Continuous models of the motion of inertial particles in laminar and turbulent flows based on the Fokker-Planck equations

Abstract The transfer of particles in laminar and turbulent flows has many applications in combustion systems, biological, environmental, nanotechnology. In the present study, a Combined Baffles Quick-Separation Device (CBQSD) is simulated numerically using the Eulerian-Lagrangian method and different turbulence models of RNG k-ε, k-ω, and RSM for 1–140 μm particles. A two-way coupling technique is employed to solve the particles’ flow. The effect of inlet flow velocity, the diameter of the splitter plane, and solid particles’ flow rate on the separation efficiency of the device is examined. The results demonstrate that the RSM turbulence model provides more appropriate results compared to RNG k-ε and k-ω models. Four thousand two hundred particles with the size distribution of 1–140 µm enter the device and 3820 particles are trapped and 380 particles leave the device. The efficiency for particles with a diameter greater than 28 µm is 100%. The complete separation of 22–28 μm particles occurs for flow rates of 10–23.5 g/s, respectively. The results reveal that the separation efficiency increases by increasing the inlet velocity, the device diameter, and the diameter of the particles.

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Fokker–Planck representations of non-Markov Langevin equations: application to delayed systems

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2018.0131 ◽

2019 ◽

Vol 377 (2153) ◽

pp. 20180131 ◽

Cited By ~ 2

Author(s):

Luca Giuggioli ◽

Zohar Neu

Keyword(s):

Langevin Equation ◽

Complex Dynamics ◽

Probability Distributions ◽

Delay Systems ◽

Langevin Equations ◽

Delayed Systems ◽

Temporal Features ◽

Fokker Planck Equations ◽

Random Fluctuations ◽

Fokker Planck

Noise and time delays, or history-dependent processes, play an integral part in many natural and man-made systems. The resulting interplay between random fluctuations and time non-locality are essential features of the emerging complex dynamics in non-Markov systems. While stochastic differential equations in the form of Langevin equations with additive noise for such systems exist, the corresponding probabilistic formalism is yet to be developed. Here we introduce such a framework via an infinite hierarchy of coupled Fokker–Planck equations for the n -time probability distribution. When the non-Markov Langevin equation is linear, we show how the hierarchy can be truncated at n = 2 by converting the time non-local Langevin equation to a time-local one with additive coloured noise. We compare the resulting Fokker–Planck equations to an earlier version, solve them analytically and analyse the temporal features of the probability distributions that would allow to distinguish between Markov and non-Markov features. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

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