On a kinetic equation for the transport of particles in turbulent flows

1991 ◽  
Vol 3 (3) ◽  
pp. 446-456 ◽  
Author(s):  
M. W. Reeks
Keyword(s):  
Kinetic Equation ◽  
Turbulent Flows

scholarly journals Kinetic equation for particle transport in turbulent flows

2020 ◽  
Vol 32 (7) ◽  
pp. 073301
Author(s):  
De-Yu Zhong ◽  
Guang-Qian Wang ◽  
Ming-Xi Zhang ◽  
Tie-Jian Li
Keyword(s):  
Kinetic Equation ◽  
Turbulent Flows ◽  
Particle Transport

CFD Application of the Diffusion-Inertia Model to Bubble Flows and Boiling Water Problems

2009 ◽  
Author(s):  
Alexander S. Filippov ◽  
Vladimir M. Alipchenkov ◽  
Nickolay I. Drobyshevsky ◽  
Roman V. Mukin ◽  
Valeri Th. Strizhov ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Kinetic Equation ◽  
Probability Density Function ◽  
Turbulent Flows ◽  
Particle Velocity ◽  
Boiling Water ◽  
Extended Version ◽  
Governing Equations ◽  
Inertia Model ◽  
Water Problems

The paper is aimed at the application of a model for simulating the dispersed turbulent flows. The model presented proceeds from a kinetic equation for the probability density function of the particle velocity distribution in turbulent flow. This approach is called the diffusion-inertia model (DIM). Applications of the model to droplet and bubble flows are presented. In the case of vaporized liquid, the interphase heat and mass transfer is introduced by adding the corresponding governing equations. This extended version of the DIM was applied to simulating the boiling water flow in a heated pipe.

Non-isothermal dispersed phase of particles in turbulent flow

2003 ◽  
Vol 475 ◽  
pp. 205-245 ◽  
Author(s):  
R. V. R. PANDYA ◽  
F. MASHAYEK
Keyword(s):  
Kinetic Equation ◽  
Phase Space ◽  
Turbulent Flows ◽  
Fluid Phase ◽  
Statistical Properties ◽  
Temperature Gradients ◽  
Particle Phase ◽  
Galilean Transformation ◽  
Mean Velocity ◽  
The Mean

In this paper we consider, for modelling and simulation, a non-isothermal turbulent flow laden with non-evaporating spherical particles which exchange heat with the surrounding fluid and do not collide with each other during the course of their journey under the influence of the stochastic fluid drag force. In the modelling part of this study, a closed kinetic or probability density function (p.d.f.) equation is derived which describes the distribution of position x, velocity v, and temperature θ of the particles in the flow domain at time t. The p.d.f. equation represents the transport of the ensemble-average (denoted by 〈 〉) phase-space density 〈W(x, v, θ, t)〉. The process of ensemble averaging generates unknown terms, namely the phase-space diffusion current j = βv〈u′W〉 and the phase-space heat current h = βθ〈t′W〉, which pose closure problems in the kinetic equation. Here, u′ and t′ are the fluctuating parts of the velocity and temperature, respectively, of the fluid in the vicinity of the particle, and βv and βθ are inverse of the time constants for the particle velocity and temperature, respectively. The closure problems are first solved for the case of homogeneous turbulence with uniform mean velocity and temperature for the fluid phase by using Kraichnan’s Lagrangian history direct interaction (LHDI) approximation method and then the method is generalized to the case of inhomogeneous flows. Another method, which is due to Van Kampen, is used to solve the closure problems, resulting in a closed kinetic equation identical to the equation obtained by the LHDI method. Then, the closed equation is shown to be compatible with the transformation constraint that is proposed by extending the concept of random Galilean transformation invariance to non-isothermal flows and is referred to as the ‘extended random Galilean transformation’ (ERGT). The macroscopic equations for the particle phase describing the time evolution of statistical properties related to particle velocity and temperature are derived by taking various moments of the closed kinetic equation. These equations are in the form of transport equations in the Eulerian framework, and are computed for the case of two-phase homogeneous shear turbulent flows with uniform temperature gradients. The predictions are compared with the direct numerical simulation (DNS) data which are generated as another part of this study. The predictions for the particle phase require statistical properties of the fluid phase which are taken from the DNS data. In DNS, the continuity, Navier–Stokes, and energy equations are solved for homogeneous turbulent flows with uniform mean velocity and temperature gradients. For the mean velocity gradient along the x2- (cross-stream) axis, three different cases in which the mean temperature gradient is along the x1-, x2-, and x3-axes, respectively, are simulated. The statistical properties related to the particle phase are obtained by computing the velocity and temperature of a large number of particles along their Lagrangian trajectories and then averaging over these trajectories. The comparisons between the model predictions and DNS results show very encouraging agreement.

Computational Fluid Dynamics Application of the Diffusion-Inertia Model to Bubble Flows and Boiling Water Problems

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Alexander S. Filippov ◽  
Vladimir M. Alipchenkov ◽  
Nickolay I. Drobyshevsky ◽  
Roman V. Mukin ◽  
Valeri F. Strizhov ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Mass Transfer ◽  
Computational Fluid Dynamics ◽  
Kinetic Equation ◽  
Turbulent Flows ◽  
Boiling Water ◽  
Extended Version ◽  
Governing Equations ◽  
Inertia Model ◽  
Water Problems

This paper is aimed at the application of a model for simulating the dispersed turbulent flows. The presented model proceeds from a kinetic equation for the probability density function of the particle velocity distribution in turbulent flow. This approach is called the diffusion-inertia model (DIM). Applications of the model to droplet and bubble flows are presented. In the case of vaporized liquid, the interphase heat and mass transfer is introduced by adding the corresponding governing equations. This extended version of the DIM was applied to simulating the boiling water flow in a heated pipe.

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