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.

Assessing sediment transport energetics with instrumented particles for above threshold of motion turbulent flows

2020 ◽  
Author(s):  
Zaid Al-Husban ◽  
Manousos Valyrakis
Keyword(s):  
Sediment Transport ◽  
Turbulent Flows ◽  
Particle Transport ◽  
Particle Interaction ◽  
Turbulent Channel Flow ◽  
Optimal Operation ◽  
Distribution Functions ◽  
Sensor Data ◽  
Flow Rates ◽  
Test Configuration

<p>Despite the fact sediment transport has been studied for decades, there is still a need to gain a further insight on the nature and driving mechanisms of bed particle motions induced by turbulent flows, for the low transport stages where the particle transport is relatively intermittent. A custom designed and prototyped instrumented particle, embedded with inertial sensors is used herein to study its transport over hydraulically rough bed surfaces. The calibration and error estimation for its sensors is also undertaken before starting the experiments, to ensure optimal operation and estimate any uncertainties.</p><p>The observations and results of this research are obtained from experiments carried out at the University of Glasgow 12 meters long and 0.9 meters wide, tilting and water recirculating flume. The flume walls comprise of smooth transparent glass that enables observing particle transport from the side (also with underwater video cameras) and the bed surface generally is layered with coarse gravel.</p><p>The particle is initially located at the upstream end of the test configuration, fully exposed to the uniform and fully developed turbulent channel flow. The top and side cameras are set in their suitable positions to monitor and study the behaviour of particle motion by capturing the dynamical features of sediment motion and to not interfere with flow field that pushes particle downstream.<span> </span></p><p>Using the sensor data to calculate the kinetic energy for a range of sets of sediment transport experiments with varying flow rates and particle densities, the probability distribution functions (PDFs) of particle transport features, such as particle’s total energy, are generated which give information about particle interaction with the surface bed during its motion. In addition, the effects of different flow rates, particle densities on particle energy are assessed.</p>

Effects of Preferential Concentration on Heat Transfer in Particle-Based Solar Receivers

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Hadi Pouransari ◽  
Ali Mani
Keyword(s):  
Heat Transfer ◽  
Turbulent Flows ◽  
Particle Transport ◽  
Three Dimensional ◽  
Stokes Number ◽  
Radiative Heating ◽  
Radiation Absorption ◽  
Order Unity ◽  
Carrier Fluid ◽  
Preferential Concentration

The working principle of particle-based solar receivers is to utilize the absorptivity of a dispersed particle phase in an otherwise optically transparent carrier fluid. In comparison to their traditional counterparts, which use a solid surface for radiation absorption, particle-based receivers offer a number of opportunities for improved efficiency and heat transfer uniformity. The physical phenomena at the core of such receivers involve coupling between particle transport, fluid turbulence, and radiative heat transfer. Previous analyses of particle-based solar receivers ignored delicate aspects associated with this three-way coupling. Namely, these investigations considered the flow fields only in the mean sense and ignored turbulent fluctuations and the consequent particle preferential concentration. In the present work, we have performed three-dimensional direct numerical simulations of turbulent flows coupled with radiative heating and particle transport over a range of particle Stokes numbers. Our study demonstrates that the particle preferential concentration has strong implications on the heat transfer statistics. We demonstrate that “for a typical setting” the preferential concentration of particles reduces the effective heat transfer between particles and the gas by as much as 25%. Therefore, we conclude that a regime with Stokes number of order unity is the least preferred for heat transfer to the carrier fluid. We also provide a 1D model to capture the effect of particle spatial distribution in heat transfer.

scholarly journals Particle transport in turbulent curved pipe flow

2016 ◽  
Vol 793 ◽  
pp. 248-279 ◽  
Author(s):  
Azad Noorani ◽  
Gaetano Sardina ◽  
Luca Brandt ◽  
Philipp Schlatter
Keyword(s):  
Turbulent Flows ◽  
Particle Transport ◽  
Carrier Phase ◽  
Solid Phase ◽  
Viscous Sublayer ◽  
Companion Paper ◽  
Current Data ◽  
Spherical Particles ◽  
Data Set ◽  
Curved Pipe

Direct numerical simulations (DNS) of particle-laden turbulent flow in straight, mildly curved and strongly bent pipes are performed in which the solid phase is modelled as small heavy spherical particles. A total of seven populations of dilute particles with different Stokes numbers, one-way coupled with their carrier phase, are simulated. The objective is to examine the effect of the curvature on micro-particle transport and accumulation. It is shown that even a slight non-zero curvature in the flow configuration strongly impact the particle concentration map such that the concentration of inertial particles with bulk Stokes number $0.45$ (based on bulk velocity and pipe radius) at the inner bend wall of mildly curved pipe becomes $12.8$ times larger than that in the viscous sublayer of the straight pipe. Near-wall helicoidal particle streaks are observed in the curved configurations with their inclination varying with the strength of the secondary motion of the carrier phase. A reflection layer, as previously observed in particle laden turbulent S-shaped channels, is also apparent in the strongly curved pipe with heavy particles. In addition, depending on the curvature, the central regions of the mean Dean vortices appear to be completely depleted of particles, as observed also in the partially relaminarised region at the inner bend. The turbophoretic drift of the particles is shown to be affected by weak and strong secondary motions of the carrier phase and geometry-induced centrifugal forces. The first- and second-order moments of the velocity and acceleration of the particulate phase in the same configurations are addressed in a companion paper by the same authors. The current data set will be useful for modelling particles advected in wall-bounded turbulent flows where the effects of the curvature are not negligible.

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