AIAA SCITECH 2023 Forum , 23-27 January 2023.
doi: 10.2514/6.2023-1004
[58]Dennis B. Finley, Todd L. Messina, Kurt Chankaya, Edwin L. Blosch and John Dreese, “Comparison of CFD-Based Simulation of External Fuel Tank Separation to Flight Test,” 52nd Aerospace Sciences Meeting, 13-17 January 2014.
doi: 10.2514/6.2014-0211
[59]Joseph Baum, Hong Luo, Rainald Loehner, Eran Goldberg and Alex Feldhun, “Application of Unstructured Adaptive Moving Body Methodology to the Simulation of Fuel Tank Separation from an F-16 Fighter,” 35th Aerospace Sciences Meeting and Exhibit, 06 January 1997 - 09 January 1997.
doi: 10.2514/6.1997-166
[60]沈心然，“穿音速流通過機翼釋放雙顆MK-82彈體之高度變化數值探討” 國立虎尾科技大學，碩士論文，民國112年。
[61]Nicholas Peters, Andrew Wissink and John Ekaterinaris, “Machine Learning-Based Surrogate Modeling Approaches for Fixed-Wing Store Separation,” Journal of Aerospace Science and Technology, Volume 133, Article 108150, February 2023.
doi: 10.1016/j.ast.2023.108150
[62]Fei Xue, Yipeng Ren, Zheng Li, Cong Xu, Dechen Wei, Xiaolu Mao and Zenghui Jaing, “Aerodynamic Characteristics of Store During Lateral Jet Assisted Separation from Cavity Using Free Drop Technique,” Chinese Journal of Aeronautics, Volume 36, Issue 1, P. 139-151, January 2023.
doi: 10.1016/j.cja.2022.07.009
[63]Wei Song, Jingang Dong, Wei Lu and Zenghui Jiang, “Trajectory and Attitude Deviations for Internal Store Separation Due to Unsteady and Quasi-Steady Test Method,” Chinese Journal of Aeronautics, Volume 35, Issue 2, P. 74-81, February 2022.
doi: 10.1016/j.cja.2021.03.007
[64]Nicholas Peters, Andrew Wissink and John Ekaterinaris, “Comparison of Data-Driven Approaches to Rotorcraft Store Separation Modeling,” Journal of Aircraft, Vol. 61, No. 1, January–February 2024.
doi: 10.2514/1.C037164