Improved scaling analysis of the transient buoyancy-driven flow induced by a linear temperature gradient

Abstract

The transient convective boundary layer flow induced by a linear temperature gradient and its subsequent intrusion flow are investigated in an open cavity with scaling analysis in this study. Scale laws quantifying the buoyancy-driven convective flow are obtained. Compared to previous similar studies, the present scaling analysis is predominantly improved by adopting a two-dimensional decomposition of the specified thermal gradient rather than following the traditional one-dimensional approach, in which way thermal restrains are greatly eliminated. Consequently, the obtained scales are much more generalised and convenient to use. They can also be extended to some problems where the previous scale laws are not handily applicable. It is demonstrated that both unsteady and steady convective boundary layers are two dimensional, which is fundamentally different from the well-known one dimensional growth in homogenous heating problems. An unsteady intrusion flow is considered in this study. Two flow Scenarios are identified for the intrusion and several possible flow regimes are found in each Scenario. A total of 120 transient cases are calculated by numerical simulations and the numerical data are compared against the scaling results. A reasonable agreement is obtained supporting the employed two-dimensional decomposition method and validating the derived scales.