Sub-additivity in combining infiltration with mechanical ventilation for single zone buildings

In determining ventilation rates, it is often necessary to combine naturally-driven infiltration, with air flows from mechanical systems. When there are balanced mechanical systems, the solution is simple additivity, because a balanced system does not impact the internal pressure of the space or the air flows through the building envelope. Unbalanced systems, however, change internal pressures and therefore can impact natural ventilation non-linearly in such a way as to make it sub-additive. Several sub-additive approaches are found in the literature, but they are not robust across the full spectrum from tight to leaky buildings and ranges of mechanical ventilation air flow rates. There are two approaches for combining natural infiltration with mechanical ventilation that require different solutions. The forward problem is to find the total air flow when adding mechanical ventilation to natural infiltration, and this application has been investigated in previous studies. The inverse problem finds the required mechanical ventilation in order to meet a total ventilation rate given a known amount of natural infiltration. This article presents the results of millions of hours of simulations of the physically correct solution, which span a broad range of climates, air leakage and structural conditions. This large dataset allows for the comparison with three literature models and the development of new robust sub-additivity models. These improved models are for use with unbalanced systems appropriate for consensus standards and guidelines for both the forward and inverse problem. They reduce errors to 1% or less and work across the air tightness spectrum.