Lagrangian Simulation of Gas-Solid Flows in Homogeneous Isotropic Turbulence

2000 ◽  
Author(s):  
Daniel Huilier
Keyword(s):  
Isotropic Turbulence ◽  
Fluid Velocity ◽  
Particle Dispersion ◽  
Lagrangian Model ◽  
Primary Concern ◽  
Inertial Particles ◽  
Lagrangian Simulation ◽  
Particle Flows ◽  
Spatio Temporal ◽  
Turbulent Particle Dispersion

Abstract A Lagrangian approach is developed to describe particle’s dispersion in a stationary, homogeneous and isotropic turbulent flow. Obviously, the particles’ dispersion is influenced by the fluid velocity fluctuations, which are classically simulated by a Monte Carlo process or Markov chains. However, some studies have shown the restrictions of these methods generating the fluid turbulent velocity and have suggested improvements to ensure that the Lagrangian model accounts for the three main effects governing the dispersion in gas-particle flows, namely the inertia, crossing trajectories and continuity effects. The first aim of this paper is to present an improved Lagrangian model which integrates the spatio-temporal characteristics of the fluid turbulence experienced by the particle. The agreement between the numerical results obtained and the analytical expressions derived by Wang and Stock (1993) will be very satisfying. Another interest is to investigate the role of the traditionally-neglected and troublesome added mass and history terms in numerical studies when long time dispersion of inertial particles is the primary concern. Indeed, we will observe that for a large range of values of the ratio of particle to fluid density, these non-stationary forces have statistically no influence on the characteristics of the turbulent particle dispersion and can be safely omitted.

An Investigation of Crossing Trajectory Effects in Turbulent Shear Flow (Keynote)

2005 ◽  
Author(s):  
Lionel Thomas ◽  
Benoiˆt Oesterle´
Keyword(s):  
Shear Flow ◽  
Isotropic Turbulence ◽  
Fluid Velocity ◽  
Stokes Number ◽  
Turbulent Shear ◽  
Inertial Particles ◽  
Turbulent Shear Flow ◽  
Velocity Magnitude ◽  
Dispersed Particles ◽  
Lagrangian Tracking

The dispersion of small inertial particles moving in a homogeneous, hypothetically stationary, shear flow is investigated using both theoretical analysis and numerical simulation, under one-way coupling approximation. In the theoretical approach, the previous studies are extended to the case of homogeneous shear flow with a corresponding anisotropic spectrum. As it is impossible to obtain a closed theoretical solution without some drastic simplifications, the motion of dispersed particles is also investigated using kinematic simulation where random Fourier modes are generated according to a prescribed anisotropic spectrum with a superimposed linear mean fluid velocity profile. The combined effects of particle Stokes number and dimensionless drift velocity (magnitude and direction) are investigated by computing the statistics from Lagrangian tracking of a large number of particles in many flow field realizations, and comparison is made between the observed effects in shear flow and in isotropic turbulence.

A Turbulent Model for Gas-Particle Jets

2000 ◽  
Vol 122 (3) ◽  
pp. 505-509 ◽  
Author(s):  
J. Garcı´a ◽  
A. Crespo
Keyword(s):  
Mixing Layer ◽  
Stokes Number ◽  
Particle Dispersion ◽  
Lagrangian Model ◽  
Grid Turbulence ◽  
Mean Velocity ◽  
Dissipation Term ◽  
Particle Flows ◽  
Integral Scales ◽  
Kolmogorov Constant

This work is concerned with turbulent diffusion in gas-particle flows. The cases studied correspond to dilute flows and small Stokes number, this implies that the mean velocity of the particles is very similar to that of the fluid element. The classical k-ε method is used to model the gas-phase, modified with additional terms for the k and ε equations, that takes into account the effect of particles on the carrier phase. The additional dissipation term included in the equation for k is due to the slip between phases at an intermediate scale, far from both the Kolmogorov and the integral scales. This term has a proportionality constant equal to 3/2 of Kolmogorov constant, C0. In this paper, a value of 3.0 has been used for this constant as suggested by Du et al., 1995, “Estimation of the Kolmogorov Constant C0 for the Langarian Structure Using a Second-Order Lagrangian Model of Grid Turbulence,” Phys. Fluids 7, (12), pp. 3083–3090. The additional source term for the ε equation is taken as proportional to ε/k, as is usually done. In all experiments analyzed the particles increased the dissipation of turbulent kinetic energy. A comparison is made between the results obtained with the model proposed in this work and the experiments of Shuen et al., 1985, “Structure of Particle-Laden Jets: Measurements and Predictions,” AIAA Journal, 23, No. 3, and Hishida et al., 1992, “Experiments on Particle Dispersion in a Turbulent Mixing Layer,” ASME Journal of Fluids Engineering, 119, pp. 181–194. [S0098-2202(00)02103-9]

Turbulent Dispersion of Heavy Particles With Nonlinear Drag

1997 ◽  
Vol 119 (1) ◽  
pp. 170-179 ◽  
Author(s):  
Renwei Mei ◽  
R. J. Adrian ◽  
T. J. Hanratty
Keyword(s):  
Isotropic Turbulence ◽  
Fluid Velocity ◽  
Interpolation Formula ◽  
Mean Value ◽  
Particle Dispersion ◽  
Turbulent Dispersion ◽  
Heavy Particles ◽  
Time Constants ◽  
The Mean ◽  
Drag Law

The analysis of Reeks (1977) for particle dispersion in isotropic turbulence is extended so as to include a nonlinear drag law. The principal issue is the evaluation of the inertial time constants, βα−1, and the mean slip. Unlike what is found for the Stokesian drag, the time constants are functions of the slip velocity and are anisotropic. For settling velocity, VT, much larger than root-mean-square of the fluid velocity fluctuations, u0, the mean slip is given by VT. For VT→0, the mean slip is related to turbulent velocity fluctuation by assuming that fluctuations in βα are small compared to the mean value. An interpolation formula is used to evaluate βα and VT in regions intermediate between conditions of VT→0 and VT≫ u0. The limitations of the analysis are explored by carrying out a Monte-Carlo simulation for particle motion in a pseudo turbulence described by a Gaussian distribution and Kraichnan’s (1970) energy spectrum.

scholarly journals Small-scale dynamics of settling, bidisperse particles in turbulence

2018 ◽  
Vol 839 ◽  
pp. 594-620 ◽  
Author(s):  
Rohit Dhariwal ◽  
Andrew D. Bragg
Keyword(s):  
Froude Number ◽  
Isotropic Turbulence ◽  
Spatial Clustering ◽  
Fluid Velocity ◽  
Vertical Motion ◽  
Collision Kernel ◽  
Small Scale ◽  
Inertial Particles ◽  
Plane Normal ◽  
The Difference

Mixing and collisions of inertial particles at the small scales of turbulence can be investigated by considering how pairs of particles move relative to each other. In real problems the two particles will have different sizes, i.e. they are bidisperse, and the effect of gravity on their motion is often important. However, how turbulence and gravity compete to control the motion of bidisperse inertial particles is poorly understood. Motivated by this, we use direct numerical simulations (DNS) to investigate the dynamics of settling, bidisperse particles in isotropic turbulence. In agreement with previous studies, we find that without gravity (i.e. $Fr=\infty$, where $Fr$ is the Froude number), bidispersity leads to an enhancement of the relative velocities, and a suppression of their spatial clustering. For $Fr<1$, the relative velocities in the direction of gravity are enhanced by the differential settling velocities of the bidisperse particles, as expected. However, we also find that gravity can strongly enhance the relative velocities in the ‘horizontal’ directions (i.e. in the plane normal to gravity). This non-trivial behaviour occurs because fast settling particles experience rapid fluctuations in the fluid velocity field along their trajectory, leading to enhanced particle accelerations and relative velocities. Indeed, the results show that even when $Fr\ll 1$, turbulence can still play an important role, not only on the horizontal motion, but also on the vertical motion of the particles. This is related to the fact that $Fr$ only characterizes the importance of gravity compared with some typical acceleration of the fluid, yet accelerations in turbulence are highly intermittent. As a consequence, there is a significant probability for particles to be in regions of the flow where the Froude number based on the local, instantaneous fluid acceleration is ${>}1$, even though the typically defined Froude number is $\ll 1$. This could imply, for example, that extreme events in the mixing of settling, bidisperse particles are only weakly affected by gravity even when $Fr\ll 1$. We also find that gravity drastically reduces the clustering of bidisperse particles. These results are strikingly different to the monodisperse case, for which recent results have shown that when $Fr<1$, gravity strongly suppresses the relative velocities in all directions, and can enhance clustering. Finally, we consider the implications of these results for the collision rates of settling, bidisperse particles in turbulence. We find that for $Fr=0.052$, the collision kernel is almost perfectly predicted by the collision kernel for bidisperse particles settling in quiescent flow, such that the effect of turbulence may be ignored. However, for $Fr=0.3$, turbulence plays an important role, and the collisions are only dominated by gravitational settling when the difference in the particle Stokes numbers is ${\geqslant}O(1)$.

Simple Stochastic Model for Particle Dispersion Including Inertia, Trajectory-Crossing, and Continuity Effects

1998 ◽  
Vol 120 (1) ◽  
pp. 186-192 ◽  
Author(s):  
Emmanuel Etasse ◽  
Charles Meneveau ◽  
Thierry Poinsot
Keyword(s):  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Dispersion Model ◽  
Particle Dispersion ◽  
Lagrangian Model ◽  
Practical Implementation ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Reynolds Number Effects ◽  
Physical Effects

An eddy-lifetime, stochastic Lagrangian model for particle dispersion in weakly laden turbulent flows is proposed, in which the interaction time-scale between particles and turbulent eddies is parametrized so as to include several physical effects. It takes into account particle inertia, crossing-trajectory effect, the possible difference in lateral and longitudinal dispersion, and some Reynolds number effects. The parametrization is based on previous results, from a theoretical dispersion model in isotropic turbulence using the trajectory-velocity independence and Gaussian approximations, as well as from Large-Eddy-Simulation. Simple fits are introduced to efficiently capture the main results from these prior studies, allowing practical implementation within the context of k – ε engineering codes. Results from simulations using the proposed approach are compared with experimental data of dispersion in decaying isotropic turbulence.

Particle dispersion in isotropic turbulence under Stokes drag and Basset force with gravitational settling

1991 ◽  
Vol 225 ◽  
pp. 481-495 ◽  
Author(s):  
Renwei Mei ◽  
Ronald J. Adrian ◽  
Thomas J. Hanratty
Keyword(s):  
Isotropic Turbulence ◽  
Fluid Velocity ◽  
Stokes Number ◽  
Particle Dispersion ◽  
Velocity Correlation ◽  
Basset Force ◽  
Stokes Drag ◽  
High Particle ◽  
Velocity Correlation Function ◽  
Density Ratios

An analysis that includes the effects of Basset and gravitational forces is presented for the dispersion of particles experiencing Stokes drag in isotropic turbulence. The fluid velocity correlation function evaluated on the particle trajectory is obtained by using the independence approximation and the assumption of Gaussian velocity distributions for both the fluid and the particle, formulated by Pismen & Nir (1978). The dynamic equation for particle motion with the Basset force is Fourier transformed to the frequency domain where it can be solved exactly. It is found that the Basset force has virtually no influence on the structure of the fluid velocity fluctuations seen by the particles or on particle diffusivities. It does, however, affect the motion of the particle by increasing (reducing) the intensities of particle turbulence for particles with larger (smaller) inertia. The crossing of trajectories associated with the gravitational force tends to enhance the effect of the Basset force on the particle turbulence. An ordering of the terms in the particle equation of motion shows that the solution is valid for high particle/fluid density ratios and to 0(1) in the Stokes number.

Lagrangian simulation of turbulent particle dispersion in electrostatic precipitators

AIChE Journal ◽  
1997 ◽  
Vol 43 (6) ◽  
pp. 1403-1413 ◽  
Author(s):  
Alfredo Soldati ◽  
Massimo Casal ◽  
Paolo Andreussi ◽  
Sanjoy Banerjee
Keyword(s):  
Particle Dispersion ◽  
Lagrangian Simulation ◽  
Electrostatic Precipitators ◽  
Turbulent Particle Dispersion

A Second Order Lagrangian Model for Irregular Ocean Waves

2005 ◽  
Vol 128 (3) ◽  
pp. 177-183 ◽  
Author(s):  
Sébastien Fouques ◽  
Harald E. Krogstad ◽  
Dag Myrhaug
Keyword(s):  
Specular Reflection ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Wave Theory ◽  
Ocean Waves ◽  
Second Order ◽  
Lagrangian Model ◽  
Lagrangian Description ◽  
Linear Wave ◽  
Irregular Solution

Synthetic aperture radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, slope, and mean curvature are studied.

scholarly journals Experiments on generation of surface waves by an underwater moving bottom

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150069 ◽  
Author(s):  
Timothée Jamin ◽  
Leonardo Gordillo ◽  
Gerardo Ruiz-Chavarría ◽  
Michael Berhanu ◽  
Eric Falcon
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Surface Deformation ◽  
Fluid Layer ◽  
Fluid Velocity ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Spatio Temporal ◽  
Experimental Findings

We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes an upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics (i.e. its spatio-temporal features) in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal high-pass filter coupled with a spatial low-pass filter. Both filter effects are often neglected in tsunami warning systems, particularly in real-time forecast. Our results display good agreement with a prevailing linear theory without any parameter fitting. Based on our experimental findings, we provide a simple theoretical approach for modelling the rapid kinematics limit that is applicable even for initially non-flat bottoms: this may be a key step for more realistic varying bathymetry in tsunami scenarios.

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