Skip to main content
SpringerLink
Log in

A unified theory for gas dynamics and aeroacoustics in viscous compressible flows. Part I. Unbounded fluid

黏性可压缩气体动力学和气动声学的统一理论基础初探(I) 无界 流动

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

This paper presents a deep reflection on the advective wave equations for velocity vector and dilatation discovered in the past decade. We show that these equations can form the theoretical basis of modern gas dynamics, because they dominate not only various complex viscous and heat-conducting gas flows but also their associated longitudinal waves, including aero-generated sound. Current aeroacoustics theory has been developing in a manner quite independently of gas dynamics; it is based on the advective wave equations for thermodynamic variables, say the exact Phillips equation of relative disturbance pressure as a representative one. However, these equations do not cover the fluid flow that generates and propagates sound waves. In using them, one has to assume simplified base-flow models, which we argue is the main theoretical obstacle to identifying sound source and achieving effective noise control. Instead, we show that the Phillips equation and alike is nothing but the first integral of the dilatation equation that also governs the longitudinal part of the flow field. Therefore, we conclude that modern aeroacoustics should merge back into the general unsteady gas dynamics as a special branch of it, with dilatation of multiple sources being a new additional and sharper sound variable.

摘要

本文是对过去十年发现的速度矢量和胀量的运流波动方程的反思和深化. 结果表明, 矢量速度方程和胀量方程不仅能刻画黏 性传热流体的各种复杂流动本身, 而且能刻画包括气动噪声在内的各种纵波在复杂流场中的非线性形成与演化, 因此它们可以构成现 代气体动力学的理论基础. 现代气动声学理论的建立是基于热力学变量的运流波动方程(例如Phillips方程), 其发展完全独立于气体动 力学. 然而, 基于热力学变量的方程不能预测产生并传播声波的各种复杂流动本身, 使得人们不得不代之以过度简化的模型, 因而导致 了声源识别的不确定性和噪声难以控制. 我们证明, Phillips方程和同类基于热力学变量的方程只不过是胀量方程的一次积分, 后者主 管了流动的纵场部分. 因此, 现代气动声学作为气体动力学的一个分支应该重新融合到气体动力学的统一理论框架之中, 同时具有多 种物理源的胀量也应该视为新的且更普适的声学变量.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. F. Mao, Y. P. Shi, L. J. Xuan, W. D. Su, and J. Z. Wu, On the governing equations for the compressing process and its coupling with other processes, Sci. China-Phys. Mech. Astron. 54, 1154 (2011).

    Article  Google Scholar 

  2. F. Mao, L. L. Kang, J. Z. Wu, J. L. Yu, A. K. Gao, W. D. Su, and X. Y. Lu, A study of longitudinal processes and interactions in compressible viscous flows, J. Fluid Mech. 893, A23 (2020).

    Article  MathSciNet  MATH  Google Scholar 

  3. R. D. Zucker, and O. Biblarz, Fundamentals of Gas Dynamics, 3rd ed. (John Wiley & Sons, New Jersey, 2020).

    Google Scholar 

  4. R. G. Davies, Aerodynamics Principles for Air Transport Pilots (CRC Press, Boca Raton, 2020).

    Book  Google Scholar 

  5. H. Schlichting, and K. Gersten, Boundary Layer Theory, 9th ed. (Springer, Berlin, 2017).

    Book  MATH  Google Scholar 

  6. M. J. Lighthill, On sound generated aerodynamically I. General theory, Proc. R. Soc. Lond. A 211, 564 (1952).

    Article  MathSciNet  MATH  Google Scholar 

  7. M. J. Lighthill, On sound generated aerodynamically II. Turbulence as a source of sound, Proc. R. Soc. Lond. A 222, 1 (1954).

    Article  MathSciNet  MATH  Google Scholar 

  8. N. Peake, and A. B. Parry, Modern challenges facing turbomachinery aeroacoustics, Annu. Rev. Fluid Mech. 44, 227 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Ihme, Combustion and engine-core noise, Annu. Rev. Fluid Mech. 49, 277 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  10. S. Karabasov, L. Ayton, X. Wu, and M. Afsar, Advances in aeroacoustics research: Recent developments and perspectives, Phil. Trans. R. Soc. A. 377, 20190390 (2019).

    Article  MathSciNet  MATH  Google Scholar 

  11. J. W. Jaworski, and N. Peake, Aeroacoustics of silent owl flight, Annu. Rev. Fluid Mech. 52, 395 (2020).

    Article  MATH  Google Scholar 

  12. H. Daryan, F. Hussain, and J. P. Hickey, Sound generation mechanism of compressible vortex reconnection, J. Fluid Mech. 933, A34 (2022).

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Wu, L. Liu, and T. Liu, Fundamental theories of aerodynamic force in viscous and compressible complex flows, Prog. Aerosp. Sci. 99, 27 (2018).

    Article  Google Scholar 

  14. J. J. Alonso, and M. R. Colonno, Multidisciplinary optimization with applications to sonic-boom minimization, Annu. Rev. Fluid Mech. 44, 505 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  15. D. Y. Ma, Modern Acoustic Theory Foundation (Science Press, Beijing, 2004).

    Google Scholar 

  16. G. K. Vallis, Essentials of Atmospheric and Oceanic Dynamics, illustrated ed. (Cambridge University Press, Cambridge, 2019).

    Book  Google Scholar 

  17. J. E. Ffowcs Williams, Aeroacoustics, Annu. Rev. Fluid Mech. 9, 447 (1977).

    Article  MATH  Google Scholar 

  18. P. Jordan, and Y. Gervais, Subsonic jet aeroacoustics: Associating experiment, modelling and simulation, Exp. Fluids 44, 1 (2008).

    Article  Google Scholar 

  19. F. Mao, Y. P. Shi, and J. Z. Wu, On a general theory for compressing process and aeroacoustics: Linear analysis, Acta Mech. Sin. 26, 355 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  20. H. Babinsky, and J. K. Harvey, Shock Wave-Boundary-Layer Interactions (Cambridge University Press, Cambridge, 2011).

    Book  MATH  Google Scholar 

  21. O. M. Phillips, On the generation of sound by supersonic turbulent shear layers, J. Fluid Mech. 9, 1 (1960).

    Article  MathSciNet  MATH  Google Scholar 

  22. D. Kochkov, J. A. Smith, A. Alieva, Q. Wang, M. P. Brenner, and S. Hoyer, Machine learning-accelerated computational fluid dynamics, Proc. Natl. Acad. Sci. USA 118, e2101784118 (2021).

    Article  MathSciNet  Google Scholar 

  23. R. D. Sandberg, and V. Michelassi, Fluid dynamics of axial turbomachinery: Blade- and stage-level simulations and models, Annu. Rev. Fluid Mech. 54, 255 (2022).

    Article  MATH  Google Scholar 

  24. C. Lagemann, K. Lagemann, S. Mukherjee, and W. Schröder, Deep recurrent optical flow learning for particle image velocimetry data, Nat. Mach. Intell. 3, 641 (2021).

    Article  Google Scholar 

  25. P. M. Danehy, R. A. Burns, D. T. Reese, J. E. Retter, and S. P. Kearney, FLEET velocimetry for aerodynamics, Annu. Rev. Fluid Mech. 54, 525 (2022).

    Article  MATH  Google Scholar 

  26. M. J. Lighthill, in Viscosity effects in sound waves of finite amplitude: Surveys in Mechanics, edited by G. K. Batchelor, and R. M. Davies (Cambridge University Press, Cambridge, 1956), pp. 250–351.

  27. L. S. G. Kovásznay, Turbulence in supersonic flow, J. Aeronaut. Sci. 20, 657 (1953).

    Article  MATH  Google Scholar 

  28. C. J. Chapman, High Speed Flow (Cambridge University Press, Cambridge, 2000).

    MATH  Google Scholar 

  29. M. Wang, J. B. Freund, and S. K. Lele, Computational prediction of flow-generated sound, Annu. Rev. Fluid Mech. 38, 483 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  30. G. M. Lilley, On the noise from jets, Noise Mechanisms AGARD-CP-131, 13.1–13.12 (1974).

  31. T. Colonius, S. K. Lele, and P. Moin, Sound generation in a mixing layer, J. Fluid Mech. 330, 375 (1997).

    Article  MATH  Google Scholar 

  32. M. E. Goldstein, An exact form of Lilley’s equation with a velocity quadrupole/temperature dipole source term, J. Fluid Mech. 443, 231 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  33. M. E. Goldstein, A generalized acoustic analogy, J. Fluid Mech. 488, 315 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  34. M. E. Goldstein, On identifying the true sources of aerodynamic sound, J. Fluid Mech. 526, 337 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  35. X. Wu, Generation of sound and instability waves due to unsteady suction and injection, J. Fluid Mech. 453, 289 (2002).

    Article  MATH  Google Scholar 

  36. D. R. Dowling, and K. G. Sabra, Acoustic remote sensing, Annu. Rev. Fluid Mech. 47, 221 (2015).

    Article  MathSciNet  Google Scholar 

  37. L. Q. Liu, J. Y. Zhu, and J. Z. Wu, Lift and drag in two-dimensional steady viscous and compressible flow, J. Fluid Mech. 784, 304 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  38. L. Q. Liu, J. Z. Wu, W. D. Su, and L. L. Kang, Lift and drag in three-dimensional steady viscous and compressible flow, Phys. Fluids 29, 116105 (2017), arXiv: 1611.09615.

    Article  Google Scholar 

  39. S. Zou, L. Liu, and J. Wu, Numerical validation and physical explanation of the universal force theory of three-dimensional steady viscous and compressible flow, Phys. Fluids 33, 036107 (2021), arXiv: 2012.11320.

    Article  Google Scholar 

  40. A. D. Pierce, Wave equation for sound in fluids with unsteady inhomogeneous flow, J. Acoust. Soc. Am. 87, 2292 (1990).

    Article  Google Scholar 

  41. W. Möehring, On vortex sound at low Mach number, J. Fluid Mech. 85, 685 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  42. S. K. Lele, and J. W. Nichols, A second golden age of aeroacoustics? Phil. Trans. R. Soc. A. 372, 20130321 (2014).

    Article  Google Scholar 

  43. R. Ewert, and J. Kreuzinger, Hydrodynamic/acoustic splitting approach with flow-acoustic feedback for universal subsonic noise computation, J. Comput. Phys. 444, 110548 (2021), arXiv: 2009.07155.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, 100871, China

    Feng Mao  (毛峰) & Jiezhi Wu  (吴介之)

  2. Shenzhen Tenfong Technology Co., LTD, Shenzhen, 518055, China

    Feng Mao  (毛峰)

  3. School of Engineering, Westlake University, Hangzhou, 310024, China

    Linlin Kang  (康林林)

  4. Department of Modern Mechanics, University of Science and Technology of China, Hefei, 230026, China

    Luoqin Liu  (刘罗勤)

  5. Physics of Fluids Group, University of Twente, 7500 AE, Enschede, The Netherlands

    Luoqin Liu  (刘罗勤)

Authors
  1. Feng Mao  (毛峰)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Linlin Kang  (康林林)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luoqin Liu  (刘罗勤)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiezhi Wu  (吴介之)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luoqin Liu  (刘罗勤).

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12102365, 91752202 and 11472016). Luoqin Liu was supported by the Hundred Talents Program of the Chinese Academy of Sciences (CAS). We thank encouragement and valuable discussions from Profs. Shu-Hai Zhang, Zhan-Sen Qian, Drs. Shu-Fan Zou, An-Kang Gao, and Zhen Li.

Electronic Supplementary Material

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mao, F., Kang, L., Liu, L. et al. A unified theory for gas dynamics and aeroacoustics in viscous compressible flows. Part I. Unbounded fluid. Acta Mech. Sin. 38, 321492 (2022). https://doi.org/10.1007/s10409-022-09033-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10409-022-09033-4

Keywords

Search

Navigation