No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
s
Effect of preferential concentration on turbulent collision rates
Abstract
The effect of particle inertia on the interparticle collision rates of a turbulentaerosol was investigated recently by Sundaram and Collins (1997) using direct numerical simulation (DNS). They observed that for values of the particle Stokes number (here defined as the ratio of the particle response time to Kolmogorov time scale) near unity, the collision frequency was enhanced by between one and two orders of magnitude. This enhancement was attributed in part to the local enrichment of the particle concentration in low-vorticity regions of the flow due to the centrifuge effect commonly referred to as preferential concentration (Eaton and Fessler 1994). Sundaram and Collins (1997) showed that the correction factor for the collision kernel in a preferentially concentrated system is g(σ), where g(r) is the particle radial distribution function and σ is the collision diameter. This paper uses DNS, in combination with statistical analysis, to study the dependence of the radial distribution function on the turbulence and particle parameters. A curve fit of the results over a broad range of the relevant dimensionless parameters enables easy estimation of g(σ). The effect of system Reynolds number over the limited range accessible by DNS is also presented. In general, the degree of preferential concentration increases with increasing Reynolds number.
© 2000 American Institute of Physics
Received 31 August 1998
Accepted 16 June 2000
/content/aip/journal/pof2/12/10/10.1063/1.1288515
1.
1.S. Sundaram and L. R. Collins, “A numerical study of the modulation of isotropic turbulence by suspended particles,” J. Fluid Mech. 379, 105 (1999).
2.
2.S. E. Elghobashi and G. C. Truesdell, “On the two-way interaction between homogeneous turbulence and dispersed particles. I: Turbulence modification,” Phys. Fluids A 5, 1790 (1993).
3.
3.K. D. Squires and J. K. Eaton, “Particle response and turbulence modification in isotropic turbulence,” Phys. Fluids A 2, 1191 (1990).
4.
4.S. E. Pratsinis and P. T. Spicer, “Competition between gas phase and surface oxidation of TiCl4 during synthesis of TiO2 particles,” Chem. Eng. Sci. 53, 1861 (1998).
5.
5.Y. Xiong and S. E. Pratsinis, “Gas phase production of particles in reactive turbulent flows,” J. Aerosol Sci. 22, 637 (1991).
6.
6.J. D. Landgrebe and S. E. Pratsinis, “Gas-phase manufacture of particulates: Interplay of chemical reaction and aerosol coagulation in the free-molecular regime,” Ind. Eng. Chem. Res. 28, 1474 (1989).
7.
7.M. B. Pinsky and A. P. Khain, “Turbulence effects on droplet growth and size distribution in clouds—A review,” J. Aerosol Sci. 28, 1177 (1997).
8.
8.R. A. Shaw, W. C. Reade, L. R. Collins, and J. Verlinde, “Preferential concentration of cloud droplets by turbulence: Effects on the early evolution of cumulus cloud droplet spectra,” J. Atmos. Sci. 55, 1965 (1998).
9.
9.R. C. Hogan, J. N. Cuzzi, and A. R. Dobrovolskis, “Scaling properties of particle density fields formed in simulated turbulent flows,” Phys. Rev. E 60, 1674 (1999).
10.
10.J. N. Cuzzi, A. R. Dobrovolskis, and R. C. Hogan, Chondrules and the Protoplanetary Disk, Chapter Turbulence, Chondrules, and Planetesimals (Cambridge University, Cambridge, 1996).
11.
11.P. G. Saffman and J. S. Turner, “On the collision of drops in turbulent clouds,” J. Fluid Mech. 1, 16 (1956).
12.
12.M. Smoluchowski, “Versuch einer mathematischen theorie der koagulationskinetic kolloider losungen,” Z. Phys. Chem., Stoechiom. Verwandtschaftsl. 92, 129 (1917).
13.
13.L.-P. Wang, A. S. Wexler, and Y. Zhou, “On the collision rate of small particles in isotropic turbulence. I. Zero-inertia case,” Phys. Fluids 10, 266 (1998).
14.
14.B. K. Brunk, D. L. Koch, and L. W. Lion, “Hydrodynamic pair diffusion in isotropic random velocity fields with application to turbulent coagulation,” Phys. Fluids 9, 2670 (1997).
15.
15.B. K. Brunk, D. L. Koch, and L. W. Lion, “Turbulent coagulation of colloidal particles,” J. Fluid Mech. 364, 81 (1998).
16.
16.B. K. Brunk, D. L. Koch, and L. W. Lion, “Observations of coagulation in isotropic turbulence,” J. Fluid Mech. 371, 81 (1998).
17.
17.J. Abrahamson, “Collision rates of small particles in a vigorously turbulent fluid,” Chem. Eng. Sci. 30, 1371 (1975).
18.
18.W. C. Reade and L. R. Collins, “Collision and coagulation in the infinite-Stokes-number regime,” Aerosol. Sci. Technol. 29, 493 (1998).
19.
19.S. Balachandar, “Particle coagulation in homogeneous turbulence,” Ph.D. thesis, Brown University, 1988.
20.
20.M. R. Maxey, “The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields,” J. Fluid Mech. 174, 441 (1987).
21.
21.K. D. Squires and J. K. Eaton, “Preferential concentration of particles by turbulence,” Phys. Fluids A 3, 1169 (1991).
22.
22.L. P. Wang and M. R. Maxey, “Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence,” J. Fluid Mech. 256, 27 (1993).
23.
23.J. K. Eaton and J. R. Fessler, “Preferential concentration of particles by turbulence,” Int. J. Multiphase Flow 20, 169 (1994).
24.
24.M. Chen, K. Kontomaris, and J. B. McLaughlin, “Direct numerical simulation of droplet collisions in a turbulent channel flow part I: Collision algorithm,” Int. J. Multiphase Flow 24, 1079 (1998).
25.
25.M. Chen, K. Kontomaris, and J. B. McLaughlin, “Direct numerical simulation of droplet collisions in a turbulent channel flow part II: Collision rates,” Int. J. Multiphase Flow 24, 1105 (1998).
26.
26.S. Sundaram and L. R. Collins, “Collision statistics in an isotropic, particle-laden turbulent suspension I. Direct Numerical Simulations,” J. Fluid Mech. 335, 75 (1997).
27.
27.L.-P. Wang, A. S. Wexler, and Y. Zhou, “Statistical mechanical descriptions of turbulent coagulation,” Phys. Fluids 10, 2647 (1998).
28.
28.V. Eswaran and S. B. Pope, “An examination of forcing in direct numerical simulations of turbulence,” Comput. Fluids 16, 257 (1988).
29.
29.C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics (Springer-Verlag, New York, 1988).
30.
30.M. R. Maxey and J. J. Riley, “Equation of motion for a small rigid sphere in a nonuniform flow,” Phys. Fluids A 26, 883 (1983).
31.
31.S. Sundaram and L. R. Collins, “Numerical considerations in simulating a turbulent suspension of finite-volume particles,” J. Comput. Phys. 124, 337 (1996).
32.
32.T. L. Hill, Statistical Thermodynamics (Addison-Wesley, Menlo Park, 1960).
33.
33.D. A. McQuarrie, Statistical Mechanics (Harper & Row, New York, 1976).
34.
34.T. L. Hill, Statistical Mechanics: Principles and Selected Applications (McGraw-Hill, New York, 1956).
35.
35.A. N. Kolmogorov, “The local structure of turbulence in an incompressible viscous fluid for very large Reynolds numbers,” Dokl. Akad. Nauk SSSR 30, 299 (1941).
36.
36.L.-P. Wang, A. S. Wexler, and Y. Zhou, “Statistical mechanical description and modeling of turbulent collision of inertial particles,” J. Fluid Mech. 415, 117 (2000).
37.
37.M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964).
38.
38.W. C. Reade and L. R. Collins, “A numerical study of the particle size distribution of an aerosol undergoing turbulent coagulation,” J. Fluid Mech. 415, 45 (2000).
39.
39.K. R. Sreenivasan and R. A. Antonia, “The phenomenology of small-scale turbulence,” Annu. Rev. Fluid Mech. 29, 435 (1997).
40.
40.J. B. McLaughlin, “Numerical computation of particles-turbulence interaction,” Int. J. Multiphase Flow 20, 211 (1994).
http://aip.metastore.ingenta.com/content/aip/journal/pof2/12/10/10.1063/1.1288515
Article metrics loading...
/content/aip/journal/pof2/12/10/10.1063/1.1288515
2000-10-01
2016-04-11
Most read this month
Article
content/aip/journal/pof2
Journal
5
3
true
Commenting has been disabled for this content