Session L37: Particle-Turbulence Interaction II

Analysis of the temperature fluctuations in particle-laden isotropic turbulence in the two-way coupling regime.

We perform direct numerical simulation of incompressible, statistically steady and isotropic turbulent flows laden with point-like particles. The fluid temperature is two-way coupled with the particle temperature and the effect of the particle inertia on the temperature statistics is investigated. Balances of the dissipation of the temperature fluctuations are derived and the amplitude of the temperature fluctuations is predicted by exploiting the Obukhov-Corrsin relation. The results show that the particles affect the temperature fluctuation and dissipation in different, non trivial ways, depending on the particle mass and heat capacity. The effect of the inertial particles on the distribution of the temperature fluctuations across the scales of the flow is characterized by means of two-particle and two-point statistics. While the fluid temperature distribution scales in a self-similar way in a wide range of particle inertia, the particle temperature statistics show a marked multifractal behavior due to the particle non-local dynamics. The interaction between the particle non-local dynamics and the ramp-cliff structure of the fluid temperature field is characterized by computing the heat flux due to the particle motion across the fluid temperature fronts.   

Acceleration of inertial particles settling by gravity in homogeneous turbulence

The acceleration events of inertial particles in turbulence are of importance in a wealth of physical phenomena, e.g., for predicting the interaction and evolution of droplets in atmospheric clouds, which are responsible for large part of the uncertainty in weather forecast. Past experimental investigations have often considered neutrally buoyant particles, neglecting the role of gravity. Recent computational investigations have in fact shown that gravity can profoundly alter the acceleration statistics. However, these studies typically make use of simplifying assumptions such as the point-particle approximation and Stokes drag formulation. We perform Lagrangian Particle Tracking to investigate acceleration statistics of heavy particles in homogeneous turbulence with negligible mean flow and shear. This is generated by two planar jet arrays that produce a homogeneous region much larger than the integral scale, minimizing the influence of boundary conditions. The particles are dilute and smaller than the Kolmogorov scales. We consider different particle types and turbulence Reynolds numbers, which allows us to distinguish between the effects of inertia and gravity on the settling velocity, acceleration variance, and acceleration distributions.   

On the multiscale mechanism generating enhanced particle settling speeds in turbulence: Part 1.

According to Maxey (J. Fluid Mech., 174:441--465, 1987), enhanced particle settling speeds in turbulence occur because of the way that inertial particles preferentially sample the fluid velocity gradient field $\nabla\bm{u}$. However, recent Direct Numerical Simulation (DNS) results in Ireland et al. (J. Fluid Mech., 796:659--711, 2016) show that the settling enhancement is strongest in a portion of the parameter space where preferential sampling of $\nabla\bm{u}$ is very weak. The results also show that the settling can be strongly enhanced with increasing Reynolds number. The analysis of Maxey does not account for these findings, partly since it was restricted to particle Stokes numbers $St\ll1$. To explain the findings, we have developed a new theoretical analysis, valid for arbitrary $St$, that employs Probability Density Function (PDF) methods, particle velocity fields constructed using averaging decompositions, and coarse-graining for the fields to reveal which scales of the turbulence contribute to the enhanced settling speeds. The results provide new insights that explain the findings in Ireland et al. In Part 2 of this talk, the theoretical descriptions will be compared to results from DNS.   

Clustering of Rapidly Settling, Low-Inertia Particle Pairs in Isotropic Turbulence. I. Drift and Diffusion Flux Closures

We present the development and analysis of a stochastic theory for characterizing the relative positions of monodisperse, low-inertia particle pairs that are settling rapidly in homogeneous isotropic turbulence.  The theory is applicable in the limits of particle Stokes number $St_\eta \ll 1$ and Froude number $Fr \ll St_\eta \ll 1$.    Here $St_\eta$~is the ratio of the particle viscous relaxation time to the Kolmogorov time scale, and $Fr$ is the ratio of the Kolmogorov scale of acceleration and the magnitude of gravitational acceleration.  In these parametric limits, closures are developed for the drift and diffusion fluxes in the probability density function (PDF) equation for the pair relative positions. The theory focuses on the relative motion of particle pairs in the dissipation regime of turbulence, i.e., for pair separations smaller than the Kolmogorov length scale.  In this regime, the theory approximates the fluid velocity field in a reference frame following the primary particle as locally linear.  We present the derivation of closure approximation  for the drift and diffusion fluxes in the PDF equation for the 
pair relative positions $\mathbf{r}$.   

The influence of Reynolds and Froude number on the motion of bidisperse inertialparticles in turbulence

Using Direct Numerical Simulations (DNS), we consider the effects of Taylor Reynolds number ($R_\lambda$), Froude number ($Fr$), and Stokes number ($St$) on the motion of bidisperse particles in turbulence. Particle accelerations play a key role in the relative motion of bidisperse particles, and we find that reducing $Fr$ enhances the accelerations, but suppresses their intermittency. Probability Density Functions (PDF) of the relative velocities show that even when the particles are settling rapidly, turbulence still plays a key role in their motion parallel to the direction of gravity, and all the more as $R_\lambda$ is increased. This occurs because although the settling velocity may be much larger than typical velocities of the turbulence, due to intermittency, there are significant regions of the flow where the turbulent velocities are of the same order as the settling velocity. Increasing $R_\lambda$ enhances the non-Gaussianity of the relative velocity PDFs, while reducing $Fr$ has the opposite effect, and for $Fr\ll 1$, the PDFs become close to Gaussian (except for weak bidispersity). Finally, we observe that low-order statistics related to collision rates, while strongly affected by $Fr$ and $St$, are only very weakly affected by $R_\lambda$ when $St\leq O(1)$.   

Field measurements of cloud droplet dynamics and spatial distribution

We present the results of a field experiment investigating the dynamics and spatial distribution of cloud droplets and their dependence on the turbulent flow properties and droplet Stokes number. These two cloud properties determine the collisional growth rate of cloud particles and the resulting precipitation rate. The experiment takes place at a high-altitude mountain research station and makes use of a movable particle tracking setup that can travel with the mean wind speed.     

Homogeneous Shear Cluster-induced Turbulence

Previous work has introduced homogeneous cluster-induced turbulence (CIT) as a canonical flow that may be studied for particle-laden flow model development. Homogeneous CIT is a two-way coupled flow in which a periodic domain of fluid is seeded with heavy, inertial particles. The momentum coupling between the phases results in turbulent-like fluctuations in the fluid phase and clustering in the particle phase that is characteristic of many particle-laden flows. As a step towards understanding particle-laden flow in boundary layers, in this work we examine the effect of homogeneous shear on CIT. We study the effects of varying the shear rate and shear direction on clustering and the dimensionality of the turbulent fluctuations. We find that at high shear rates, regardless of the shear direction, the turbulent fluctuations approach a one-component state and the clusters disappear. Horizontally oriented shear tends to impede the trajectory towards the one-component state. At low shear rates, the dynamics remain close to CIT regardless of the shear direction. Finally, we evaluate a Reynolds Stress Model by comparing its predictions with the simulation results in this study.