An Example of Solution Multiplicity in a Building with Bi-directional Flow Openings

We addressed the question of whether the assumption of unidirectional flow found in previous studies has led to the existence of two stable ventilation solutions in a two-opening building. The findings of multiple solutions in building ventilation raise the question of whether the macroscopic flow analysis and/or computational fluid dynamics simulations can provide sufficient accuracy to predict airflow patterns for guiding practical design of natural and hybrid ventilation. We extended previous analyses of a building with two unidirectional flow openings to one with two bi-directional flow openings. We considered natural ventilation driven by combined thermal buoyancy and opposing wind forces. A Newton–Rapson method was used to solve the non-linear governing equations for air-flows and a Runge–Kutta method was used for heat balance in the building. The airflow and heat balance calculations are fully coupled. We found that two stable solution sexisted under a certain combination of identical natural driving forces and a certain combination of large openings with bi-directional flows. The existence of the two stable solutions diminished when the vertical distance between the two openings was equal to or less than the opening height. This observation reveals that the assumption of unidirectional flow has indeed led to the existence of two stable solutions under these conditions for the simple building considered. These results provide more evidence of the existence of multiple solutions for building ventilation in general building configurations and also suggest the need for careful examination of the underlying physical assumptions in the solution multiplicity analyses.