Decaying versus stationary turbulence in particle-laden isotropic turbulence: Heavy particle statistics modifications

2013 ◽  
Vol 25 (3) ◽  
pp. 033303 ◽  
Author(s):  
Abouelmagd H. Abdelsamie ◽  
Changhoon Lee
Keyword(s):  
Isotropic Turbulence ◽  
Heavy Particle ◽  
Stationary Turbulence ◽  
Particle Statistics

scholarly journals A Lagrangian direct-interaction approximation for homogeneous isotropic turbulence

1997 ◽  
Vol 345 ◽  
pp. 307-345 ◽  
Author(s):  
SHIGEO KIDA ◽  
SUSUMU GOTO
Keyword(s):  
Energy Spectrum ◽  
Differential Equations ◽  
Isotropic Turbulence ◽  
Longitudinal Velocity ◽  
Direct Interaction ◽  
Homogeneous Isotropic Turbulence ◽  
Velocity Correlation ◽  
Stationary Turbulence ◽  
Direct Interaction Approximation ◽  
Velocity Derivative

A set of integro-differential equations in the Lagrangian renormalized approximation (Kaneda 1981) is rederived by applying a perturbation method developed by Kraichnan (1959), which is based upon an extraction of direct interactions among Fourier modes of a velocity field and was applied to the Eulerian velocity correlation and response functions, to the Lagrangian ones for homogeneous isotropic turbulence. The resultant set of integro-differential equations for these functions has no adjustable free parameters. The shape of the energy spectrum function is determined numerically in the universal range for stationary turbulence, and in the whole wavenumber range in a similarly evolving form for the freely decaying case. The energy spectrum in the universal range takes the same shape in both cases, which also agrees excellently with many measurements of various kinds of real turbulence as well as numerical results obtained by Gotoh et al. (1988) for a decaying case as an initial value problem. The skewness factor of the longitudinal velocity derivative is calculated to be −0.66 for stationary turbulence. The wavenumber dependence of the eddy viscosity is also determined.

A consequence of the zero fourth cumulant approximation

1962 ◽  
Vol 13 (3) ◽  
pp. 369-382 ◽  
Author(s):  
Edward E. O'Brien ◽  
George C. Francis
Keyword(s):  
Energy Spectrum ◽  
Numerical Computation ◽  
Root Mean Square ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Passive Scalar ◽  
Turbulent Energy ◽  
Length Scale ◽  
Mean Square ◽  
Stationary Turbulence

Recent investigations by Kraichnan (1961) and Ogura (1961) have raised doubts concerning the usefulness of the zero fourth cumulant approximation in turbulence dynamics. It appears extremely tedious to examine, by numerical computation, the consequences of this approximation on the turbulent energy spectrum although the appropriate equations have been established by Proudman & Reid (1954) and Tatsumi (1957). It has proved possible, however, to compute numerically the sequences of an analogous assumption when applied to an isotropic passive scalar in isotropic turbulence.The result of such computation, for specific initial conditions described herein, and for stationary turbulence, is that the scalar spectrum does develop negative values after a time approximately $2 \Lambda | {\overline {(u^2)}} ^{\frac {1}{2}}$, Where Λ is a length scale typical of the energy-containing components of both the turbulent and scalar spectra and $\overline {(u^2)}^{\frac {1}{2}}$ is the root mean square turbulent velocity.

A family of stochastic models for two-particle dispersion in isotropic homogeneous stationary turbulence

1994 ◽  
Vol 279 ◽  
pp. 69-99 ◽  
Author(s):  
M. S. Borgas ◽  
B. L. Sawford
Keyword(s):  
Quadratic Form ◽  
Stochastic Models ◽  
Stokes Equations ◽  
Probability Distributions ◽  
Particle Dispersion ◽  
Relative Dispersion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stationary Turbulence ◽  
Particle Statistics

A family of Lagrangian stochastic models for the joint motion of particle pairs in isotropic homogeneous stationary turbulence is considered. The Markov assumption and well-mixed criterion of Thomson (1990) are used, and the models have quadratic-form functions of velocity for the particle accelerations. Two constraints are derived which formally require that the correct one-particle statistics are obtained by the models. These constraints involve the Eulerian expectation of the ‘acceleration’ of a fluid particle with conditioned instantaneous velocity, given either at the particle, or at some other particle's position. The Navier-Stokes equations, with Gaussian Eulerian probability distributions, are shown to give quadratic-form conditional accelerations, and models which satisfy these two constraints are found. Dispersion calculations show that the constraints do not always guarantee good one-particle statistics, but it is possible to select a constrained model that does. Thomson's model has good one-particle statistics, but is shown to have unphysical conditional accelerations. Comparisons of relative dispersion for the models are made.

Numerical Study of Noise from Isotropic Turbulence

1997 ◽  
Vol 05 (03) ◽  
pp. 317-336 ◽  
Author(s):  
A. Witkowska ◽  
D. Juvé ◽  
J. G. Brasseur
Keyword(s):  
Isotropic Turbulence ◽  
Numerical Study ◽  
Acoustic Power ◽  
Turnover Time ◽  
Turbulence Structure ◽  
Sound Generation ◽  
Acoustic Analogy ◽  
Eddy Simulation ◽  
Stationary Turbulence ◽  
Theoretical Predictions

A numerical study of sound radiation by isotropic turbulence is carried out by combining turbulence simulation with Lighthill's acoustic analogy. In the first study we analyze sound generation by decaying isotropic turbulence obtained both with 643 Direct Numerical Simulation (DNS) and 163 Large Eddy Simulation (LES). Both simulations lead to similar results for acoustic power, in agreement with the numerical results of Sarkar and Hussaini, but slightly different from theoretical predictions of Proudman and Lilley. In the second study we analyze sound generation by forced stationary turbulence, simulated with 1283 DNS using a forcing scheme which preserves turbulence structure. The acoustic power computed from the stationary turbulence is in good agreement with results obtained for decaying isotropic turbulence. The acoustic spectrum shows that the characteristic frequency of the generated sound is approximately four times the inverse eddy turnover time. The contributions of different turbulence scales to the generated noise are computed separately from filtered velocity fields. For the low Reynolds number turbulence analyzed, the scales which most contribute to noise generation are 2–3 times smaller than the energy-containing scales and lie between the energy and dissipation-rate spectral peaks.

scholarly journals A Lagrangian Stochastic Model for the concentration fluctuations

2005 ◽  
Vol 5 (3) ◽  
pp. 3621-3639
Author(s):  
L. Mortarini ◽  
E. Ferrero
Keyword(s):  
Stochastic Model ◽  
Isotropic Turbulence ◽  
Concentration Fluctuations ◽  
Inertial Subrange ◽  
Lagrangian Stochastic Model ◽  
Theoretical Predictions ◽  
The Mean ◽  
Probability Density Function Pdf ◽  
Mean Concentration ◽  
Particle Statistics

Abstract. A Lagrangian Stochastic Model for the two-particles dispersion, aiming at simulating the pollutant concentration fluctuations, is presented. Three model versions (1-D, 2-D and 3-D) are tested. Firstly the ability of the model to reproduce the two-particle statistics in a homogeneous isotropic turbulence is discussed, comparing the model results with theoretical predictions in terms of the probability density function (PDF) of the particles separation and its statistics. Then, the mean concentration and its fluctuations are considered and the results presented. The influence of the PDF of the particle separation on the concentration fluctuations is shown and discussed. We found that the separation PDF in the inertial subrange is not gaussian and this fact influences the predicted concentration fluctuations.

scholarly journals The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational effects

2016 ◽  
Vol 796 ◽  
pp. 617-658 ◽  
Author(s):  
Peter J. Ireland ◽  
Andrew D. Bragg ◽  
Lance R. Collins
Keyword(s):  
Reynolds Number ◽  
Relative Velocity ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Inertial Particles ◽  
Inertial Particle ◽  
Physical Mechanisms ◽  
Preferential Sampling ◽  
Velocity Statistics ◽  
Particle Statistics

In this study, we analyse the statistics of both individual inertial particles and inertial particle pairs in direct numerical simulations of homogeneous isotropic turbulence in the absence of gravity. The effect of the Taylor microscale Reynolds number, $R_{{\it\lambda}}$, on the particle statistics is examined over the largest range to date (from $R_{{\it\lambda}}=88$ to 597), at small, intermediate and large Kolmogorov-scale Stokes numbers $St$. We first explore the effect of preferential sampling on the single-particle statistics and find that low-$St$ inertial particles are ejected from both vortex tubes and vortex sheets (the latter becoming increasingly prevalent at higher Reynolds numbers) and preferentially accumulate in regions of irrotational dissipation. We use this understanding of preferential sampling to provide a physical explanation for many of the trends in the particle velocity gradients, kinetic energies and accelerations at low $St$, which are well represented by the model of Chun et al. (J. Fluid Mech., vol. 536, 2005, pp. 219–251). As $St$ increases, inertial filtering effects become more important, causing the particle kinetic energies and accelerations to decrease. The effect of inertial filtering on the particle kinetic energies and accelerations diminishes with increasing Reynolds number and is well captured by the models of Abrahamson (Chem. Engng Sci., vol. 30, 1975, pp. 1371–1379) and Zaichik & Alipchenkov (Intl J. Multiphase Flow, vol. 34 (9), 2008, pp. 865–868), respectively. We then consider particle-pair statistics, and focus our attention on the relative velocities and radial distribution functions (RDFs) of the particles, with the aim of understanding the underlying physical mechanisms contributing to particle collisions. The relative velocity statistics indicate that preferential sampling effects are important for $St\lesssim 0.1$ and that path-history/non-local effects become increasingly important for $St\gtrsim 0.2$. While higher-order relative velocity statistics are influenced by the increased intermittency of the turbulence at high Reynolds numbers, the lower-order relative velocity statistics are only weakly sensitive to changes in Reynolds number at low $St$. The Reynolds-number trends in these quantities at intermediate and large $St$ are explained based on the influence of the available flow scales on the path-history and inertial filtering effects. We find that the RDFs peak near $St$ of order unity, that they exhibit power-law scaling for low and intermediate $St$ and that they are largely independent of Reynolds number for low and intermediate $St$. We use the model of Zaichik & Alipchenkov (New J. Phys., vol. 11, 2009, 103018) to explain the physical mechanisms responsible for these trends, and find that this model is able to capture the quantitative behaviour of the RDFs extremely well when direct numerical simulation data for the structure functions are specified, in agreement with Bragg & Collins (New J. Phys., vol. 16, 2014a, 055013). We also observe that at large $St$, changes in the RDF are related to changes in the scaling exponents of the relative velocity variances. The particle collision kernel closely matches that computed by Rosa et al. (New J. Phys., vol. 15, 2013, 045032) and is found to be largely insensitive to the flow Reynolds number. This suggests that relatively low-Reynolds-number simulations may be able to capture much of the relevant physics of droplet collisions and growth in the adiabatic cores of atmospheric clouds.

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.

scholarly journals A Lagrangian Stochastic Model for the concentration fluctuations

2005 ◽  
Vol 5 (9) ◽  
pp. 2539-2545 ◽  
Author(s):  
L. Mortarini ◽  
E. Ferrero
Keyword(s):  
Stochastic Model ◽  
Isotropic Turbulence ◽  
Concentration Fluctuations ◽  
Inertial Subrange ◽  
Lagrangian Stochastic Model ◽  
Theoretical Predictions ◽  
The Mean ◽  
Probability Density Function Pdf ◽  
Mean Concentration ◽  
Particle Statistics

Abstract. A Lagrangian Stochastic Model for the two-particles dispersion, aiming at simulating the pollutant concentration fluctuations, is presented. Three model versions (1-D, 2-D and 3-D) are tested. Firstly the ability of the model to reproduce the two-particle statistics in a homogeneous isotropic turbulence is discussed, comparing the model results with theoretical predictions in terms of the probability density function (PDF) of the particles separation and its statistics. Then, the mean concentration and its fluctuations are considered and the results presented. The influence of the PDF of the particle separation on the concentration fluctuations is shown and discussed. We found that the separation PDF in the inertial subrange is not gaussian and this fact influences the predicted concentration fluctuations.

Sign in / Sign up

Export Citation Format

Share Document