Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T15:58:04.714Z Has data issue: false hasContentIssue false
  • English
  • Français

Temporal Evolution and Scaling of Mixing in Turbulent Thermal Convection for Inhomogeneous Boundary Conditions

Part of: Optics, electromagnetic theory - General

Published online by Cambridge University Press:  11 July 2017

Yikun Wei ,
Hua-Shu Dou ,
Zuchao Zhu ,
Zhengdao Wang ,
Yuehong Qian  and
Haihong Xue
Yikun Wei
Affiliation:
Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310023, China
Hua-Shu Dou*
Affiliation:
Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310023, China
Zuchao Zhu
Affiliation:
Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310023, China
Zhengdao Wang
Affiliation:
Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200444, China
Yuehong Qian
Affiliation:
Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200444, China
Haihong Xue
Affiliation:
Department of Pediatric, Xinhua Hospital, School of Medicine, Shanghai Jiaotong University, Shanghai 200240, China
*
*Corresponding author. Email:huashudou@yahoo.com (H.-S. Dou)
Get access

Abstract

Numerical simulations of two-dimensional (2D) turbulent thermal convection for inhomogeneous boundary condition are investigated using the lattice Boltzmann method (LBM). This study mainly appraises the temporal evolution and the scaling behavior of global quantities and of small-scale turbulence properties. The research results show that the flow is dominated by large-scale structures in the turbulence regime. Mushroom plumes emerge at both ends of each heat source, and smaller plumes increasingly rise. It is found that the gradient of root mean-square (rms) vertical velocities and the gradient of the rms temperature in the bottom boundary layer decreases with time evolution. It is further observed that the temporal evolution of the Kolmogorov scale, the kinetic-energy dissipation rates and thermal dissipation rates agree well with the theoretical predictions. It is also observed that there is a range of linear scaling in the 2nd-order structure functions of the velocity and temperature fluctuations and mixed velocity-temperature structure function.

Keywords

Thermal convectionTurbulenceinhomogeneous boundary conditionsLattice Boltzmann method

MSC classification

Secondary: 78A48: Composite media; random media
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 5 , October 2017 , pp. 1035 - 1051
Copyright
Copyright © Global-Science Press 2017 

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

[1] Hartmann, D. L., Moy, L. A. and Fu, Q., Tropical convection and the energy balance at the top of the atmosphere, J. Clim., 14 (2011), pp. 4495–4511.2.0.CO;2>CrossRefGoogle Scholar
[2] Marshall, J. and Schott, F., Open-ocean convection: observations, theory, and models, Rev. Geophys., 37 (1999), pp. 1–64.CrossRefGoogle Scholar
[3] Cardin, P. and Olson, P., Chaotic thermal convection in a rapidly rotating spherical shell: consequences for flow in the outer core, Phys. Earth Planet. Inter., 82 (1994), pp. 235–259.Google Scholar
[4] Lohse, D. and Xia, K. Q., Small-scale properties of turbulent Rayleigh-Bénard convection, Annu. Rev. Fluid. Mech., 42 (2010), pp. 335–364.Google Scholar
[5] Chilla, F. and Schumacher, J., New perspectives in turbulent Rayleigh-Bénard convection, Eur. Phys. J. E, 35 (2012), pp. 58–82.CrossRefGoogle ScholarPubMed
[6] Ahlers, G., Grossmann, S. and Lohse, D., Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection, Rev. Mod. Phys., 81 (2009), pp. 503–537.CrossRefGoogle Scholar
[7] Bailon, J. C., Emran, M. S. and Schumacher, J., Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection, J. Fluid Mech., 655 (2010), pp. 152–173.Google Scholar
[8] Biferale, L., A note on the fluctuations of dissipation scale in turbulence, Phys. Fluids, 20 (2008), pp. 031703–031709.Google Scholar
[9] Chill, F. and Schumacher, J., New perspectives in turbulent Rayleigh-Bénard convection, Euro. J. Phys. E, 35 (2012), pp. 58–67.CrossRefGoogle Scholar
[10] Seiden, G., Pattern forming system in the presence of different symmetry-breaking mechanisms, Phys. Rev. Lett., 101 (2008), pp. 214503–214507.Google Scholar
[11] Freund, G. and Pesch, W., Rayleigh-Bénard convection in the presence of spatial temperature modulations, J. Fluid. Mech., 673 (2011), pp. 318–348.CrossRefGoogle Scholar
[12] Weiss, S., Seiden, G. and Bodenschatz, E., Pattern formation in spatially forced thermal convection, New J. Phys., 14 (2011), pp. 053010–053019.Google Scholar
[13] Ripesi, P., Biferale, L., Sbragaglia, M. and Wirth, A., Natural convection with mixed insulating and conducting boundary conditions: low- and high-Rayleigh-number regimes, J. Fluid. Mech., 742 (2014), pp. 636–663.Google Scholar
[14] Biferake, L. and Procaccia, I., Anisotropy in turbulent flows and in turbulent transport, Phys. Rep., 2005, 414 (2005), pp. 143–164.Google Scholar
[15] Chertkov, M., Phenomenology of Rayleigh-Taylor turbulence, Phys. Rev. Lett., 91 (2003), pp. 115001–115010.Google Scholar
[16] Succi, S., The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, 2005.Google Scholar
[17] Chen, S. and Doolen, G., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30 (1998), pp. 329–345.Google Scholar
[18] Aidun, C. K., Lattice-Boltzmann method for complex flows, Annu. Rev. Fluid. Mech., 42 (2010), pp. 439–472.Google Scholar
[19] Qian, Y. H., D'Humieres, D. and Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys. Lett., 17 (1992), pp. 479–484.Google Scholar
[20] Inamuro, T., Yoshino, M., Inoue, H., Mizuno, R. and Ogino, F., A lattice Boltzmann method for a binary miscible fluid mixture and its application to a heat-transfer problem, J. Comput. Phys., 179 (2002), pp. 201–215.Google Scholar
[21] Guo, Z. L., Shi, B. C., A coupled lattice BGK model for the Boussinesq equations, Int. J. Numer. Meth. Fluids, 39 (2002), pp. 325–342.Google Scholar
[22] Azwadi, C. S. and Rosdzimin, A., Simulation of natural convection heat transfer in an enclosure using lattice Boltzmann method, J. Mekanikal., 27 (2008), pp. 42–50.Google Scholar
[23] Peng, Y., Shu, C. and Chew, Y. T., Simplified thermal lattice Boltzmann model for incompressible thermal flows, Phys. Rev. E, 68 (2003), pp. 026701–026708.Google Scholar
[24] Shan, X., Simulation of RayleighBénard convection using a lattice Boltzmann method, Phys. Rev. E, 55 (1997), pp. 2780–2788.CrossRefGoogle Scholar
[25] He, X., Chen, S. and Doolen, G. D., A novel thermal model for the lattice Boltzmann method in incompressible limit, J. Comput. Phys., 146 (1998), pp. 282–300.CrossRefGoogle Scholar
[26] Chen, S., Simulating compositional convection in the presence of rotation by lattice Boltzmann model, Int. J. Thermal Sci., 49 (2010). pp. 2093–2107.Google Scholar
[27] Wei, Y. K., Wang, Z. D., Yang, J. F., Dou, H. S. and Qian, Y. H., A simple lattice Boltzmann model for turbulence Rayleigh-Bénard thermal convection, Comput. Fluids, 118 (2015), pp. 167–171.Google Scholar
[28] Peng, Y., Shu, C. and Chew, Y. T., A Three-dimensional incompressible thermal lattice Boltzmann model and its application to simulate natural convection in a cubic cavity, J. Comput. Phys., 193 (2003), pp. 260–274.CrossRefGoogle Scholar
[29] Peng, Y., Shu, C. and Chew, Y. T., Three-dimensional lattice kinetic scheme and its application to simulate incompressible viscous thermal flows, Commun. Comput. Phys., 2 (2007), pp. 239–254.Google Scholar
[30] Li, Q., Luo, K., He, Y. and Tao, W., Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices, Phys. Rev. E, 85 (2012), pp. 016710–016717.CrossRefGoogle ScholarPubMed
[31] Karlin, I. V., Sichau, D. and Chikatamarla, S. S., Consistent two-population lattice Boltzmann model for thermal flows, Phys. Rev. E, 88 (2013), pp. 063310–063318.Google Scholar
[32] Prasianakis, N. I., Chikatamarla, S. S., Karlin, I. V., Ansumali, S. and Boulouchos, K., Entropic lattice Boltzmannmethod for simulation of thermal flows, Math. Comput. Simul., 72 (2006), pp. 179–183.Google Scholar
[33] Frapolli, N., Chikatamarla, S. and Karlin, I., Multispeed entropic lattice Boltzmann model for thermal flows, Phys. Rev. E, 90 (2014), pp. 043306–043315.Google Scholar
[34] Hamlington, P. E., Krasnov, D., Boeck, T. and Schumacher, J., Local dissipation scales and energy dissipation rate moments in channel flow, J. Fluid. Mech., 701 (2012), pp. 419–429.CrossRefGoogle Scholar
[35] Zhou, Q., Temporal evolution and scaling of mixing in two-dimensional Rayleigh-Taylor turbulence, Phys. Fluilds, 25 (2013), pp. 08510701–08510717.Google Scholar
[36] Clever, R. M. and Busse, F. H., Transition to time-dependent convection, J. Fluid Mech., 65 (1974), pp. 625–645.Google Scholar