Skip to main content Accessibility help
×
Home

On the dynamics of air bubbles in Rayleigh–Bénard convection

  • Jin-Tae Kim (a1), Jaewook Nam (a2), Shikun Shen (a1), Changhoon Lee (a2) (a3) and Leonardo P. Chamorro (a1) (a4) (a5)...

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.

Copyright

Corresponding author

Email address for correspondence: lpchamo@illinois.edu

References

Hide All
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, 10911112.
Batchelor, G. K. 1950 The application of the similarity theory of turbulence to atmospheric diffusion. Q. J. R. Meteorol. Soc. 76 (328), 133146.
Bourgoin, M., Ouellette, N. T., Xu, H., Berg, J. & Bodenschatz, E. 2006 The role of pair dispersion in turbulent flow. Science 311 (5762), 835838.
Bourgoin, M. & Xu, H. 2014 Focus on dynamics of particles in turbulence. New J. Phys. 16 (8), 085010.
Brown, E., Funfschilling, D. & Ahlers, G. 2007 Anomalous Reynolds-number scaling in turbulent Rayleigh–Bénard convection. J. Stat. Mech. Theor. Exp. 2007 (10), P10005.
Bunner, B. & Tryggvason, G. 2003 Effect of bubble deformation on the properties of bubbly flows. J. Fluid Mech. 495, 77118.
Choi, J.-I., Yeo, K. & Lee, C. 2004 Lagrangian statistics in turbulent channel flow. Phys. Fluids 16, 779793.
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops and Particles. Dover Publications.
Craven, P. & Wahba, G. 1978 Smoothing noisy data with spline functions. Numer. Math. 31 (4), 377403.
Elghobashi, S. 1994 On predicting particle-laden turbulent flows. Appl. Sci. Res. 52 (4), 309329.
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, 97121.
Fouxon, I., Shim, G., Lee, S. & Lee, C. 2018 Multifractality of tine bubbles in turbulence due to lift. Phys. Rev. Fluids 3, 124305.
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), 44954511.
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.
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.
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, 306316.
La Porta, A., Voth, G. A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2001 Fluid particle accelerations in fully developed turbulence. Nature 409 (6823), 10171019.
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), 92379242.
Lee, C., Yeo, K. & Choi, J.-I. 2004 Intermittent nature of acceleration in near wall turbulence. Phys. Rev. Lett. 92, 144502.
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.
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335364.
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. 343348. VDE.
Magnaudet, J. & Eames, I. 2000 The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32 (1), 659708.
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.
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.
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.
Mazzitelli, I. M. & Lohse, D. 2003 On the relevance of the lift force in bubbly turbulence. J. Fluid Mech. 488, 283313.
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), 465538.
Mougin, G. & Magnaudet, J. 2001 Path instability of a rising bubble. Phy. Rev. Lett. 88 (1), 014502.
Ni, R., Huang, S.-D. & Xia, K.-Q. 2012 Lagrangian acceleration measurements in convective thermal turbulence. J. Fluid Mech. 692, 395419.
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.
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), 10931098.
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375404.
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, 201212.
Zhou, Q., Sun, C. & Xia, K.-Q. 2007 Morphological evolution of thermal plumes in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 98 (7), 074501.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

On the dynamics of air bubbles in Rayleigh–Bénard convection

  • Jin-Tae Kim (a1), Jaewook Nam (a2), Shikun Shen (a1), Changhoon Lee (a2) (a3) and Leonardo P. Chamorro (a1) (a4) (a5)...

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.