Particle Dispersion in Fine Scales of Homogeneous Isotropic Turbulence

2007 ◽  
Author(s):  
M. Sato ◽  
M. Tanahashi ◽  
T. Miyauchi
Keyword(s):  
Isotropic Turbulence ◽  
Major Axis ◽  
Stokes Number ◽  
High Energy ◽  
Energy Dissipation Rate ◽  
Particle Dispersion ◽  
Fine Scale ◽  
Number Density ◽  
Homogeneous Isotropic Turbulence ◽  
Preferential Concentration

Direct numerical simulations of homogeneous isotropic turbulence laden with particles have been conducted to clarify the relationship between particle dispersion and coherent fine scale eddies in turbulence. Dispersion of 106 particles are analyzed for several particle Stokes numbers. The spatial distributions of particles depend on their Stokes number, and the Stokes number that causes preferential concentration of particles is closely related to the time scale of coherent fine scale eddies in turbulence. On the plane perpendicular to the rotating axes of fine scale eddies, number density of particle with particular Stokes number is low at the center of the fine scale eddy, and high in the regions with high energy dissipation rate around the eddy. The maximum number density can be observed at about 1.5 to 2.0 times the eddy radius on the major axis of the fine scale eddy.

Lift Force Effects on the Behavior of Bubbles in Homogeneous Isotropic Turbulence

2005 ◽  
Author(s):  
Mustapha Abbad ◽  
Benoiˆt Oesterle´
Keyword(s):  
Relative Velocity ◽  
Lift Force ◽  
Isotropic Turbulence ◽  
Stokes Number ◽  
Rise Velocity ◽  
Homogeneous Isotropic Turbulence ◽  
Preferential Concentration ◽  
Coupling Approximation ◽  
Lagrangian Tracking ◽  
Small Bubbles

The influence of lift forces on the dispersion of small bubbles is numerically studied in a homogeneous isotropic turbulence generated by random Fourier modes, under one-way coupling approximation. The effects of bubble Stokes number and mean relative velocity are investigated by computing the statistics from Lagrangian tracking of a large number of bubbles in many flow field realizations, and comparison is provided between the results obtained with and without taking the lift force into account. The effects of preferential concentration, which are known to reduce the terminal rise velocity of bubbles, are also investigated. The lift force is found to drastically modify the correlations and integral time scales of the fluid seen by the bubbles in their fluctuating motion, and to significantly enhance the accumulation of bubbles in high vorticity regions.

scholarly journals Reynolds-number dependence of turbulence enhancement on collision growth

2016 ◽  
Vol 16 (19) ◽  
pp. 12441-12455 ◽  
Author(s):  
Ryo Onishi ◽  
Axel Seifert
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Stokes Number ◽  
Homogeneous Isotropic Turbulence ◽  
Collision Efficiency ◽  
Cloud Droplets ◽  
Clustering Effect ◽  
Reynolds Number Dependence ◽  
Coagulation Kernel

Abstract. This study investigates the Reynolds-number dependence of turbulence enhancement on the collision growth of cloud droplets. The Onishi turbulent coagulation kernel proposed in Onishi et al. (2015) is updated by using the direct numerical simulation (DNS) results for the Taylor-microscale-based Reynolds number (Reλ) up to 1140. The DNS results for particles with a small Stokes number (St) show a consistent Reynolds-number dependence of the so-called clustering effect with the locality theory proposed by Onishi et al. (2015). It is confirmed that the present Onishi kernel is more robust for a wider St range and has better agreement with the Reynolds-number dependence shown by the DNS results. The present Onishi kernel is then compared with the Ayala–Wang kernel (Ayala et al., 2008a; Wang et al., 2008). At low and moderate Reynolds numbers, both kernels show similar values except for r2 ∼ r1, for which the Ayala–Wang kernel shows much larger values due to its large turbulence enhancement on collision efficiency. A large difference is observed for the Reynolds-number dependences between the two kernels. The Ayala–Wang kernel increases for the autoconversion region (r1, r2 < 40 µm) and for the accretion region (r1 < 40 and r2 > 40 µm; r1 > 40 and r2 < 40 µm) as Reλ increases. In contrast, the Onishi kernel decreases for the autoconversion region and increases for the rain–rain self-collection region (r1, r2 > 40 µm). Stochastic collision–coalescence equation (SCE) simulations are also conducted to investigate the turbulence enhancement on particle size evolutions. The SCE with the Ayala–Wang kernel (SCE-Ayala) and that with the present Onishi kernel (SCE-Onishi) are compared with results from the Lagrangian Cloud Simulator (LCS; Onishi et al., 2015), which tracks individual particle motions and size evolutions in homogeneous isotropic turbulence. The SCE-Ayala and SCE-Onishi kernels show consistent results with the LCS results for small Reλ. The two SCE simulations, however, show different Reynolds-number dependences, indicating possible large differences in atmospheric turbulent clouds with large Reλ.

Preferential concentration driven instability of sheared gas–solid suspensions

2015 ◽  
Vol 770 ◽  
pp. 85-123 ◽  
Author(s):  
M. Houssem Kasbaoui ◽  
Donald L. Koch ◽  
Ganesh Subramanian ◽  
Olivier Desjardins
Keyword(s):  
Turning Point ◽  
Fluid Velocity ◽  
Density Wave ◽  
Multiple Scale ◽  
Stokes Number ◽  
Particle Number Density ◽  
Simple Shear Flow ◽  
Number Density ◽  
Preferential Concentration ◽  
Algebraic Instability

We examine the linear stability of a homogeneous gas–solid suspension of small Stokes number particles, with a moderate mass loading, subject to a simple shear flow. The modulation of the gravitational force exerted on the suspension, due to preferential concentration of particles in regions of low vorticity, in response to an imposed velocity perturbation, can lead to an algebraic instability. Since the fastest growing modes have wavelengths small compared with the characteristic length scale ($U_{g}/{\it\Gamma}$) and oscillate with frequencies large compared with ${\it\Gamma}$, $U_{g}$ being the settling velocity and ${\it\Gamma}$ the shear rate, we apply the WKB method, a multiple scale technique. This analysis reveals the existence of a number density mode which travels due to the settling of the particles and a momentum mode which travels due to the cross-streamline momentum transport caused by settling. These modes are coupled at a turning point which occurs when the wavevector is nearly horizontal and the most amplified perturbations are those in which a momentum wave upstream of the turning point creates a downstream number density wave. The particle number density perturbations reach a finite, but large amplitude that persists after the wave becomes aligned with the velocity gradient. The growth of the amplitude of particle concentration and fluid velocity disturbances is characterised as a function of the wavenumber and Reynolds number ($\mathit{Re}=U_{g}^{2}/{\it\Gamma}{\it\nu}$) using both asymptotic theory and a numerical solution of the linearised equations.

Direct numerical simulation of turbulence modulation by particles in compressible isotropic turbulence

2017 ◽  
Vol 832 ◽  
pp. 438-482 ◽  
Author(s):  
Qi Dai ◽  
Kun Luo ◽  
Tai Jin ◽  
Jianren Fan
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Rotational Motion ◽  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Stokes Number ◽  
Systematic Investigation ◽  
Turbulence Modulation ◽  
Physical Mechanisms ◽  
Preferential Concentration

In this paper, a systematic investigation of turbulence modulation by particles and its underlying physical mechanisms in decaying compressible isotropic turbulence is performed by using direct numerical simulations with the Eulerian–Lagrangian point-source approach. Particles interact with turbulence through two-way coupling and the initial turbulent Mach number is 1.2. Five simulations with different particle diameters (or initial Stokes numbers, $St_{0}$) are conducted while fixing both their volume fraction and particle densities. The underlying physical mechanisms responsible for turbulence modulation are analysed through investigating the particle motion in the different cases and the transport equations of turbulent kinetic energy, vorticity and dilatation, especially the two-way coupling terms. Our results show that microparticles ($St_{0}\leqslant 0.5$) augment turbulent kinetic energy and the rotational motion of fluid, critical particles ($St_{0}\approx 1.0$) enhance the rotational motion of fluid, and large particles ($St_{0}\geqslant 5.0$) attenuate turbulent kinetic energy and the rotational motion of fluid. The compressibility of the turbulence field is suppressed for all the cases, and the suppression is more significant if the Stokes number of particles is close to 1. The modifications of turbulent kinetic energy, the rotational motion and the compressibility are all related with the particle inertia and distributions, and the suppression of the compressibility is attributed to the preferential concentration and the inertia of particles.

Direct Numerical Simulations of Colliding Particles Suspended in Homogeneous Isotropic Turbulence

2009 ◽  
Author(s):  
M. Ernst ◽  
M. Sommerfeld
Keyword(s):  
Numerical Simulations ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Stokes Number ◽  
Direct Numerical Simulations ◽  
Spherical Particles ◽  
Collision Rate ◽  
Homogeneous Isotropic Turbulence ◽  
And Performance ◽  
Fluid Behaviour

Direct numerical simulations of particle-laden homogeneous isotropic turbulence are performed to characterize the collision rate as a function of different particle properties. The fluid behaviour is computed using a three-dimensional Lattice Boltzmann Method including a spectral forcing scheme to generate the turbulence field. Under assumption of mass points, the transport of spherical particles is modelled in a Lagrangian frame of reference. In the simulations the influence of the particle phase on the fluid flow is neglected. The detection and performance of inelastic interparticle collisions are based on a deterministic collision model. Different studies with monodisperse particles are considered. According to the executed simulations, particles with small Stokes number possess a collision rate similar to the prediction of Saffman and Turner [1], whereas particles with larger Stokes numbers behave similarly to the theory of Abrahamson [2].

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.

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