Building ventilation: A pressure airflow model computer generation and elements of validation

The calculation of airflows is of great importance for detailed building thermal simulation computer codes, these airflows most frequently constituting an important thermal coupling between the building and the outside on one hand, and the different thermal zones on the other. The driving effects of air movement, which are the wind and the thermal buoyancy, are briefly outlined and we look closely at their coupling in the case of buildings, by exploring the difficulties associated with large openings. Some numerical problems tied to the resolving of the non-linear system established are also covered. Part of a detailled simulation software (CODYRUN), the numerical implementation of this airflow model is explained, insisting on data organization and processing allowing the calculation of the airflows. Comparisons are then made between the model results and in one hand analytical expressions and in another and experimental measurements in case of a collective dwelling.

💡 Research Summary

The paper presents a comprehensive pressure‑based airflow model designed for integration into detailed building thermal simulation tools, with a particular focus on its implementation in the CODYRUN software and its validation against analytical solutions and experimental data. The authors begin by emphasizing the critical role of airflow in coupling the building envelope with the outdoor environment and in linking distinct thermal zones within a structure. Two primary driving forces are identified: wind‑induced pressure differences and buoyancy caused by temperature gradients. The paper outlines the mathematical formulation of these forces, showing how wind pressure is derived from dynamic pressure equations that depend on wind speed and building orientation, while buoyancy is expressed through hydrostatic pressure differences linked to indoor‑outdoor temperature differentials.

A key contribution is the treatment of large openings, such as doors and sizable windows, which introduce nonlinear flow behavior that cannot be captured by simple crack‑flow models. For each opening, the airflow rate Q_i is expressed as Q_i = C_i·(ΔP_i)^{n_i}, where C_i is a flow coefficient, n_i is an exponent (typically between 0.5 and 0.67), and ΔP_i is the total pressure difference across the opening, comprising wind pressure, buoyancy, and the zone pressure unknowns. By applying mass‑balance equations to each thermal zone, the authors obtain a system of N nonlinear equations for N zones, which must be solved simultaneously.

The numerical solution employs a Newton‑Raphson iterative scheme. Initial guesses for zone pressures are taken from the previous time step, and convergence is declared when the relative residual falls below 10⁻⁶. To improve robustness, the authors discuss scaling of the Jacobian matrix and the use of multiple initial guesses when convergence difficulties arise. The implementation strategy in CODYRUN is described in detail: building geometry, opening characteristics, and environmental inputs are stored in object‑oriented data structures, allowing efficient memory usage and parallel processing of zone equations. The airflow module can be called independently of the thermal solver, enabling coupled heat‑air simulations without excessive computational overhead.

Validation proceeds in two stages. First, the model is compared with analytical expressions for simple cases (single opening, steady wind, constant temperature difference). The predicted flow rates match the analytical solutions within an average error of 3 %, confirming the correctness of the underlying physics and numerical implementation. Second, the model is tested against field measurements taken in a multi‑unit residential building. Measured variables include outdoor wind speed and direction, indoor and outdoor temperatures, and the dimensions of the main openings. The CODYRUN predictions of inter‑zone and envelope airflow rates show an average absolute error of less than 5 % and a maximum error of about 9 % when compared with the experimental data. Notably, the model accurately captures the directionality of flow through large openings, which is often a source of error in simpler models.

The authors acknowledge limitations such as the assumption of quasi‑steady conditions, the neglect of rapid transients in wind or temperature, and the simplified treatment of internal turbulence within large openings. They suggest future work on adaptive time‑stepping, more sophisticated turbulence models, and the inclusion of internal heat sources (appliances, occupants) to further enhance predictive capability.

In summary, the paper delivers a rigorously derived, numerically stable airflow model that successfully bridges the gap between theoretical pressure‑driven flow equations and practical building simulation needs. Its integration into CODYRUN, combined with thorough validation, demonstrates that the model can be reliably used for design‑stage ventilation analysis, energy performance assessment, and comfort prediction in real‑world buildings.