To model runoff, the so called Nusselt solution is used. It describes a steady parallel flow with a parabolic velocity profile. The Nusselt solution for fluid flow is a good first approximation, although some assumptions have to be made when using it. First, the liquid film should be thin enough so that the film does not become unstable. On the other hand, the film should be thick enough to minimize the influence of surface forces. Furthermore we neglect surface tension and assume that the surrounded air has zero density and viscosity. Finally, the pressure is presumed to be constant over the film thickness. In the simulations, only the two-dimensional case is considered. As a consequence, the formation of the typical “fingering pattern” on a facade due to the instability of the moisture front, could cannot yet be taken into account.
All these assumptions lead to the problem that we can only simulate already formed liquid films and we are still looking for a way to model the first moments when the liquid film forms. One assumption is remarkable. Huppert already discovered in 1982 that neglecting surface tension doesn’t influence the flow speed of the moisture film.
If we implement this theory in a finite element method that is used to asses moisture transport in building materials (HAMFEM) we come to the following conclusions for some rain showers during a one hour rain event. However that a large amount of the excess water that can’t be absorbed by the sample runs down and out the system, the mass increase of the sample itself is notable higher. This is the result of a postponed drying phase and a longer wetting phase. This is depicted in figure 1.
However, when considered phenomena like dirt- or white washing of the facade, it could be important to have an idea of the frequency at which runoff occurs and to incorporate also the third dimension and surface tension in the model to enable the calculation of the typical “fingering pattern” on wetted facades. When phenomena concerning deterioration are considered, it might be important to make long term assessments of the wall using measured weather data.
Thijs Van den Brande is a PhD-student at the Builing Physics Section, KU Leuven. This research have been obtained in the framework of the research project FWO G.0448.10N, ‘Strategies for moisture modelling of historical buildings in order to reduce damage risks’, funded by the FWO-Flanders