Turbulence and heat transfer on a rotating, heated half soap bubble

He, Xiaoqiu; Bragg, Andrew D.; Xiong, Yongliang; Fischer, Patrick

doi:10.1017/jfm.2021.610

Cited by 6 publications

(16 citation statements)

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“…The terms involving S and F are the external cooling and friction terms, respectively, which model the heat exchange and friction due to the the cold air surrounding the bubble. These terms are required in order for the DNS to attain non-trivial steady-state regimes, and are discussed in details in the study of Bruneau et al 51 and He et al 52 . Analogous terms are also routinely used when performing DNS of two-dimension turbulence on flat geometries 53 .…”

Section: Methods a Governing Equationsmentioning

confidence: 99%

“…In our DNS we use S = 0.06 and F = 0.06, which are the values that have already been shown to be suitable in previous studies 51,52 . The boundary conditions used are u = 0 and T 0 = 1 on the bubble equator.…”

Section: Methods a Governing Equationsmentioning

confidence: 99%

“…DNS of the half soap bubble were first performed by Xiong et al 50 , and Bruneau et al 51 used the DNS to show that the scaling behaviour of Re and Nu are very similar to that in standard RBC, with the DNS yielding Nu ∼ Ra 0.30 and Nu ∼ Ra 0.49 . He et al 52 further extended the model to investigate the impact of bubble rotation on the convective flow and showed that Nu is not effected by even strong rotation, while Re decreases considerably with increasing rotation 52 .…”

Section: Soap Bubblementioning

confidence: 99%

“…It means that when (T − T 0 )/T 0 > 0, then for φ ∈ [0, π), B θ will lead to convective motion towards the North pole, while for φ ∈ (π, 2π), B θ will act to stabilize and stratify the flow. Therefore, while for δ = 0, heating at the equator generates buoyancy forces leading to convection and (for sufficiently large Ra) turbulence over the entire surface of the bubble 52 , for δ = π/2, buoyancy forces leading to convection and turbulence can arise for φ ∈ [0, π), whereas for φ ∈ (π, 2π) the buoyancy forces will quench the turbulence and stratify the flow. Note also that since B θ = −((T − T 0 )/T 0 ) cos θ sin φ , then the buoyancy forces that produce convection in the region φ ∈ [0, π) will be strongest near φ = π/2.…”

Section: B Tilt Leads To Stable Stratification For the Hemispherical ...mentioning

confidence: 99%

“…The numerical simulations are conducted by the homebrew code which is introduced in details in previous studies 51,52 . Here we give a brief overview of the numerical methods used in the DNS.…”

Section: Direct Numerical Simulationsmentioning

confidence: 99%

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

He,

Xiong,

Bragg

et al. 2022

Preprint

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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 Ra ∈ [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 behaviour of the Nusselt number Nu and Reynolds number Re are different in these two regimes, with Nu ∝ Ra 0.3 for the DPR and Nu ∝ Ra 0.24 for the SPR. Concerning Re, the scaling in the DPR lies between Re ∝ Ra 0.48 and Re ∝ Ra 0.53 depending on Ra and δ , while in the SPR, the scaling lies between Re ∝ Ra 0.44 and Re ∝ Ra 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 ∝ Ra −0.23 in the DPR, and ε T B ∝ Ra −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 ∝ Ra −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 ∝ Ra −0.27 . For the turbulent dissipation rates, the results indicate the scaling ε T B ∝ Ra −0.18 and ε u B ∝ Ra −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. I. INTRODUCTIONTurbulent thermal convection is ubiquitous in nature and plays a significant role in large scale flows on the Earth, such as the cyclones in the atmosphere and the circulation of the deep oceans 1 . Convective flows are also vital for a great number of industrial applications, for example cooling systems on chip-boards 2 . The fluid motion in turbulent thermal convection is driven by buoyancy which arises due to temperature gradients imposed by boundary conditions 3 . In these flows, the a) Also at

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Section: Methods a Governing Equationsmentioning

confidence: 99%

Section: Methods a Governing Equationsmentioning

confidence: 99%

Section: Soap Bubblementioning

confidence: 99%

Section: B Tilt Leads To Stable Stratification For the Hemispherical ...mentioning

confidence: 99%

Section: Direct Numerical Simulationsmentioning

confidence: 99%

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

He,

Xiong,

Bragg

et al. 2022

Preprint

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Spectra and structure functions of the temperature and velocity fields in supergravitational thermal turbulence

et al. 2022

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We analyse the power spectra and structure functions (SFs) of the temperature and radial velocity fields, calculated in the radial and azimuthal directions, in annular centrifugal Rayleigh-B\'{e}nard convection (ACRBC) for Rayleigh number Ra $ \in [{10^8},{10^{11}}]$, Prandtl number Pr = 10.7, and inverse Rossby number $\rm{Ro}^{-1} = 16$ using the spatial data obtained by quasi-two-dimensional direct numerical simulation. Bolgiano and Obukhov-like (BO59-like) scalings for the energy spectrum in both the azimuthal and radial directions and thermal spectrum in the azimuthal direction are observed. The range of BO59-like scaling becomes wider as Ra increases. At $\rm{Ra} = 10^{11}$, it is found that BO59-like scaling ${E_u}({k_r}) \sim {k_r}^{ - 11/5}$ spans nearly two decades for the energy spectrum calculated in the radial direction. Power-law fittings in the range larger than the Bolgiano scales, the scaling exponents of transverse and longitudinal velocity SFs versus the order coincide with the theoretical prediction of BO59 scaling $\zeta _p^u = 3p/5$ basically. The second-order temperature SFs exhibit a gradual transition from the Obukhov-Corrsin behaviour at scales smaller than the Bolgiano scales to the BO59 behaviour at scales larger than the Bolgiano scales. The slopes from the 3rd to 6th-order temperature SFs are similar, which is similar to classical Rayleigh-B\'{e}nard convection and Rayleigh-Taylor turbulence. The probability density functions (p.d.f.) of temperature fluctuations $\delta T/{\sigma _T}$ reveal the cold plumes are strong and the p.d.f. in different regions at high Ra are similar. The stronger turbulent-mixing and larger centrifugal buoyancy in ACRBC may result in the BO59-like scaling.

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

Xiong

Bragg

et al. 2022

Physics of Fluids

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We use 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∈[0o,90o], the Rayleigh number is varied between Ra∈[3*106, 3*109]. 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 behaviour of the Nusselt number and Reynolds number are different in these two regimes, with Nu∝Ra0.3 for the DPR and Nu∝Ra0.24 for the SPR. Concerning Re, the scaling in the DPR lies between Re∝Ra0.48 and Re∝Ra0.53 depending on Ra and δ, while in the SPR, the scaling lies between Re∝Ra0.44 and Re∝Ra0.45 depending on δ. The turbulent thermal and kinetic energy dissipation rates (εT' and εu', respectively) are also very different in the DPR and SPR. The PDFs of the normalized logεT' and logεu' 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 logεT' and logεu' 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 different scaling.

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Turbulence and heat transfer on a rotating, heated half soap bubble

Abstract: Abstract

Cited by 6 publications

References 68 publications

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

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

Spectra and structure functions of the temperature and velocity fields in supergravitational thermal turbulence

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

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