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基于逆向增广Burgers方程的声爆反演技术研究——超声速民机气动专栏

顾奕然1,黄江涛2,陈树生1,刘德园1,高正红3   

  1. 1. 西北工业大学
    2. 中国空气动力研究与发展中心
    3. 西北工业大学航空学院
  • 收稿日期:2021-08-20 修回日期:2021-10-20 出版日期:2021-10-21 发布日期:2021-10-21
  • 通讯作者: 陈树生

Research on acoustic explosion inversion technology based on inverse augmented Burgers equation

  • Received:2021-08-20 Revised:2021-10-20 Online:2021-10-21 Published:2021-10-21
  • Contact: Shu-Sheng CHEN

摘要: 声爆问题一直是制约超声速客机发展的障碍之一,因此低声爆设计技术在超声速客机的设计中尤为重要。逆向增广Burgers方程可将中场声压信号反演至近场,能够为低声爆反设计工作提供优化目标。本文围绕逆向增广Burgers方程展开研究,运用算子分裂法和正则化伪抛物型方程法对逆向方程进行数值求解,并求取对应的反向等效面积。本文借助第二届、第三届声爆预测研讨会(SBPW-2,SBPW-3)发布的三个标准算例,对数值方法的收敛性、求解准确度、不同中场高度及不同周向角下反演技术的计算精度进行了研究。研究还针对逆向增广Burgers方程的特点,探讨了在中场设置目标波形进行反设计方法的可行性,并对声压信号中高频分量的传播特性进行了研究。研究认为上述方法能够较为准确地完成中场至近场的声压信号反演计算,并且使用中场目标波形代替地面目标波形能减轻反演距离对反演计算过程的影响。

关键词: 声爆, 逆向增广Burgers方程, 超声速客机, 低声爆反设计, 反向等效面积

Abstract: Sonic boom has always been one of the obstacles restricting the development of supersonic airliner. Hence, low sonic boom design technology is particularly important in the design of supersonic airliner. The inverse augmented Burgers equation can invert the mid-field sound pressure signal to the near-field, which can provide optimization objectives for the design of low sonic boom inverse design. This paper focuses on the inverse augmented Burgers equation. The operator splitting technique and the pseudoparabolic equation method are used to numerically solve the inverse equation, and the corresponding reversed equivalent-area is calculated. With the help of three standard examples published in the second and third sonic boom predic-tion workshop (sbpw-2, sbpw-3), the convergence of the numerical method, the accuracy of the solution, and the calculation accuracy of the inversion technique under different field heights and different rolling angles are studied. According to the characteristics of inverse augmented Burgers equation, the feasibility of setting target waveform in mid-field for inverse de-sign method is discussed, and the propagation characteristics of high-frequency components in sound pressure signal are studied. The research shows that the above method can accurately complete the inversion calculation of sound pressure sig-nal from mid-field to near-field, and using mid-field target waveform instead of ground target waveform can reduce the in-fluence of inversion distance on the inversion calculation process.

Key words: Sonic boom, Inverse augmented Burgers equation, Supersonic airliner, Low sonic boom inverse design, Reversed Equivalent-Areas

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