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

An analysis of particle concentrations formed in direct numerical simulatio ns of forced three-dimensional (3-D) turbulence is described, Up to 48 mill ion 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 par ameter 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 (Re-lam bda) 40, 80, and 140 were studied. We present several new results for conce ntration measures utilized in previous studies as well as measures introduc ed in this paper. The measures are compared and contrasted on a finer St gr id than presented in previous work and are analyzed as functions of Re-lamb da and spatial binning scale. The measures are based on (a) deviations of t he concentration PDF (probability density function) from the PDF of a unifo rm particle field, (b) the correlation dimension (D-2) for both 3-D and two -dimensional concentrations, and (c) the relative St-dependent concentratio ns contained in a localized region of space. Measure (c) is motivated by th e observation that the total and St-dependent concentrations are linearly c orrelated. The concentration measures reveal St dependencies that are insen sitive to the Reynolds number of the flow with each measure having its own characteristic shape. The widths and maxima of St functions for measures ex plicitly constructed on a single spatial binning scale showed a very weak d ependence on bin sizes ranging from 2 to 6 times the Kolmogorov length scal e. We conclude that the measures studied in this paper reveal a universalit y that may persist to much higher Reynolds numbers. (C) 2001 American Insti tute of Physics.