## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Analysis and correlation of fluid motions in natural thermal convection in a cylindrical vessel

**ABSTRACT**

A natural thermal convection system is set up in a cylindrical vessel with aspect ratio of 2 having a temperature gradient in the vertical direction, and the fluid motions due to convection are investigated. The 2-dimensional velocity field along the plane passing through the diameter of the vessel is obtained using particle image velocimetry. The results indicate that the convection is in the transition stage and the mean velocity fields show two pairs of counter-rotating circulations. The mean motions are predominant in the vertical direction under the influence of the temperature gradient, while the fluctuations in the x and y directions have the same order of magnitude. Probability density functions of fluctuation velocities at seven characteristic points show different behaviors. The space-time correlations in the regions where the circulations interact exhibit the iso-correlation lines predicted by the elliptical approximation hypothesis. The space-time correlations of the stream wise and vertical fluctuations show distinct movements which imply the existence of anisotropy around the interaction region.

**KEYWORDS**

PAPER SUBMITTED: 2018-06-05

PAPER REVISED: 2018-09-10

PAPER ACCEPTED: 2018-11-10

PUBLISHED ONLINE: 2019-04-14

- Ahlers, G., Turbulent Convection. Physics, 2 (2009), 74, pp. 1-7
- He, X., et al., Transition to the Ultimate State of Turbulent Rayleigh-Bénard Convection. Physical Review Letters, 108 (2013), 2, 014503
- Chong, K., et al., Effect of Prandtl Number on Heat Transport Enhancement in Rayleigh-Bénard Convection Under Geometrical Confinement. Physical Review Fluids, 3 (2018), 1, 013501
- Kaczorowski, M., et al., Turbulent Flow in the Bulk of Rayleigh-Bénard Convection: Aspect-ratio Dependence of the Small-scale Properties. Journal of Fluid Mechanics, 722 (2013), 5, pp. 596-617
- Ni, R., et al., Reversals of the Large-Scale Circulation in Quasi-2D Rayleigh-Bénard Convection. Journal of Fluid Mechanics, 778 (2015), R5
- Xi, H., et al., Higher-Order Flow Modes in Turbulent Rayleigh-Bénard Convection. Journal of Fluid Mechanics, 805 (2016), pp. 31-51
- He, X., et al., Logarithmic Spatial Variations and Universal f−1Powerspectra of Temperature Fluctuations in Turbulent Rayleigh-Bénard Convection. Physical Review Letters, 112 (2014), 174501
- He, X., et al., Reynolds Numbers and the Elliptic Approximation Near the Ultimate State of Turbulent Rayleigh-Benard Convection. New Journal of Physics, 17 (2015), 063028
- Taylor, G., The spectrum of turbulence. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, London, England, 1938, Vol. 919, pp. -490
- He, G., et al., On the Computation of Space-Time Correlations by Large-Eddy Simulation. Physics of Fluids, 11 (2003), 16, pp. 319-330
- He, G., et al., Elliptic Model for Space-Time Correlations in Turbulent Shear Flows. Physical Review E, 73 (2006), 055303
- Zhao, X., et al., Space-Time Correlations of Fluctuating Velocities in Turbulent Shear Flows. Physical Review E, 79 (2009), 046316
- He, X., et al., Small-Scale Turbulent Fluctuations Beyond Taylor's Frozen-Flow Hypothesis. Physical Review E, 81 (2010), 065303
- Guo, L., et al., LES Prediction of Space-Time Correlations in Turbulent Shear Flows. Acta Mechanica Sinica, 4 (2012), 28, pp. 993-998
- Wallace, J., Space-Time Correlations in Turbulent Flow: a Review. Theoretical & Applied Mechanics Letters, 2(2014), 4, 4022003
- Geng, C., et al., Taylor's Hypothesis in Turbulent Channel Flow Considered Using a Transport Equation Analysis. Physics of Fluids, 2 (2015), 27, pp. 15
- He, G., et al., Space-Time Correlations and Dynamic Coupling in Turbulent Flows. Annual Review of Fluid Mechanics, 1 (2017), 49, pp. 51-70
- Zhou, Q., et al., Experimental Investigation of Longitudinal Space-Time Correlations of the Velocity Field in Turbulent Rayleigh-Bénard Convection. Journal of Fluid Mechanics, 3 (2011), 683, pp. 94-111
- Hogg, J., et al., Reynolds-Number Measurements for Low-Prandtl-Number Turbulent Convection of Large-Aspect-Ratio Samples. Journal of Fluid Mechanics, 5 (2013), 725, pp. 664-680
- Wang, W., et al., TRPIV Investigation of Space-Time Correlation in Turbulent Flows over Flat and Wavy Walls. Acta Mechanica Sinica, 4 (2014), 30, pp. 468-479
- Wang, W., et al., Convection and Correlation of Coherent Structure in Turbulent Boundary Layer Using Tomographic Particle Image Velocimetry. Chinese Physics B, 10(2014), 23, pp. 323-333
- Yang, S., et al., Heat Transfer. Beijing: Higher Education Press, 2006 (in Chinese)