This study was an attempt to analyze convective flow patternsunder conditions applicable to fires in high rise buildings when naturalconvection alone is the most important driving force. The primaryaim of this investigation was to consider the turbulent flow in verticalshafts caused by hot gases entering the bottom of the shaft which isalready filled with a cooler (denser) gas, and hence creating an unstable density field.
The small scale model used to study this problem consisted of a vertical tube of dense fluid placed in an infinite (less dense) fluidenvironment. General scaling laws were developed for the variation ofdensity with time for the flow set up in the model. Also, an analyticalmodel was developed to account for the observed mixing rates in thissimple configuration.
In the analysis, the diffusion equation was solved and found tobe in agreement with the small scale model. The mixing coefficientfor this unstable system is
See abstract for formula
where the constant, 0.28, was determined empirically, and thefundamental time scale that characterizes the mixing in the vertical columnis
See abstract for formula
Later, the above techniques were used to investigate in a moresuperficial way the effects on the mixing rates of geometric variations,limited external environments, changes in the internal geometry of theshafts, gas density ration, and heat transfer.
