A simplified numerical model for rainwater runoff on building facades: Possibilities and limitations

A simplified numerical model for rainwater runoff on building facades is presented, evaluated and discussed. The variation of runoff film thickness is described by a first-order hyperbolic partial differential equation. This equation is derived from the continuity equation, to which the wind-driven rain (WDR) intensity and the capillary absorption flux by the wall are added as source/sink terms, and from the adoption of the parabolic velocity profile of the Nusselt solution for a simplified representation of thin film flow. Two major model simplifications are the adoption of the Nusselt solution for (1) statistically-steady, developed films, in spite of actual wave behaviour, and for (2) transient, developing films, in spite of the actual moving contact line complexity. Both simplifications are directly related to surface tension effects. Concerning the first simplification, a selective review of the literature, including experimental laboratory data, confirms the validity of the Nusselt solution for representing the time-averaged properties of thin film flow, up to film Reynolds numbers of 1000, in spite of the actual wave behaviour. Concerning the second simplification, the runoff model is evaluated by a comparison with available on-site measurements of rainwater runoff from a building facade exposed to WDR, indicating a fair qualitative and quantitative agreement. Specific attention is given to a discussion of the possibilities and limitations of the runoff model. The runoff model can easily be integrated into 2D and 3D building envelope heat-air-moisture transfer (BE-HAM) models, but further research on the simplifications and assumptions of the runoff model is required.