Mechanical Engineering - Theses
Permanent URI for this collection
Search Results
1 - 1 of 1
-
ItemBoundary layer and bulk dynamics in vertical natural convection( 2017)Results from direct numerical simulations of vertical natural convection at Rayleigh numbers 10^5–10^9 and Prandtl number 0.709 are found to support a generalised applicability of the Grossmann–Lohse (GL) theory, which was originally developed for Rayleigh–Bénard convection. In accordance with the GL theory, we show that the normalised mean boundary- layer thicknesses of the velocity and temperature fields obey the laminar-like Prandtl– Blasius–Pohlhausen scaling, corresponding to the “classical” state. 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. 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. On closer scrutiny of the boundary layers, we find evidence that the boundary layers are undergoing a transition from the classical state to the “ultimate” shear-dominated state. In particular, we observe near-wall higher-shear patches that occupy increasingly larger fractions of the wall-areas. These higher-shear patches exhibit turbulent features, for instance (i) the patches appear streaky, reminiscent of the characteristic near- wall streaks in canonical wall-bounded turbulence, (ii) the local mean temperature profile yields a logarithmic variation, in agreement with the logarithmic law of the wall for mean temperature, and (iii) the local Nusselt number follows an effective Rayleigh number power-law scaling exponent of 0.37, consistent with the logarithmically corrected 1/2 power-law scaling predicted for ultimate thermal convection. We reason that both turbulent and laminar-like boundary layers coexist in the transitional regime of vertical natural convection, consistent with the findings reported for Rayleigh–Bénard convection and Taylor–Couette flows. When the walls are instead removed and boundary layers eliminated, the new setup mimics turbulent bulk-dominated thermal convection. We refer to this new setup as homogeneous vertical natural convection. A direct application of scaling arguments to the governing equations of this new setup yields the asymptotic 1/2 power-law scaling relations for the Nusselt and Reynolds numbers, in accordance to previous theoretical predictions of turbulent bulk-dominated thermal convection. Results from direct numerical simulation of the new setup further supports the predicted 1/2 power- law relations. When employing bulk quantities for the wall-bounded setup, we too find the aforementioned 1/2 power-law scaling. This extended result suggests that the 1/2 power-law scaling relation may even be present at lower Rayleigh numbers provided the appropriate quantities in the turbulent bulk flow are employed for the definitions of the Rayleigh, Reynolds and Nusselt numbers. Lastly, we perform a straightforward assessment of the mixing efficiency in vertical natural convection. The value is predicted and found to be approximately 0.5, which suggests that the dissipation rate of kinetic energy is directly proportional to the rate at which gravitational potential energy is readily available for conversion.