- Access by Xinjiang University
Model for the radial distribution function of polydisperse inertial spheres settling in homogeneous, isotropic turbulence
Phys. Rev. Fluids 7, 104602 – Published 7 October, 2022
DOI: https://doi.org/10.1103/PhysRevFluids.7.104602
Abstract
While particle inertia is widely known to cause substantial clustering of monodisperse particles in turbulent flows, differential sedimentation of polydisperse particles can rapidly decorrelate their relative positions and attenuate clustering. This paper presents a simple analytical model for the radial distribution function (RDF) of inertial particles settling in homogeneous, isotropic turbulence over a broad range of particle Stokes numbers, settling parameters, size ratios, and interparticle separations. We first draw on previous theories and direct-numerical simulations (DNS) to develop a simple comprehensive fit for the RDF of monodisperse particles without sedimentation. Even in the absence of gravity, the relative positions of polydisperse particles decorrelate as a result of turbulent accelerations, which have been treated as an acceleration-driven relative diffusivity of unequal size particles balancing the radial diffusion and drift resulting from turbulent shearing motions. We develop a similar model to describe the orientational averaged pair distribution function or RDF in the presence of differential sedimentation. The model is validated by comparison with DNS results for polydisperse settling particles. Juxtaposition of the model predictions with a variety of experimental measurements provides a perspective on current empirical knowledge of the RDF of sedimenting particles in turbulence. A sample calculation is then performed to illustrate the effect of preferential concentration in the presence of differential sedimentation on the coalescence rate of cloud droplets.
Physics Subject Headings (PhySH)
Article Text
References (33)
- O. Ayala, B. Rosa, L.-P. Wang, and W. Grabowski, Effects of turbulence on the geometric collision rate of sedimenting droplets. Part 1. Results from direct numerical simulation, New J. Phys. 10, 075015 (2008).
- L. Pan, P. Padoan, J. Scalo, A. G. Kritsuk, and M. L. Norman, Turbulent clustering of protoplanetary dust and planetesimal formation, Astrophys. J. 740, 6 (2011).
- J. Chun, D. L. Koch, S. L. Rani, A. A, and L. R. Collins, Clustering of aerosol particles in isotropic turbulence, J. Fluid Mech. 536, 219 (2005).
- A. D. Bragg, P. J. Ireland, and L. R. Collins, Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence, Phys. Rev. E 92, 023029 (2015).
- L. I. Zaichik and V. M. Alipchenkov, Pair dispersion and preferential concentration of particles in isotropic turbulence, Phys. Fluids 15, 1776 (2003).
- H. Xu and E. Bodenschatz, Motion of inertial particles with size larger than Kolmogorov scale in turbulent flows, Physica D 237, 2095 (2008).
- L. I. Zaichik and V. M. Alipchenkov, Refinement of the probability density function model for preferential concentration of aerosol particles in isotropic turbulence, Phys. Fluids 19, 113308 (2007).
- L. I. Zaichik and V. M. Alipchenkov, Statistical models for predicting pair dispersion and particle clustering in isotropic turbulence and their applications, New J. Phys. 11, 103018 (2009).
- P. Ireland, A. Bragg, and L. Collins, The effect of reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational effects, J. Fluid Mech. 796, 617 (2016).
- P. Ireland, A. Bragg, and L. Collins, The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 2. Simulations with gravitational effects, J. Fluid Mech. 796, 659 (2016).
- A. D. Bragg and L. R. Collins, New insights from comparing statistical theories for inertial particles in turbulence: I. Spatial distribution of particles, New J. Phys. 16, 055013 (2014).
- R. Dhariwal and A. Bragg, Small-scale dynamics of settling, bidisperse particles in turbulence, J. Fluid Mech. 839, 594 (2018).
- S. L. Rani, V. K. Gupta, and D. L. Koch, Clustering of rapidly settling, low-inertia particle pairs in isotropic turbulence. Part 1. Drift and diffusion flux closures, J. Fluid Mech. 871, 450 (2019).
- O. Ayala, B. Rosa, and L.-P. Wang, Effects of turbulence on the geometric collision rate of sedimenting droplets. Part 2. Theory and parameterization, New J. Phys. 10, 075016 (2008).
- J. Lu, H. Nordsiek, and R. A. Shaw, Clustering of settling charged particles in turbulence: Theory and experiments, New J. Phys. 12, 123030 (2010).
- J. P. Salazar, J. De Jong, L. Cao, S. H. Woodward, H. Meng, and L. R. Collins, Experimental and numerical investigation of inertial particle clustering in isotropic turbulence, J. Fluid Mech. 600, 245 (2008).
- E.-W. Saw, R. A. Shaw, J. P. Salazar, and L. R. Collins, Spatial clustering of polydisperse inertial particles in turbulence: II. Comparing simulation with experiment, New J. Phys. 14, 105031 (2012).
- A. J. Petersen, L. Baker, and F. Coletti, Experimental study of inertial particles clustering and settling in homogeneous turbulence, J. Fluid Mech. 864, 925 (2019).
- M. A. Yavuz, R. P. J. Kunnen, G. J. F. Van Heijst, and H. J. H. Clercx, Extreme Small-Scale Clustering of Droplets in Turbulence Driven by Hydrodynamic Interactions, Phys. Rev. Lett. 120, 244504 (2018).
- J. Dhanasekaran, A. Roy, and D. L. Koch, Collision rate of bidisperse, hydrodynamically interacting spheres settling in a turbulent flow, J. Fluid Mech. 912, A5 (2021).
- W. C. Reade and L. R. Collins, Effect of preferential concentration on turbulent collision rates, Phys. Fluids 12, 2530 (2000).
- S. L. Rani, R. Dhariwal, and D. L. Koch, Clustering of rapidly settling, low-inertia particle pairs in isotropic turbulence. Part 2. Comparison of theory and DNS, J. Fluid Mech. 871, 477 (2019).
- L. I. Zaichik, O. Simonin, and V. M. Alipchenkov, Collision rates of bidisperse inertial particles in isotropic turbulence, Phys. Fluids 18, 035110 (2006).
- L. Pan and P. Padoan, Turbulence-induced relative velocity of dust particles. I. Identical particles, Astrophys. J. 776, 12 (2013).
- R. Dhariwal, S. L. Rani, and D. L. Koch, Stochastic theory and direct numerical simulations of the relative motion of high-inertia particle pairs in isotropic turbulence, J. Fluid Mech. 813, 205 (2017).
- W. W. Grabowski and L.-P. Wang, Growth of cloud droplets in a turbulent environment, Annu. Rev. Fluid Mech. 45, 293 (2013).
- B. Brunk, D. Koch, and L. Lion, Hydrodynamic pair diffusion in isotropic random velocity fields with application to turbulent coagulation, Phys. Fluids 9, 2670 (1997).
- A. D. Bragg, A. L. Hammond, R. Dhariwal, and H. Meng, Hydrodynamic interactions and extreme particle clustering in turbulence, J. Fluid Mech. 933, A31 (2022).
- A. B. Kostinski and R. A. Shaw, Fluctuations and luck in droplet growth by coalescence, Bull. Am. Meteorol. Soc. 86, 235 (2005).
- S. G. Lasher-trapp, W. A. Cooper, and A. M. Blyth, Broadening of droplet size distributions from entrainment and mixing in a cumulus cloud, Quart. J. R. Meteorol. Soc. 131, 195 (2005).
- S. G. Lasher-Trapp, C. A. Knight, and J. M. Straka, Early radar echoes from ultragiant aerosol in a cumulus congestus: Modeling and observations, J. Atmos. Sci. 58, 3545 (2001).
- P. Vaillancourt, M. Yau, P. Bartello, and W. W. Grabowski, Microscopic approach to cloud droplet growth by condensation. Part II: Turbulence, clustering, and condensational growth, J. Atmos. Sci. 59, 3421 (2002).
- R. Davis, The rate of coagulation of a dilute polydisperse system of sedimenting spheres, J. Fluid Mech. 145, 179 (1984).
