一种高效的组合动导数分量数值模拟算法
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摘要
基于传统网格速度法,发展了在流场网格不变的情况下,数值模拟沉浮运动、纯俯仰运动和俯仰振荡运动的算法,提出了一套直接求解旋转阻尼导数和洗流时差导数的方法,该方法不需要实时更新网格,减少了计算时间和所需内存,避免了负体积的出现。首先通过NACA 0006的阵风响应和NACA 0012翼型的强迫俯仰振荡,验证了程序和方法的正确性;然后数值模拟了BFM(basic finner missile)标准模型的沉浮运动、纯俯仰运动和俯仰振荡运动,并计算了其旋转阻尼导数、洗流时差导数和组合动导数,所得结果与动网格方法和风洞试验值吻合,最大误差不超过4%,进一步验证了该方法的正确性。
Based on the field velocity approach,an effective method was presented for numerical simulating of floating motion,pure pitch motion and pitching oscillation,and then the lag of wash derivative and the pitch-damping derivative was directly calculated,without the mesh movement.Without the need to update the grid in real time,this approach reduced the time and memory required for computation,and avoided the negative volume.Numerical results were validated by comparison with the experiment results for NACA 0006 airfoil with gust response and NACA 0012 airfoil with forced oscillation.To validate the applicability for the present method farther,pitching combined dynamic derivative and its individual components were calculated from load history of the unsteady flow around a standard research configuration,known as the basic finner missile(BFM).Predicted results showed a good a-greement with the available wind tunnel data,the maximum error was no more than 4%.
Based on the field velocity approach,an effective method was presented for numerical simulating of floating motion,pure pitch motion and pitching oscillation,and then the lag of wash derivative and the pitch-damping derivative was directly calculated,without the mesh movement.Without the need to update the grid in real time,this approach reduced the time and memory required for computation,and avoided the negative volume.Numerical results were validated by comparison with the experiment results for NACA 0006 airfoil with gust response and NACA 0012 airfoil with forced oscillation.To validate the applicability for the present method farther,pitching combined dynamic derivative and its individual components were calculated from load history of the unsteady flow around a standard research configuration,known as the basic finner missile(BFM).Predicted results showed a good a-greement with the available wind tunnel data,the maximum error was no more than 4%.
引文
[1]陶洋,范召林,赵忠良.基于CFD的带控制舵导弹的动导数计算[J].航空动力学报,2010,25(1):102-106.TAO Yang,FAN Zhaolin,ZHAO Zhongliang.Prediction of dynamic damping coefficient of basic finnner based on CFD[J].Journal of Aerospace Power,2010,25(1):102-106.(in Chinese)
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[3]RONCH A D,VALLESPIN D.Computation of dynamic derivatives using CFD[R].AIAA-2010-4817,2010.
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[7]范晶晶,阎超,李悦军.飞行器大迎角下俯仰静、动导数的数值计算[J].航空学报,2009,30(10):1846-1850.FAN Jingjing,YAN Chao,LI Yuejun.Computation of vehicle pitching static and dynamic derivatives at high angles of attack[J].Acta Aeronautica et Astronautica Sincia,2009,30(10):1846-1850.(in Chinese)
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[9]席柯,阎超,黄宇,等.俯仰阻尼导数分量的CFD数值模拟[J].北京航空航天大学学报,2015,41(2):222-227.XI Ke,YAN Chao,HUANG Yu.Numerical simulation of individual components of pitch-damping coefficient sum[J].Journal of Beijing University of Aeronautics and Astronautics,2015,41(2):222-227.(in Chinese)
[10]米百刚,詹浩,王斑.基于刚性动网格技术的动导数数值模拟[J].航空动力学报,2014,29(11):2659-2664.MI Baigang,ZHAN Hao,WANG Ban.Numerical simulation of dynamic derivatives based on rigid moving mesh technique[J].Journal of Aerospace Power,2014,29(11):2659-2664(in Chinese)
[11]阎超.计算流体力学方法及应用[M].北京:北京航空航天大学出版社,2006:18-25.
[12]PARAMESWARAN V,BAEDER J D.Indicial aerodynamics in compressible flow-direct computational fluid dynamic calculations[J].Journal of Aircraft,1997,34(1):131-133.
[13]SINGH R,BAEDER J D.Direct calculation of threedimensional indicial lift response using computational fluid dynamic[J].Journal of Aircraft,1997,34(4):465-471.
[14]郭东,徐敏,陈士橹.基于网格速度法的非定常流场模拟和动导数计算[J].西北工业大学学报,2012,30(5):784-788.GUO Dong,XU Min,CHEN Shilu.An effective computation method based on field velocity approach for unsteady flow simulation and obtaining dynamic derivatives[J].Journal of Northwestern Polytechnical University,2012,30(5):784-788.(in Chinese)
[15]LOMAX H T.Indicial aerodynamics,AGARD manual of aeroelasticity:Part 2NATO[R].Advisory Group for Aerospace Research and Development,1968.
[16]LI Jie,HUANG Shouzhi,JIANG Shengju,et al.Unsteady viscous flow simulations by a fully implicit method with deforming grid[R].AIAA-2005-1221,2005.
[17]USELTON B L,JENKE L M.Experiment missile pitching-and-rolling damping characteristics at large angles of attack[J].Journal of Spacecraft,1977,14(4):241-247.
[2]OKTAY E,AKAY H U.CFD predictions of dynamic derivatives for missiles[R].AIAA-2002-0276,2002.
[3]RONCH A D,VALLESPIN D.Computation of dynamic derivatives using CFD[R].AIAA-2010-4817,2010.
[4]袁先旭,张涵信,谢昱飞.基于CFD方法的俯仰静、动导数数值计算[J].空气动力学学报,2005,23(4):458-463.YUAN Xianxu,ZHANG Hanxin,XIE Yufei.The pitching static/dynamic derivative computation based on CFD method[J].Acta Aerodynamic Sincia,2005,23(4):458-463.(in Chinese)
[5]SOO H P,YOONSIK K,JANG H K.Prediction of dynamic damping coefficients using unsteady dual-time stepping method[R].AIAA-2002-0715,2000.
[6]米百刚,詹浩,樊华羽.飞行器组合及单独动导数数值求解方法研究[J].西北工业大学学报,2015,33(4):540-545.MI Baigang,ZHAN Hao,FAN Huayu.Calculation combined and single dynamic derivatives of flight vehicle[J].Journal of Northwestern Polytechnical University,2015,33(4):540-545.(in Chinese)
[7]范晶晶,阎超,李悦军.飞行器大迎角下俯仰静、动导数的数值计算[J].航空学报,2009,30(10):1846-1850.FAN Jingjing,YAN Chao,LI Yuejun.Computation of vehicle pitching static and dynamic derivatives at high angles of attack[J].Acta Aeronautica et Astronautica Sincia,2009,30(10):1846-1850.(in Chinese)
[8]叶川,马东立.利用CFD技术计算飞行器动导数[J].北京航空航天大学学报,2013,39(2):196-200.YE Chuan,MA Dongli.Aircraft dynamic derivatives calculation using CFD techniques[J].Journal of Beijing University of Aeronautics and Astronautics,2013,39(2):196-200.(in Chinese)
[9]席柯,阎超,黄宇,等.俯仰阻尼导数分量的CFD数值模拟[J].北京航空航天大学学报,2015,41(2):222-227.XI Ke,YAN Chao,HUANG Yu.Numerical simulation of individual components of pitch-damping coefficient sum[J].Journal of Beijing University of Aeronautics and Astronautics,2015,41(2):222-227.(in Chinese)
[10]米百刚,詹浩,王斑.基于刚性动网格技术的动导数数值模拟[J].航空动力学报,2014,29(11):2659-2664.MI Baigang,ZHAN Hao,WANG Ban.Numerical simulation of dynamic derivatives based on rigid moving mesh technique[J].Journal of Aerospace Power,2014,29(11):2659-2664(in Chinese)
[11]阎超.计算流体力学方法及应用[M].北京:北京航空航天大学出版社,2006:18-25.
[12]PARAMESWARAN V,BAEDER J D.Indicial aerodynamics in compressible flow-direct computational fluid dynamic calculations[J].Journal of Aircraft,1997,34(1):131-133.
[13]SINGH R,BAEDER J D.Direct calculation of threedimensional indicial lift response using computational fluid dynamic[J].Journal of Aircraft,1997,34(4):465-471.
[14]郭东,徐敏,陈士橹.基于网格速度法的非定常流场模拟和动导数计算[J].西北工业大学学报,2012,30(5):784-788.GUO Dong,XU Min,CHEN Shilu.An effective computation method based on field velocity approach for unsteady flow simulation and obtaining dynamic derivatives[J].Journal of Northwestern Polytechnical University,2012,30(5):784-788.(in Chinese)
[15]LOMAX H T.Indicial aerodynamics,AGARD manual of aeroelasticity:Part 2NATO[R].Advisory Group for Aerospace Research and Development,1968.
[16]LI Jie,HUANG Shouzhi,JIANG Shengju,et al.Unsteady viscous flow simulations by a fully implicit method with deforming grid[R].AIAA-2005-1221,2005.
[17]USELTON B L,JENKE L M.Experiment missile pitching-and-rolling damping characteristics at large angles of attack[J].Journal of Spacecraft,1977,14(4):241-247.