Ultimate heat transfer in ‘wall-bounded’ convective turbulence

Kawano, Kimiko; Motoki, Shingo; Shimizu, Masaki; Kawahara, Genta

doi:10.1017/jfm.2020.867

Cited by 13 publications

(28 citation statements)

References 42 publications

(129 reference statements)

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“…Finally, following the argument in Kawano et al. (2021), we would like to suggest the possibility of the ultimate state in practical applications. Let us consider a wall perforated with many fine holes connected to an adjacent constant-pressure plenum chamber.…”

Section: Resultsmentioning

confidence: 83%

“…wall-normal velocity on the permeable wall (Kawano et al. 2021). Let us further suppose that the thickness of the porous wall is of the order of the channel half-width .…”

Section: Resultsmentioning

confidence: 99%

“…2001; Kawano et al. 2021). We impose the no-slip, permeable and isothermal conditions, on the walls, where () represents the ‘permeability’ parameter, and the impermeable conditions are recovered for , while implies zero pressure fluctuations and an unconstrained wall-normal velocity.…”

Section: Governing Equations and Numerical Simulationsmentioning

confidence: 99%

“…The present DNS code is based on the one developed for turbulent thermal convection between permeable walls (Kawano et al. 2021). The governing equations (2.1)–(2.3) are discretised employing the spectral Galerkin method based on the Fourier–Chebyshev expansions.…”

Section: Governing Equations and Numerical Simulationsmentioning

confidence: 99%

“…Recently, Kawano et al. (2021) have found that the ultimate heat transfer can be achieved in turbulent thermal convection between permeable walls. In their study, the wall-normal transpiration velocity on the wall is assumed to be proportional to the local pressure fluctuations.…”

Section: Introductionmentioning

confidence: 99%

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The ultimate state of turbulent permeable-channel flow

et al. 2021

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Direct numerical simulations have been performed for heat and momentum transfer in internally heated turbulent shear flow with constant bulk mean velocity and temperature, $u_{b}$ and $\theta _{b}$ , between parallel, isothermal, no-slip and permeable walls. The wall-normal transpiration velocity on the walls $y=\pm h$ is assumed to be proportional to the local pressure fluctuations, i.e. $v=\pm \beta p/\rho$ (Jiménez et al., J. Fluid Mech., vol. 442, 2001, pp. 89–117). The temperature is supposed to be a passive scalar, and the Prandtl number is set to unity. Turbulent heat and momentum transfer in permeable-channel flow for the dimensionless permeability parameter $\beta u_b=0.5$ has been found to exhibit distinct states depending on the Reynolds number $Re_b=2h u_b/\nu$ . At $Re_{b}\lesssim 10^4$ , the classical Blasius law of the friction coefficient and its similarity to the Stanton number, $St\approx c_{f}\sim Re_{b}^{-1/4}$ , are observed, whereas at $Re_{b}\gtrsim 10^4$ , the so-called ultimate scaling, $St\sim Re_b^0$ and $c_{f}\sim Re_b^0$ , is found. The ultimate state is attributed to the appearance of large-scale intense spanwise rolls with the length scale of $O(h)$ arising from the Kelvin–Helmholtz type of shear-layer instability over the permeable walls. The large-scale rolls can induce large-amplitude velocity fluctuations of $O(u_b)$ as in free shear layers, so that the Taylor dissipation law $\epsilon \sim u_{b}^{3}/h$ (or equivalently $c_{f}\sim Re_b^0$ ) holds. In spite of strong turbulence promotion there is no flow separation, and thus large-amplitude temperature fluctuations of $O(\theta _b)$ can also be induced similarly. As a consequence, the ultimate heat transfer is achieved, i.e. a wall heat flux scales with $u_{b}\theta _{b}$ (or equivalently $St\sim Re_b^0$ ) independent of thermal diffusivity, although the heat transfer on the walls is dominated by thermal conduction.

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Section: Resultsmentioning

confidence: 83%

“…wall-normal velocity on the permeable wall (Kawano et al. 2021). Let us further suppose that the thickness of the porous wall is of the order of the channel half-width .…”

Section: Resultsmentioning

confidence: 99%

Section: Governing Equations and Numerical Simulationsmentioning

confidence: 99%

Section: Governing Equations and Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The ultimate state of turbulent permeable-channel flow

et al. 2021

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Asymptotic ultimate regime of homogeneous Rayleigh–Bénard convection on logarithmic lattices

Barral

Dubrulle

2023

J. Fluid Mech.

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We investigate how the heat flux $Nu$ scales with the imposed temperature gradient $Ra$ in homogeneous Rayleigh–Bénard convection using one-, two- and three-dimensional simulations on logarithmic lattices. Logarithmic lattices are a new spectral decimation framework which enables us to span an unprecedented range of parameters ( $Ra$ , $Re$ , $\Pr$ ) and test existing theories using little computational power. We first show that known diverging solutions can be suppressed with a large-scale friction. In the turbulent regime, for $\Pr \approx 1$ , the heat flux becomes independent of viscous processes (‘asymptotic ultimate regime’, $Nu\sim Ra ^{1/2}$ with no logarithmic correction). We recover scalings coherent with the theory developed by Grossmann and Lohse, for all situations where the large-scale frictions keep a constant magnitude with respect to viscous and diffusive dissipation. We also identify another turbulent friction-dominated regime at $\Pr \ll 1$ , where deviations from the Grossmann and Lohse prediction are observed. These two friction-dominated regimes may be relevant in some geophysical or astrophysical situations, where large-scale friction arises due to rotation, stratification or magnetic field.

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Turbulent thermal convection in mixed porous–pure fluid domains

Hamtiaux

Papalexandris

2023

J. Fluid Mech.

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In this paper, we report on a direct numerical simulation (DNS) study of turbulent thermal convection in mixed porous–pure fluid domains. The computational domain consists of a cavity that contains a porous medium placed right above the bottom wall. The solid matrix is internally heated which, in turn, induces the convective motions of the fluid. The Rayleigh number of the flow in the pure fluid region above the porous medium is of the order of $10^7$ . In our study, we consider cases of different sizes of the porous medium, as well as cases with both uniform and non-uniform heat loading of the solid matrix. For each case, we analyse the convective structures in both the porous and the pure fluid domains and investigate the effect of the porous medium on the emerging flow patterns above it. Results for the flow statistics, as well as for the Nusselt number and each of its components, are also presented herein. Further, we make comparisons of the flow properties in this pure fluid region with those in Rayleigh–Bénard convection. Our simulations predict that, depending on the area coverage, the large-scale circulation above the porous medium can be in a single-roll, dual-roll or intermediate state. Also, when the area coverage increases, the temperatures inside it increase due to reduced fluid circulation. Accordingly, when the area coverage increases, then the Nusselt number becomes smaller whereas the Rayleigh number is increased.

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Ultimate heat transfer in ‘wall-bounded’ convective turbulence

Abstract: Abstract

Cited by 13 publications

References 42 publications

The ultimate state of turbulent permeable-channel flow

The ultimate state of turbulent permeable-channel flow

Asymptotic ultimate regime of homogeneous Rayleigh–Bénard convection on logarithmic lattices

Turbulent thermal convection in mixed porous–pure fluid domains

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