Some examples of solution multiplicity in natural ventilation

This paper shows that under certain conditions, multiple solutions for the flow rate exist in a natural ventilation system, induced by the non-linear interaction between buoyancy and wind forces. Under certain physical simplifications, the system is governed in steady state by a non-linear algebraic equation or a system of equations. Three examples are given here: a single-zone building with two openings, a channel with two end openings, and a two-zone building with two openings in each zone. Analytical and numerical solutions are presented. It is shown that in all three cases the flow rate exhibits hysteresis. These results have significant implications for multi-zone modelling of natural ventilation and smoke spread in buildings. An experimental investigation using a small-scale model in a water tunnel confirms that two steady-state solutions exist for a single-zone building.