Buoyancy-Driven Flow in a Two-Story Compartment

In this study we develop a theoretical model for the buoyancy-driven flow in a two-story compartment. In particular, the influence of the vent area $(A^{*}∕H^2)$ and the upper story height $\left(\beta \right)$ on the evolution of the “first front” is presented. We note that the steady-state thickness $({\tilde{h}}_{1s};{\tilde{h}}_{1s,m})$ of the buoyant fluid accumulated on the ceiling in the lower story and the filling time for the upper story decrease as the vent area increases. Before the upper story is fully filled, the flow may become “stack driven” by the buoyant fluid in the upper story. For sufficiently high upper story and large vent area, the buoyant fluid in the lower story can be completely drained. The upper story serves as a “buffer zone” which helps to reduce the accumulated buoyant fluid in the lower story.