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Analytical and Numerical Solution of the Equation for the Probability Density Function of the Particle Velocity in a Turbulent Flow

  • GENERAL PROBLEMS OF TRANSPORT THEORY
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Journal of Engineering Physics and Thermophysics Aims and scope

A study has been made of the random motion of inertial particles in a homogeneous isotropic turbulent gas flow. Fluctuations of the gas velocity along the particle path were modeled by the Gaussian random process with a finite time of degeneracy of the autocorrelation function. A closed equation has been obtained for the probability density function of the particle velocity, for which two methods of numerical solution have been proposed: using the finite-difference scheme and using one based on direct numerical modeling of an empirical probability density function. The empirical probability density function was obtained as a result of the averaging of random particle paths, which are a solution of a system of ordinary stochastic differential equations. The results of numerical calculation have been compared with the analytical solution describing the dynamics of the probability density function of the particle-velocity distribution.

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Authors and Affiliations

  1. N. É. Bauman Moscow State Technical University, 5 2nd Baumanskaya Str., Moscow, 105005, Russia

    I. V. Derevich & A. K. Klochkov

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  1. I. V. Derevich
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  2. A. K. Klochkov
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Correspondence to I. V. Derevich.

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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 93, No. 5, pp. 1081–1092, September–October, 2020.

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Derevich, I.V., Klochkov, A.K. Analytical and Numerical Solution of the Equation for the Probability Density Function of the Particle Velocity in a Turbulent Flow. J Eng Phys Thermophy 93, 1043–1054 (2020). https://doi.org/10.1007/s10891-020-02206-4

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  • DOI: https://doi.org/10.1007/s10891-020-02206-4

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