Multiple steady states in combined buoyancy and wind driven natural ventilation: The conditions for multiple solutions and the critical point for initial conditions

Abstract

Natural ventilation systems may have multiple steady states in the combined buoyancy and wind driven mode in a single space. In this paper, dynamical system analysis is applied both graphically and quantitatively to investigate the multiple steady state behavior of such a natural ventilation system. The necessary conditions for the system to have multiple steady states are derived for a single space combined wind and buoyancy driven natural ventilation system. Distinct from previous studies, the derivation comes from the transient dynamical system behaviors of the system rather than from the steady state equations, and it can be applied to more general cases. Based on the dynamical system analysis, the quantitative relation between the initial temperature and the final steady state is investigated for the single space case. The unstable steady state, which cannot physically exist in reality, is the critical point of the initial value in determining the final (steady) state of the system.