Session Q09: Particle-laden Flows: Particle-Turbulence Interaction II

On the incipient sediment suspension downstream of three-dimensional wall-mounted obstacles.

The incipient sediment suspension downstream of thin square shaped tab with various inclination angles was studied using theoretical and experimental arguments. Sediment distribution characteristics and wake flows under various tab inclinations and incoming velocities were studied using volumetric particle tracking velocimetry and particle image velocimetry. Results indicate that sediment suspension occurred right downstream of obstacles due to enhanced local turbulent intensities. Sediment volumetric fraction was highly influenced by wake turbulent kinetic energy for low inclination angles (i.e., obstacles nearly parallel to incoming flow). However, for high inclination angles, sediment suspension was dominated and suppressed by distinct downward velocities resulting in lower volumetric fraction. Revised Rouse number, supported by flow measurements, was proposed to allow us to quantitatively depict the coupled influence of turbulent mixing load and vertical flows across various inclination angles and incoming velocities.   

When is settling important for particle concentrations in wall-bounded turbulent flows?

The role of settling on inertial particle concentrations in a wall-bounded turbulence is explored. While it may be thought that settling can be ignored when the Stokes settling velocity $v_s$ is small compared with the fluid friction velocity $u_\tau$, we show that even in this regime the settling may make a leading order contribution to the concentration profiles. This is because the importance of settling is determined by the size of $v_s$ compared with the turbophoretic velocity, not compared with $u_\tau$. We explain this in the context of the particle mean-momentum equation, and show that in general, there always exists a region in the boundary layer where settling cannot be neglected, no matter how small $v_s/u_\tau$ is (provided it is finite). Direct numerical simulations confirm the arguments, and show that even for $v_s/u_\tau = O(10^−2)$, the near wall particle concentration can be orders of magnitude larger than for the case where $v_s/u_\tau= 0$, and for $v_s/u_\tau = O(10^−3)$ enhancements of up to a factor of two are observed. It is also found that even for $v_s/u_\tau = O(10^−2)$, the preferential sampling of ejection events in the boundary layer by the inertial particles is profoundly modified compared with the $v_s/u_\tau=0$ case.   

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

In 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. Monchaux \& Dejoan (Phys. Rev. Fluids 2, 104302, 2017) showed using DNS that even when the particle mass loading is small, although the effect of the particles on the global flow properties is weak, the particles can still strongly modify the local flow in their vicinity by dragging the surrounding fluid down as they fall, significantly influencing their settling velocities. We show using DNS that this enhancement due to two-way coupling in the dilute regime disappears as the Reynolds number increases, and we explain this using our multiscale theory. We also consider denser regimes, and explain how the fluid-dragging effect competes with the preferential sweeping mechanism at different scales in the flow.   

Skin-friction drag modulation and riblet-like clusters in a semi-dilute particle-laden turbulent channel flow at $Re_\tau = 180$

In this study, we explore how coherent structures near the wall can be modulated by particles to help alter the skin-friction drag that is produced by them. This can help regulate the overall mass flow rate of the fluid by increasing or decreasing the overall drag caused by the skin-friction generated near the wall due to these coherent structures. We explore this modulation within Euler-Lagrange simulations of a four-way coupled turbulent particle-laden channel flow at $Re_\tau = 180$. Two separate cases are run at a lower ($St^+ = 6$) and higher inertia ($St^+ = 30$). The particles are present at a semi-dilute concentration, i.e., such that the average volume fraction is low ($2.4 10^-4 – 7.2 10^-4$), but mass loading is significant ($M = 0.2 – 0.6$). The results show that Particle inertia is vital to the type of modulation near the wall. Particles with a lower inertia ($St^+=6$) tend to enhance the drag, decreasing the overall mass flow rate. Due to their inertia, these particles move towards the wall, where they form small and fragmented clusters without significant coherence. Contrastingly, particles at $St^+ = 30$ cause a redaction of drag and an increase in the mass flow rate. These higher inertia particles accumulate near the walls and form very long longitudinal clusters akin to riblets that align with the flow low speed streaks. We measure the contribution of the particles to the total shear stress, and show how this directly relates to the change in the mass flow rate.   

On the roles of clustered inertial particles in inter-phase, cross-scale momentum transfer

Inter-phase, cross-scale transfer of turbulence kinetic energy (TKE) of two-way coupled homogeneous isotropic turbulence is examined using a wavelet multiresolution analysis. Locally in space, clusters of the critical particles (St_k = 1) are not definite energy sources or sinks. Cross-scale transfer estimated using the subfilter-scale energy flux Π_SFS does not indicate a definite direction of energy transfer in the spectral space at positions where St_k = 1 particles accumulate. Local Π_SFS is not necessarily amplified by the clusters, although the mean downscale transfer is enhanced. Wavelet statistics conditioned on coarse-grained number density support the same conclusions. Clusters of St_k = 1 particles are associated with a co-existence of down- and upscale energy transfer.  Regions devoid of St_k = 1 particles are characterized by the in-scale energy transfer (Π_SFS ≈ 0), while the inverse is not true. The critical particles create nonlocal modulations of turbulence, although they are accumulated locally in space. In addition, the analysis supports \textit{a priori}, a validity of the subgrid-scale (SGS) Stokes number useful for analyzing the SGS modeling of two-way coupled particle-laden turbulence.   

A Large Eddy Simulation (LES) study to capture turbulence attenuation for turbulent channel flows

The presence of particles leads to turbulence modulation in particle-laden turbulent flows. In the present study, turbulence attenuation is observed with Smagorinsky and dynamic Smagorinsky models for two Reynolds numbers of 3300 and 5600 based on average gas velocity and channel width. The turbulence intensities decrease with an increase in particle loading, after a critical loading (CPVL) a sudden drop in the fluid fluctuations is observed. At low volume fractions, LES models predict the turbulence attenuation with high accuracy (> 80%) but fail to predict the volume loading at which turbulence collapse happens. It is found that an inaccurate prediction of the turbulent energy production is the source of error in CPVL prediction which is caused by the “modeling error” in LES models.   

Tomo-PIV measurements of a freely moving sphere in a turbulent boundary layer

Time resolved tomo-PIV was used to track nearly neutrally buoyant hydrogel spheres in a fully developed, turbulent boundary layer. The spheres were refractive index matched and were ``tagged" by spokes of tracer particles. Spheres (D⁺ ≈ 70, superscript "+" denotes inner wall scaling) were released one by one from the bottom at about 5δ (Re_δ ≈ 8000) upstream of the measurement volume. Sphere centroid positions were tracked in the buffer and logarithmic layers. The imaged spokes were converted into point clouds and their translational and rotational motion were determined using the iterative closest point algorithm. Sphere Reynolds numbers did not exceed 100, and no signs of sphere wake shedding were detected. It was found that besides their translational motion, the spheres exhibited significant rotation. The spheres were found in proximity of fragmented hairpin-like packets that induced ejection and sweep motions affecting the spheres' trajectories. All investigated spheres approached the wall at a lower velocity than their terminal settling velocity. We show that besides the drag force, both shear-induced and rotation induced lift forces are important in the transverse motion of the spheres.    

Inertial particles in a Kolmogorov channel flow

We investigate, by means of analytical and numerical methods, the effects of heavy particles on the linear stability and on the turbulent drag of a Kolmogorov channel flow.

Particles are modeled in the framework of an Eulerian two-way coupling model: a continuum density transported by a compressible velocity field which exchanges momentum with the fluid phase.

In the case of laminar flow, we find that particles can either stabilize or destabilize the flow depending on the particle Stokes number and on the mass fraction. 

In the case of a turbulent Kolmogorov flow, we find that particles always reduce the mean flow with respect to the pure fluid case and therefore enhance the drag coefficient.

Turbulence suppression is observed to be stronger for particles of smaller inertia. This surprising result is understood by mapping the equations for dusty flow to a Newtonian flow with an effective forcing rescaled by the increased fluid density.