Kinematic and Thermodynamic Effects on Particle Clustering in Turbulent Flows

Abstract

Particle-laden flows are ubiquitous in numerous state-of-the-art engineering applications such as dispersed metallic particle combustion, particle solar collectors, and cold spray manufacturing. In such thermal applications, ensuring a uniform distribution of particles within a carrier fluid is critical, yet inertial particles intrinsically cluster in turbulent flows. In past investigations, particle clustering was treated as a purely kinematic problem, and typically, the variable temperature effects of both the particles and the gas were neglected. This is perplexing, as the increase in carrier gas temperature increases viscosity, which concomitantly enhances the coupling force between the fluid and the particles. Thus, it is plausible that particle clustering is influenced not only by kinematics but also by local thermodynamics. This line of thinking has motivated the scientific questions that underpin the present work.

To understand the role of thermodynamics on particle clustering, direct numerical simulations (DNS) were carried out to analyze the clustering behavior of heated dispersed particles in homogeneous isotropic turbulence (HIT) and subsonic jet flows; the study was then extended to explore particle-laden supersonic jet flows. In these analyses, the continuum and particulate phases were modeled with the Eulerian and Lagrangian point-particle approaches, respectively. The fluid-particle energy was coupled with two-way coupling (TWC), while momentum exchange between the two phases was modeled with one-way coupling (OWC) and TWC. The analysis of the simulations led to the discovery of a novel particle clustering mechanism called viscous capturing (VC), in which preformed particle clusters create hot spots. The higher temperature of the gas in these hot spots led to regions with higher local viscosity, termed viscous clouds. The increased drag on the particles in the viscous clouds makes it hard for the clustered particles to leave the clusters, and it also aids in capturing more particles passing through the viscous clouds. This ultimately enhances particle clustering. An opposite particle clustering behavior was observed in a carrier phase with liquid-like viscosity (viscosity decreases with temperature rise), where particle heating resulted in superior particle dispersion.

Furthermore, the VC effect was found to increase with the rise in particle loading density. This is because, at higher particle loading density, the two prerequisites of VC are satisfied: (1) particles should be clustered before particle heating is initiated, and (2) these clusters should be large and unevenly distributed in the flow. In these viscous clouds, the fluid-particle and particle-particle slip velocities were found to be well-correlated, which further aids in keeping particles clustered. Apart from these conditions, particles should be uniformly heated for VC to take effect.

The HIT helps to isolate the effect of turbulence on particle clustering but lacks generalizability or the mean shear of more relevant particle-laden flow configurations, such as a jet flow. In subsonic jets, even a moderate rise in local gas viscosity can initiate VC, which results in higher clustering of heated particles as compared to unheated particles. This is because the introduction of particles within the jet core, which causes particles to be close to each other, also satisfies the two prerequisites of VC and retains particles within the jet. Thus, instead of individual viscous clouds compared to the HIT case, the entire central region of the jet acts as a viscous cloud. Even the particles with a higher radial velocity component remained within the jet, as they were unable to cross the sharp temperature gradient at the outer edge of the jet due to their propensity to collect at the location of a sharp scalar gradient. Thus, heated particles are essentially restrained within the jet.

On the other hand, in supersonic jet flows, it was determined that particles of different inertia have a distinct axial location where they start dispersing radially (xᵣ). This xᵣ is marked with a local Stokes number of St* ≈ 0.6. A new metric was also introduced to estimate xᵣ for practical applications. Particle dispersion was also influenced by the compressibility effects, where larger particles were found to have a higher propensity to settle in high-density gradient and dilatation regions of the flow.