基于传递函数法的大展弦比机翼阵风响应分析
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摘要
将传递函数法应用于大展弦比机翼的阵风响应分析。首先,基于二元机翼的运动方程和准定常片条理论建立机翼的阵风响应微分方程,对其进行Laplace变换,并转换为状态空间方程形式。然后,运用传递函数方法,获得机翼响应在频域的解析解,通过Laplace数值逆变换求得机翼在时域内的响应。通过与已有文献结果对比,验证了本文方法的正确性。最后,采用该方法求解了"1-cos"型阵风和连续大气湍流作用下的机翼响应,并对结果进行了分析讨论。
The semi-analytical and semi-numerical transfer function method is applied to study the highaspect-ratio wing gust response. First, the wing gust response equations are established by combining the beam bend vibration model and the steady aerodynamic model, which are transformed by the Laplace transformation into the state-space form. Then, the analytical solution in the frequency domain is obtained by using the transfer function method. The transient response of the wing in the time domain is obtained by the numerical inversion of the Laplace transforms. By comparing with the results in the existing literature, the method is validated. Finally, the response of the wing for the One-Minus-Cosine gust and the continuous atmospheric turbulence is solved and analyzed.
The semi-analytical and semi-numerical transfer function method is applied to study the highaspect-ratio wing gust response. First, the wing gust response equations are established by combining the beam bend vibration model and the steady aerodynamic model, which are transformed by the Laplace transformation into the state-space form. Then, the analytical solution in the frequency domain is obtained by using the transfer function method. The transient response of the wing in the time domain is obtained by the numerical inversion of the Laplace transforms. By comparing with the results in the existing literature, the method is validated. Finally, the response of the wing for the One-Minus-Cosine gust and the continuous atmospheric turbulence is solved and analyzed.
引文
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2 Chahine GL.Interaction between an oscillating bubble and a free surface.Journal of Fluids Engineering,1977,99(4):709-716
3 Moulin B,Karpel M.Gust loads alleviation using special control surfaces.Journal of Aircraft,2015,44(1):17-25
4谢正桐,周文伯.超声速机翼-尾翼对突风动态响应的数值方法.空气动力学学报,1996(3):344-348Xie Zhengtong,Zhou Wenbo.A numerical method of the wing-tail combination’s unsteady response to gust.Acta Aerodynamica Sinica,1996(3):344-348(in Chinese)
5 Yang G,Obayashi S.Numerical analyses of discrete gust response for an aircraft.Journal of Aircraft,2012,41(6):1353-1359
6 Parameswaran B,Baeder JD.Indicial aerodynamics in compressible flow-direct computational fluid dynamic calculations.Journal of Aircraft,1997,34(1):131-133
7 Singh R,Baeder JD.Direct calculation of three-dimensional indicial lift response using computational fluid dynamics.Journal of Aircraft,1997,34(4):465-471
8 Raveh DE,Zaide A.Numerical simulation and reduced-order modeling of airfoil gust response.AIAA Journal,2006,44(8):1826-1834
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10顾宁.基于CFD的机翼阵风响应及减缓计算.[硕士论文].南京:南京航空航天大学,2013Gu Ning.CFD-based gust response and alleviation research of aircraft wing.[Master Thesis].Nanjing:Nanjing University of Aeronautics and astronautics,2013(in Chinese)
11周建平,雷勇军.分布参数系统的传递函数方法.北京:科学出版社,2010Zhou Jianping,Lei Yongjun.Transfer Function Method of Distributed Parameter System.Beijing:Science Press,2010(in Chinese)
12段静波,周洲,江涛.基于曲梁模型的大展弦比大柔性机翼颤振分析.西北工业大学学报,2016,34(5):774-782Duan Jingbo,Zhou Zhou,Jiang Tao.A method for flutter of the very flexible wing with high-aspect-ratio based on curve beam model.Northwestern Polytechnical University,2016,34(5):774-782(in Chinese)
13段静波,江涛.带外挂机翼颤振分析的传递函数方法.振动与冲击,2017,36(10):109-116Duan Jingbo,Jiang Tao.Transfer function method for the flutter of aircraft wings with an external store.Journal of Vibration and Shock,2017,36(10):109-116(in Chinese)
14 Valsa J,Brancik L.Approximate formulae for numerical inversion of Laplace transforms.International Journal of Numerical Modelling:Electronic Networks,Devices and Fields,1998,11(3):153-166
15赵永辉.气动弹性力学与控制.北京:科学出版社,2006Zhao Yonghui.Aeroelastic Mechanics and Control.Beijing:Science Press,2006(in Chinese)
2 Chahine GL.Interaction between an oscillating bubble and a free surface.Journal of Fluids Engineering,1977,99(4):709-716
3 Moulin B,Karpel M.Gust loads alleviation using special control surfaces.Journal of Aircraft,2015,44(1):17-25
4谢正桐,周文伯.超声速机翼-尾翼对突风动态响应的数值方法.空气动力学学报,1996(3):344-348Xie Zhengtong,Zhou Wenbo.A numerical method of the wing-tail combination’s unsteady response to gust.Acta Aerodynamica Sinica,1996(3):344-348(in Chinese)
5 Yang G,Obayashi S.Numerical analyses of discrete gust response for an aircraft.Journal of Aircraft,2012,41(6):1353-1359
6 Parameswaran B,Baeder JD.Indicial aerodynamics in compressible flow-direct computational fluid dynamic calculations.Journal of Aircraft,1997,34(1):131-133
7 Singh R,Baeder JD.Direct calculation of three-dimensional indicial lift response using computational fluid dynamics.Journal of Aircraft,1997,34(4):465-471
8 Raveh DE,Zaide A.Numerical simulation and reduced-order modeling of airfoil gust response.AIAA Journal,2006,44(8):1826-1834
9顾宁,陆志良,张家齐等.基于CFD的机翼突风响应计算.航空学报,2011,32(5):785-791Gu Ning,Lu Zhiliang,Zhang Jiaqi,et al.CFD-based analysis for gust response of aircraft wing.Acta Aeronautica Et Astronautica Sinica,2011,32(5):785-791(in Chinese)
10顾宁.基于CFD的机翼阵风响应及减缓计算.[硕士论文].南京:南京航空航天大学,2013Gu Ning.CFD-based gust response and alleviation research of aircraft wing.[Master Thesis].Nanjing:Nanjing University of Aeronautics and astronautics,2013(in Chinese)
11周建平,雷勇军.分布参数系统的传递函数方法.北京:科学出版社,2010Zhou Jianping,Lei Yongjun.Transfer Function Method of Distributed Parameter System.Beijing:Science Press,2010(in Chinese)
12段静波,周洲,江涛.基于曲梁模型的大展弦比大柔性机翼颤振分析.西北工业大学学报,2016,34(5):774-782Duan Jingbo,Zhou Zhou,Jiang Tao.A method for flutter of the very flexible wing with high-aspect-ratio based on curve beam model.Northwestern Polytechnical University,2016,34(5):774-782(in Chinese)
13段静波,江涛.带外挂机翼颤振分析的传递函数方法.振动与冲击,2017,36(10):109-116Duan Jingbo,Jiang Tao.Transfer function method for the flutter of aircraft wings with an external store.Journal of Vibration and Shock,2017,36(10):109-116(in Chinese)
14 Valsa J,Brancik L.Approximate formulae for numerical inversion of Laplace transforms.International Journal of Numerical Modelling:Electronic Networks,Devices and Fields,1998,11(3):153-166
15赵永辉.气动弹性力学与控制.北京:科学出版社,2006Zhao Yonghui.Aeroelastic Mechanics and Control.Beijing:Science Press,2006(in Chinese)