Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-25T23:01:52.335Z Has data issue: false hasContentIssue false

A new time scale for turbulence modulation by particles

Published online by Cambridge University Press:  09 October 2019

Izumi Saito*
Affiliation:
Department of Physical Science and Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan
Takeshi Watanabe
Affiliation:
Department of Physical Science and Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan
Toshiyuki Gotoh
Affiliation:
Department of Physical Science and Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan
*
Email address for correspondence: [email protected]

Abstract

A new time scale for turbulence modulation by particles is introduced. This time scale is inversely proportional to the number density and the radius of particles, and can be regarded as a counterpart of the phase relaxation time, an important time scale in cloud physics, which characterizes the interaction between turbulence and cloud droplets by condensation–evaporation. Scaling analysis and direct numerical simulations of dilute inertial particles in homogeneous isotropic turbulence suggest that turbulence modulation by particles with a fixed mass-loading parameter can be expressed as a function of the Damköhler number, which is defined as the ratio of the turbulence large-eddy turnover time to the new time scale.

Type
JFM Rapids
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111133.Google Scholar
Boivin, M., Simonin, O. & Squires, K. D. 1998 Direct numerical simulation of turbulence modulation by particles in isotropic turbulence. J. Fluid Mech. 375, 235263.Google Scholar
Crowe, C. T., Schwarzkopf, J. D., Sommerfeld, M. & Tsuji, Y. 2011 Multiphase Flows with droplets and Particles, 2nd edn. CRC Press.Google Scholar
Devenish, B. J., Bartello, P., Brenguier, J.-L., Collins, L. R., Grabowski, W. W., IJzermans, R. H. A., Malinowski, S. P., Reeks, M. W., Vassilicos, J. C., Wang, L.-P. et al. 2012 Droplet growth in warm turbulent clouds. Q. J. R. Meteorol. Soc. 138, 14011429.Google Scholar
Elghobashi, S. 1994 On predicting particle-laden turbulent flows. Appl. Sci. Res. 52, 309329.Google Scholar
Elghobashi, S. & Truesdell, G. C. 1993 On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: turbulence modification. Phys. Fluids 5, 17901801.Google Scholar
Gore, R. A. & Crowe, C. T. 1991 Modulation of turbulence by a dispersed phase. Trans. ASME J. Fluids Engng 113, 304307.Google Scholar
Gotoh, T., Suehiro, T. & Saito, I. 2016 Continuous growth of cloud droplets in cumulus cloud. New J. Phys. 18, 043042.Google Scholar
Grabowski, W. W. & Wang, L.-P. 2013 Growth of cloud droplets in a turbulent environment. Annu. Rev. Fluid Mech. 45, 293324.Google Scholar
Korolev, A. V. & Mazin, I. P. 2003 Supersaturation of water vapor in clouds. J. Atmos. Sci. 60, 29572974.Google Scholar
Kostinski, A. B. 2009 Simple approximations for condensational growth. Environ. Res. Lett. 4, 015005.Google Scholar
Kulick, J. D., Fessler, J. R. & Eaton, J. K. 1994 Particle response and turbulence modification in fully developed channel flow. J. Fluid Mech. 277, 109134.Google Scholar
Kussin, J. & Sommerfeld, M. 2002 Experimental studies on particle behaviour and turbulence modification in horizontal channel flow with different wall roughness. Exp. Fluids 33, 143159.Google Scholar
Lanotte, A. S., Seminara, A. & Toschi, F. 2009 Cloud droplet growth by condensation in homogeneous isotropic turbulence. J. Atmos. Sci. 66, 16851697.Google Scholar
Paris, A. D. & Eaton, J. K.2001 Turbulence attenuation in a particle-laden channel flow. Rep. TSD-137, Department of Mechanical Engineering, Stanford University.Google Scholar
Poelma, C., Westerweel, J. & Ooms, G. 2007 Particle–fluid interactions in grid-generated turbulence. J. Fluid Mech. 589, 315351.Google Scholar
Politovich, M. K. & Cooper, W. A. 1988 Variability of the supersaturation in cumulus clouds. J. Atmos. Sci. 45, 20642086.Google Scholar
Saito, I. & Gotoh, T. 2018 Turbulence and cloud droplets in cumulus clouds. New J. Phys. 20, 023001.Google Scholar
Saito, I., Gotoh, T. & Watanabe, T. 2019 Broadening of cloud droplet size distributions by condensation in turbulence. J. Met. Soc. Japan 97, 867891.Google Scholar
Sardina, G., Picano, F., Brandt, L. & Caballero, R. 2015 Continuous growth of droplet size variance due to condensation in turbulent clouds. Phys. Rev. Lett. 115, 15.Google Scholar
Shaw, R. A. 2003 Particle-turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech. 35, 183227.Google Scholar
Squires, K. D. & Eaton, J. K. 1993 Particle response and turbulence modification in isotropic turbulence. Phys. Fluids 2, 11911203.Google Scholar
Sundaram, S. & Collins, L. R. 1996 Numerical considerations in simulating a turbulent of finite-volume particles. J. Comput. Phys. 124, 337350.Google Scholar
Sundaram, S. & Collins, L. R. 1999 A numerical study of the modulation of isotropic turbulence by suspended particles. J. Fluid Mech. 379, 105143.Google Scholar
Tagawa, Y., Mercado, J. M., Prakash, V. N., Calzavarini, E., Sun, C. & Lohse, D. 2012 Three-dimensional Lagrangian Voronoï analysis for clustering of particles and bubbles in turbulence. J. Fluid Mech. 693, 201215.Google Scholar
Tanaka, T. & Eaton, J. K. 2008 Classification of turbulence modification by dispersed spheres using a novel dimensionless number. Phys. Rev. Lett. 101, 114502.Google Scholar
Tanaka, T. & Eaton, J. K. 2010 Sub-Kolmogorov resolution partical image velocimetry measurements of particle-laden forced turbulence. J. Fluid Mech. 643, 177206.Google Scholar
Tennekes, H. T. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.Google Scholar
Vaillancourt, P. A. & Yau, M. K. 2000 Review of particle-turbulence interactions and consequences for cloud physics. Bull. Am. Meteorol. Soc. 81, 285298.Google Scholar
Vaillancourt, P. A., Yau, M. K. & Grabowski, W. W. 2001 Microscopic approach to cloud droplet growth by condensation. Part 1: Model description and results without turbulence. J. Atmos. Sci. 58, 19451964.Google Scholar
Vreman, A. W. 2016 Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres. J. Fluid Mech. 796, 4085.Google Scholar