Stokes and Reynolds number dependence of preferential particle concentration in simulated three-dimensional turbulence

Abstract

An analysis of particle concentrations formed in direct numerical simulations of forced three-dimensional (3-D) turbulence is described. Up to 48 million particles responding passively to the flow with response times ranging from 0.2 to 6 times the dissipation time of the fluid were evolved together until the concentration field reached a statistical stationary state. The Stokes number (St), defined at the dissipation time scale, was the sole parameter used to characterize the particle–fluid coupling in the regime where particles preferentially concentrate. Concentrations resulting from three simulations equilibrating at the Taylor microscale Reynolds numbers (Reλ) 40, 80, and 140 were studied. We present several new results for concentration measures utilized in previous studies as well as measures introduced in this paper. The measures are compared and contrasted on a finer St grid than presented in previous work and are analyzed as functions of Reλ and spatial binning scale. The measures are based on (a) deviations of the concentration PDF (probability density function) from the PDF of a uniform particle field, (b) the correlation dimension (D2) for both 3-D and two-dimensional concentrations, and (c) the relative St-dependent concentrations contained in a localized region of space. Measure (c) is motivated by the observation that the total and St-dependent concentrations are linearly correlated. The concentration measures reveal St dependencies that are insensitive to the Reynolds number of the flow with each measure having its own characteristic shape. The widths and maxima of St functions for measures explicitly constructed on a single spatial binning scale showed a very weak dependence on bin sizes ranging from 2 to 6 times the Kolmogorov length scale. We conclude that the measures studied in this paper reveal a universality that may persist to much higher Reynolds numbers.