On the Average Settling Rate of Heavy Particles in Decaying Homogeneous Isotropic Turbulence

1998 ◽  
Vol 14 (3) ◽  
pp. 111-118
Author(s):  
C. Y. Yang ◽  
U. Lei
Keyword(s):  
Time Scale ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Solid Particles ◽  
Settling Rate ◽  
Stationary Turbulence ◽  
Turbulence Decay ◽  
Decaying Turbulence ◽  
Inertia Response

ABSTRACTThe average settling rate of spherical solid particles, 〈vs〉, under a body force field is studied numerically in decaying homogeneous isotropic turbulent flows generated by the direct numerical simulation of the continuity and Navier-Stokes equations. The increase of the average settling rate, 〈Δvs〉, is maximized when Tp/Tk ≈ 1 and vd/u′ ≈ 0.5, and is of order 0.lu′, which is qualitatively similar to that in stationary turbulence. Here 〈Δvs〉 = 〈vs〉 − vd, Tp is the particle's relaxation time, Tk is the Kolmogorov time scale, vd is the settling rate of particles in still fluid, and u′ is the root mean square of the fluid velocity fluctuation. However, the magnitude of the maximum value of 〈Δvs〉 in decaying turbulence is substantially greater (about 40%) than that in the corresponding stationary turbulence due to the inertia response of particles to turbulence decay. Although 〈Δvs〉/u′ does not reach a stationary state as the flow is evolving, it is a slowly time varying function for the parameters of interest as Tp (≈ Tk when 〈Δvs〉 is maximized) is in general of one order less than the time scale of turbulence decay.

Motion of Descending Solid Particles and Local Flow Around the Particles in Downward Turbulent Water Duct Flow (Keynote)

2011 ◽  
Author(s):  
Yoshimichi Hagiwara ◽  
Hideto Fujii ◽  
Katsutoshi Sakurai ◽  
Takashi Kuroda ◽  
Atsuhide Kitagawa
Keyword(s):  
Reynolds Number ◽  
Time Scale ◽  
High Speed ◽  
Fluid Velocity ◽  
Stokes Number ◽  
Solid Particles ◽  
Duct Flow ◽  
Local Flow ◽  
Particle Reynolds Number ◽  
Turbulent Water

The Stokes number, the ratio of the particle time scale to flow time scale, is a promising quantity for estimating changes in statistics of turbulence due to particles. First, we explored the Stokes numbers in some recent studies. Secondly, we discussed the results of our direct numerical simulation for turbulent flow with a high-density particle in a vertical duct. In the discussion, we defined the particle Reynolds number from the mean fluid velocity in the near-particle region at any time. We evaluated a new local Stokes number for the particle. It is found that the Stokes number is effective for the prediction of the distance between the particle center and one wall. Finally, we carried out experiments for turbulent water flow with aluminum balls of 1 mm in diameter in a vertical channel. The motions of aluminum balls and tracer particles in the flow were captured with a high-speed video camera. We found that the experimental results for the time changes in the wall-normal distance of the ball and the particle Reynolds number for the ball are similar to the predicted results.

On the emergence of non-classical decay regimes in multiscale/fractal generated isotropic turbulence

2014 ◽  
Vol 756 ◽  
pp. 816-843 ◽  
Author(s):  
Marcello Meldi ◽  
Hugo Lejemble ◽  
Pierre Sagaut
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Time Scale ◽  
Isotropic Turbulence ◽  
Initial Kinetic Energy ◽  
Grid Turbulence ◽  
Production Term ◽  
Turbulence Decay ◽  
Turbulence Production

AbstractThe present paper addresses the issue of finding key parameters that may lead to the occurrence of non-classical decay regimes for fractal/multiscale generated grid turbulence. To this aim, a database of numerical simulations has been generated by the use of the eddy-damped quasi-normal Markovian (EDQNM) model. The turbulence production in the wake of the fractal/multiscale grid is modelled via a turbulence production term based on the forcing term developed for direct numerical simulations (DNS) purposes and the dynamics of self-similar wakes. The sensitivity of the numerical results to the simulation parameters has been investigated successively. The analysis is based on the observation of both the time evolution of the turbulent energy spectrum $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}E(k,t)$ and the decay of the flow statistical quantities, such as the turbulent kinetic energy $\mathcal{K}(t)$ and the energy dissipation rate $\varepsilon (t)$. A satisfactory agreement with existing experimental data published by different research teams is observed. In particular, it is observed that the key parameter that governs the nature of turbulence decay is $\alpha ={d/U_{\infty }}\, {(\varepsilon (0)/\mathcal{K}(0))}={d/L(0)} \, {(\sqrt{\mathcal{K}(0)}/U_{\infty })}$ (with $d$ the bar diameter and $U_{\infty }$ the upstream uniform velocity), which measures the ratio of the time scale largest grid bar $d/U_{\infty }$ to the turbulent time scale $\mathcal{K}(0)/\varepsilon (0)$. Two asymptotic behaviours for $\alpha \rightarrow + \infty $ and $\alpha \rightarrow 0$ are identified: (i) a fast algebraic decay law regime for rapidly decaying production terms, due to strongly modified initial kinetic energy spectrum and (ii) a real exponential decay regime associated with strong, very slowly decaying production terms. The present observations are in full agreement with conclusions drawn from recent fractal grid experiments, and it provides a physical scenario for occurrence of anomalous decay regime which encompasses previous hypotheses.

scholarly journals Vorticity moments in four numerical simulations of the 3D Navier–Stokes equations

2013 ◽  
Vol 732 ◽  
pp. 316-331 ◽  
Author(s):  
Diego A. Donzis ◽  
John D. Gibbon ◽  
Anupam Gupta ◽  
Robert M. Kerr ◽  
Rahul Pandit ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Numerical Solutions ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Random Initial Conditions ◽  
Decaying Turbulence ◽  
High Reynolds

AbstractThe issue of intermittency in numerical solutions of the 3D Navier–Stokes equations on a periodic box ${[0, L] }^{3} $ is addressed through four sets of numerical simulations that calculate a new set of variables defined by ${D}_{m} (t)= {({ \varpi }_{0}^{- 1} {\Omega }_{m} )}^{{\alpha }_{m} } $ for $1\leq m\leq \infty $ where ${\alpha }_{m} = 2m/ (4m- 3)$ and ${[{\Omega }_{m} (t)] }^{2m} = {L}^{- 3} \int \nolimits _{\mathscr{V}} {\vert \boldsymbol{\omega} \vert }^{2m} \hspace{0.167em} \mathrm{d} V$ with ${\varpi }_{0} = \nu {L}^{- 2} $. All four simulations unexpectedly show that the ${D}_{m} $ are ordered for $m= 1, \ldots , 9$ such that ${D}_{m+ 1} \lt {D}_{m} $. Moreover, the ${D}_{m} $ squeeze together such that ${D}_{m+ 1} / {D}_{m} \nearrow 1$ as $m$ increases. The values of ${D}_{1} $ lie far above the values of the rest of the ${D}_{m} $, giving rise to a suggestion that a depletion of nonlinearity is occurring which could be the cause of Navier–Stokes regularity. The first simulation is of very anisotropic decaying turbulence; the second and third are of decaying isotropic turbulence from random initial conditions and forced isotropic turbulence at fixed Grashof number respectively; the fourth is of very-high-Reynolds-number forced, stationary, isotropic turbulence at up to resolutions of $409{6}^{3} $.

Direct Numerical Simulation of Mixing of a Passive in Decaying Turbulence

1999 ◽  
Author(s):  
P. Deb ◽  
Pradip Majumdar
Keyword(s):  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Scalar Dissipation ◽  
Step Method ◽  
Fractional Step Method ◽  
Mixing Processes ◽  
Turbulent Reactive Flows ◽  
Decaying Turbulence

Abstract Research on turbulent mixing processes is of great interest to those working on turbulent-reactive flows. In this paper, a detailed study has been performed for the evolution of scalar fields of different initial integral scales in decaying, homogeneous and isotropic turbulence using DNS technique. Passive scalar mixing in a cubical decaying, homogeneous, isotropic turbulence field is considered. The three-dimensional incompressible Navier-Stokes equations together with scalar equation are solved using Fractional Step Method. The convective and diffusive terms in governing equations are discretised by Compact Finite Difference Scheme. The 32 × 32 × 32 uniform staggered grids are used. The present simulation is performed at Taylor Reynolds number of 28.83. In this paper, the evolution of scalar RMS and scalar dissipation rate for different integral length scales has been presented. The initial velocity vector and Probability Density Function (PDF) of scalar at different eddy turn over time have also been presented.

scholarly journals Refinement of a Previous Hypothesis of the Lyapunov Analysis of Isotropic Turbulence

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Nicola de Divitiis
Keyword(s):  
Structure Function ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Longitudinal Velocity ◽  
Navier Stokes ◽  
Lyapunov Analysis ◽  
Velocity Difference ◽  
Navier Stokes Equations ◽  
Previous Hypothesis ◽  
Kolmogorov Theory

The purpose of this paper is to improve a hypothesis of the previous work of N. de Divitiis (2011) dealing with the finite-scale Lyapunov analysis of isotropic turbulence. There, the analytical expression of the structure function of the longitudinal velocity differenceΔuris derived through a statistical analysis of the Fourier transformed Navier-Stokes equations and by means of considerations regarding the scales of the velocity fluctuations, which arise from the Kolmogorov theory. Due to these latter considerations, this Lyapunov analysis seems to need some of the results of the Kolmogorov theory. This work proposes a more rigorous demonstration which leads to the same structure function, without using the Kolmogorov scale. This proof assumes that pair and triple longitudinal correlations are sufficient to determine the statistics ofΔurand adopts a reasonable canonical decomposition of the velocity difference in terms of proper stochastic variables which are adequate to describe the mechanism of kinetic energy cascade.

Modeling of the Vortex-Structure in a Particle-Laden Mixing-Layer

2005 ◽  
Author(s):  
Jens A. Melheim ◽  
Stefan Horender ◽  
Martin Sommerfeld
Keyword(s):  
Vortex Structure ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Mixing Layer ◽  
Equation Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Calculated Concentration ◽  
Langevin Model ◽  
Particle Velocities

Numerical calculations of a particle-laden turbulent horizontal mixing-layer based on the Eulerian-Lagrangian approach are presented. Emphasis is given to the determination of the stochastic fluctuating fluid velocity seen by the particles in anisotropic turbulence. The stochastic process for the fluctuating velocity is a “Particle Langevin equation Model”, based on the Simplified Langevin Model. The Reynolds averaged Navier-Stokes equations are closed by the standard k-epsilon turbulence model. The calculated concentration profile and the mean, the root-mean-square (rms) and the cross-correlation terms of the particle velocities are compared with particle image velocimetry (PIV) measurements. The numerical results agree reasonably well with the PIV data for all of the mentioned quantities. The importance of the modeled vortex structure “seen” by the particles is discussed.

Scale-dependent alignment, tumbling and stretching of slender rods in isotropic turbulence

2018 ◽  
Vol 860 ◽  
pp. 465-486 ◽  
Author(s):  
Nimish Pujara ◽  
Greg A. Voth ◽  
Evan A. Variano
Keyword(s):  
Isotropic Turbulence ◽  
Fluid Velocity ◽  
Inertial Range ◽  
Small Scale ◽  
Strain Rate Tensor ◽  
Scaling Exponents ◽  
Slender Body Theory ◽  
Velocity Statistics ◽  
Rigid Rods ◽  
Dissipation Range

We examine the dynamics of slender, rigid rods in direct numerical simulation of isotropic turbulence. The focus is on the statistics of three quantities and how they vary as rod length increases from the dissipation range to the inertial range. These quantities are (i) the steady-state rod alignment with respect to the perceived velocity gradients in the surrounding flow, (ii) the rate of rod reorientation (tumbling) and (iii) the rate at which the rod end points move apart (stretching). Under the approximations of slender-body theory, the rod inertia is neglected and rods are modelled as passive particles in the flow that do not affect the fluid velocity field. We find that the average rod alignment changes qualitatively as rod length increases from the dissipation range to the inertial range. While rods in the dissipation range align most strongly with fluid vorticity, rods in the inertial range align most strongly with the most extensional eigenvector of the perceived strain-rate tensor. For rods in the inertial range, we find that the variance of rod stretching and the variance of rod tumbling both scale as $l^{-4/3}$, where $l$ is the rod length. However, when rod dynamics are compared to two-point fluid velocity statistics (structure functions), we see non-monotonic behaviour in the variance of rod tumbling due to the influence of small-scale fluid motions. Additionally, we find that the skewness of rod stretching does not show scale invariance in the inertial range, in contrast to the skewness of longitudinal fluid velocity increments as predicted by Kolmogorov’s $4/5$ law. Finally, we examine the power-law scaling exponents of higher-order moments of rod tumbling and rod stretching for rods with lengths in the inertial range and find that they show anomalous scaling. We compare these scaling exponents to predictions from Kolmogorov’s refined similarity hypotheses.

scholarly journals Modeling Free Surface Flows Using Stabilized Finite Element Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Deepak Garg ◽  
Antonella Longo ◽  
Paolo Papale
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Computer Code ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Element Method

This work aims to develop a numerical wave tank for viscous and inviscid flows. The Navier-Stokes equations are solved by time-discontinuous stabilized space-time finite element method. The numerical scheme tracks the free surface location using fluid velocity. A segregated algorithm is proposed to iteratively couple the fluid flow and mesh deformation problems. The numerical scheme and the developed computer code are validated over three free surface problems: solitary wave propagation, the collision between two counter moving waves, and wave damping in a viscous fluid. The benchmark tests demonstrate that the numerical approach is effective and an attractive tool for simulating viscous and inviscid free surface flows.

scholarly journals Cloud droplet diffusional growth in homogeneous isotropic turbulence: bin microphysics versus Lagrangian superdroplet simulations

2020 ◽  
Author(s):  
Wojciech W. Grabowski ◽  
Lois Thomas
Keyword(s):  
Fluid Flow ◽  
Time Scale ◽  
Isotropic Turbulence ◽  
Spectral Width ◽  
Small Scale ◽  
Computational Domain ◽  
Homogeneous Isotropic Turbulence ◽  
Diffusional Growth ◽  
Droplet Concentration ◽  
Bin Microphysics

Abstract. Increase of the spectral width of initially monodisperse population of cloud droplets in homogeneous isotropic turbulence is investigated applying a finite-difference fluid flow model combined with either Eulerian bin microphysics or Lagrangian particle-based scheme. The turbulence is forced applying a variant of the so-called linear forcing method that maintains the mean turbulent kinetic energy (TKE) and the TKE partitioning between velocity components. The latter is important for maintaining the quasi-steady forcing of the supersaturation fluctuations that drive the increase of the spectral width. We apply a large computational domain, 643 m3, one of the domains considered in Thomas et al. (2020). The simulations apply 1 m grid length and are in the spirit of the implicit large eddy simulation (ILES), that is, with explicit small-scale dissipation provided by the model numerics. This is in contrast to the scaled-up direct numerical simulation (DNS) applied in Thomas et al. (2020). Two TKE intensities and three different droplet concentrations are considered. Analytic solutions derived in Sardina et al. (2015), valid for the case when the turbulence time scale is much larger than the droplet phase relaxation time scale, are used to guide the comparison between the two microphysics simulation techniques. The Lagrangian approach reproduces the scalings relatively well. Representing the spectral width increase in time is more challenging for the bin microphysics because appropriately high resolution in the bin space is needed. The bin width of 0.5 μm is only sufficient for the lowest droplet concentration, 26 cm−3. For the highest droplet concentration, 650 cm−3, even an order of magnitude smaller bin size is not sufficient. The scalings are not expected to be valid for the lowest droplet concentration and the high TKE case, and the two microphysics schemes represent similar departures. Finally, because the fluid flow is the same for all simulations featuring either low or high TKE, one can compare point-by-point simulation results. Such a comparison shows very close temperature and water vapor point-by-point values across the computational domain, and larger differences between simulated mean droplet radii and spectral width. The latter are explained by fundamental differences in the two simulation methodologies, numerical diffusion in the Eulerian bin approach and relatively small number of Lagrangian particles that are used in the particle-based microphysics.

scholarly journals CFD SIMULATION OF EROSION BY PARTICLE COLLISION IN U-BEND AND HELICAL TYPE PIPES

2020 ◽  
Vol 14 (2) ◽  
pp. 1-13
Author(s):  
Mohammad Sheikh Mamoo ◽  
Ataallah Soltani Goharrizi ◽  
Bahador Abolpour
Keyword(s):  
Mass Flow ◽  
Mean Curvature ◽  
Particle Density ◽  
Fluid Velocity ◽  
Diameter Ratio ◽  
Solid Particles ◽  
Pipe Diameter ◽  
Design Parameters ◽  
Curvature Radius ◽  
Rate Of Penetration

Erosion caused by solid particles in curve pipes is one of the major concerns in the oil and gas industries. Small solid particles flow with a carrier liquid fluid and impact the inner wall of the piping, valves, and other equipment. These components face a high risk of solid particle erosion due to the constant collision, which may result in equipment malfunctioning and even failure. In this study, the two-way coupled Eulerian-Lagrangian method with the Oka erosion and Grant and Tabakoff particle-wall rebound models approach is employed to simulate the liquid-solid flow in U-bend and helical pipes using computational fluid dynamics. The effects of operating parameters (inlet fluid velocity and temperature, particle density and diameter, and mass flow rate) and design parameters (mean curvature radius/pipe diameter ratio) are investigated on the erosion of these tubes walls. It is obtained that increasing the fluid velocity and temperature, particle mass flow and particle density increase the penetration rate, particle diameter affects the rate of penetration, and increasing mean curvature radius/pipe diameter ratio decreases the rate of penetration.

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