Using advanced wall functions in the computation of buoyant Flows

This study explores the potential of a recently developed wallfunction strategy for the economical and reliable prediction of natural convection flows. This strategy involves the use of large nearwall control volumes and the analytical solution of simplified, boundarylayer forms of the momentum and enthalpy transport equations to provide wall boundary conditions for momentum, temperature and also turbulence parameters. The simpler, conventional wallfunction strategy, based on the loglaw, has also been employed for baseline comparisons. These nearwall modeling strategies have been combined with different highReynoldsnumber turbulence models, which include the k-, a basic form of the secondmoment closure, and a more elaborate secondmoment closure which satisfies a number of physical realisability constraints, including the 2component limit. In the secondmoment computations, in addition to the generalized gradient diffusion hypothesis, more complex algebraic expressions have been employed for the modeling of the turbulent heat fluxes. They involve solution of transport equations for the temperature fluctuation and its dissipation rate. Three types of test cases have been computed; a square cavity with differentially heated vertical walls, a tall cavity with similar heating arrangements and a square cavity with unstable stratification. The resulting comparisons show that the more elaborate wall function shows distinctive predictive advantages. In comparison to the use of lowRe models is highly costeffective and in some cases also results in superior predictions. The k- model when used with the new nearwall approach, is satisfactory in most cases. Of the secondmoment closures, the realizable version, used with the additional transport equations, yields the most satisfactory flow and thermal predictions.