Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-06T08:27:47.490Z Has data issue: false hasContentIssue false
  • English
  • Français

On the dynamics of air bubbles in Rayleigh–Bénard convection

Published online by Cambridge University Press:  18 March 2020

Jin-Tae Kim ,
Jaewook Nam ,
Shikun Shen ,
Changhoon Lee Open the ORCID record for Changhoon Lee [Opens in a new window]  and
Leonardo P. Chamorro Open the ORCID record for Leonardo P. Chamorro [Opens in a new window]
Jin-Tae Kim
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois, Urbana, IL61801, USA
Jaewook Nam
Affiliation:
Department of Computational Science and Engineering, Yonsei University, Seoul03722, Korea
Shikun Shen
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois, Urbana, IL61801, USA
Changhoon Lee
Affiliation:
Department of Computational Science and Engineering, Yonsei University, Seoul03722, Korea Department of Mechanical Engineering, Yonsei University, Seoul03722, Korea
Leonardo P. Chamorro*
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois, Urbana, IL61801, USA Department of Civil and Environmental Engineering, University of Illinois, Urbana, IL61801, USA Department of Aerospace Engineering, University of Illinois, Urbana, IL61801, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamics of air bubbles in turbulent Rayleigh–Bénard (RB) convection is described for the first time using laboratory experiments and complementary numerical simulations. We performed experiments at $Ra=5.5\times 10^{9}$ and $1.1\times 10^{10}$, where streams of 1 mm bubbles were released at various locations from the bottom of the tank along the path of the roll structure. Using three-dimensional particle tracking velocimetry, we simultaneously tracked a large number of bubbles to inspect the pair dispersion, $R^{2}(t)$, for a range of initial separations, $r$, spanning one order of magnitude, namely $25\unicode[STIX]{x1D702}\leqslant r\leqslant 225\unicode[STIX]{x1D702}$; here $\unicode[STIX]{x1D702}$ is the local Kolmogorov length scale. Pair dispersion, $R^{2}(t)$, of the bubbles within a quiescent medium was also determined to assess the effect of inhomogeneity and anisotropy induced by the RB convection. Results show that $R^{2}(t)$ underwent a transition phase similar to the ballistic-to-diffusive ($t^{2}$-to-$t^{1}$) regime in the vicinity of the cell centre; it approached a bulk behavior $t^{3/2}$ in the diffusive regime as the distance away from the cell centre increased. At small $r$, $R^{2}(t)\propto t^{1}$ is shown in the diffusive regime with a lower magnitude compared to the quiescent case, indicating that the convective turbulence reduced the amplitude of the bubble’s fluctuations. This phenomenon associated to the bubble path instability was further explored by the autocorrelation of the bubble’s horizontal velocity. At large initial separations, $R^{2}(t)\propto t^{2}$ was observed, showing the effect of the roll structure.

JFM classification

Drops and Bubbles: Bubble dynamics Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 891 , 25 May 2020 , A7
Copyright
© The Author(s), 2020. Published by 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

Alméras, E., Mathai, V., Lohse, D. & Sun, C. 2017 Experimental investigation of the turbulence induced by a bubble swarm rising within incident turbulence. J. Fluid Mech. 825, 1091–1112.CrossRefGoogle Scholar
Batchelor, G. K. 1950 The application of the similarity theory of turbulence to atmospheric diffusion. Q. J. R. Meteorol. Soc. 76 (328), 133–146.CrossRefGoogle Scholar
Bourgoin, M., Ouellette, N. T., Xu, H., Berg, J. & Bodenschatz, E. 2006 The role of pair dispersion in turbulent flow. Science 311 (5762), 835–838.CrossRefGoogle ScholarPubMed
Bourgoin, M. & Xu, H. 2014 Focus on dynamics of particles in turbulence. New J. Phys. 16 (8), 085010.Google Scholar
Brown, E., Funfschilling, D. & Ahlers, G. 2007 Anomalous Reynolds-number scaling in turbulent Rayleigh–Bénard convection. J. Stat. Mech. Theor. Exp. 2007 (10), P10005.Google Scholar
Bunner, B. & Tryggvason, G. 2003 Effect of bubble deformation on the properties of bubbly flows. J. Fluid Mech. 495, 77–118.CrossRefGoogle Scholar
Choi, J.-I., Yeo, K. & Lee, C. 2004 Lagrangian statistics in turbulent channel flow. Phys. Fluids 16, 779–793.CrossRefGoogle Scholar
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops and Particles. Dover Publications.Google Scholar
Craven, P. & Wahba, G. 1978 Smoothing noisy data with spline functions. Numer. Math. 31 (4), 377–403.CrossRefGoogle Scholar
Elghobashi, S. 1994 On predicting particle-laden turbulent flows. Appl. Sci. Res. 52 (4), 309–329.CrossRefGoogle Scholar
Ern, P., Risso, F., Fabre, D. & Magnaudet, J. 2012 Wake-induced oscillatory paths of bodies freely rising or falling in fluids. Annu. Rev. Fluid Mech. 44, 97–121.CrossRefGoogle Scholar
Fouxon, I., Shim, G., Lee, S. & Lee, C. 2018 Multifractality of tine bubbles in turbulence due to lift. Phys. Rev. Fluids 3, 124305.CrossRefGoogle Scholar
Hartmann, D. L., Moy, L. A. & Fu, Q. 2001 Tropical convection and the energy balance at the top of the atmosphere. J. Clim. 14 (24), 4495–4511.2.0.CO;2>CrossRefGoogle Scholar
Kim, J.-T., Kim, D., Liberzon, A. & Chamorro, L. P. 2016a Three-dimensional particle tracking velocimetry for turbulence applications: case of a jet flow. J. Vis. Exp. (108), e53745.CrossRefGoogle Scholar
Kim, J.-T., Shen, S., Dimarco, S. L., Jin, Y. & Chamorro, L. P. 2018 Lagrangian acceleration in Rayleigh–Bénard convection at various aspect ratios. Phys. Rev. Fluids 3 (11), 113502.CrossRefGoogle Scholar
Kim, J.-T., Zhang, Z., Liberzon, A., Zhang, Y. & Chamorro, L. P. 2016b On the Lagrangian features of circular and semicircular jets via 3D particle tracking velocimetry. Exp. Therm. Fluid Sci. 77, 306–316.CrossRefGoogle Scholar
La Porta, A., Voth, G. A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2001 Fluid particle accelerations in fully developed turbulence. Nature 409 (6823), 1017–1019.CrossRefGoogle ScholarPubMed
Lakkaraju, R., Stevens, R. J., Oresta, P., Verzicco, R., Lohse, D. & Prosperetti, A. 2013 Heat transport in bubbling turbulent convection. Proc. Natl Acad. Sci. USA 110 (23), 9237–9242.CrossRefGoogle ScholarPubMed
Lee, C., Yeo, K. & Choi, J.-I. 2004 Intermittent nature of acceleration in near wall turbulence. Phys. Rev. Lett. 92, 144502.CrossRefGoogle ScholarPubMed
Liot, O., Gay, A., Salort, J., Bourgoin, M. & Chillà, F. 2016 Inhomogeneity and Lagrangian unsteadiness in turbulent thermal convection. Phys. Rev. Fluids 1 (6), 064406.CrossRefGoogle Scholar
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335–364.CrossRefGoogle Scholar
Luetteke, F., Zhang, X. & Franke, J. 2012 Implementation of the Hungarian method for object tracking on a camera monitored transportation system. In ROBOTIK 2012; 7th German Conference on Robotics, pp. 343–348. VDE.Google Scholar
Magnaudet, J. & Eames, I. 2000 The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32 (1), 659–708.CrossRefGoogle Scholar
Mathai, V., Huisman, S. G., Sun, C., Lohse, D. & Bourgoin, M. 2018a Dispersion of air bubbles in isotropic turbulence. Phy. Rev. Lett. 121 (5), 054501.CrossRefGoogle Scholar
Mathai, V., Prakash, V. N., Brons, J., Sun, C. & Lohse, D. 2015 Wake-driven dynamics of finite-sized buoyant spheres in turbulence. Phy. Rev. Lett. 115 (12), 124501.CrossRefGoogle ScholarPubMed
Mathai, V., Zhu, X., Sun, C. & Lohse, D. 2018b Flutter to tumble transition of buoyant spheres triggered by rotational inertia changes. Nat. Commun. 9 (1), 1792.CrossRefGoogle Scholar
Mazzitelli, I. M. & Lohse, D. 2003 On the relevance of the lift force in bubbly turbulence. J. Fluid Mech. 488, 283–313.CrossRefGoogle Scholar
McKenzie, D. P., Roberts, J. M. & Weiss, N. O. 1974 Convection in the Earth’s mantle: towards a numerical simulation. J. Fluid Mech. 62 (3), 465–538.CrossRefGoogle Scholar
Mougin, G. & Magnaudet, J. 2001 Path instability of a rising bubble. Phy. Rev. Lett. 88 (1), 014502.CrossRefGoogle ScholarPubMed
Ni, R., Huang, S.-D. & Xia, K.-Q. 2012 Lagrangian acceleration measurements in convective thermal turbulence. J. Fluid Mech. 692, 395–419.CrossRefGoogle Scholar
Ni, R. & Xia, K.-Q. 2013 Experimental investigation of pair dispersion with small initial separation in convective turbulent flows. Phys. Rev. E 87 (6), 063006.Google ScholarPubMed
Roghair, I., Mercado, J. M., Annaland, M. V. S., Kuipers, H., Sun, C. & Lohse, D. 2011 Energy spectra and bubble velocity distributions in pseudo-turbulence: numerical simulations versus experiments. Intl J. Multiphase Flow 37 (9), 1093–1098.CrossRefGoogle Scholar
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375–404.CrossRefGoogle Scholar
Vasiliev, A., Sukhanovskii, A., Frick, P., Budnikov, A., Fomichev, V., Bolshukhin, M. & Romanov, R. 2016 High Rayleigh number convection in a cubic cell with adiabatic sidewalls. Intl J. Heat Mass Transfer 102, 201–212.CrossRefGoogle Scholar
Zhou, Q., Sun, C. & Xia, K.-Q. 2007 Morphological evolution of thermal plumes in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 98 (7), 074501.CrossRefGoogle ScholarPubMed