Sealing properties of particle density fields formed in simulated turbulent flows

Direct numerical simulations of particle concentrations in fully developed three-dimensional turbulence were carried out in order to study the nonunif orm structure of the particle density field. Three steady-state turbulent f luid fields with Taylor microscale Reynolds numbers (Re-lambda) of 40, 80, and 140 were generated by solving the Navier-Stokes equations with pseudosp ectral methods. Large-scale forcing was used to drive the turbulence and ma intain temporal stationarity. The response of the particles to the fluid wa s parametrized by the particle Stokes number St, defined as the ratio of th e particle's stopping time to the mean period of eddies on the Kolmogorov s cale (eta) In this paper, we consider only passive particles optimally coup led to these eddies (St approximate to 1) because of their tendency to conc entrate more than particles with lesser or greater St values. The trajector ies of up to 70 x 10(6) particles were tracked in the equilibrated turbulen t hows until the particle concentration field reached a statistically stati onary state. The nonuniform structure of the concentration fields was chara cterized by the multifractal singularity spectrum f(alpha), derived from me asures obtained after binning particles into cells ranging from 2 eta to 15 eta in size. We observed strong systematic variations of f(alpha) across t his scale range in all three simulations and conclude that the particle con centration held is not statistically self-similar across the scale range ex plored. However, spectra obtained at the 2 eta, 4 eta, and 8 eta scales of each flow case were found to be qualitatively similar;This result suggests that the local structure of the particle concentration field may be flow in dependent. The singularity spectra found for 2 eta-sized cells were used to predict concentration distributions in good agreement with those obtained directly from the particle data. This singularity spectrum has a shape simi lar to the analogous spectrum derived for the inertial-range energy dissipa tion fields sf experimental turbulent flows at Re-lambda = 110 and 1100. Ba sed on this agreement, and the expectation that both dissipation and partic le concentration are controlled by the same cascade process, we hypothesize that singularity spectra similar to the ones found in this work provide a good characterization of the spatially averaged statistical properties of p referentially concentrated particles in higher Re-lambda turbulent flows. [ S1063-651X(99)00807-7].