Simultaneous solutions of coupled thermal airflow problem for natural ventilation in buildings

Natural and hybrid ventilation can be sustainable building ventilation strategies, where airflow is driven naturally by thermal buoyancy and/or wind forces other than pure mechanical means. The simulation and design of these systems need to consider the combined impact of thermal and airflow transport behaviors. The numerical solution of such combined thermal airflow problems often employs a segregate and iterative approach. Either the air temperatures in the thermal problem or the air pressures in the airflow problem are solved separately with the other parameter known from a previous iteration. The newly solved parameters are then substituted successively into the other calculation. For highly coupled thermal airflow problems, the segregate method can cause solution fluctuation or even divergence when relaxation factors are not carefully selected to avoid abrupt changes of air parameters in the successive substitution procedure. This article investigated two nonsegregate methods to solve thermal and airflow problems simultaneously. In the fully simultaneous method, air temperatures and pressures for all rooms of a building are solved simultaneously using a single Jacobian matrix. In the semi-simultaneous method, a Jacobian matrix for the air temperature and pressure of one room is solved when air temperatures and pressures of other rooms are kept as constants. The same procedure is then repeated for each room of a building. In both cases, relaxation factors are not required. The simultaneous solution methods are demonstrated for a two-zone building with thermal buoyancy-driven flows and validated for an experimental study of combined wind and buoyancy forces in a light well. It was shown that the simultaneous solvers provide stable solutions without using any relaxation in both cases. The predicted results also agree reasonably well with the experimental data.