Dimensionless analytical solutions for steady-state fire smoke spread through high-rise shaft

Analytical solutions in terms of dimensionless numbers for the smoke spread through high-rise shafts during fires are essential to provide a fundamental understanding of smoke transport physics, which is a complex coupled heat and mass transfer problem. Existing solutions are often dimensional based on simplification of the problem such as assuming adiabatic conditions. In order to obtain the dimensionless analytical solutions, energy balance equation, mechanical energy equation and mass balance equation were established for smoke spread in high-rise buildings under both mechanical and natural venting conditions. Experiments were designed and conducted on two scaled shafts with different sizes and materials, and the measured results were compared to the dimensionless analytical solutions. It was found that the dimensionless analytical solutions could predict temperature profiles, mass flow rate and neutral plane level accurately. The effect of the adiabatic assumption on the accuracy was also discussed. For example, due to the adiabatic assumption, the error of the calculated mass flow rate required during mechanical venting to maintain a high-rise shaft smoke free was found to increase with a dimensionless number, ω, defined by the geometrical and thermal properties of the shaft.