Modeling façade degradation risks on a cubic building: The impact of spatial wetting- and drying patterns on the hygrothermal response

Abstract

HAM models have proven their value for analyzing moisture-related pathologies by assessing hygrothermal responses to environmental exposure. In this study, a coupling between CFD and HAM is developed to capture spatial wetting and drying effects, which allows to identify façade degradation patterns. Wind-driven rain (WDR) and evaporation significantly influence the hygrothermal performance and durability of façades, particularly in heritage and renovation. In traditional HAM modeling, WDR and convective heat transfer coefficients (CHTC) are often simplified by applying generic, uniform values across the façade. However, this approximation fails to account for the spatial and temporal variations in WDR and neglects the significant variations in CHTC due to the surrounding velocity flow field. These oversimplifications can limit the validity and accuracy of hygrothermal predictions. This study presents a novel approach by externally coupling CFD simulations with HAM modeling to capture the spatial distribution of WDR and CHTC on building façades. Steady Reynolds-averaged Navier-Stokes equations and Eulerian-multiphase simulations are performed to calculate the wind flow and the rain trajectories with turbulent dispersion of raindrops. Using a cubic low-rise building as a case, the coupled model evaluates the effects of wind and rain exposure on façade deterioration, including frost degradation, salt crystallization, and algae growth. Results indicate that conventional approaches tend to underestimate critical rain loads, while drying potential is overestimated. It highlights how spatial variations in WDR and drying influence degradation mechanisms, emphasizing the need for more detailed spatial analyses. This integrated method provides valuable insights into risks posed by moisture exposure and drying dynamics, offering practical applications for targeted renovation strategies and improved preservation of building materials.

Keywords

hygrothermal response surface pathology wind-driven rain convective drying CFD-HAM

Introduction

Moisture-related building pathologies, such as frost degradation, rotting of embedded wood beams, algae growth and salt efflorescence affect a significant portion of existing buildings across many regions (De Vos et al., 2020). In large areas of Europe, wind-driven rain (WDR) is the primary cause of moisture accumulation, often exceeding a building’s drying capacity, which relies primarily on surface evaporation (Hens, 2017). For a reliable analysis of moisture risks, an accurate assessment of the combined effect of wetting and drying should be implemented together with a hygrothermal study.

Wind-driven rain is defined as the rain that impacts the building envelope due to a horizontal wind component. The extent of rain exposure depends on the wind flow in both the immediate and broader surroundings of a building (Blocken and Carmeliet, 2004). For example, the velocity field around a building in an urban environment will have lower wind speeds than in an open field. This results in reduced rain exposure, as raindrops have a smaller horizontal component, causing the rain trajectory to align more parallel to the façade (Blocken et al., 2010). Various methods exist to determine the amount of wind-driven rain on a façade, including measurements, semi-empirical formulas, and numerical simulations based on Computational Fluid Dynamics (CFD; Blocken and Carmeliet, 2004). Measuring WDR is a time-consuming and challenging task. Measurement errors can be substantial and highly dependent on the available equipment and the specific location, both spatially on the façade and geographically for the building itself. Nevertheless, despite the challenges, measurements remain essential for the development and validation of both semi-empirical and CFD-based methods and should be carried out whenever possible. Semi-empirical methods provide a quick and straightforward approach to estimating WDR on building facades, but only offer rough approximations. These methods rely on correlations between meteorological data, building geometry, and topography; however, limited datasets and varying model assumptions often result in significant discrepancies from actual measurements (Blocken et al., 2010; Kubilay et al., 2014a, 2014b). The usage of numerical methods, including CFD, facilitates a comprehensive examination of WDR-exposure and is validated across several field measurements (Blocken and Carmeliet, 2007; Khalilzadeh et al., 2019; Kubilay et al., 2013, 2014). However, this method is not without significant preparation and computational demands. Blocken and Carmeliet (2010) reviewed various methods for estimating WDR intensity, noting CFD’s strengths in detailed spatial and temporal rain analysis on complex building shapes. Choi (1991, 1993, 1994, 2002) developed a steady-state CFD method for WDR using Reynolds-averaged Navier-Stokes (RANS) equations with a Lagrangian particle tracking (LPT) model, which was later expanded by Blocken and Carmeliet (2002) for transient events. Afterward, Huang and Li (2010) demonstrated that an Eulerian multiphase (EM) model with RANS can accurately simulate WDR on the windward facade of an isolated low-rise building while reducing the computational demand by $~ 10$ times. Kubilay et al. (2013) validated the EM model for WDR by comparing its results with measurement data on a historical building featuring a high-rise tower. Kubilay et al. (2015a) further developed the EM model by incorporating turbulent dispersion of raindrops for time-averaged WDR calculations. This enhancement improved accuracy by reducing deviations from field measurements, particularly in capturing the behavior of smaller droplets.

Increased moisture levels do not necessarily entail an increased threat, provided the building materials can adequately dry out again. However, wetting–drying cycles may still contribute to material aging and degradation such as reduced mechanical strength and increased cracking in timber (Ferreira et al., 2023). The drying process of the façade mainly occurs through evaporation of water from the porous building material to the surrounding air (Steskens et al., 2009). Surface evaporation is determined by the transport of heat and moisture, which is dominated by the velocity field over the surface. The convective heat transfer coefficient (CHTC) and vapor transfer coefficient (CVTC) are typically used to model these respective transport processes (Defraeye et al., 2011, 2012). The CHTC is often used to estimate the CVTC by means of the heat and mass transfer analogy, also known as the Lewis analogy. The distribution of transfer exchanges across the building envelope is complex and, in the same way as the WDR, influenced by the wind velocity field, wind direction and speed around the building, as well as by the geometry of the building itself (Defraeye et al., 2011, 2012; Montazeri et al., 2015; Montazeri and Blocken, 2017, 2018; Zhou et al., 2023). Determining the CHTC of building façades can be achieved through different four methods: simplified analytical approximations, on-site measurements, wind tunnel experiments, or numerical simulations using CFD. On-site measurements for CHTC capture complex real-world conditions but are often limited to a few spatial and temporal points. They typically rely on a one-dimensional energy balance for building surfaces and use heated plates on facades. A major limitation is the lack of control over boundary conditions, like wind speed, direction, temperature, and humidity. Wind-tunnel measurements offer controlled boundary conditions, providing high-resolution CHTC data. However, such studies are mainly done on flat plates or bluff bodies like cubes at low Reynolds numbers with thin turbulent boundary layers. While flat-plate experiments can mimic full-scale conditions, building flow complexity raises questions about their validity for such applications. Reduced-scale models of buildings used in wind tunnels may not fully meet similarity requirements due to much lower Reynolds numbers, limiting data applicability for real buildings (Montazeri et al., 2015; Montazeri and Blocken, 2017, 2018). Semi-empirical models offer a quick approximation; however, they typically consider only a single uniform value, which is derived from wind speed measurements at 10 m in an open field. This approach often results in an overestimation, which is conservative in energy calculations but may not be in hygrothermal calculations. CFD simulations address many limitations of on-site and wind-tunnel measurements by providing whole-field data across all points in the computational domain. Unlike reduced-scale wind-tunnel tests, CFD can operate at full scale, avoiding issues with similarity requirements and enabling convenient parametric studies.

In the conventional approach for hygrothermal simulations, semi-empirical methods are applied for WDR loads which consider a uniform value over the façade. The same applies for the CHTC and CVTC and such assumptions consequently lead to high systematic errors and uncertainties in assessing moisture risk on building façades, as they lack insights on moisture distribution across different façade locations. This limitation makes it unclear which areas have the highest moisture risk, often resulting in uniform moisture protection measures across the entire façade and even the whole building envelope. Next to that, the simplified approach also fails to relate the actual degradation patterns on buildings with simulation results, limiting systematic validation in case-studies, in turn reinforcing the uncertainty and scepsis in the combination of hygrothermal models and degradation models.

Several researchers have already used CFD to map driving rain, or to determine generalized expressions for CHTC. However, most of them did not address the combined effects of wetting and drying, and are typically limited to the exposure analysis, neglecting the hygrothermal response necessary to assess building performance. By coupling the wind flow field from CFD with hygrothermal behavior, the spatial distribution of WDR loads and transfer coefficients across the façade can be analyzed, enabling detailed assessment of surface degradation risks such as salt crystallization, frost damage, and algae growth. An external coupling was chosen over an internal integration to minimize computational demands, allowing flexibility to analyze various wall assemblies and renovation strategies without recalculating wind field velocities for each simulation and time step.

Methodology

A summary of the workflow for an external coupling of CFD and HAM is presented in Figure 1. Initially, (1) CFD is used to calculate the wind velocity field around a building. This flow field is then utilized to determine the CHTC, CVTC (2), and at the same time used as the boundary conditions for a follow-up CFD simulation in which the rain trajectory and WDR across the entire building envelope is determined (1). So, in this first part of the workflow, the wetting and drying is determined over the spatial domain of the façade. In a following step, the CHTC, CVTC, and the WDR flux are used as the boundary conditions for hygrothermal simulations (3). These provide insight into the heat and moisture content in the façade. Lastly, the hygrothermal response is translated into a performance risk assessment by means of numerical prediction models for salt, frost, and algae (4).

Wind and rain field

The subject of this study is a cube with dimensions of 10 m × 10 m × 10 m. A simplified cube was chosen for computational efficiency and to focus on airflow characteristics in a controlled setup. To calculate the velocity field around the cube, the simpleFoam solver from the OpenFOAM8 software (OpenCFD Ltd, 2013) is used. An incompressible turbulent wind flow with steady Reynolds-averaged Navier-Stokes equations is modeled using the k–ε turbulence model (Launder and Sharma, 1974). A reference wind speed, U₁₀, of 10 m/s was applied for 16 different orientations, ranging from 0° to 337.5°, with a constant increment of 22.5°. This value was selected as a representative speed for the purposes of this study. A single reference wind speed was modeled, with the wind flow field scaled in subsequent steps based on the assumption that, for flows around sharp-edged bluff bodies, the locations of flow separation remain unchanged by variations in the Reynolds number (Kubilay et al., 2013, 2014). Considering neutral conditions during rain, the wind speed inlet profile follows the conventional logarithmic law (Richards and Hoxey, 1993), as shown below for equation (a). Meanwhile, the inlet profiles for the turbulent quantities, k and ε, are specified according to the following expressions in (b) and (c):

(a) U (y) = \frac{u_{ABL}^{*}}{κ} \ln (\frac{y + y_{0}}{y_{0}})

(b) k (y) = \frac{u_{ABL}^{* 2}}{C_{μ}^{0.5}}

(c) ε (y) = \frac{u_{ABL}^{* 3}}{κ (y + y_{0})}

With: U(y) the mean wind speed at height y above the ground, $u_{ABL}^{*}$ the atmospheric boundary layer (ABL) friction velocity, κ the von Karman constant 0.41, $y_{0}$ the aerodynamic roughness length, and $C_{μ}$ the turbulent viscosity coefficient 0.09 (Richards and Hoxey, 1993).

In the rain phase, the wind-driven rain solver developed by Kubilay et al. (2013, 2014, 2015a, 2015b) is used to calculate the rain droplet trajectories. The continuity and momentum equations of the rain droplets are calculated with the Eulerian multiphase (EM) model based on the previously simulated but scaled wind-flow field. As an input, 32 wind speeds are modeled running from 0 to 15.5 m/s with an increment of 0.5 m/s. The rainfall intensities are varied with a finer resolution at lower intensity, namely from 0 to 3 mm/h with an increment of 0.1 and then 3.5, 4, 4.5, 5, 10, 30 mm/h for the higher intensity. The selection of the wind speed and rainfall intensity ranges is based on their representation in the Moisture Reference Year (MRY) developed by Vandemeulebroucke for the Brussels climate, as illustrated in Figure 3. The rain inlet boundaries, raindrop velocity and rain phase fraction, are imposed at the inlet and top boundaries. The raindrop-size distribution by Best (1950) and terminal velocities by Gunn and Kinzer (1949) are used. It is important to note that the droplets leave the domain when they make contact with a surface, such as the building walls and the ground, this implies that splashing and runoff is not considered in the moisture exposure. For more information and validation of the solver, the author refers to Kubilay et al. (2013, 2014, 2015).

Figure 2 provides an overview of the computational domain and grid refinement over the cube, which is located parallel to the boundary box. The domain has a square base measuring 310 m × 310 m with a height of 160 m. This provides 150 m of free field on each side of the cube, in accordance with the best practice guidelines of Franke et al. (2007). The grid was generated using the blockMesh tool in OpenFOAM, with grid refinement increasing as the wall boundaries are approached. Each side of the cube is divided into 1600 cells, with each cell’s centroid serving as a point for which a hygrothermal simulation is conducted in the subsequent phase. The computational domain consists of 4,776,000 hexahedral cells.

Hygrothermal boundary conditions

The imposed flux for WDR, along with the CHTC and CVTC needed for the hygrothermal model, are calculated at the centroid of the mesh cells on the four side walls of the cube. A MRY dataset published by Vandemeulebroucke for Brussels is used as a base for the calculations (Vandemeulebroucke et al., 2022). Brussels is the capital of Belgium. It has an oceanic climate, with mild winters and warm summers, and precipitation occurring throughout the year. The mean temperature and precipitation over the MRY are 10.3°C and 1011 mm, respectively.

Figure 3 illustrates the histogram for rainfall intensity on the left and the wind rose during rain events on the right. The figures show that the predominant wind orientation is southwest and that the majority of wind flow at 10 m stays below 10 m/s with an average velocity of 4.3 m/s. The majority of rainfall events have intensities below 5 mm/h, which suggests that smaller raindrops (less than 2 mm diameter) dominate during these periods.

The CHTC, CVTC, and WDR are determined using the formulas provided below:

(a) R_wdr=η·R_h

(b) CHTC= 4+4. v_local

At each hourly time step of the MRY, the wind-driven rain, R_wdr [mm/h], was calculated according to equation (a), based on the MRY climate data. In the calculation, the R_h represents the hourly horizontal rainfall intensity [mm/h] and η the specific catch ratio [-]. For each hour in the MRY, the corresponding catch ratio is determined by matching the wind speed, orientation, and rainfall intensity to the results of the pre-simulated CFD rain simulations. When an exact match for the wind speed, orientation, or rainfall intensity is not available in the CFD results, linear interpolation is applied across the three variables to derive the appropriate catch ratio. This ensures that the imposed WDR accurately reflects the environmental conditions at each hour in the MRY. The CHTC is calculated according to equation (b) from EN6946:2007. Here the v_local is the wind speed adjacent to the surface. The v_local is determined by matching the pre-simulated wind field with corresponding wind orientation and speed, from the scaled velocity field. The distance from the wall to the velocity evaluation point, d_loc, is not uniformly defined in literature. A distance of 0.3 m is recommended by ASHRAE Task Group (1975) and used in various studies (Blocken et al., 2009; Montazeri et al., 2015). Additionally, a distance of 1.0 m has been adopted by Sharples (1984) and other authors (Blocken et al., 2009; Loveday and Taki, 1996). In this study, a sensitivity analysis is conducted with different values for d_loc both in the turbulent boundary layer as well as further away from the wall. These are compared with the conventional approach in HAM simulations, where d_loc is equivalent to the distance between the wall and the local climate station, which can easily span several kilometers. At last, the CVTC is calculated by multiplying the CHTC with 6.10–9 km/W (EN 6964, 2007) as shown in equation (c).

Hygrothermal modeling

In the following step, 1D hygrothermal simulations were conducted using Delphin 6.1 (2023) with the pre-calculated boundary conditions. The hygrothermal simulations are constructed in accordance with the 12-step framework SAMiRA proposed by Vanderschelden et al. (2022, 2025). This study focusses on a single-wall configuration, specifically a solid brick wall with internal lime plaster. The brick layer, comprising 450 mm thick old building brick Dresden ZP, exemplifies a conventional heritage wall in Belgian dwellings (Le Noir, 2017). The primary material characteristics are included in Table 1 below. The grid resolution is set in such a way that, when the grid is halved, the temperature and humidity remain within a 1 K and 5% difference, respectively according to EN15026:2023. As mentioned previously, the boundary conditions (WDR, CHTC, and CVTC) for the exterior surface are determined based on CFD calculations and the climatological data from the MRY of Brussels. Next to that, the MRY is used to define the remaining parameters such as relative humidity, temperature, and radiation, both shortwave and longwave. The indoor climate is defined by an adaptive indoor climate model according to EN 15026 with an increased moisture load (plus 5%). For the indoor heat and vapor transfer coefficients, respectively 7.63 W/m²K and 2.5e−08 s/m, are used. The saved outputs are the temperature, humidity, and moisture content on the exterior surface, together with the ice content in the outer layers up to a depth of 10 mm, with an increment of 1 mm.

Table 1.

Material properties for brick ZP and the historical lime plaster used in the hygrothermal modeling.

Name	Density ρ	Specific heat capacity	Open porosity	W _sat	W _cap	Thermal conductivity λ	Capillary absorption A_w	Vapor diffusion resistance µ
	kg/m³	J/kgK	m³/m³	m³/m³	m³/m³	W/mK	kg/m²s^0.5	-
Plaster	1800	850	0.3017	0.285	0.2526	0.82	0.127	12
Brick	1981	841	0.2526	0.1643	0.16	0.89	0.05	45

Hygrothermal response behavior

In the final step, the hygrothermal response was analyzed using several performance criteria. As wind-driven rain and convective drying predominantly affect surfaces, only surface degradation was considered in the calculations. Three different types of façade deterioration were evaluated: degradation caused by freeze-thaw cycles, deterioration due to salt crystallization-dissolution, and biological colonization of the façade by algae. Although the most reliable models from literature were adopted, their predictive accuracy remains limited by the variability of masonry properties and the simplification of 1D simulations, which cannot fully capture the complexity of moisture and salt transport. As the degradation models also carry inherent uncertainty, their systematic validation lies outside the scope of this work but will be addressed in future research through comparison with observed façade degradation patterns.

The assessment of frost damage to the exterior layers is conducted through the calculation of freeze-thaw cycles (FTC) and the determination of the Ω-factor. The ice model from Delphin is used to calculate the ice mass density and the ice volume percentage within the pore structure. This is in relation to the capillary pressure within the pores, whereby freezing point depression is considered. In order to analyze the FTC, the threshold value of 25% as proposed by Mensinga et al. (2010) is employed to calculate a cycle for relative comparison. The FTC provides relative insights on the sensitivity to wetting and drying, but does not provide an accurate risk assessment considering the actual freeze-thaw sensitivity of specific materials. The Ω-factor, which quantifies the relative change in dynamic elasticity modulus after freeze-thaw cycles, is particularly useful in hygrothermal studies due to its clear threshold for frost damage (Ω > 0.3), as defined in EN 12371:2010 (2010). A value exceeding this threshold typically indicates significant deterioration, such as the formation of cracks or the detachment of fragments. In this paper, the Ω-factor is applied by assigning an Ω-factor to each freeze-thaw event based on the most extreme freezing temperature and saturation degree, following the method of Feng et al. (2019) and Janssens et al. (2024).

In heritage structures, the formation of salt crystals represents a considerable threat to masonry structures, largely due to the phase transitions that occur within the pore system of materials. The degradation is quantified by counting the number of crystallization-dissolution cycles, wherein a phase transition occurs when the crystallization pressure surpasses the material’s tensile strength. Among the different salts encountered in practice, sodium chloride (e.g. halite, H) and sodium sulfate (e.g. thenardite–mirabilite, TM) are the most widespread and damaging in masonry façades (Balksten and Strandberg-de Bruijn, 2021; Grossi et al., 2011). Their frequent occurrence, either separately or together in a mixture, and their distinct crystallization behavior justify treating them as key representatives in hygrothermal degradation studies. The sodium sulfate solution, should be regarded as a coupled thenardite–mirabilite system, where repeated phase transitions between the two forms generate crystallization pressures, exceeding the tensile strength of brick and mortar (Balksten and Strandberg-de Bruijn, 2021; Grossi et al., 2011).

The crystallization cycles in this study were evaluated at the wall surface and at a depth of 5 mm using different temporal resolutions, namely hourly, 12-hourly, and daily. Following Janssens et al. (2025), a depth of 5 mm was selected as the reference depth: surface efflorescence is largely esthetic, whereas subflorescence just below the surface is the most relevant for material damage, where moisture and salt transport interact most strongly. This interpretation is consistent with Balksten and Strandberg-de Bruijn (2021), who emphasizes that real degradation risks occur in the near-surface zone of masonry rather than at the exposed surface itself. Note that, the impact that salts have on the hygrothermal behavior of walls are not yet included in current simulation models.

For halite, a phase transition occurs when the daily humidity drops below the critical threshold of 75.3% (Grossi et al., 2011). In contrast, for the mixture of thenardite-mirabilite, the critical threshold is temperature-dependent and follows the following function according to:

R H_{crit} = 59.11 + 0.87549 . T when T < 22.5 ° C

Algae growth on external walls primarily affects the esthetic appearance of buildings and may increase surface moisture retention. While not a direct structural threat, it indicates conditions that are favorable for other biological colonization (e.g. moss or higher plants growing in cracks), which in turn can contribute to material degradation and, indirectly, to structural risks. Recent studies emphasize that algae and other microorganisms play an important role as precursors or facilitators of broader biodeterioration processes on building envelopes (Chen et al., 2025; Dakal and Cameotra, 2012).

To predict algae growth under varying environmental conditions, two mathematical models are applied in this study: the Modified Avrami’s Model (MAV), developed by Quagliarini et al. (2021), and Miyauchi et al.’s (2008) Mathematical Model (MM). The MAV-Model is based on laboratory-accelerated growth tests, simulating algae colonization on substrates under controlled conditions. MAV uses an exponential growth equation, shown below, to simulate the colonization of algae on substrates.

X (t) = (1 - \exp (- K (t - t 1)^{n})) * \frac{A_{c}}{A_{t}}

Where X(t) is the colonization coverage of algae over time t, K [-] is a specific growth rate kinetics coefficient temporal dependent on the substrate surface and temperature, t1 is the latency time corresponding to the first appearance of algal spots which is determined by the open porosity and roughness of the substrate, n [-] is Avrami’s exponent, A_c/A_t [-] represents the maximum ratio of the area covered by algae to the total surface area of the substrate. Due to the presence of pits and depressions, as well as moisture retained in the surface pores, achieving complete coverage of the surface is not feasible. This model focuses on the positive growth phase and does not account for population decline, predicting that algae will grow significantly when relative humidity exceeds 98% (Figure 4).

The MM-Model, introduced by Miyauchi, uses field data to predict algae growth and incorporates environmental indices such as moisture content, temperature, and solar radiation, making it more flexible for natural environmental conditions. The growth rate of algae, denoted as dN/dt is calculated as in the following:

{\begin{matrix} \frac{dN}{dt} = G . r_{0} . N \\ G = g_{w} . g_{T} . (G_{0} + (1 - G_{0}) * g_{s} \end{matrix}

Here, the G [-] is the given for the integrated environmental index, r₀ [-] is the constant growing rate when G = 1 equal to 0.0026, N [cells/m²] is the base algae population density where N₀ is considered 1. The environmental index is determined by the moisture content index, g_W, the temperature index, g_T, and the solar radiation index, g_S, visualized in Figure 5.

Results

Wind-driven rain, wetting pattern

Figure 6 shows the in-plane average wind velocity for both the horizontal and vertical center plane over an annual period in Brussels. Figure 6(a) shows a typical airflow pattern around a building, consistent with the 2021 ASHRAE Handbook. An upwind vortex forms at the front of the building, while a larger recirculation zone appears at the rear. Panel (b) showcases the mean wind flow in the horizontal plane at an elevation of 5 m, where both the upwind vortex and two recirculation zones situated in the rear are visible. The predominant wind direction in Brussels is from the southwest, with an average speed of approximately 4 m/s. Figure 6(a) and (b) show that the south and west façades experience the highest average wind speeds, while those facing north and east experience significantly lower speeds. Consequently, the latter façades are subjected to reduced levels of wind-driven rain. Furthermore, on an annual basis, they undergo less convective drying.

In Figure 7, an overview of the distribution of the annual wind-driven rain for the different facades, at four distinct orientations, is shown. When focusing on the wetting behavior of the facades, it is clear that the south side has the highest WDR load with a local maximum of 780 mm/year. The lowest WDR load is found on the east side where the WDR remains below 100 mm/year on the whole surface. On each façade, it is visible that the top corners and the downwind edge, with a southwest dominant wind, are exposed to the highest amount of rainwater and the lowest rain load is found at the bottom corner. In comparison with traditional implementations of the wind-driven rain in hygrothermal simulations, three reference semi-empirical WDR loads were calculated according to ISO 15927-3 (EN 15927, 2009) and visualized with a dashed line. The lowest reference is based on the default values from Delphin (C_r C_t O W = 0.2). It uses a factor for terrain roughness C_r of 1.007, a factor for topography C_t of 1, an obstacle factor O of 0.8, a wall factor W of 0.4 and a correction factor RE of 0.7. The second reference has the same assumption as the first but the RE is set to 1 (C_r C_t O W = 0.3). The highest values for C_r C_t O W according to ISO 15927-3 yield a total of 0.6, which represents the most critical situation in a terrain category I without any obstacles and a wall factor of 0.5. Even though these three references together cover the range of WDR loads found on the façade, the results highlight important shortcomings. First of all, in practice typically a single WDR exposure is considered, omitting the spatial variability of the façade. Secondly, the default settings will often entail a significant underestimation of realistic WDR loads for large parts of the façade. Thirdly, even when extreme values are selected in the semi-empirical approach, peak intensities at the top of the façade are underestimated by up to 40%.

Convective drying pattern

The calculation for the convective drying is done with the local wind velocity adjacent to the wall, yet no clear distance to the wall, (v_loc) is prescribed in literature or standards.

Figures 8 and 9 illustrate the impact of the distance considered for local wind speed on the South façade. In Figure 8, distances from 1 mm up to 250 mm are considered within the boundary layer of the surface, whereas distances of 300–1000 mm are considered outside the boundary layer. All local wind speeds have a spatial distribution calculated by means of CFD, except for the “Field” distance. The field distance represents the most common approach in HAM modeling, where local wind speed is assumed constant across the entire façade and where the value is equal to the measured velocity by the climate station. For this purpose, the wind speed from the MRY at a height of 10 m is applied. In general in free field, a greater distance is correlated with higher wind speeds, which in turn promote increased moisture and heat transfer and drying. The impact is also visible for the different performance risks. The performance models in Figure 8(a) can be classified into two distinct groups. The first category, which includes the Avrami and Miyauchi indices, is characterized as a dose-response model. In contrast, the second category, including salt and frost models, determines the number of cycles based on a threshold. As the distance of the local wind speed from the surface increases, the index shows a reduction in the first type, whereas the threshold-based models have an increase in cycles. The latter observation may be explained by larger fluctuations around the threshold due to increased drying from higher wind speeds, for example, in the field. In the case of frost damage, higher wind speed increase the heat exchange, in turn decreasing the temperature in the brick, increasing the ice mass density. The sensitivity analysis shows that the largest variation occurs between 1 and 250 mm, where the strong boundary-layer influence results in unstable values for the different degradation predictions. Once beyond 300 mm, the spread between 300 and 500 mm, and in some cases even up to 1000 mm, is relatively small, meaning the results are only weakly sensitive to the exact choice in this range.

In Figure 8(b), the impact of reference wind speed to calculate CHTC and CVTC is visualized for the Avrami index at various heights on the south façade, located 2.5 m from the edge. At the top of the surface, the greatest damage is observed when wind speeds from within the boundary layer are considered. Beyond 300 mm from the surface, a similar damage index is observed for greater distances. A more pronounced difference between the distance for v_loc is visible at the lower part of the façade, clearly showing that the assumption of using field wind speed for the entire façade overestimates drying at lower façade heights. This overestimation leads to an underestimation of algae growth at these heights, which, in reality, would be even more pronounced due to splash back and rising damp. The latter is visualized spatially in Figure 9. The degradation distribution on the south façade is examined for three different distances for wind speed reference: 300 mm, 1000 mm, and the field distance. The degradation patterns reveal that the distribution under field conditions, the most prevalent approach in current practice, resembles the wind-driven rain pattern. At shorter distances, with the closest being 300 mm, the degradation pattern does not fully align with the rain pattern but instead reflects a combination of both rain and drying patterns. With regard to the growth of algae, as represented by the Avrami index, this results in an increase in algae on the downside wind side (the left side of the façade). This is due to the elevated wind-driven rain load and limited drying on this side. The distribution of ice volume, at the bottom of the figure, demonstrates the opposite effect, with a reduction on the left side of the façade. This phenomenon can be attributed to the correlation between a longer distance from the wall and higher wind speeds, which in turn facilitates a more rapid and extensive heat exchange between the wall and its surroundings. Consequently, the field distance experiences accelerated and enhanced cooling, leading to an increase in ice content.

Both analyses in Figure 8 support the choice of 300 mm as a robust reference, it is consistent with ASHRAE guidance, yields nearly the same outcomes as larger distances, and avoids the uniform over-drying tendency of the façade associated with a field wind speed approach.

In the subsequent analyses a distance of 300mm was used to determine v_loc in accordance with ASHRAE guidelines. Figure 10 illustrates the spatial distribution of the CHTC across the various façades of the cube. The obtained pattern serves as an indicator for the CHTC, the CVTC, and consequently the drying of the four façades. The highest average CHTC values, consistent with the distribution of WDR, are observed on the south and west façades, with maximum values exceeding 20 W/m²K. This indicates that regions with elevated wind-driven rain are not necessarily the most vulnerable to deteriorate due to the accelerated drying observed in these areas. The highest CHTC values are observed on the south and west façades, situated near the top and the opposite downwind edge. In contrast, the north and east façades exhibit lower CHTC values, with a maximum of 17 W/m²K observed near the edges of the façade. Higher values on these façades are concentrated at the center and the upwind edge.

Frost degradation pattern

Figure 11 presents the spatial distribution of the frost damage indicator (Ω value) at different depths from the exterior surface, ranging from 1 to 10 mm. At shallow depths (1–3 mm), high Ω values (>0.5) dominate the upper façade regions, indicating that frost damage is most critical in the near-surface zone. With increasing depth, the intensity of the damage indicator decreases and the patterns smooth out, reflecting the damped influence of surface boundary conditions on the moisture content and temperature fluctuations. By 5–6 mm, the critical zones are still present but significantly attenuated. At 8 mm depth the Ω values are largely homogenized, while at 10 mm the indicator vanishes entirely, suggesting negligible frost risk from this depth onward. Based on this, a depth of 3 mm is used in further analyses, as it represents the most critical for frost degradation.

In Figure 12, the frost risk assessment is visualized at a plane on 3 mm depth from the surface, with the FTC calculations shown in the top row and the Ω value calculations in the bottom row. It can be observed that both approaches yield comparable results in terms of pattern. A clear distinct distribution of degradation across all façades can be seen, where the different patterns of both drying potential and driven rain can be recognized within the FTC and Ω patterns. On each façade, places with high rainfall also show increased risk of damage (up to 12 cycles), whereas places with minimal WDR entail little frost damage. However, the critical WDR zones do not coincide with the critical frost damage. Due to the dominant southwest wind direction during rainfall, the highest damage occurs on the west and south façade. On the north façade a low freeze-thaw risk is observed for the bottom to middle part of the façade, as could be expected based on the low WDR loads. However, at the top side rather high FTC values are found: even though the WDR are similar to the bottom of the south façade, the frost degradation on the north is higher due to the lower temperature and overall lower drying potential. This highlights the impact of drying, and in turn, the complexity of selecting correct parameters in simplified simulations. The same effect of the drying is also evident on the south and west façade, where the highest amounts of rainfall do not entail the highest frost damage because of higher drying rates. The most critical zone for frost damage on the cubic building is located on the west façade at the edges with the center point of the critical zone at a height of 8 m in the Ω approach and at 7.5 m for the FTC. This critical zone was determined based on the frost at a depth of 3 mm which showed to be most critical over the first 10 mm depth in this case for a 450 mm wall.

A comparison can be made between the results of the present frost-risk simulations and those reported by Mandinec et al. (2025). Their study focused on brick façade deterioration, specifically spalled and replaced bricks, using drone imagery. They observed that damage concentrated at façade edges and in mid-to-upper zones, particularly on south-facing façades exposed to wind-driven rain. The present simulation results similarly identify critical zones at the edges and above the middle of façades. Both approaches show that deterioration is not dictated by rainfall intensity alone but by the interaction of exposure, drying capacity and local boundary conditions.

Algae growth pattern

Figure 13 illustrates the spatial distribution of the Avrami index for the four façades on top (a) and the Miyauchi index below (b). The degree of algae growth on a given façade is partly determined by the amount of precipitation. The Avrami index, which considers temperature and humidity as a proxy, indicates that the highest growth is observed on the south façade, followed by the west, north, and east façades. The Miyauchi index, which also accounts for radiation, indicates that the west façade is the most critical, closely followed by the south façade. The Miyauchi model indicates higher growth rates on the north and east façades relative to the Avrami model, which is likely due to the reduced radiation on the northern façade. The Avrami model demonstrates a clear interplay between wetting and drying, delineating critical zones. On the southern and western façades, higher algal growth is observed near the upper and downwind edges, with a value of 0.4. However, this is not the sole critical area; another key area is identified at a height of approximately 7.5 m. This area is characterized by sufficient wetting combined with limited drying, which promotes algae growth.

Salt crystallizations pattern

Figure 14 provides a visual representation of the findings from the salt study conducted on the façades. The upper row (a) shows the number of cycles at a depth of 5 mm from the exterior surface for a halite salt solution, whereas the lower row similarly represents the number of cycles for a thenardite-mirabilite solution (b). As explained above, the 5 mm depth was selected as the reference plane because it represents the most relevant zone for crystallization damage, in line with Janssens et al. (2025). The comparison between the patterns for the halite and thenardite-mirabilite crystallization cycles indicates comparable levels of deterioration across the four orientations, with a comparable order of magnitude for the number of cycles. The same critical orientations come to front, and the locations of the critical zones on these façades also coincide. The southern and western façades are subjected to the lowest number of cycles, with a maximum of 60. In contrast, the highest number of cycles occurs in the lower regions of the northern façade, with values above 100. It is worth noting that the observed damage patterns are inverse to those previously discussed in the context of frost and algae growth. In the case of salt degradation areas with lower, but not minimal, wind-driven rainfall experience the most salt crystallization. This is because regions exposed to higher wind-driven rain in masonry façades tend to maintain excessive moisture levels, preventing salts from undergoing dissolution due to insufficient drying periods. Conversely, areas with minimal rainfall, such as the ground edge of the buildings, are not the most critical as they lack sufficient humidity for phase changes necessary for salt crystallization.

Discussion

This study demonstrates how external coupling of CFD with hygrothermal modeling enhances the understanding of spatial wetting and drying patterns and their role in façade degradation. The work should be regarded as a methodological proof-of-concept, as several simplifications were necessary to balance feasibility and insight.

While the use of a cubic geometry facilitates a controlled research on the wind-driven rain and drying patterns, it does not fully represent the complexities of real-world environments. In practice, urban topography, building height, and surrounding obstacles significantly influence the wind field and consequently the WDR. Nonetheless, the cubic reference geometry is well-established in building physics and wind engineering, as it allows systematic evaluation of exposure mechanisms without interference from case-specific complexities.

As summarized by Vanderschelden et al. (2025), the present study applied the minimum requirements of hygrothermal modeling, with simplified input and model parameters. One-dimensional simulations, though widely applied and standardized (EN 15026, 2023), cannot reproduce the full three-dimensional complexity of moisture transport in masonry. Features such as joints, cracks, mortar heterogeneity, or localized defects may strongly influence degradation in practice. While 1D models provide useful insights into relative differences between exposure scenarios, they inevitably introduce uncertainty in absolute predictions and may underestimate local effects. The simulations also assumed deterministic material properties, whereas historical variability in brick production can lead to a wide range of hygrothermal responses. Incorporating stochastic parameters would therefore allow a more representative sensitivity analysis and strengthen predictive values. Climate input was represented by a MRY for Brussels, which provides a consistent basis for relative assessment but does not fully capture the absolute severity of long-term degradation. Seasonal and inter-annual variations in rainfall and drying may accelerate or slow deterioration compared to the MRY baseline. Moreover, additional moisture sources such as runoff, splash-off, and rising damp were not included, although they could further increase risks in practice, particularly in the lower façade regions where drying is weakest. Addressing these aspects through multi-dimensional simulations, stochastic material properties, long-term climate data, and additional boundary conditions would provide a more comprehensive picture, but at the expense of substantially higher computational demand and storage.

The methodology has not yet been validated through systematic field observations, and the results should therefore be interpreted as relative risk distributions rather than absolute predictions of façade performance. As a partial check, the simulated frost-risk patterns were compared with degradation maps reported by Mandinec et al. (2025), which revealed similar critical zones at façade edges and in mid-to-upper regions. This agreement suggests that the approach can capture relevant degradation mechanisms, but systematic field validation remains essential. Ongoing work within our group focuses on detailed mapping of façade deterioration to provide the empirical datasets required for more rigorous comparison between simulations and observed degradation.

Conclusions

In order to study the impact of the spatial distribution of wind and wind-driven rain on the hygrothermal response and degradation patterns of facades, an externally coupled approach of CFD and HAM simulations has been developed. The wind and rain flow around a cubic low-rise building is determined by utilizing steady Reynolds-Averaged Navier-Stokes (RANS) equations and Eulerian multiphase CFD simulations. Based on the resulting flow field, the WDR, CHTC, and CVTC are calculated and employed as boundary conditions for HAM modeling. The hygrothermal behavior was modeled for a solid 450 mm masonry construction in the four orientations/sides of a cubic building in a free field. Each façade was subdivided into 1600 cells, and a one-dimensional hygrothermal simulation was conducted for each cell over a 1-year period using Delphin 6.1. The risk assessment focuses on surface degradation related to frost cycles, salt crystallizations, and algae growth. The patterns of individual performance risks are used to study the relative impact of wetting and drying patterns.

The results demonstrate the substantial influence of the spatial distribution of wetting and drying on the risk of frost, algae, and salt degradation, as well as their spatial patterns on building facades. For frost degradation, the west façade is the most susceptible, with a maximum FTC of 14 and an Ω value of 0.7. The critical frost zone is not situated in the area with the highest WDR, rather, it is located at a height of 7.5 m, where drying is more limited. A comparable pattern is seen in the case of algae growth, with the south façade exhibiting the highest overall growth. However, the maximum growth is once again concentrated at a height of 7.5 m. In contrast, the pattern observed in the case of salt crystallization is notably different. Here, the critical façade is located on the north side. The highest degradation is not observed in the upper half of the façade but instead in the lower section, with a central point between 1 and 2 m.

The results of this study indicate that typical hygrothermal analysis (HAM) studies often underestimate the exposure to precipitation and overlook the importance of variability in drying rates. Furthermore, the use of field wind speeds as opposed to speeds adjacent to the wall in calculating transfer coefficients results in a significant overestimation of drying. This overestimation leads to higher calculated cycles (such as FTC), while dose-response models such as the algae growth model tend to be underestimated. When lower wind-driven rain loads and higher drying rates are assumed, moisture-related risks are underestimated in the conventional approach to hygrothermal simulations.

Footnotes

ORCID iDs

Bruno Vanderschelden

Ayta çKubilay

Nathan Van Den Bossche

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research was supported through the Brain 2.0 initiative from Belspo Project no. B2/212/P2/CLIMPACTH.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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