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探月飞船返回地球时将以第二宇宙速度再入地球大气层，面临极其严苛的气动环境，因此对于再入气动过载的分析具有重要意义. 再入运动方程是一组非线性很强的常微分方程，数值方法计算量大，不适用于在线任务. 因此，本文采用一种近似解法对气动过载进行分析. 首先，基于匹配渐进展开方法将再入纵向运动解在大气外层区域与内层区域分别展开，得到统一形式的闭型近似解，在此基础上分段求解气动过载，并与精确解进行对比分析. 其次，利用闭型近似解，通过当前状态反解虚拟初始条件，在此基础上提出初次过载峰值的解析预测方法，并分析了不同条件下预测的相对误差变化规律. 最后，基于过载峰值的解析预测对飞船的初次再入过程进行卸载，将飞船在再入过程中耗散的总能量进行重新分配，并通过蒙特卡罗飞行仿真试验验证了卸载方法的有效性.Reentry velocity of lunar module reaches the second cosmic velocity, which could make the aerodynamic environment insupportable. So it is essential to analysis the reentry aerodynamic load. The equation of motion for reentry vehicle is a group of ordinary differential equations, and numerical methods are inadequate for online mission because their computation amount is too large. An analytical method of solving the reentry equation of motion is proposed in this paper to analyze the reentry aerodynamic load. First, matched asymptotic method is used to obtain solutions of longitudinal equation of motion in outer and inner region independently and combine them to obtain a unified closed-form solution. Reentry aerodynamic load has been analyzed in three fragments using the closed-form solution, and approximate solution of load is compared with the exact solution. Second, suppositional initial conditions are obtained by solving the closed-form solution using current state, then an analytical method of predicting the first load peak is proposed, and the relative prediction error is analyzed for different bank angles. Third, the load relief method based on load peak prediction is proposed, which can redistribute the total dissipated energy in the whole reentry process, and the validity of the method is verified by Monte Carlo simulation.
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Keywords:
- reentry aerodynamic load /
- matched asymptotic expansion /
- closed-form approximate solution /
- load relief
[1] Bairstow S H 2006 Ph. D. Dissertation (Massachusetts: Massachusetts Institute of Techlonogy)
[2] Hwang I, Li J, Du D 2009 J. Dyn. Sys. Meas. Control. 131 051010
[3] Wu H B, Zhang Y F, Mei F X 2006 Acta Phys. Sin. 55 4987 (in Chinese) [吴惠彬, 张永发, 梅凤翔 2006 物理学报 55 4987]
[4] Zhang R C, Wang L H, Yue C Q 2007 Acta Phys. Sin. 56 3050 (in Chinese) [张睿超, 王连海, 岳成庆 2007 物理学报 56 3050]
[5] Hereman W, Banerjee P, Korpel A 1986 J. Phys. A 19 19
[6] Wang M L, Zhou Y B, Li Z B 1996 Phys. Lett. A 26 6027
[7] Mei F X, Wu H B, Zhang Y F 2006 Chin. Phys. 15 1662
[8] Hereman W, Takaota M 1990 J. Phys. A 23 4805
[9] Panigrahi M, Dash P C 1999 Phys. Lett. A 261 284
[10] Li Z B, Pan S Q 2001 Acta Phys. Sin. 50 402 (in Chinese) [李志斌, 潘素起 2001 物理学报 50 402]
[11] Zhao H Y 1997 Reentry Dynamics and Guidance (Changsha: National University of Defense Technology Press) p114 (in Chinese) [赵汉元 1997 飞行器再入动力学和制导 (长沙: 国防科技大学出版社) 第114页]
[12] Loh W H 1965 AIAA J. 3 1688
[13] Mititelu G 2009 Celest. Mech. Dyn. Astr. 103 327
[14] Gorbonos D, Kol B 2005 Class. Quantum. Grav. 22 3935
[15] Burke W L 1971 J. Math. Phys. 12 401
[16] Gorbonos D, Kol B 2004 J. High Energy Phys. 2004 53
[17] Lin W T, Lin Y H, Mo J Q 2012 Chin. Phys. B 21 010204
[18] Shi Y Y, Pottsepp L, Eckstein M C 1970 AIAA J. 9 736
[19] Vinh N X, Kuo Z S 1996 1996 AIAA/AAS Astrodynamics Conference, San Diego, America, July 29-31, 1996 p212
[20] Kluever C A 2008 J. Guidance. 31 1531
[21] Mease K D, McCreary F A 1985 12th Atmospheric Flight Mechanics Conference Snowmass, America, August 19-21, 1985 p408
[22] Lu P 2008 J. Guidance. 31 1067
[23] Shen H X, Zhou J P, Peng Q B, Li H Y 2012 Sci. China Tech. Sci. 55 2561
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[1] Bairstow S H 2006 Ph. D. Dissertation (Massachusetts: Massachusetts Institute of Techlonogy)
[2] Hwang I, Li J, Du D 2009 J. Dyn. Sys. Meas. Control. 131 051010
[3] Wu H B, Zhang Y F, Mei F X 2006 Acta Phys. Sin. 55 4987 (in Chinese) [吴惠彬, 张永发, 梅凤翔 2006 物理学报 55 4987]
[4] Zhang R C, Wang L H, Yue C Q 2007 Acta Phys. Sin. 56 3050 (in Chinese) [张睿超, 王连海, 岳成庆 2007 物理学报 56 3050]
[5] Hereman W, Banerjee P, Korpel A 1986 J. Phys. A 19 19
[6] Wang M L, Zhou Y B, Li Z B 1996 Phys. Lett. A 26 6027
[7] Mei F X, Wu H B, Zhang Y F 2006 Chin. Phys. 15 1662
[8] Hereman W, Takaota M 1990 J. Phys. A 23 4805
[9] Panigrahi M, Dash P C 1999 Phys. Lett. A 261 284
[10] Li Z B, Pan S Q 2001 Acta Phys. Sin. 50 402 (in Chinese) [李志斌, 潘素起 2001 物理学报 50 402]
[11] Zhao H Y 1997 Reentry Dynamics and Guidance (Changsha: National University of Defense Technology Press) p114 (in Chinese) [赵汉元 1997 飞行器再入动力学和制导 (长沙: 国防科技大学出版社) 第114页]
[12] Loh W H 1965 AIAA J. 3 1688
[13] Mititelu G 2009 Celest. Mech. Dyn. Astr. 103 327
[14] Gorbonos D, Kol B 2005 Class. Quantum. Grav. 22 3935
[15] Burke W L 1971 J. Math. Phys. 12 401
[16] Gorbonos D, Kol B 2004 J. High Energy Phys. 2004 53
[17] Lin W T, Lin Y H, Mo J Q 2012 Chin. Phys. B 21 010204
[18] Shi Y Y, Pottsepp L, Eckstein M C 1970 AIAA J. 9 736
[19] Vinh N X, Kuo Z S 1996 1996 AIAA/AAS Astrodynamics Conference, San Diego, America, July 29-31, 1996 p212
[20] Kluever C A 2008 J. Guidance. 31 1531
[21] Mease K D, McCreary F A 1985 12th Atmospheric Flight Mechanics Conference Snowmass, America, August 19-21, 1985 p408
[22] Lu P 2008 J. Guidance. 31 1067
[23] Shen H X, Zhou J P, Peng Q B, Li H Y 2012 Sci. China Tech. Sci. 55 2561
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