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The effect of tilt on turbulent thermal convection for a heated soap bubble

Publication ,  Journal Article
He, XQ; Xiong, YL; Bragg, AD; Fischer, P; Kellay, H
Published in: Physics of Fluids
October 1, 2022

We use direct numerical simulation (DNS) to explore the effect of tilt on two-dimensional turbulent thermal convection on a half-soap bubble that is heated at its equator. In the DNS, the bubble is tilted by an angle δ ∈ [0 °, 90 °], the Rayleigh number is varied between R a ∈ [3 × 10 6, 3 × 10 9], and the Prandlt number is fixed at Pr = 7. The DNS reveals two qualitatively different flow regimes: the dynamic plume regime (DPR) and the stable plume regime (SPR). In the DPR, small dynamic plumes constantly emerge from random locations on the equator and dissipate on the bubble. In the SPR, the flow is dominated by a single large and stable plume rising from the lower edge of the bubble. The scaling behavior of the Nusselt number Nu and Reynolds number Re is different in these two regimes, with N u ∝ R a 0.3 for the DPR and N u ∝ R a 0.24 for the SPR. Concerning Re, the scaling in the DPR lies between R e ∝ R a 0.48 and R e ∝ R a 0.53 depending on Ra and δ, while in the SPR, the scaling lies between R e ∝ R a 0.44 and R e ∝ R a 0.45 depending on δ. The turbulent thermal and kinetic energy dissipation rates (ϵ T ′ and ϵ u ′, respectively) are also very different in the DPR and SPR. The probability density functions (PDF) of the normalized log ϵ T ′ and log ϵ u ′ are close to a Gaussian PDF for small fluctuations but deviate considerably from a Gaussian at large fluctuations in the DPR. In the SPR, the PDFs of normalized log ϵ T ′ and log ϵ u ′ deviate considerably from a Gaussian PDF even for small values. The globally averaged thermal energy dissipation rate due to the mean temperature field was shown to exhibit the scaling 〈ϵ 〈T 〉 〉 B ∝ R a - 0.23 in the DPR and 〈ϵ 〈T 〉 〉 B ∝ R a - 0.28 in the SPR. The globally averaged kinetic energy dissipation rate due to the mean velocity field is shown to exhibit the scaling 〈ϵ 〈u 〉 〉 B ∝ R a - 0.47 in the DPR (the exponent reduces from 0.47 to 0.43 as δ is increased up to 30°). In the SPR, the behavior changes considerably to 〈ϵ 〈u 〉 〉 B ∝ R a - 0.27. For the turbulent dissipation rates, the results indicate the scaling 〈ϵ T ′ 〉 B ∝ R a - 0.18 and 〈ϵ u ′ 〉 B ∝ R a - 0.29 in the DPR. However, the dependencies of 〈ϵ T ′ 〉 B and 〈ϵ u ′ 〉 B on Ra cannot be described by power-laws in the SPR.

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Published In

Physics of Fluids

DOI

EISSN

1089-7666

ISSN

1070-6631

Publication Date

October 1, 2022

Volume

34

Issue

10

Related Subject Headings

  • Fluids & Plasmas
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

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He, X. Q., Xiong, Y. L., Bragg, A. D., Fischer, P., & Kellay, H. (2022). The effect of tilt on turbulent thermal convection for a heated soap bubble. Physics of Fluids, 34(10). https://doi.org/10.1063/5.0118074
He, X. Q., Y. L. Xiong, A. D. Bragg, P. Fischer, and H. Kellay. “The effect of tilt on turbulent thermal convection for a heated soap bubble.” Physics of Fluids 34, no. 10 (October 1, 2022). https://doi.org/10.1063/5.0118074.
He XQ, Xiong YL, Bragg AD, Fischer P, Kellay H. The effect of tilt on turbulent thermal convection for a heated soap bubble. Physics of Fluids. 2022 Oct 1;34(10).
He, X. Q., et al. “The effect of tilt on turbulent thermal convection for a heated soap bubble.” Physics of Fluids, vol. 34, no. 10, Oct. 2022. Scopus, doi:10.1063/5.0118074.
He XQ, Xiong YL, Bragg AD, Fischer P, Kellay H. The effect of tilt on turbulent thermal convection for a heated soap bubble. Physics of Fluids. 2022 Oct 1;34(10).

Published In

Physics of Fluids

DOI

EISSN

1089-7666

ISSN

1070-6631

Publication Date

October 1, 2022

Volume

34

Issue

10

Related Subject Headings

  • Fluids & Plasmas
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences