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摘要: 为了提高飞机穿越大气紊流场时的实时飞行仿真逼真度, 提出了三维空间大气紊流场的生成与扩展方法。采用Von Karman模型, 在频域空间直接进行蒙特卡罗法随机抽样, 经三维傅立叶逆变换得到三维空间大气紊流场。基于傅立叶变换的复共轭对称特性, 生成实的紊流场。在飞行仿真过程中, 对预先生成的无因次紊流场进行有因次化, 保证紊流场尺度和强度随飞行高度动态变化。运用基于对称扩展的紊流场扩展方法, 保证生成的局部空间紊流场有效扩展为大范围连续紊流场。仿真结果表明: 生成的三维紊流场在对称扩展前、后均符合Von Karman模型, 且与基于紊流场相关函数矩阵的生成方法相比, 新算法计算速度快, 存储空间需求少, 更适于实时飞行仿真。Abstract: In order to improve the real-time flight simulation fidelity of aircraft through turbulence field, the generation and extension methods of 3D atmospheric turbulence field were put forward.Based on Von Karman model, spatial turbulence field was generated in frequency domain by using Monte Carlo method and transformed back to time domain by using 3D Fourier inverse transform.The conjugate characteristic of Fourier transform was applied to guarantee the realism of turbulence field in time domain.During flight simulation, the integral scale and intensity of turbulence field changed with flight altitude by dimensioning the non-dimensional turbulence field which had been generated in advance.A symmetrical turbulence extension method was presented to make sure that the local field could be effectively extended to wide range and continuous field.Simulation result indicates that turbulence field conforms to Von Karman model before and after symmetrical extension, compared to the generation method based on correlation function matrix, the new algorithms have faster generation speed and less storage space, so they are suitable for real-time flight simulation.
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表 1 傅立叶变换的复共轭对称关系
Table 1. Conjugate relations in Fourier transform
一维对称性 X(M-k)=X*(k), Im X(M/2)=0 二维对称性 X(M1-k1, 0)=X*(k1, 0), Im X(M1/2, 0)=0 X(0, M2-k2)=X*(0, k2),
Im X(0, M2/2)=0X(M1-k1, M2-k2)=X*(k1, k2),
Im X(M1/2, M2/2)=0三维对称性 X(M1-k1, 0, 0)=X*(k1, 0, 0),
Im X(M1/2, 0, 0)=0X(0, M2-k2, 0)=X*(0, k2, 0),
Im X(0, M2/2, 0)=0X(0, 0, M3-k3)=X*(0, 0, k3),
Im X(0, 0, M3/2)=0X(M1-k1, M2-k2, 0)=X*(k1, k2, 0),
Im X(M1/2, M2/2, 0)=0X(M1-k1, 0, M3-k3)=X*(k1, 0, k3),
Im X(M1/2, 0, M2/2)=0X(0, M2-k2, M3-k3)=X*(0, k2, k3),
Im X(0, M2/2, M3/2)=0X(M1-k1, M2-k2, M3-k3)=X*(k1, k1, k3),
Im X(M1/2, M2/2, M3/2)=0
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