Session Q10: Turbulence: Particle-Laden Flows (3:55pm - 4:40pm CST)

Numerical investigation of finite-time singularity of particle-laden flow

This study aims at investigation of finite-time singularity of particle velocity gradient by collision using a new approach. The motion of particle is derived in Eulerian frame under the assumption that velocity of particles is a smooth function in space, and is uniquely determined by the position of a particle. The derived equation of particle motion looks simple, but the solution is determined by a very complex process. In particular, the particle velocity gradient can easily go to infinity within a finite time due to the quadratic nonlinearity when the motion of particle is driven by turbulence. The discontinuity of the particle velocity gradient physically means a collision between two particles. Thus, a detailed investigation of the process of particle velocity gradients going to infinity allows a rigorous mathematical description of particle collisions in turbulence. Using this concept, the singularity of particle velocity gradient for various Stokes numbers and gravity factors is investigated firstly in a simple and intuitional Taylor-Green vortex flow and then in two-dimension turbulent flow. Detailed results will be presented in the meeting.   

Numerical Forcing of Dense Particle-Laden HIT Flows

Particle-laden flows are common to many scientific and engineering applications. One particular area of interest is high mass loading of particles in turbulent flows, which is commonly found in sprays and fluidized beds, among other applications. As a step in that direction, this paper introduces filtered linear forcing (FLF) as a tool for studying dense, low Mach number, particle-laden homogeneous isotropic turbulence (HIT) flows, and the strategy is compared to ordinary linear forcing (OLF). OLF is an effective way to generate isotropic turbulence in a periodic domain, and FLF algorithm applies a low-pass filter to the source term in the OLF algorithm in order to attain flows at higher Reynolds Number. An in-house finite volume code is used to implement an Eulerian framework to solve the gas phase transport equations, and Lagrangian equations are used to solve the liquid phase. In this study, particles with Stokes Number $St$ $\geq$ 1 in HIT flow are analyzed, as their behavior is different from smaller $St$ particles, wherein $St\geq 1$ particles have inertia and non-trivial slip compared to the gas phase. After achieving statistical stationarity, the particle clustering is compared between the FLF and OLF techniques, and the numerical stability is tested and compared as well.   

Capturing velocity gradients and particle rotation rates in turbulence

Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate, shape-dependent orientational dynamics, which sensitively depends on the particle history. In this contribution, we systematically develop a reduced-order model for the small-scale dynamics of turbulence, which captures the velocity gradient statistics along particle paths. The analysis of the resulting stochastic dynamical system allows us to identify the emergence of non-Gaussian statistics and non-trivial temporal correlations of vorticity and strain, as previously reported from experiments and simulations. Based on these insights, we use our model to compute the orientational statistics of anisotropic particles in turbulence, enabling modeling applications for complex particulate flows.   

Fluctuation-induced force mediated by turbulent fluctuations

Understanding hydrodynamic interaction forces between large particles aggregates or objects is important in a range of problems encountered in industrial and natural flows. Here we report a long-range attraction force mediated by turbulent fluctuations between two large anisotropic objects, beam, exposed to the wave-driven turbulence. In this system, we show that the magnitude of the force is a function of two parameters: the beam separation and the energy injection rate. A model is proposed that describes how this attraction force depends on the change of energy and structure of the confined turbulent flow. The physical mechanism responsible for this attraction force is related to the nontrivial coupling of the Lagrangian structure of the flow with the cavity formed by the beams. These results provide valuable insights in force generation mediated by turbulent fluctuations and in the recent discovery of turbulence-driven propulsion.   

The role of two-way coupling and preferential sweeping on particle settling velocities in turbulence

In a recent article (Tom \& Bragg, J. Fluid Mech., 871, pp. 244--270, 2019), we used theory and Direct Numerical Simulations (DNS) to explore how the preferential sweeping mechanism that generates enhanced particle settling velocities in turbulence operates at different scales of the flow. We showed that the scales that contribute to preferential sweeping depend on the particle Stokes number, settling parameter, and the flow Reynolds number. That analysis, however, assumed one-way coupling. When the particle mass loading is small, although the effect of the particles on the global flow properties is weak, the particles may nevertheless strongly modify the local flow in their vicinity, dragging the surrounding fluid down with them as they fall, significantly influencing their settling velocities (Monchaux \& Dejoan, Phys. Rev. Fluids 2, 104302, 2017). We use theory and DNS to explore how this fluid-dragging effect introduced by two-way coupling competes with the preferential sweeping mechanism at different scales in the flow, and for different particle and flow parameters. The analysis provides new insights into the scales where one mechanism dominates over the other, and the parameter regimes where two-way coupling effects are important for particle settling velocities.   

New Measurements of Inertial Particle Relative Velocity and Radial Distribution Function down to Near-contact Separations in Isotropic Turbulence Reveals Hydrodynamic Interaction Effects

Understanding particle collision mechanisms in isotropic turbulence is important to applications such as droplet coalescence. It is known that particles with finite Stokes numbers (\textit{St}) experience enhanced clustering due to turbulence, measured by the radial distribution function $g(r)$, and increased inward relative velocities, measured by the mean inward radial relative velocity $\langle w_{r}(r)\rangle^{\mathrm{-}}$, compared to inertia-free particles. However, collision occurs when particles are near contact. When their separation distance $r$ approaches the collision radius, particle pairs begin to experience hydrodynamic interactions (HI). Yavuz et al. (2018) (Phys Rev Lett 120 244504) observed $g(r)$ enhancement by HI; however their data exhibited significant scatter at $r$/$a=O$(10), ($a$: particle radius). We used a new high-resolution particle tracking technique by LaVision$^{\mathrm{1}}$ and optimized it for small-$r$ measurements of particles in a fan-driven enclosed isotropic turbulence chamber. This enabled high-resolution measurements of $g(r)$ and $\langle w_{r}(r)\rangle^{\mathrm{-}}$ down to near contact ($r$/$a=$2.07) using particles of different radii (2.5$\mu $m\textless $a$\textless 22.5$\mu $m) and inertia (0.1\textless \textit{St}\textless 3.7). When $r$/$a$\textless $O$(10), we observe that $g(r)$ varies as $r^{\mathrm{-6}}$, and $\langle w_{r}(r)\rangle ^{\mathrm{-\thinspace }}$begins to increase drastically. In this talk we explore how inertia affects clustering and relative velocities of particle pairs near contact through HI as well as turbulence.   

Turbulent Channel Flow of Suspensions over Porous Media.

In this study, we discuss the flow of turbulent suspension of non-Brownian and non-colloidal, rigid spherical particles in a Newtonian fluid over a porous wall. We consider suspension flows where the volume fraction ranges changes from 0 to 0.2 with different wall porous permeability, while porosity is constant at 0.6. Direct numerical simulations (DNS) with an immersed boundary method (IBM) are employed to resolve the particles and flow phase and coupled with the volume-averaged Navier-Stokes (VANS) to solve the flow within the porous layer. The results show that the mean velocity profiles are significantly altered by the presence of the particles in the fluid region when increasing the permeability of the porous layer. At the highest volume fraction investigated here, 0.2, the velocity fluctuation intensities and the Reynolds shear stress are found to decrease. The overall drag is found to grow with the volume fraction.   

Extended lifetime of respiratory droplets in a turbulent vapor puff

We numerically study a respiratory event with a turbulent jet together with 5000 exhaled droplets using a Lagrangian-Eurlerian approach. In our simulation, droplets are coupled to the ambient velocity, temperature and humidity fields such that we realistically account for the droplet evaporation in a respiratory event. In this study, we focus on cases with different ambient relative humidity (RH) with ambient temperature at $20^oC$ and exhaled vapor at $34^oC$. We found that for RH$=50\%$, the lifetime of the droplets with initial diameter of $10\mu m$ can be extended by up to 30 times as compared to the lifetime estimation by W. F. Wells (1934). The substantial increase in lifetime is attributed to the collective effects during droplet evaporation and the role of the respiratory humidity. The amount of lifetime extension even become more pronounced for larger RH, for example, the extension can go up to 200 times for RH$=90\%$. Our tool is a starting point for larger parameter studies, and our findings on extended lifetimes have implications on airborne disease transmission such as the pandemic of COVID-19.   

Resonant Alignment of Prolate Ellipsoids in Taylor-Couette Flow

Neutrally buoyant spheres have been observed to preferentially concentrate in Taylor-Couette flow. This phenomenon can be attributed to Faxen forces (Henderson et al. 2007) or a balance between shear gradient and wall effects (Majji & Morris 2018). But, the precise influence of particle shape on preferential clustering in Taylor-Couette flow is unknown. Using direct numerical simulations with the immersed boundary method, we show that prolate ellipsoids (Elongated spheroids, $\ell/d=0.1$ with $\ell$ the particle major axis and $d$ the gap-width between the cylinders) tend to get trapped at the Taylor vortex core for a specific range of Taylor numbers. Furthermore, trapped ellipsoids have their axis of revolution aligned with the tangent along the cylinder. This preferential clustering at the vortex core is a finite size effect and is therefore greatly enhanced when the ellipsoids are doubled in size. The clustering and alignment of the ellipsoids are shown to be linked to local flow regions where the axial vorticity of the Taylor vortex is lowest.   

Interscale energy transfer of liquid velocity fluctuations in a particle-laden plume.

We present an analysis of the interscale energy transfer inside a particle-laden plume. The experimental dataset analyzed was recently published (Bordoloi et al. 2020, J. Fluid Mech., 896:A19) in which stereoscopic particle image velocity (SPIV) was used to measure the interstitial fluid velocity fields at a plume centerplane. The single-phase Karman-Howarth-Monin (KHM) equation is adapted to multiphase turbulent flows by including the phase-indicator function. Implications of our analysis on turbulence modeling are discussed.