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Experimental study of the effects of droplet number density on turbulence-driven polydisperse droplet size growth

Published online by Cambridge University Press:  23 April 2021

M. Shyam Kumar ,
Manikandan Mathur Open the ORCID record for Manikandan Mathur [Opens in a new window]  and
S.R. Chakravarthy
M. Shyam Kumar
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai600036, India
Manikandan Mathur*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai600036, India
S.R. Chakravarthy
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai600036, India
*
†Email address for correspondence: [email protected]
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Abstract

Interaction of polydisperse droplets in a turbulent air flow features prominently in a wide range of phenomena, such as warm rain initiation as an example. In the current study, we present an experimental investigation on the effects of initial droplet field characteristics on the maximum droplet size growth. By performing experiments in a vertically oriented air flow facility, the air flow turbulence was able to be controlled through the mean flow velocity and an active turbulence generator. The initial droplet field characteristics (droplet diameter range of 0–120 $\mathrm {\mu }$m) were varied using spray nozzles of different flow numbers. Based on quantitative measurements of the droplet size distribution at various spatial locations using phase Doppler interferometry (PDI), we estimated the droplet size growth rate $R$ as a function of turbulence intensity $I$, initial droplet number density $\rho _N$ and initial mean droplet size $\bar {D}$. For each ($\rho _N$, $\bar {D}$), we observed the occurrence of an optimum turbulence intensity $I^*$, with the corresponding maximum droplet size growth rate being $R^*$. Two different trends were observed. When $\rho _N$ and $\bar {D}$ were simultaneously increased and decreased, respectively, their competing influences resulted in small variations in $R^*$. In contrast, when $\bar {D}$ was held constant with a corresponding Stokes number $St$ smaller than unity, there existed a threshold $\rho _N$ above which $R^*$ increased rapidly with $\rho _N$. These trends were then understood through long-distance microscopy (LDM) measurements. Beyond the aforementioned threshold $\rho _N$, the fraction of uncorrelated small-sized $(St<1)$ droplet pairs was found to rapidly increase with $\rho _N$. Further detailed analysis of droplet tracking in the LDM images identified that the velocity fluctuations in the small-sized droplet pairs being induced by close encounters with inertial droplets was the underlying mechanism for the rapid increase of $R^*$ with $\rho _N$. This mechanism potentially explains how droplet collisions can be enhanced in small droplets if the droplet field is sufficiently polydisperse.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Drops and Bubbles: Breakup/coalescence Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 917 , 25 June 2021 , A12
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Abrahamson, J. 1975 Collision rates of small particles in a vigorously turbulent fluid. Chem. Engng Sci. 30 (11), 1371–1379.CrossRefGoogle Scholar
Adrian, R.J. & Yao, C.S. 1986 Power spectra of fluid velocities measured by laser doppler velocimetry. Exp. Fluids 5 (1), 17–28.CrossRefGoogle Scholar
Aliseda, A., Cartellier, A., Hainaux, F. & Lasheras, J.C. 2002 Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 468, 77–105.CrossRefGoogle Scholar
Bachalo, W.D. 1997 Measurement techniques for turbulent two-phase flow research. Presented at the International Symposium on Multiphase Fluid, Non-Newtonian Fluid and Physicochemical Fluid Flows (ISMNP), October 7–9, 1997, Beijing, China.Google Scholar
Balachandar, S. & Eaton, J.K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.CrossRefGoogle Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A.S. & Toschi, F. 2010 Intermittency in the velocity distribution of heavy particles in turbulence. J. Fluid Mech. 646, 527–536.CrossRefGoogle Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A.S. & Toschi, F. 2011 Spatial and velocity statistics of inertial particles in turbulent flows. J. Phys.: Conf. Ser. 333, 012003.Google Scholar
Bec, J., Celani, A., Cencini, M. & Musacchio, S. 2005 Clustering and collisions of heavy particles in random smooth flows. Phys. Fluids 17 (7), 073301.CrossRefGoogle Scholar
Benedict, L.H., Nobach, H. & Tropea, C. 2000 Estimation of turbulent velocity spectra from laser doppler data. Meas. Sci. Technol. 11 (8), 1089–1104.CrossRefGoogle Scholar
Blaisot, J.B. & Yon, J. 2005 Droplet size and morphology characterization for dense sprays by image processing: application to the diesel spray. Exp. Fluids 39 (6), 977–994.CrossRefGoogle Scholar
Bordás, R., Roloff, C., Thévenin, D. & Shaw, R.A. 2013 Experimental determination of droplet collision rates in turbulence. New J. Phys. 15 (4), 045010.CrossRefGoogle Scholar
Borée, J., Ishima, T. & Flour, I. 2001 The effect of mass loading and inter-particle collisions on the development of the polydispersed two-phase flow downstream of a confined bluff body. J. Fluid Mech. 443, 129–165.CrossRefGoogle Scholar
Bracco, A., Chavanis, P.H., Provenzale, A. & Spiegel, E.A. 1999 Particle aggregation in a turbulent Keplerian flow. Phys. Fluids 11 (8), 2280–2287.CrossRefGoogle Scholar
Chen, S., Yau, M.K. & Bartello, P. 2018 Turbulence effects of collision efficiency and broadening of droplet size distribution in cumulus clouds. J. Atmos. Sci. 75 (1), 203–217.CrossRefGoogle Scholar
Coleman, S.W. & Vassilicos, J.C. 2009 A unified sweep-stick mechanism to explain particle clustering in two-and three-dimensional homogeneous, isotropic turbulence. Phys. Fluids 21 (11), 113301.CrossRefGoogle Scholar
Devenish, B.J., et al. 2012 Droplet growth in warm turbulent clouds. Q. J. R. Meteorol. Soc. 138 (667), 1401–1429.CrossRefGoogle Scholar
Dooley, P.N. & Quinlan, N.J. 2009 Effect of eddy length scale on mechanical loading of blood cells in turbulent flow. Ann. Biomed. Engng 37 (12), 2449.CrossRefGoogle ScholarPubMed
Dou, Z., Ireland, P.J., Bragg, A.D., Liang, Z., Collins, L.R. & Meng, H. 2018 Particle-pair relative velocity measurement in high-Reynolds-number homogeneous and isotropic turbulence using 4-frame particle tracking velocimetry. Exp. Fluids 59 (2), 30.CrossRefGoogle Scholar
Eaton, J.K. & Fessler, J.R. 1994 Preferential concentration of particles by turbulence. Intl J. Multiphase Flow 20, 169–209.CrossRefGoogle Scholar
Falkovich, G., Fouxon, A. & Stepanov, M.G. 2002 Acceleration of rain initiation by cloud turbulence. Nature 419 (6903), 151.CrossRefGoogle ScholarPubMed
Falkovich, G. & Pumir, A. 2007 Sling effect in collisions of water droplets in turbulent clouds. J. Atmos. Sci. 64 (12), 4497–4505.CrossRefGoogle Scholar
Freud, E. & Rosenfeld, D. 2012 Linear relation between convective cloud drop number concentration and depth for rain initiation. J. Geophys. Res. 117, D02207.Google Scholar
Ghosh, S., Davila, J., Hunt, J.C.R., Srdic, A., Fernando, H.J.S. & Jonas, P.R. 2005 How turbulence enhances coalescence of settling particles with applications to rain in clouds. Proc. R. Soc. Lond. A 461 (2062), 3059–3088.Google Scholar
Good, G.H., Ireland, P.J., Bewley, G.P., Bodenschatz, E., Collins, L.R. & Warhaft, Z. 2014 Settling regimes of inertial particles in isotropic turbulence. J. Fluid Mech. 759, R3.CrossRefGoogle Scholar
Gore, R.A. & Crowe, C.T. 1991 Modulation of turbulence by a dispersed phase. Trans. ASME J. Fluids Engng 113 (2), 304–307.CrossRefGoogle Scholar
Goto, S. & Vassilicos, J.C. 2008 Sweep-stick mechanism of heavy particle clustering in fluid turbulence. Phys. Rev. Lett. 100 (5), 054503.CrossRefGoogle ScholarPubMed
Grabowski, W.W. & Wang, L.-P. 2013 Growth of cloud droplets in a turbulent environment. Annu. Rev. Fluid Mech. 45, 293–324.CrossRefGoogle Scholar
Gualtieri, P., Picano, F., Sardina, G. & Casciola, C.M. 2012 Statistics of particle pair relative velocity in the homogeneous shear flow. Physica D 241 (3), 245–250.CrossRefGoogle Scholar
Gualtieri, P., Picano, F., Sardina, G. & Casciola, C.M. 2013 Clustering and turbulence modulation in particle-laden shear flows. J. Fluid Mech. 715, 134–162.CrossRefGoogle Scholar
Hassan, Y.A. & Canaan, R.E. 1991 Full-field bubbly flow velocity measurements using a multiframe particle tracking technique. Exp. Fluids 12 (1–2), 49–60.CrossRefGoogle Scholar
Jacobs, C.N., Merchant, W., Jendrassak, M., Limpasuvan, V., Gurka, R. & Hackett, E.E. 2016 Flow scales of influence on the settling velocities of particles with varying characteristics. PloS One 11 (8), e0159645.CrossRefGoogle ScholarPubMed
James, M. & Ray, S.S. 2017 Enhanced droplet collision rates and impact velocities in turbulent flows: the effect of poly-dispersity and transient phases. Sci. Rep. 7 (1), 12231.CrossRefGoogle ScholarPubMed
Kumar, M.S., Chakravarthy, S.R. & Mathur, M. 2019 Optimum air turbulence intensity for polydisperse droplet size growth. Phys. Rev. Fluids 4 (7), 074607.CrossRefGoogle Scholar
Langmuir, I. 1948 The production of rain by a chain reaction in cumulus clouds at temperatures above freezing. J. Meteorol. 5 (5), 175–192.2.0.CO;2>CrossRefGoogle Scholar
Larsen, M.L., Kostinski, A.B. & Tokay, A. 2005 Observations and analysis of uncorrelated rain. J. Atmos. Sci. 62 (11), 4071–4083.CrossRefGoogle Scholar
Maxey, M.R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.CrossRefGoogle Scholar
Monchaux, R., Bourgoin, M. & Cartellier, A. 2010 Preferential concentration of heavy particles: a voronoïanalysis. Phys. Fluids 22 (10), 103304.CrossRefGoogle Scholar
Monchaux, R., Bourgoin, M. & Cartellier, A. 2012 Analyzing preferential concentration and clustering of inertial particles in turbulence. Intl J. Multiphase Flow 40, 1–18.CrossRefGoogle Scholar
Mulla, I.A., Sampath, R. & Chakravarthy, S.R. 2019 Interaction of lean premixed flame with active grid generated turbulence. Heat Mass Transfer 55 (7), 1887–1899.CrossRefGoogle Scholar
Nicolai, C., Jacob, B., Gualtieri, P. & Piva, R. 2014 Inertial particles in homogeneous shear turbulence: experiments and direct numerical simulation. Flow Turbul. Combust. 92 (1–2), 65–82.CrossRefGoogle Scholar
Nobach, H., Müller, E. & Tropea, C. 1998 Efficient estimation of power spectral density from laser doppler anemometer data. Exp. Fluids 24 (5–6), 499–509.CrossRefGoogle Scholar
Pan, L. & Padoan, P. 2013 Turbulence-induced relative velocity of dust particles. I. Identical particles. Astrophys. J. 776 (1), 12.CrossRefGoogle Scholar
Parthasarathy, R.N. & Faeth, G.M. 1990 Turbulence modulation in homogeneous dilute particle-laden flows. J. Fluid Mech. 220, 485–514.CrossRefGoogle Scholar
Pinsky, M., Khain, A. & Krugliak, H. 2008 Collisions of cloud droplets in a turbulent flow. Part 5. Application of detailed tables of turbulent collision rate enhancement to simulation of droplet spectra evolution. J. Atmos. Sci. 65 (2), 357–374.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Pruppacher, R.H. & Klett, J.D. 1997 Microphysics of Clouds and Precipitation, vol 18. Atmospheric and Oceanographic Sciences Library. Kluwer Academic Publishers.Google Scholar
Qiu, H.-H. & Sommerfeld, M. 1992 A reliable method for determining the measurement volume size and particle mass fluxes using phase-doppler anemometry. Exp. Fluids 13 (6), 393–404.CrossRefGoogle Scholar
Reade, W.C. & Collins, L.R. 2000 Effect of preferential concentration on turbulent collision rates. Phys. Fluids 12 (10), 2530–2540.CrossRefGoogle Scholar
Reveillon, J. & Vervisch, L. 2005 Analysis of weakly turbulent dilute-spray flames and spray combustion regimes. J. Fluid Mech. 537, 317–347.CrossRefGoogle Scholar
Saffman, P.G.F. & Turner, J.S. 1956 On the collision of drops in turbulent clouds. J. Fluid Mech. 1 (1), 16–30.CrossRefGoogle Scholar
Sahu, S., Hardalupas, Y. & Taylor, A.M.K.P. 2016 Droplet–turbulence interaction in a confined polydispersed spray: effect of turbulence on droplet dispersion. J. Fluid Mech. 794, 267–309.CrossRefGoogle Scholar
Shao, X., Wu, T. & Yu, Z. 2012 Fully resolved numerical simulation of particle-laden turbulent flow in a horizontal channel at a low Reynolds number. J. Fluid Mech. 693, 319–344.CrossRefGoogle Scholar
Squires, K.D. & Eaton, J.K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids A 3 (5), 1169–1178.CrossRefGoogle Scholar
Sumbekova, S., Cartellier, A., Aliseda, A. & Bourgoin, M. 2017 Preferential concentration of inertial sub-Kolmogorov particles: the roles of mass loading of particles, stokes numbers, and Reynolds numbers. Phys. Rev. Fluids 2 (2), 024302.CrossRefGoogle Scholar
Sundaram, S. & Collins, L.R. 1997 Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations. J. Fluid Mech. 335, 75–109.CrossRefGoogle Scholar
Tratnig, A. & Brenn, G. 2010 Drop size spectra in sprays from pressure-swirl atomizers. Intl J. Multiphase Flow 36 (5), 349–363.CrossRefGoogle Scholar
Vaillancourt, P.A. & Yau, M.K. 2000 Review of particle–turbulence interactions and consequences for cloud physics. Bull. Am. Meteorol. Soc. 81 (2), 285–298.2.3.CO;2>CrossRefGoogle Scholar
Voßkuhle, M., Pumir, A., Lévêque, E. & Wilkinson, M. 2014 Prevalence of the sling effect for enhancing collision rates in turbulent suspensions. J. Fluid Mech. 749, 841–852.CrossRefGoogle Scholar
Wang, L.-P. & Grabowski, W.W. 2009 The role of air turbulence in warm rain initiation. Atmos. Sci. Lett. 10 (1), 1–8.CrossRefGoogle Scholar
Wang, L.-P., Xue, Y., Ayala, O. & Grabowski, W.W. 2006 Effects of stochastic coalescence and air turbulence on the size distribution of cloud droplets. Atmos. Res. 82 (1), 416–432.CrossRefGoogle Scholar
Wilkinson, M., Mehlig, B. & Bezuglyy, V. 2006 Caustic activation of rain showers. Phys. Rev. Lett. 97 (4), 048501.CrossRefGoogle ScholarPubMed