scholarly journals The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 2. Simulations with gravitational effects

2016 ◽  
Vol 796 ◽  
pp. 659-711 ◽  
Author(s):  
Peter J. Ireland ◽  
Andrew D. Bragg ◽  
Lance R. Collins
Keyword(s):  
Reynolds Number ◽  
Single Particle ◽  
Isotropic Turbulence ◽  
Distribution Functions ◽  
Particle Collision ◽  
Collision Kernel ◽  
Finite Domain ◽  
Inertial Particles ◽  
Inertial Particle ◽  
Wide Range

In Part 1 of this study (Ireland et al., J. Fluid Mech., vol. 796, 2016, pp. 617–658), we analysed the motion of inertial particles in isotropic turbulence in the absence of gravity using direct numerical simulation (DNS). Here, in Part 2, we introduce gravity and study its effect on single-particle and particle-pair dynamics over a wide range of flow Reynolds numbers, Froude numbers and particle Stokes numbers. The overall goal of this study is to explore the mechanisms affecting particle collisions, and to thereby improve our understanding of droplet interactions in atmospheric clouds. We find that the dynamics of heavy particles falling under gravity can be artificially influenced by the finite domain size and the periodic boundary conditions, and we therefore perform our simulations on larger domains to reduce these effects. We first study single-particle statistics that influence the relative positions and velocities of inertial particles. We see that gravity causes particles to sample the flow more uniformly and reduces the time particles can spend interacting with the underlying turbulence. We also find that gravity tends to increase inertial particle accelerations, and we introduce a model to explain that effect. We then analyse the particle relative velocities and radial distribution functions (RDFs), which are generally seen to be independent of Reynolds number for low and moderate Kolmogorov-scale Stokes numbers $St$. We see that gravity causes particle relative velocities to decrease by reducing the degree of preferential sampling and the importance of path-history interactions, and that the relative velocities have higher scaling exponents with gravity. We observe that gravity has a non-trivial effect on clustering, acting to decrease clustering at low $St$ and to increase clustering at high $St$. By considering the effect of gravity on the clustering mechanisms described in the theory of Zaichik & Alipchenkov (New J. Phys., vol. 11, 2009, 103018), we provide an explanation for this non-trivial effect of gravity. We also show that when the effects of gravity are accounted for in the theory of Zaichik & Alipchenkov (2009), the results compare favourably with DNS. The relative velocities and RDFs exhibit considerable anisotropy at small separations, and this anisotropy is quantified using spherical harmonic functions. We use the relative velocities and the RDFs to compute the particle collision kernels, and find that the collision kernel remains as it was for the case without gravity, namely nearly independent of Reynolds number for low and moderate $St$. We conclude by discussing practical implications of the results for the cloud physics and turbulence communities and by suggesting possible avenues for future research.

Collision statistics of inertial particles in two-dimensional homogeneous isotropic turbulence with an inverse cascade

2014 ◽  
Vol 745 ◽  
pp. 279-299 ◽  
Author(s):  
Ryo Onishi ◽  
J. C. Vassilicos
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Particle System ◽  
Stochastic Simulations ◽  
Collision Kernel ◽  
Inertial Particles ◽  
Two Dimensional ◽  
Homogeneous Isotropic Turbulence ◽  
Local Flow ◽  
Reynolds Number Dependence

AbstractThis study investigates the collision statistics of inertial particles in inverse-cascading two-dimensional (2D) homogeneous isotropic turbulence by means of a direct numerical simulation (DNS). A collision kernel model for particles with small Stokes number ($\mathit{St}$) in 2D flows is proposed based on the model of Saffman & Turner (J. Fluid Mech., vol. 1, 1956, pp. 16–30) (ST56 model). The DNS results agree with this 2D version of the ST56 model for $\mathit{St}\lesssim 0.1$. It is then confirmed that our DNS results satisfy the 2D version of the spherical formulation of the collision kernel. The fact that the flatness factor stays around 3 in our 2D flow confirms that the present 2D turbulent flow is nearly intermittency-free. Collision statistics for $\mathit{St}= 0.1$, 0.4 and 0.6, i.e. for $\mathit{St}<1$, are obtained from the present 2D DNS and compared with those obtained from the three-dimensional (3D) DNS of Onishi et al. (J. Comput. Phys., vol. 242, 2013, pp. 809–827). We have observed that the 3D radial distribution function at contact ($g(R)$, the so-called clustering effect) decreases for $\mathit{St}= 0.4$ and 0.6 with increasing Reynolds number, while the 2D $g(R)$ does not show a significant dependence on Reynolds number. This observation supports the view that the Reynolds-number dependence of $g(R)$ observed in three dimensions is due to internal intermittency of the 3D turbulence. We have further investigated the local $\mathit{St}$, which is a function of the local flow strain rates, and proposed a plausible mechanism that can explain the Reynolds-number dependence of $g(R)$. Meanwhile, 2D stochastic simulations based on the Smoluchowski equations for $\mathit{St}\ll 1$ show that the collision growth can be predicted by the 2D ST56 model and that rare but strong events do not play a significant role in such a small-$\mathit{St}$ particle system. However, the probability density function of local $\mathit{St}$ at the sites of colliding particle pairs supports the view that powerful rare events can be important for particle growth even in the absence of internal intermittency when $\mathit{St}$ is not much smaller than unity.

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.

scholarly journals Analysis of the forward and backward in time pair-separation probability density functions for inertial particles in isotropic turbulence

2017 ◽  
Vol 830 ◽  
pp. 63-92 ◽  
Author(s):  
Andrew D. Bragg
Keyword(s):  
Probability Density ◽  
Isotropic Turbulence ◽  
Probability Density Functions ◽  
Density Functions ◽  
Inertial Particles ◽  
Mean Square ◽  
Inertial Particle ◽  
Particle Pair ◽  
Pair Separation ◽  
Dissipation Range

In this paper we investigate, using theory and direct numerical simulations (DNS), the forward in time (FIT) and backward in time (BIT) probability density functions (PDFs) of the separation of inertial particle pairs in isotropic turbulence. In agreement with our earlier study (Bragg et al., Phys. Fluids, vol. 28, 2016, 013305), where we compared the FIT and BIT mean-square separations, we find that inertial particles separate much faster BIT than FIT, with the strength of the irreversibility depending upon the final/initial separation of the particle pair and their Stokes number $St$. However, we also find that the irreversibility shows up in subtle ways in the behaviour of the full PDF that it does not in the mean-square separation. In the theory, we derive new predictions, including a prediction for the BIT/FIT PDF for $St\geqslant O(1)$, and for final/initial separations in the dissipation regime. The prediction shows how caustics in the particle relative velocities in the dissipation range affect the scaling of the pair-separation PDF, leading to a PDF with an algebraically decaying tail. The predicted functional behaviour of the PDFs is universal, in that it does not depend upon the level of intermittency in the underlying turbulence. We also analyse the pair-separation PDFs for fluid particles at short times, and construct theoretical predictions using the multifractal formalism to describe the fluid relative velocity distributions. The theoretical and numerical results both suggest that the extreme events in the inertial particle-pair dispersion at the small scales are dominated by their non-local interaction with the turbulent velocity field, rather than due to the strong dissipation range intermittency of the turbulence itself. In fact, our theoretical results predict that for final/initial separations in the dissipation range, when $St\gtrsim 1$, the tails of the pair-separation PDFs decay faster as the Taylor Reynolds number $Re_{\unicode[STIX]{x1D706}}$ is increased, the opposite of what would be expected for fluid particles.

scholarly journals On the transition between turbulence regimes in particle-laden channel flows

2018 ◽  
Vol 845 ◽  
pp. 499-519 ◽  
Author(s):  
Jesse Capecelatro ◽  
Olivier Desjardins ◽  
Rodney O. Fox
Keyword(s):  
Reynolds Number ◽  
Fluid Phase ◽  
Stokes Number ◽  
Channel Flows ◽  
High Mass ◽  
Inertial Particles ◽  
Mass Loading ◽  
Two Phase ◽  
Phase Dynamics ◽  
Wide Range

Turbulent wall-bounded flows exhibit a wide range of regimes with significant interaction between scales. The fluid dynamics associated with single-phase channel flows is predominantly characterized by the Reynolds number. Meanwhile, vastly different behaviour exists in particle-laden channel flows, even at a fixed Reynolds number. Vertical turbulent channel flows seeded with a low concentration of inertial particles are known to exhibit segregation in the particle distribution without significant modification to the underlying turbulent kinetic energy (TKE). At moderate (but still low) concentrations, enhancement or attenuation of fluid-phase TKE results from increased dissipation and wakes past individual particles. Recent studies have shown that denser suspensions significantly alter the two-phase dynamics, where the majority of TKE is generated by interphase coupling (i.e.  drag) between the carrier gas and clusters of particles that fall near the channel wall. In the present study, a series of simulations of vertical particle-laden channel flows with increasing mass loading is conducted to analyse the transition from the dilute limit where classical mean-shear production is primarily responsible for generating fluid-phase TKE to high-mass-loading suspensions dominated by drag production. Eulerian–Lagrangian simulations are performed for a wide range of particle loadings at two values of the Stokes number, and the corresponding two-phase energy balances are reported to identify the mechanisms responsible for the observed transition.

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 ${\geqslant}O(1)$.

scholarly journals Inertial particle acceleration in strained turbulence

2015 ◽  
Vol 785 ◽  
pp. 31-53 ◽  
Author(s):  
C.-M. Lee ◽  
Á. Gylfason ◽  
P. Perlekar ◽  
F. Toschi
Keyword(s):  
Particle Acceleration ◽  
Strain Rate ◽  
Probability Density ◽  
Energy Dissipation Rate ◽  
Distribution Functions ◽  
Inertial Particles ◽  
Inertial Particle ◽  
Mean Flow ◽  
The Mean ◽  
Mean Strain

The dynamics of inertial particles in turbulence is modelled and investigated by means of direct numerical simulation of an axisymmetrically expanding homogeneous turbulent strained flow. This flow can mimic the dynamics of particles close to stagnation points. The influence of mean straining flow is explored by varying the dimensionless strain rate parameter $Sk_{0}/{\it\epsilon}_{0}$ from 0.2 to 20, where $S$ is the mean strain rate, $k_{0}$ and ${\it\epsilon}_{0}$ are the turbulent kinetic energy and energy dissipation rate at the onset of straining. We report results relative to the acceleration variances and probability density functions for both passive and inertial particles. A high mean strain is found to have a significant effect on the acceleration variance both directly by an increase in the frequency of the turbulence and indirectly through the coupling of the fluctuating velocity and the mean flow field. The influence of the strain on the normalized particle acceleration probability distribution functions is more subtle. For the case of a passive particle we can approximate the acceleration variance with the aid of rapid-distortion theory and obtain good agreement with simulation data. For the case of inertial particles we can write a formal expression for the accelerations. The magnitude changes in the inertial particle acceleration variance and the effect on the probability density function are then discussed in a wider context for comparable flows, where the effects of the mean flow geometry and of the anisotropy at small scales are present.

Experimental and numerical investigation of inertial particle clustering in isotropic turbulence

2008 ◽  
Vol 600 ◽  
pp. 245-256 ◽  
Author(s):  
JUAN P. L. C. SALAZAR ◽  
JEREMY DE JONG ◽  
LUJIE CAO ◽  
SCOTT H. WOODWARD ◽  
HUI MENG ◽  
...  
Keyword(s):  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Experimental System ◽  
Collision Kernel ◽  
Inertial Particle ◽  
Particle Clustering ◽  
Glass Spheres ◽  
Preferential Concentration ◽  
Particle Imaging ◽  
Good Agreement

This paper presents the first detailed comparisons between experiments and direct numerical simulations (DNS) of inertial particle clustering in nearly isotropic ‘box turbulence’. The experimental system consists of a box 38cm in each dimension with fans in the eight corners that sustain nearly isotropic turbulence in the centre of the box. We inject hollow glass spheres with a mean diameter of 6 μm and measure the locations of several hundred particles in a 1 cm3 volume in the centre of the box using three-dimensional digital holographic particle imaging. We observe particle concentration fluctuations that result from inertial clustering (sometimes called ‘preferential concentration’). The radial distribution function (RDF), a statistical measure of clustering, has been calculated from the particle position field. We select this measure because of its relevance to the collision kernel for particles. DNS of the equivalent system, with nearly perfect parameter overlap, have also been performed. We observe good agreement between the RDF predictions of the DNS and the experimental observations, despite some challenges in the interpretation of the experiments. The results provide important guidance on ways to improve the measurement.

Three-Dimensional Measurement of Aerosol Particle Clustering in Homogeneous Isotropic Turbulence

2003 ◽  
Author(s):  
Lujie Cao ◽  
Gang Pan ◽  
Hui Meng
Keyword(s):  
Isotropic Turbulence ◽  
Imaging System ◽  
Three Dimensional ◽  
Theoretical Models ◽  
Particle Collision ◽  
Collision Kernel ◽  
Particle Clustering ◽  
Coagulation Rate ◽  
Holographic Imaging ◽  
Preferential Concentration

Due to the inertial mismatch between dense particles and lighter surrounding gas, aerosol particles in the size range 1 to 10 μm cluster in a flow field. This phenomenon, sometimes referred to as preferential concentration, can increase the particle coagulation rate by as much as two orders of magnitude. Many direct numerical simulation (DNS) studies have been conducted to study preferential concentration and various theoretical models have been proposed to predict the effect of clustering on particle collision rate. However, to date there is very little experimental data available to validate DNS results and theoretical models. In this study, we apply our state-of-the-art holographic imaging system to measure the 3D position of particles in a turbulence chamber. Nearly homogenous isotropic turbulence is generated in the center of the chamber by use of eight fans mounted in the corners. With our holographic imaging system, individual particles can be measured simultaneously and hence we are able to calculate particle radial distribution function (RDF), a statistical measure of particle clustering and a key variable in collision kernel. In this paper we report the first experimental 3D RDF to date. Comparison between our 3D RDF and 2D RDF results shows that significant bias exists in experimental results obtained using 2D experimental techniques.

On the role of gravity and shear on inertial particle accelerations in near-wall turbulence

2010 ◽  
Vol 658 ◽  
pp. 229-246 ◽  
Author(s):  
V. LAVEZZO ◽  
A. SOLDATI ◽  
S. GERASHCHENKO ◽  
Z. WARHAFT ◽  
L. R. COLLINS
Keyword(s):  
Isotropic Turbulence ◽  
Response Times ◽  
Quantitative Agreement ◽  
Wall Turbulence ◽  
Wall Region ◽  
Inertial Particles ◽  
Inertial Particle ◽  
Homogeneous And Isotropic Turbulence ◽  
Near Wall

Recent experiments in a turbulent boundary layer by Gerashchenko et al. (J. Fluid Mech., vol. 617, 2008, pp. 255–281) showed that the variance of inertial particle accelerations in the near-wall region increased with increasing particle inertia, contrary to the trend found in homogeneous and isotropic turbulence. This behaviour was attributed to the non-trivial interaction of the inertial particles with both the mean shear and gravity. To investigate this issue, we perform direct numerical simulations of channel flow with suspended inertial particles that are tracked in the Lagrangian frame of reference. Three simulations have been carried out considering (i) fluid particles, (ii) inertial particles with gravity and (iii) inertial particles without gravity. For each set of simulations, three particle response times were examined, corresponding to particle Stokes numbers (in wall units) of 0.9, 1.8 and 11.8. Mean and r.m.s. profiles of particle acceleration computed in the simulation are in qualitative (and in several cases quantitative) agreement with the experimental results, supporting the assumptions made in the simulations. Furthermore, by comparing results from simulations with and without gravity, we are able to isolate and quantify the significant effect of gravitational settling on the phenomenon.

Numerical Investigation on Head-On Collisions of Binary Micro-Droplets by an Improved Multiphase Lattice Boltzmann Flux Solver

2016 ◽  
Author(s):  
Y. Wang ◽  
C. Shu
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann ◽  
Weber Number ◽  
Density Ratio ◽  
Distribution Functions ◽  
Time Step ◽  
Large Density ◽  
Wide Range ◽  
Large Density Ratio ◽  
Critical Weber Number

Head-on collisions of binary micro-droplets are of great interest in both academic research and engineering applications. Numerical simulation of this problem is challenging due to complex interfacial changes and large density ratio between different fluids. In this work, the recently proposed lattice Boltzmann flux solver (LBFS) is applied to study this problem. The LBFS is a finite volume method for the direct update of macroscopic flow variables at cell centers. The fluxes of the LBFS are reconstructed at each cell interface through lattice moments of density distribution functions (DDFs). As compared with conventional multiphase lattice Boltzmann method, the LBFS can be easily applied to study complex multiphase flows with large density ratio. In addition, external forces can be implemented more conveniently and the tie-up between the time step and mesh spacing is also removed. Moreover, it can deal with complex boundary conditions directly as those do in the conventional Navier-Stokes solvers. At first, the reliability of the LBFS is validated by simulating a micro-droplet impacting on a dry surface at density ratio 832 (air to water). The obtained result agrees well with experimental measurement. After that, numerical simulations of head-on collisions of two micro droplets are carried out to examine different collisional behaviors in a wide range of Reynolds numbers and Weber numbers of 100 ≤ Re ≤ 2000 and 10 ≤ We ≤ 500. A phase diagram parameterized by these two control parameters is obtained to classify the outcomes of these collisions. It is shown that, at low Reynolds number (Re=100), two droplets will be coalescent into a bigger one for all considered Weber numbers. With the increase of the Reynolds number, separation of the collision into multiple droplets appears and the critical Weber number for separation is decreased. When the Reynolds number is sufficiently high, the critical Weber number for separation is between 20 and 25.

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