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Register a new userSpectral characterisation of inertial particle clustering in turbulence
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Clustering of inertial particles is important for many types of astrophysical and geophysical turbulence, but it has been studied predominately for incompressible flows. Here we study compressible flows and compare clustering in both compressively (irrotationally) and vortically (solenoidally) forced turbulence. Vortically and compressively forced flows are driven stochastically either by solenoidal waves or by circular expansion waves, respectively. For compressively forced flows, the power spectra of the density of inertial particles are a particularly sensitive tool for displaying particle clustering relative to the density enhancement. We use both Lagrangian and Eulerian descriptions for the particles. Particle clustering through shock interaction is found to be particularly prominent in turbulence driven by spherical expansion waves. It manifests itself through a double-peaked distribution of spectral power as a function of Stokes number. The two peaks are associated with two distinct clustering mechanisms; shock interaction for smaller Stokes numbers and the centrifugal sling effect for larger values. The clustering of inertial particles is associated with the formation of caustics. Such caustics can only be captured in the Lagrangian description, which allows us to assess the relative importance of caustics in vortically and irrotationally forced turbulence. We show that the statistical noise resulting from the limited number of particles in the Lagrangian description can be removed from the particle power spectra, allowing us a more detailed comparison of the residual spectra. We focus on the Epstein drag law relevant for rarefied gases, but show that our findings apply also to the usual Stokes drag.
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From new detailed experimental data, we found that the Radial Distribution Function (RDF) of inertial particles in turbulence grows explosively with $r^{-6}$ scaling as the collision radius is approached. We corrected a theory by Yavuz et al. (Phys. Rev. Lett. 120, 244504 (2018)) based on hydrodynamic interactions between pairs of weakly inertial particles, and demonstrate that even this corrected theory cannot explain the observed RDF behavior. We explore several alternative mechanisms for the discrepancy that were not included in the theory and show that none of them are likely the explanation, suggesting new, yet to be identified physical mechanisms are at play.
Multiscale statistical analyses of inertial particle distributions are presented to investigate the statistical signature of clustering and void regions in particle-laden incompressible isotropic turbulence. Three-dimensional direct numerical simulations of homogeneous isotropic turbulence at high Reynolds number ($Re_lambda gtrsim 200$) with up to $10^9$ inertial particles are performed for Stokes numbers ranging from $0.05$ to $5.0$. Orthogonal wavelet analysis is then applied to the computed particle number density fields. Scale-dependent skewness and flatness values of the particle number density distributions are calculated and the influence of Reynolds number $Re_lambda$ and Stokes number $St$ is assessed. For $St sim 1.0$, both the scale-dependent skewness and flatness values become larger as the scale decreases, suggesting intermittent clustering at small scales. For $St le 0.2$, the flatness at intermediate scales, i.e. for scales larger than the Kolmogorov scale and smaller than the integral scale of the flow, increases as $St$ increases, and the skewness exhibits negative values at the intermediate scales. The negative values of the skewness are attributed to void regions. These results indicate that void regions at the intermediate sales are pronounced and intermittently distributed for such small Stokes numbers. As $Re_lambda$ increases, the flatness increases slightly. For $Re_lambda ge 328$, the skewness shows negative values at large scales, suggesting that void regions are pronounced at large scales, while clusters are pronounced at small scales.
In a shear flow particles migrate to their equilibrium positions in the microchannel. Here we demonstrate theoretically that if particles are inertial, this equilibrium can become unstable due to the Saffman lift force. We derive an expression for the critical Stokes number that determines the onset of instable equilibrium. We also present results of lattice Boltzmann simulations for spherical particles and prolate spheroids to validate the analysis. Our work provides a simple explanation of several unusual phenomena observed in earlier experiments and computer simulations, but never interpreted before in terms of the unstable equilibrium.
Recently, the nature of viscoelastic drag-reducing turbulence (DRT), especially maximum drag reduction (MDR) state, has become a focus of controversy. It has long been regarded as polymers-modulated inertial turbulence (IT), but is challenged by the newly proposed concept of elasto-inertial turbulence (EIT). This study is to re-picture DRT in parallel plane channels by introducing dynamics of EIT based on statistical and budget analysis for a series of flow regimes from the onset of DR to EIT. Energy conversion between velocity fluctuations and polymers as well as polymeric pressure redistribution effect are of particular concern, based on which a new energy self-sustaining process (SSP) of DRT is re-pictured. The numerical results indicate that at low Reynolds number (Re), the flow enters laminar regime before EIT-related SSP is formed with the increase of elasticity, whereas, at moderate Re, EIT-related SSP can get involved and survive from being relaminarized. This somehow explains the reason why relaminarization is observed for small Re while the flow directly enters MDR and EIT at moderate Re. Moreover, with the proposed energy picture, the newly discovered phenomenon that the streamwise velocity fluctuations lag behind those in wall-normal direction can be well explained. The re-pictured SSP certainly justify that IT nature is gradually replaced by that of EIT in DRT with the increase of elasticity.
In this paper we numerically investigate the influence of dissipation during particle collisions in an homogeneous turbulent velocity field by coupling a discrete element method to a Lattice-Boltzmann simulation with spectral forcing. We show that even at moderate particle volume fractions the influence of dissipative collisions is important. We also investigate the transition from a regime where the turbulent velocity field significantly influences the spatial distribution of particles to a regime where the distribution is mainly influenced by particle collisions.
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