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.

Numerical Simulation of Heavy Particle Dispersion—Scale Ratio and Flow Decay Considerations

1994 ◽  
Vol 116 (1) ◽  
pp. 154-163 ◽  
Author(s):  
Lian-Ping Wang ◽  
David E. Stock
Keyword(s):  
Numerical Simulation ◽  
Time Scale ◽  
Dispersion Coefficient ◽  
Fluid Velocity ◽  
Heavy Particle ◽  
Particle Dispersion ◽  
Heavy Particles ◽  
Velocity Scale ◽  
Scale Ratio ◽  
Diffusivity Ratio

Lagrangian statistical quantities related to the dispersion of heavy particles were studied numerically by following particle trajectories in a random flow generated by Fourier modes. An experimental fluid velocity correlation was incorporated into the flow. Numerical simulation was performed with the use of nonlinear drag. The simulation results for glass beads in a nondecaying turbulent air showed a difference between the horizontal dispersion coefficient and vertical dispersion coefficient. This difference was related to the differences of both the velocity scale and the time scale between the two direction. It was shown that for relatively small particle sizes the particle time scale ratio dominates the value of the diffusivity ratio. For large particles, the velocity scale ratio reaches a value of 1/2 and thus fully determines the diffusivity ratio. Qualitative explanation was provided to support the numerical findings. The dispersion data for heavy particles in grid-generated turbulences were successfully predicted by the simulation when flow decay was considered. As a result of the reduction in effective inertia and the increase in effective drift caused by the flow decay, the particle dispersion coefficient in decaying flow decreases with downstream location. The particle rms fluctuation velocity has a slower decay rate than the fluid rms velocity if the drift parameter is large. It was also found that the drift may substantially reduce the particle rms velocity.

scholarly journals Extreme events in computational turbulence

2015 ◽  
Vol 112 (41) ◽  
pp. 12633-12638 ◽  
Author(s):  
P. K. Yeung ◽  
X. M. Zhai ◽  
Katepalli R. Sreenivasan
Keyword(s):  
Extreme Events ◽  
Isotropic Turbulence ◽  
Temporal Evolution ◽  
Energy Dissipation Rate ◽  
Mean Value ◽  
Small Scale ◽  
Homogeneous And Isotropic Turbulence ◽  
The Mean ◽  
Grid Points ◽  
Vortex Tubes

We have performed direct numerical simulations of homogeneous and isotropic turbulence in a periodic box with 8,1923grid points. These are the largest simulations performed, to date, aimed at improving our understanding of turbulence small-scale structure. We present some basic statistical results and focus on “extreme” events (whose magnitudes are several tens of thousands the mean value). The structure of these extreme events is quite different from that of moderately large events (of the order of 10 times the mean value). In particular, intense vorticity occurs primarily in the form of tubes for moderately large events whereas it is much more “chunky” for extreme events (though probably overlaid on the traditional vortex tubes). We track the temporal evolution of extreme events and find that they are generally short-lived. Extreme magnitudes of energy dissipation rate and enstrophy occur simultaneously in space and remain nearly colocated during their evolution.

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.

scholarly journals Passive Front Propagation in Intense Turbulence: Early Transient and Late Statistically Stationary Stages of the Front Area Evolution

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 5102
Author(s):  
Vladimir A. Sabelnikov ◽  
Andrei N. Lipatnikov
Keyword(s):  
Isotropic Turbulence ◽  
Front Surface ◽  
High Ratio ◽  
Turbulent Dispersion ◽  
Material Surface ◽  
Constant Density ◽  
Length Scale ◽  
Fluid Consumption ◽  
Turbulent Reynolds Number ◽  
The Mean

The influence of statistically stationary, homogeneous isotropic turbulence (i) on the mean area of a passive front propagating in a constant-density fluid and, hence, (ii) on the mean fluid consumption velocity u¯T is explored, particularly in the case of an asymptotically high turbulent Reynolds number, and an asymptotically high ratio of the Kolmogorov velocity to a constant speed u0 of the front. First, a short early transient stage is analyzed by assuming that the front remains close to a material surface that coincides with the front at the initial instant. Therefore, similarly to a material surface, the front area grows exponentially with time. This stage, whose duration is much less than an integral time scale of the turbulent flow, is argued to come to an end once the volume of fluid consumed by the front is equal to the volume embraced due to the turbulent dispersion of the front. The mean fluid consumption velocity averaged over this stage is shown to be proportional to the rms turbulent velocity u′. Second, a late statistically stationary regime of the front evolution is studied. A new length scale characterizing the smallest wrinkles of the front surface is introduced. Since this length scale is smaller than the Kolmogorov length scale ηK under conditions of the present study, the front is hypothesized to be a bifractal with two different fractal dimensions for wrinkles larger and smaller than ηK. Finally, a simple scaling of u¯T∝u′ is obtained for this late stage as well.

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.

The mean value of the fluctuations in pressure and pressure gradient in a turbulent fluid

1938 ◽  
Vol 34 (4) ◽  
pp. 534-539
Author(s):  
A. E. Green
Keyword(s):  
Unit Volume ◽  
Isotropic Turbulence ◽  
Fluid Motion ◽  
Mean Value ◽  
Mean Square ◽  
Turbulent Fluid ◽  
Dissipation Of Energy ◽  
The Mean ◽  
Rate Of Dissipation ◽  
Image Position

1. Taylor has shown (1) that two characteristic lengthsλ and λη may be defined for turbulent fluid motion. The length λ, which is connected with the dissipation of energy, is, for isotropic turbulence, given bywhere is the mean rate of dissipation of energy per unit volume and represents the mean square value of any component of velocity. The length λη can be defined in terms of thuswhere For isotropic turbulence Taylor assumed thatwhere B is a constant. Since the turbulence is isotropic,and so, from (1), (2), (3) and (4) we have

Turbulent Diffusion of Heavy-Particles in Turbulent Jets

1992 ◽  
Vol 114 (4) ◽  
pp. 667-671 ◽  
Author(s):  
A. A. Mostafa
Keyword(s):  
Diffusion Coefficient ◽  
Shear Flows ◽  
Fluid Velocity ◽  
Gas Diffusion ◽  
Particle Dispersion ◽  
Turbulent Dispersion ◽  
Turbulent Shear ◽  
Jet Flows ◽  
Particle Diffusion ◽  
Two Phase

The turbulent dispersion of heavy suspended particles in turbulent shear flows is analyzed when crossing trajectory effects are important. A semiempirical expression for particle diffusion coefficient is developed via a comparison with experimental data of two-phase turbulent jet flows. This expression gives the particle momentum diffusion coefficient in terms of the gas diffusion coefficient, mean relatively velocity, and root mean square of the fluctuating fluid velocity. The proposed expression is used in a two-phase flow mathematical model to predict different particle-laden jet flows. The good agreement between the predictions and data suggests that the developed expression for particle diffusion coefficient is reasonably accurate in predicting particle dispersion in turbulent free shear flows.

Direct simulation of particle dispersion in a decaying isotropic turbulence

1992 ◽  
Vol 242 ◽  
pp. 655-700 ◽  
Author(s):  
S. Elghobashi ◽  
G. C. Truesdell
Keyword(s):  
Particle Motion ◽  
Isotropic Turbulence ◽  
Particle Dispersion ◽  
Time Development ◽  
Solid Particles ◽  
Mean Square ◽  
Lagrangian Velocity ◽  
The Mean ◽  
Simulation Results ◽  
Surrounding Fluid

Dispersion of solid particles in decaying isotropic turbulence is studied numerically. The three-dimensional, time-dependent velocity field of a homogeneous, non-stationary turbulence was computed using the method of direct numerical simulation (DNS). A numerical grid containing 963 points was sufficient to resolve the turbulent motion at the Kolmogorov lengthscale for a range of microscale Reynolds numbers starting from Rλ = 25 and decaying to Rλ = 16. The dispersion characteristics of three different solid particles (corn, copper and glass) injected in the flow, were obtained by integrating the complete equation of particle motion along the instantaneous trajectories of 223 particles for each particle type, and then performing ensemble averaging. The three different particles are those used by Snyder & Lumley (1971), referred to throughout the paper as SL, in their pioneering wind-tunnel experiment. Good agreement was achieved between our DNS results and the measured time development of the mean-square displacement of the particles.The simulation results also include the time development of the mean-square relative velocity of the particles, the Lagrangian velocity autocorrelation and the turbulent diffusivity of the particles and fluid points. The Lagrangian velocity frequency spectra of the particles and their surrounding fluid, as well as the time development of all the forces acting on one particle are also presented. In order to distinguish between the effects of inertia and gravity on the dispersion statistics we compare the results of simulations made with and without the buoyancy force included in the particle motion equation. A summary of the significant results is provided in §7 of the paper.The main objective of the paper is to enhance the understanding of the physics of particle dispersion in a simple turbulent flow by examining the simulation results described above and answering the questions of how and why the dispersion statistics of a solid particle differ from those of its corresponding fluid point and surrounding fluid and what influences inertia and gravity have on these statistics.

Long-period modulated superstructures in Pd-12.5 at.%Ce and Pd-15 at.%Ce alloys

1990 ◽  
Vol 48 (4) ◽  
pp. 164-165
Author(s):  
Noriyuki Kuwano ◽  
Masaru Itakura ◽  
Kensuke Oki
Keyword(s):  
Electron Microscopy ◽  
Mean Value ◽  
Heavy Elements ◽  
Arc Furnace ◽  
X Ray ◽  
Long Period ◽  
Ultra High Purity ◽  
Heat Treated ◽  
Atomic Scattering ◽  
The Mean

Pd-Ce alloys exhibit various anomalies in physical properties due to mixed valences of Ce, and the anomalies are thought to be strongly related with the crystal structures. Since Pd and Ce are both heavy elements, relative magnitudes of (fcc-fpd) are so small compared with <f> that superlattice reflections, even if any, sometimes cannot be detected in conventional x-ray powder patterns, where fee and fpd are atomic scattering factors of Ce and Pd, and <f> the mean value in the crystal. However, superlattices in Pd-Ce alloys can be analyzed by electron microscopy, thanks to the high detectability of electron diffraction. In this work, we investigated modulated superstructures in alloys with 12.5 and 15.0 at.%Ce.Ingots of Pd-Ce alloys were prepared in an arc furnace under atmosphere of ultra high purity argon. The disc specimens cut out from the ingots were heat-treated in vacuum and electrothinned to electron transparency by a jet method.

Partition Coefficient Ratios and Tumour Perfusion Studied with 85mKr and 133Xe

1987 ◽  
Vol 26 (06) ◽  
pp. 253-257
Author(s):  
M. Mäntylä ◽  
J. Perkkiö ◽  
J. Heikkonen
Keyword(s):  
Partition Coefficient ◽  
Partition Coefficients ◽  
Regional Blood Flow ◽  
Blood Perfusion ◽  
Compartmental Analysis ◽  
Malignant Tumour ◽  
Mean Value ◽  
Perfusion Rate ◽  
Biological Variables ◽  
The Mean

The relative partition coefficients of krypton and xenon, and the regional blood flow in 27 superficial malignant tumour nodules in 22 patients with diagnosed tumours were measured using the 85mKr- and 133Xe-clearance method. In order to minimize the effect of biological variables on the measurements the radionuclides were injected simultaneously into the tumour. The distribution of the radiotracers was assumed to be in equilibrium at the beginning of the experiment. The blood perfusion was calculated by fitting a two-exponential function to the measuring points. The mean value of the perfusion rate calculated from the xenon results was 13 ± 10 ml/(100 g-min) [range 3 to 38 ml/(100 g-min)] and from the krypton results 19 ± 11 ml/(100 g-min) [range 5 to 45 ml/(100 g-min)]. These values were obtained, if the partition coefficients are equal to one. The equations obtained by using compartmental analysis were used for the calculation of the relative partition coefficient of krypton and xenon. The partition coefficient of krypton was found to be slightly smaller than that of xenon, which may be due to its smaller molecular weight.

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