TY - JOUR

T1 - Vertical natural convection

T2 - Application of the unifying theory of thermal convection

AU - Ng, Chong Shen

AU - Ooi, Andrew

AU - Lohse, Detlef

AU - Chung, Daniel

N1 - Publisher Copyright:
© 2015 Cambridge University Press.

PY - 2015/1/6

Y1 - 2015/1/6

N2 - Results from direct numerical simulations of vertical natural convection at Rayleigh numbers 1.0 × 105-1.0 × 109 and Prandtl number 0:709 support a generalised applicability of the Grossmann-Lohse (GL) theory, which was originally developed for horizontal natural (Rayleigh-Bénard) convection. In accordance with the GL theory, it is shown that the boundary-layer thicknesses of the velocity and temperature fields in vertical natural convection obey laminar-like Prandtl-Blasius-Pohlhausen scaling. Specifically, the normalised mean boundary-layer thicknesses scale with the.1=2-power of a wind-based Reynolds number, where the 'wind' of the GL theory is interpreted as the maximum mean velocity. Away from the walls, the dissipation of the turbulent fluctuations, which can be interpreted as the 'bulk' or 'background' dissipation of the GL theory, is found to obey the Kolmogorov-Obukhov-Corrsin scaling for fully developed turbulence. In contrast to Rayleigh-Bénard convection, the direction of gravity in vertical natural convection is parallel to the mean flow. The orientation of this flow presents an added challenge because there no longer exists an exact relation that links the normalised global dissipations to the Nusselt, Rayleigh and Prandtl numbers. Nevertheless, we show that the unclosed term, namely the global-averaged buoyancy flux that produces the kinetic energy, also exhibits both laminar and turbulent scaling behaviours, consistent with the GL theory. The present results suggest that, similar to Rayleigh-Bénard convection, a pure power-law relationship between the Nusselt, Rayleigh and Prandtl numbers is not the best description for vertical natural convection and existing empirical relationships should be recalibrated to better reflect the underlying physics.

AB - Results from direct numerical simulations of vertical natural convection at Rayleigh numbers 1.0 × 105-1.0 × 109 and Prandtl number 0:709 support a generalised applicability of the Grossmann-Lohse (GL) theory, which was originally developed for horizontal natural (Rayleigh-Bénard) convection. In accordance with the GL theory, it is shown that the boundary-layer thicknesses of the velocity and temperature fields in vertical natural convection obey laminar-like Prandtl-Blasius-Pohlhausen scaling. Specifically, the normalised mean boundary-layer thicknesses scale with the.1=2-power of a wind-based Reynolds number, where the 'wind' of the GL theory is interpreted as the maximum mean velocity. Away from the walls, the dissipation of the turbulent fluctuations, which can be interpreted as the 'bulk' or 'background' dissipation of the GL theory, is found to obey the Kolmogorov-Obukhov-Corrsin scaling for fully developed turbulence. In contrast to Rayleigh-Bénard convection, the direction of gravity in vertical natural convection is parallel to the mean flow. The orientation of this flow presents an added challenge because there no longer exists an exact relation that links the normalised global dissipations to the Nusselt, Rayleigh and Prandtl numbers. Nevertheless, we show that the unclosed term, namely the global-averaged buoyancy flux that produces the kinetic energy, also exhibits both laminar and turbulent scaling behaviours, consistent with the GL theory. The present results suggest that, similar to Rayleigh-Bénard convection, a pure power-law relationship between the Nusselt, Rayleigh and Prandtl numbers is not the best description for vertical natural convection and existing empirical relationships should be recalibrated to better reflect the underlying physics.

KW - Turbulence simulation

KW - Turbulence theory

KW - Turbulent convection

KW - 2023 OA procedure

UR - http://www.scopus.com/inward/record.url?scp=84927142901&partnerID=8YFLogxK

U2 - 10.1017/jfm.2014.712

DO - 10.1017/jfm.2014.712

M3 - Article

SN - 0022-1120

VL - 764

SP - 349

EP - 361

JO - Journal of fluid mechanics

JF - Journal of fluid mechanics

ER -