Cascade model for particle concentration and enstrophy in fully developed turbulence with mass-loading feedback

Scale dependence of multiplier distributions for particle concentration, enstrophy, and dissipation in the inertial range of homogeneous turbulence

Turbulent flows preferentially concentrate inertial particles depending on their stopping time or Stokes number, which can lead to significant spatial variations in the particle concentration. Cascade models are one way to describe this process in statistical terms. Here, we use a direct numerical simulation (DNS) dataset of homogeneous, isotropic turbulence to determine probability distribution functions (PDFs) for cascade multipliers, which determine the ratio by which a property is partitioned into subvolumes as an eddy is envisioned to decay into smaller eddies. We present a technique for correcting effects of small particle numbers in the statistics. We determine multiplier PDFs for particle number, flow dissipation, and enstrophy, all of which are shown to be scale dependent. However, the particle multiplier PDFs collapse when scaled with an appropriately defined local Stokes number. As anticipated from earlier works, dissipation and enstrophy multiplier PDFs reach an asymptote for sufficiently small spatial scales. From the DNS measurements, we derive a cascade model that is used it to make predictions for the radial distribution function (RDF) for arbitrarily high Reynolds numbers, Re, finding good agreement with the asymptotic, infinite Re inertial range theory of Zaichik and Alipchenkov [New J. Phys. 11, 103018 (2009)NJOPFM1367-263010.1088/1367-2630/11/10/103018]. We discuss implications of these results for the statistical modeling of the turbulent clustering process in the inertial range for high Reynolds numbers inaccessible to numerical simulations.

Multifractality in individual honeybee behavior hints at colony-specific social cascades: Reanalysis of radio-frequency identification data from five different colonies

Honeybees (Apis mellifera) exhibit complex coordination and interaction across multiple behaviors such as swarming. This coordination among honeybees in the same colony is remarkably similar to the concept of informational cascades. The multifractal geometry of cascades suggests that multifractal measures of individual honeybee activity might carry signatures of these colony-wide coordinations. The present work reanalyzes time stamps of entrances to and exits from the hive captured by radio-frequency identification (RFID) sensors reading RFID tags on individual bees. Indeed, both multifractal spectrum width for individual bees' inter-reading interval series and differences of those widths from surrogates significantly predicted not just whether the individual bee's hive had a mesh enclosure but also predicted the specific membership of individual bees in one of five colonies. The significant effects of multifractality in matching honeybee activity to type of colony and, further, matching individual honeybees to their exact home colony suggests that multifractality quantifies key features of the colony-wide interactions across many scales. This relevance of multifractality to predicting colony type or colony membership adds additional credence to the cascade metaphor for colony organization. Perhaps, multifractality provides a new tool for exploring the relationship between individual organisms and larger, more complex social behaviors.

Numerical study of particle-vortex interaction and turbulence modulation in swirling jets

This study carried out a direct numerical simulation of gas-solid swirling jet flow, focusing on the particle-vortex interaction and mechanisms of turbulence modulation. Two cases of flows with either a constant particle flow rate or a constant particle mass loading are simulated. The typical instantaneous particle-vortex interactions are illustrated and analyzed, as well as the spectrum representations and the projections of them. The results show that the small particles (St<1) and light-mass loadings augment the vortices of the large-scale range in the power spectrum representation by shifting the peaks of wave numbers from small to large values as they pass through the large vortices and break them into smaller scales. The large particles and heavy-mass loadings suppress greatly the large scales of vortices, transferring the turbulent kinetic energy from large to relatively smaller scales of vortices, resulting in turbulence augmentation in the large wave numbers and turbulence attenuation in the range of small wave numbers. Moreover, by comparison between the two cases, it is found that the turbulence modulation is more highly sensitive to the effect of mass loadings rather than the dynamical response property of particles. The well-known knowledge on modulation of turbulence is true under the condition of the same mass loading. However, the situation becomes very complicated when the mass loading changes. Finally, these conclusions are verified by the analysis of energy spectrum and dissipation.

Two-fluid approach for direct numerical simulation of particle-laden turbulent flows at small Stokes numbers

A two-fluid approach is proposed for direct numerical simulation of particle-laden turbulent flows in two-way coupling where the particle Stokes number is small. An Eulerian velocity field is calculated for the particle phase through a truncated series expansion in terms of the velocity and acceleration of the fluid phase [M. R. Maxey, J. Fluid Mech. 174, 441 (1987)]. This expansion is valid for particles with a sufficiently small Stokes number defined as the ratio of particle time constant to the Kolmogorov time scale. The transport equation of the Eulerian concentration field of particles (particle volume fraction) is solved along with the fluid-phase equations for which the effect of the particles on the fluid phase is taken into account through source terms in the momentum equations. For the assessment purposes, particle-laden decaying isotropic turbulence is studied. The results obtained through the proposed two-fluid approach are compared against those obtained by the trajectory approach in which the particle equations are solved in the Lagrangian framework. It is shown that there is a good agreement between various fluid-phase statistics obtained by these approaches for different small Stokes numbers and mean particle concentrations.