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Simultaneous Solutions of Coupled Thermal Airflow Problem for Natural Ventilation in Buildings



Steven J. Emmerich, William S. Dols, Liangzhu (Leon) Wang


Natural and hybrid ventilation are 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 thus need to consider mutual impact of the thermal and the air behaviors. A numerical solution of such thermal airflow problems often follows a segregate and iterative manner. Either the air temperature in the thermal problem or the air pressure in the airflow problem is solved separately with the other parameter known from a previous iteration. The newly solved parameter is then substituted successively in the other problem. For highly coupled thermal airflow problems, the segregate method could 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 paper investigated two non-segregate 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 by 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, relaxations are not required. The simultaneous solution methods are demonstrated by a two-zone building with thermal buoyancy-driven flows, and validated by 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.
Hvac&R Research


combined airflow and heat transfer model energy analysis multizone model natural ventilation


Emmerich, S. , Dols, W. and , L. (2011), Simultaneous Solutions of Coupled Thermal Airflow Problem for Natural Ventilation in Buildings, Hvac&R Research, [online], (Accessed June 19, 2024)


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Created May 11, 2011, Updated February 19, 2017