Law of the wall for a temporally evolving vertical natural convection boundary layer

Ke, Junhao; Williamson, N.; Armfield, S.W.; Norris, Stuart; Komiya, Atsuki

doi:10.1017/jfm.2020.621

Cited by 19 publications

(70 citation statements)

References 42 publications

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“…The present study follows our previous work in Ke et al (2020), where the near-wall dynamics of the temporally developing turbulent NCBL adjacent to a vertical isothermal wall was investigated. In the present study, we investigate the bulk mean flow (later identified as the plume-like region in § 3) of the turbulent NCBL in terms of the integral model framework outlined by .…”

Section: Introductionmentioning

confidence: 94%

“…Grossmann & Lohse 2000, 2001 where a bulk-dominated ultimate turbulent regime is thought to be achieved at very high Grashof numbers. Our previous work on the temporally developing NCBL in Ke et al (2020) also investigated the law of the wall in the near-wall region for the NCBL using DNS. That study showed that the mean temperature profile for the turbulent NCBL appears self-similar and follows a log-law; whereas such a log-law is modified for the mean streamwise velocity profile due to the additional buoyancy in the near-wall region, and that the near-wall buoyancy becomes increasingly weak such that the NCBL would be asymptotic to momentum-dominated behaviour in the limit of higher Grashof number.…”

Section: Introductionmentioning

confidence: 99%

“…This technique has also been adapted by a number of flows that are generally thought spatially developing (see e.g. Abedin et al 2009;Abedin, Tsuji & Hattori 2010;Kozul, Chung & Monty 2016;Ke et al 2019Ke et al , 2020.…”

Section: Introductionmentioning

confidence: 99%

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High Grashof number turbulent natural convection on an infinite vertical wall

Williamson

Armfield

et al. 2021

J. Fluid Mech.

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The present study concerns a temporally evolving turbulent natural convection boundary layer (NCBL) adjacent to an isothermally heated vertical wall, with Prandtl number 0.71. Three-dimensional direct numerical simulations (DNS) are carried out to investigate the turbulent flow up to $\textit {Gr}_\delta =1.21\times 10^8$ , where $\textit {Gr}_\delta$ is the Grashof number based on the boundary layer thickness $\delta$ . In the near-wall region, there exists a constant heat flux layer, similar to previous studies for the spatially developing flows (e.g. George & Capp, Intl J. Heat Mass Transfer, vol. 22, 1979, pp. 813–826). Beyond a wall-normal distance $\delta _i$ , the NCBL can be characterised as a plume-like region. We find that this region is well described by a self-similar integral model with profile coefficients (cf. van Reeuwijk & Craske, J. Fluid Mech., vol. 782, 2015, pp. 333–355) which are $\textit {Gr}_\delta$ -independent after $\textit {Gr}_\delta =10^7$ . In this Grashof number range both the outer plume-like region and the near-wall boundary layer are turbulent, indicating the beginning of the so-called ultimate turbulent regime (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56; Grossmann & Lohse, Phys. Fluids, vol. 23, 2011, 045108). Solutions to the self-similar integral model are analytically obtained by solving ordinary differential equations with profile coefficients empirically obtained from the DNS results. In the present study, we have found the wall heat transfer of the NCBL is directly related to the top-hat scales which characterise the plume-like region. The Nusselt number is found to follow $\textit {Nu}_\delta \propto \textit {Gr}_\delta ^{0.381}$ , slightly higher than the empirical $1/3$ -power-law correlation reported for spatially developing NCBLs at lower $\textit {Gr}_\delta$ , but is shown to be consistent with the ultimate heat transfer regime with a logarithmic correction suggested by Grossmann & Lohse (Phys. Fluids, vol. 23, 2011, 045108). By modelling the near-wall buoyancy force, we show that the wall shear stress would scale with the bulk velocity only at asymptotically large Grashof numbers.

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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

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High Grashof number turbulent natural convection on an infinite vertical wall

Williamson

Armfield

et al. 2021

J. Fluid Mech.

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“…The numerical solver has been validated by a number of natural convection studies and the grid resolution is found sufficient for DNS [4,15]. The DNS data used in the present study has also been previously reported in [5].…”

Section: Methodsmentioning

confidence: 91%

“…To initiate laminar-turbulent transition, stream-wise and spanwise perturbations, given by equation (5), are augmented to the laminar temperature solution (4).…”

Section: Methodsmentioning

confidence: 99%

Integral modelling of an unsteady natural convection boundary layer

Ke¹

2020

Australasian Fluid Mechanics Conference (AFMC)

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The study concerns an unsteady natural convection boundary layer (NCBL) over a geometrically unbounded vertical isothermal wall with Prandtl number of Pr = 0.71. A threedimensional direct numerical simulation (DNS) is carried out to investigate the NCBL. In the present study we identify the plume-like region of the NCBL by a wall-normal distance δ i at which point the molecular diffusion matches the magnitude of the turbulent heat flux. Based on the DNS data, we have found that the plume-like region of the turbulent NCBL can be well described by the integral model supplied by proper boundary conditions at δ i . The profile coefficients obtained from the integral model appears independent of the growth of the boundary layer thickness, indicating the outer part plume-like region is self-similar.

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