Equations of Multimoment Hydrodynamics in the Problem of Flowing Around a Sphere. 1. Construction of Asymmetric Distributions of Hydrodynamic Values

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

The equations of multimoment hydrodynamics are used to interpret flows behind the sphere that do not have axial symmetry. The equations of multimoment hydrodynamics follow from the equations for pair distribution functions. The derivation of the equations is free from approximations similar to the Boltzmann hypothesis. In accordance with the general approach, the pair function is represented as an infinite series of products of trajectory invariants with unknown coefficients. A finite number of terms are preserved in this series, which make it possible to construct asymmetric distributions of hydrodynamic values. Analytical expressions for the principal hydrodynamic values are presented. Solutions of nonlinear differential equations for unknown coefficients will make it possible to trace the evolution of the observed asymmetric flows, culminating in pronounced turbulence.

Full Text

Restricted Access

About the authors

I. V. Lebed

Institute of Applied Mechanics of the Russian Academy of Sciences

Author for correspondence.
Email: lebed-ivl@yandex.ru
Russian Federation, Moscow

References

  1. L.G. Loitsyanskii. Mechanics of Liquids and Gases. Oxford: Pergamon, 1966.
  2. Mikhalkin V.N., Sumskoi S.I., Tereza A.M. et al. // Russ. J. Phys. Chem. B 2022. V. 16. P. 629.
  3. Lebed I.V., Umanskii S.Y. // Russ. J. Phys. Chem. B. 2007. V. 1. P. 52. https://doi.org/10.1134/S1990793107010071
  4. I.V. Lebed. The Foundations of Multimoment Hydrodynamics. Part 1: Ideas, Methods and Equations. N-Y: Nova Science Publishers, 2018.
  5. Lebed I.V. // Chem. Phys. Lett. 1990. V. 165. № 1-2. P. 226, https://doi.org/10.1016/0009-2614(90)85433-D
  6. Lebed I.V. // Physica A. 2019. V. 515. P. 715. https://doi.org/10.1016/j.physa.2018.09.166
  7. Lebed I.V. // Physica A. 2019. V. 524. P. 325. https://doi.org/10.1016/j.physa.2019.04.086
  8. Lebed I.V. // Chem. Phys. Rep. 1997. V. 16. P. 1263.
  9. Lebed I.V. // Russ. J. Phys. Chem. B. 2014. V. 8. P. 240. https://doi.org/10.1134/S1990793114020171
  10. Kiselev A.Ph., Lebed I.V. // Chaos, Solitons, Fractals. 2021. V. 142. №110491, http:// doi.org/10.1016/j.chaos.2020.110491
  11. Lebed I.V. // Russ. J. Phys. Chem. B. 2022. V. 16. P. 370. http:// doi.org/10.1134/S199079312202018X
  12. Lebed I.V. // Russ. J. Phys. Chem. B. 2023. V. 17. P. 1194. https://doi.org/10.1134/S1990793123050056
  13. Lebed I.V. // Russ. J. Phys. Chem. B. 2023. V. 17. P. 1414. https://doi.org/10.1134/S1990793123060179
  14. Lebed I.V. // Russ. J. Phys. Chem. B. 2024. V. 18. P. 1296. https://doi.org/10.1134/S1990793124700957
  15. Lebed I.V. // Russ. J. Phys. Chem. B. 2024. V. 18. P. 1405. https://doi.org/10.1134/S1990793124700969

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Fig. 1. XYZ coordinate system rigidly connected with the centre of the sphere. The Z axis coincides in direction with the velocity of the impinging flow U0; r, θ, φ - spherical coordinates of the vector x; R1 - velocity integration region.

Download (88KB)
Indexing metadata

Copyright (c) 2025 Russian Academy of Sciences