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

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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.

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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

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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.

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