Influence of Wind-Driven Rain on the Thermal Conductivity of Building Envelopes with Different Cement-Lime Coatings

Wind-driven rain (WDR) can be an important moisture source for building facades and therefore is of great concern in civil engineering. Wind-driven rain or driving rain is rain that is given a horizontal velocity component by wind. WDR intensity depends on several parameters such as building geometry, surroundings, terrain topography, position on the facade, wind velocity, wind direction, rainfall intensity and raindrop-size distribution. Wind-driven rain research is important within a number of research areas including Earth sciences, meteorology and building science. As one of the most important moisture sources, it affects the hydrothermal performance and durability of facades. Consequences of its destructive effect can take many forms. Moisture accumulation in porous materials can lead to water penetration, frost damage, moisture induced salt migration, discoloration by efflorescence, structural cracking due to thermal and moisture gradients, increased thermal lost due to the raised thermal conductivity, aesthetics etc. [1 and 2]. Computational Fluid Dynamics (CFD) simulations can be a valuable alternative to measurements and semi-empirical methods. According to the STN EN 15 026 [3], WDR load should be involved in building envelope heat-air-moisture (HAM) simulation. This leads to the need for accurate information on the spatial distribution of surface wetting and, therefore, CFD simulations with their high resolution are very useful. The use of various simulation programs has increased with development of computers. Programs for simulation of heat-air and moisture transport in building envelope uses non-steady boundary condition – outdoor climate data sets – test reference years (TRY) [4]. Test reference years are used in building science for many purposes. Generally, there are two types of test reference years: energy TRY (to calculate the energy consumption) and moisture reference year (to analyze the moisture problems in building envelopes). The methodology for creation of moisture TRY from long term observation is analyzed and described by Sanders [4]. This paper deals with influence of WDR on the building envelope in terms of thermal conductivity. Low rise building was simulated in CFD software OpenFOAM using Eulerian multiphase model for rain phase and determined rain load was used as an input for HAM simulation in WUFI. Two different wall constructions which were used differ in the core layer and also in exterior coatings. The influence of wind-driven rain load on the thermal conductivity for the aerated concrete and aerated clay brick was established.


Introduction
Wind-driven rain (WDR) can be an important moisture source for building facades and therefore is of great concern in civil engineering. Wind-driven rain or driving rain is rain that is given a horizontal velocity component by wind. WDR intensity depends on several parameters such as building geometry, surroundings, terrain topography, position on the facade, wind velocity, wind direction, rainfall intensity and raindrop-size distribution. Wind-driven rain research is important within a number of research areas including Earth sciences, meteorology and building science. As one of the most important moisture sources, it affects the hydrothermal performance and durability of facades. Consequences of its destructive effect can take many forms. Moisture accumulation in porous materials can lead to water penetration, frost damage, moisture induced salt migration, discoloration by efflorescence, structural cracking due to thermal and moisture gradients, increased thermal lost due to the raised thermal conductivity, aesthetics etc. [1 and 2].
Computational Fluid Dynamics (CFD) simulations can be a valuable alternative to measurements and semi-empirical methods. According to the STN EN 15 026 [3], WDR load should be involved in building envelope heat-air-moisture (HAM) simulation. This leads to the need for accurate information on the spatial distribution of surface wetting and, therefore, CFD simulations with their high resolution are very useful.
The use of various simulation programs has increased with development of computers. Programs for simulation of heat-air and moisture transport in building envelope uses non-steady boundary condition -outdoor climate data sets -test reference years (TRY) [4]. Test reference years are used in building science for many purposes. Generally, there are two types of test reference years: energy TRY (to calculate the energy consumption) and moisture reference year (to analyze the moisture problems in building envelopes). The methodology for creation of moisture TRY from long term observation is analyzed and described by Sanders [4].
This paper deals with influence of WDR on the building envelope in terms of thermal conductivity. Low rise building was simulated in CFD software OpenFOAM using Eulerian multiphase model for rain phase and determined rain load was used as an input for HAM simulation in WUFI. Two different wall constructions which were used differ in the core layer and also in exterior coatings. The influence of wind-driven rain load on the thermal conductivity for the aerated concrete and aerated clay brick was established.

Computational domain
The computational domain for the simulated building with dimensions 775 x 1600 x 420 m is shown in Fig. 1 and consists of 4,876,875 tetrahedral cells. The blockage ratio of the domain is 0.1 % and the distances of the modelled building between the domain boundaries are according to the guidelines of Franke et al. [5]. material base is more or less the same. FeinPutz has smooth and EdelPutz scraped surface. The material parameters are summarized in Table 2. The measured properties from previous research [6 and 7] are highlighted. The rest of properties are from the WUFI software database, mostly measured by Fraunhofer Institute for Building Physics.

Wind and rain phase
Computer code OpenFOAM was used for numerical simulation. It is an open-source, implicit, segregated and double precision solver. Eulerian multiphase model [8] was used for the rain phase instead of commonly used and more time consuming Langrangian particle tracking model. This model enables to reduce the computational expense to model a long rain event which is discretised into 1 min or 10 min time steps. CFD simulations are made for a limited number of horizontal rainfall intensity and wind velocity couples. The wind-flow field in the domain is solved for wind velocity U 10 = 10 m/s and wind-flow fields for other reference wind velocities (1, 2, 3 and 10 m/s) are obtained by linear scaling.
In Fig. 2, we can see a wind flow field showing the mean wind velocity on the vertical mid-plane through both buildings. The wind flow on the high building is clearly influenced by the lower building. Typical flow features as the standing vortex, the downflow from the stagnation point, large vortices behind the building, and flow restoration behind the building are visible.

Reference wall constructions
Two walls with two different traditional coatings (totally four variants) from Baumit were used for the heat-air and moisture simulation (HAM) -see Table 1. The basic difference between EdelPutz and FeinPutz is the final surface of the coating. The Detailed construction of the reference walls Table 1 Aerated where U(y) is the mean streamwise wind velocity at height y above the ground plane, u* ABL the ABL friction velocity, k the von Karman constant (used 0.41 in the present study), and y 0 the aerodynamic roughness length. In the paper, an aerodynamic roughness length of 0.5 is chosen which represents a landscape totally and quite regularly covered with similar-size large objects according to the Davenport roughness classification [10 and 11]. The Aerodynamic boundary layer (ABL) friction velocity, u* ABL , is chosen to obtain the desired reference wind speed, U 10 , at a height of 10 m (in this study 10 m/s). In Fig. 3 we can see the difference of raindrop trajectories with different wind velocity and raindrop diameter. The higher the wind velocity, the more inclined the trajectories are. Behind the obstruction the turbulent flow occurs which influences the The inlet profile of the mean wind velocity is defined by the typical log-law expression [9]:

Determination of wind-driven rain load
The global catch ratios for six positions on the facade (Fig. 5) are summarized in Table 3. It was obtained through the numerical model for the measured rain event on 4-5 November 2012 [12].
trajectories. With using each reference wind-flow field, specific catch ratio distributions are calculated for various diameters (Fig. 4) of raindrops (diameters from 0.5 to 1 mm in steps of 0.1 mm, from 1 to 2 in steps of 0.2 and from 2 to 6 in steps of 1 mm). Catch ratio distributions are obtained for a list of reference horizontal rainfall intensities R h (0, 0.1, 0.5, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 25, and 30 mm/h, catch ratio chart in Fig.  5) using the droplet size distribution as input [12]. The global catch ratio for selected rain event is obtained by summation over

Results and discussions
From Figs. 6 and 7 we can clearly see the difference between the WDR load and its influence on the water content in the aerated clay brick. In Tables 5 and 6 we can see how the increased water content is reflected in thermal conductivity (Fig. 8), especially in the upper positions and the aerated clay brick wall where the difference is very big. The thermal resistance decreases up to 45 % for the aerated clay brick wall (TSF) with smooth FeinPutz coatings. With the aerated concrete wall, the values are not so high. In the bottom part of the building (m5), the values of thermal conductivity are significantly lower.
More detailed information about the rain event is stated in [12]. The rain lasted for 9 hours with cumulative horizontal rainfall 44.5 mm/m 2 .
From Fig. 4, which represents specific catch ratios, we can clearly see the difference of WDR load on the facade which is highest in the upper part and especially in the top corners. For the determination of WDR load on the facade, three positions on the facade were selected (Fig. 5), concretely m1 with the highest catch ratio, m2 with overall value for the upper part and m5 for the lower part of the building. Catch ratio chart for the position m2 is shown in Fig. 5 and it depends on the wind velocity and rain intensity. The catch ratios from the numerical model are transformed to the proportion factor ( Table 3). The proportion factor in the HAM simulation program WUFI defines the position on the facade.

HAM simulation in WUFI
For simulation in WUFI software, two different wall types with different coatings were used. According to the previous research [14], climatic year 2010 for Bratislava (mean temperature 9.5°C, horizontal rain sum 1012 mm/m 2 ) were used as the outer boundary condition. As input for the numerical model was used only rainfall with corresponding wind direction (wind-driven rain which affects the facade -raindrops hit the windward north-west facade). The initial moisture for used materials was typical built-in moisture according to the WUFI database. The inner boundary condition was derived from outer according to the STN EN 15026:2007. Figs. 6 and 7 represent the average annual course of water content in the core layer (ACB and ACC) in the 5 th year after the construction of building. Table 4 shows the annual averages of water content for selected positions.
Mean annual water content in the core layer of simulated walls

Conclusion
It was demonstrated that the wind-driven rain load has crucial influence on the water content in the wall for the windward oriented facades with exterior coatings based on the traditionally cement-lime material base. The water content values, especially for the aerated clay brick, can be different for different producers because they differ in the shape of the cavities, clay etc. Moreover, the water transport model in WUFI is not ideal considering the materials with cavities (all materials in WUFI are treated as porous material). Also the difference for other manufactures of cement-lime coatings can be different. Each producer has his own manufacturing secrets and different ingredients and mixing ratios.
In the end, we offer a recommendation based on the results of the research. For the windward facades of buildings higher than 10 meters, the usage of cement-lime coatings is not recommended without any other protection (e.g. water repellent paint) because the thermal resistance will be significantly decreased.