Overview of three state-of-the-art wind-driven rain assessment models and comparison based on model theory

Transcription

1 Accepted for publication in Building and Environment Overview of tree state-of-te-art wind-driven rain assessment models and comparison based on model teory B. Blocken (a), J. Carmeliet (b,c) (a) Building Pysics and Systems, Eindoven University of Tecnology, P.O. box 513, 5600 MB Eindoven, Te Neterlands (b) Cair of Building Pysics, Swiss Federal Institute of Tecnology ETHZ, ETH-Hönggerberg, CH-8093 Züric, Switzerland (c) Laboratory for Building Tecnologies, Swiss Federal Laboratories for Materials Testing and esearc, Empa, Überlandstrasse 129, CH-8600 Dübendorf, Switzerland Abstract In te past, different calculation models for wind-driven rain (WD) ave been developed and progressively improved. Today, te models tat are most advanced and most frequently used are te semi-empirical model in te ISO Standard for WD (ISO), te semi-empirical model by Straube and Burnett (SB) and te CFD model by Coi, extended by Blocken and Carmeliet. Eac of tese models is quite different, and to te knowledge of te autors, no comparison of tese models as yet been performed. Tis paper first presents a detailed overview of te tree models, including new insigts in similarities between tese models and relations wit recent researc results. Based on tis overview, it provides a comparison focused on te extent to wic te different influencing parameters of WD are implemented in te models. It sows tat te implementation of te influencing parameters is most pronounced for te CFD model, less pronounced for te ISO model and least pronounced for te SB model. It is also sown tat in te two semi-empirical models, te values of te wall factor W (for ISO) and te rain admittance function AF (for SB), wic ave te same definition in bot models, can differ more tan a factor 2 from eac oter. Te two models can terefore provide very different results. Tey also require differently defined reference wind speed values as input. Te overview and te comparison in tis paper provide te basis for future comparison studies and future improvements of te semi-empirical models. Keywords: Driving rain; building facade; Computational Fluid Dynamics (CFD); eat, air, moisture transfer (HAM); ygrotermal modelling 1. Introduction Wind-driven rain (WD), also referred to as driving rain, is one of te most important moisture sources for building facades. It is an essential boundary condition for te analysis of te ygrotermal beaviour and durability of istorical and contemporary building facade components [1-10]. WD is governed by a wide range of parameters: building geometry, position on te building facade, environment topograpy, wind speed, wind direction, orizontal rainfall intensity and raindrop-size distribution. WD is very complex and caracterised by a ig spatial and temporal variability. Terefore, assessing te intensity of WD impinging on building facades is a difficult task. Given its complexity, it is not surprising tat, in spite of many decades of intensive researc work, WD is still an active researc topic and muc work remains to be done. Tree main categories of metods exist for assessing te intensity of WD on building facades: measurements, semi-empirical models and numerical simulation based on Computational Fluid Dynamics (CFD). Te term semi-empirical refers to models wit a teoretical basis and wit coefficients tat are at least partly determined from measurements. A general review of tese tree categories of metods can be found in [4]. Measurements are time-consuming, expensive and often impractical. ecent researc as revealed tat WD measurements are also very prone to error [11-13]. In addition, measurements made on te facades of a particular building at a particular site, ave limited applicability to oter facades of oter buildings at oter sites. Tis awareness as driven researcers to develop calculation models, wic ave been progressively improved trougout te years. Today, te models tat are most advanced and most frequently used are te semi-empirical model in te ISO Standard for WD assessment [14] (ISO model), te semi-empirical model by Straube [15] and Straube and Burnett [16] (SB model) and te CFD model by Coi [17-19], extended into te Corresponding autor: Bert Blocken, Building Pysics and Systems, Eindoven University of Tecnology, P.O.Box 513, 5600 MB Eindoven, te Neterlands. Tel.: +31 (0) , Fax +31 (0) address: b.j.e.blocken@tue.nl 1

2 time domain by Blocken and Carmeliet [20,21]. Eac of tese models is quite different and, to te knowledge of te autors, no comparison of tese models as yet been performed. Tis paper provides a detailed overview of te tree WD models and a comparison of tese models by focusing on teir underlying teory and concepts, and te resulting capabilities and limitations. It specifically aims at providing furter insigts into te model teory, wic, for te semi-empirical models, extend considerably beyond te information available in te original documents. New insigts in te similarities between models are provided, and several model features are discussed based on recent researc results. Te overview also supports te comparison study. Te overview and comparison study in tis paper are intended to support future comparison studies and future improvements of te two semi-empirical models. Te paper contains seven sections. In section 2, te common background of te two semi-empirical models is outlined. In sections 3 to 5, eac model is presented and discussed separately. Section 6 compares te models in terms of implementation of te influencing parameters of WD. Te models are also compared in terms of calculation cost and accuracy. Finally, section 7 (summary and conclusions) concludes te paper. 2. Background of te two semi-empirical models Te information presented in tis section is for a large part similar to tat in [4], but is repeated ere because it is essential for te remainder of tis paper. Bot te ISO and te SB model are based on te WD relationsip, wic itself is based on a simple teoretical formula. If we assume tat all raindrops are of te same size and tat te wind flow is uniform (no increase of wind speed wit eigt), steady and orizontal, te intensity of WD passing troug an imaginary vertical surface can be expressed as [22-24]: wdr U = (1) V t were wdr is te WD intensity troug te imaginary vertical surface, is te unobstructed orizontal rainfall intensity (i.e. te intensity of rainfall falling troug a orizontal plane, as measured by a standard rain gauge wit a orizontal orifice), U is te wind speed and V t is te raindrop terminal velocity of fall. In tis equation, te wind direction is assumed to be perpendicular to te vertical surface at all times. It assumes no deflection of wind or raindrops by te vertical surface and ence is a measure for te free or free-field WD. Hoppestad [22] proposed te following formula based on Eq. (1): = κ U (2) wdr He called tis equation te WD relationsip and te factor κ te WD coefficient. On-site measured values for κ wit free-standing WD gauges at different locations in Norway ranged from to Later, Lacy [24,25] refined Eqs. (1-2) by employing te empirical relationsips tat express te median raindrop size as a function of [26] and te terminal velocity of fall of suc raindrops [27], yielding: = U (3) 0.88 wdr were (s/m) is te WD coefficient tat results from te adopted empirical relationsips. As te empirical expression for median raindrop size represents an average of different measurements, also te value of te WD coefficient in Eq. (3) sould be considered an average value. Te exponent 0.88 as often been omitted in WD researc. Eq. (2) and (3) and te associated WD coefficients were derived and measured for free-field conditions. Te WD intensity in free-field conditions can be very different from te WD intensity on a building facade, because of te strongly disturbed wind-flow pattern around te building. To take tis effect into account, an adapted WD coefficient α was introduced in te WD relationsip, as well as a factor cosθ: wdr 0.88 = α U cosθ (4) Tis is te WD relationsip for WD on buildings. θ is te angle in a orizontal plane between te wind direction and te normal to te facade, also called te wind incidence angle. U is a wind speed, wic as often not been clearly defined in early WD researc. It can be assumed but not confirmed tat it is te reference wind speed measured at te standard meteorological eigt of 10 m. Note tat adding cosθ implies tat only te component of te reference wind velocity vector normal to te facade is considered. Tis is called te cosine projection metod [28]. Many researcers measuring WD on buildings found a very large variation of α wit te size of te building and across te building facade: values from 0.02 s/m (9% of 0.222) [24, 29] to 0.26 s/m 2

3 (120% of 0.222) [30] ave been reported. For te present study, for all tree models, te WD coefficient α will be unambiguously defined as in Eq. (4). 3. Te semi-empirical model in te ISO Standard Before describing and discussing te features of tis model, te development istory of te ISO Standard for WD assessment is briefly presented. Te reason is te need for clarification amongst te many different standard draft versions tat ave been developed Development istory of wind-driven rain standards Te ISO Standard of 2009, wic is te subject of tis paper, is te result of a sequence of standards and draft standards, starting from te BSI (Britis Standards Institution) Draft for Development 93 [31], wic was superseded in 1992 by te improved BS 8104 Code of practice for assessing exposure of walls to wind-driven rain [32]. Tis code was based on a long series of WD measurements on buildings at a large number of locations witin te UK. Furter expansion, based on work by Sanders [1], led to te European Standard Draft PrEN in 1997 [33]. Tis Standard Draft is closely related to BS 8104, but it replaced te traditional WD index/wd map approac to determine WD exposure [4] by te WD relationsip given in Eq. 4. Te main reason for tis was tat extensive WD index maps witin Europe only existed for te UK. Tis Standard Draft provided a procedure to analyse ourly weater data (wind speed, wind direction, orizontal rainfall intensity) in order to obtain an estimate of te WD amount impinging on a building facade or wall of any given orientation ( metod1 ). Te 1997 version of te Draft was extended in 2006 to include a different metod ( metod2 ) for tose countries in wic simultaneous ourly wind and rain measurement data were not available [34]. Metod2 is not based on te WD relationsip. Instead it uses 12-ourly averaged wind data and a qualitative recording of te presence and intensity of rain (i.e. te present weater code for rain) to calculate te spell lengt during wic masonry is moistened, aving a mean return period of 10 years. Note tat metod2 did not occur in earlier versions of te Standard. It is clearly more limited, less quantitative and terefore inferior to te metod based on te WD relationsip, but it was needed to guarantee applicability of te European Standard Draft in all European countries. Tis version of te Standard Draft as been converted into ISO Standard in 2009: Hygrotermal performance of buildings Calculation and presentation of climatic data Part 3: Calculation of a driving rain index for vertical surfaces from ourly wind and rain data. [14]. Only metod1 of tis Standard will be addressed in tis paper Model description Metod1 in te ISO Standard (ISO) provides a procedure to calculate two quantities [14]: (1) te annual average index (as a measure for average WD exposure) and (2) te spell index (as a measure for maximum or peak WD exposure). Te procedure consists of two steps. First, te airfield index is calculated, wic refers to WD in free-field conditions, i.e. witout buildings present, and related to a smoot grass-covered terrain (airfield). Next, tis airfield index is converted to a wall index by correction factors to take into account te differences between free-field WD (as in Eq. 2) and WD impinging on te building. Te correction factors are te rougness coefficient, te topograpy coefficient, te obstruction factor and te wall factor. Note tat te word index as been inerited from earlier WD researc; it is used in te ISO Standard to refer to WD amounts, expressed in L/m² or mm Airfield indices Te airfield ourly index is defined as te quantity of driving rain tat would occur on a vertical wall of given orientation per square meter of wall during 1 at a eigt at 10 m above ground level in te middle of an airfield, at te geograpical location of te wall [14]. Te airfield annual index is te airfield index for a given wall orientation totalled over one year. Te calculation is performed wit at least 10 (and preferably 20 or 30) years of ourly values of wind speed, wind direction and orizontal rainfall intensity from te nearest meteorological station: I A U10.. cosθ = (5) 9 N were te airfield annual index I A is expressed in L/m²a (a = annum), U 10 is te reference wind speed (unobstructed streamwise wind speed at 10 m eigt) and N is te number of years of available data. Te summation is taken over all ours wen cosθ is positive, i.e. te ours wen te wall is windward. Te airfield spell index is defined as te airfield index for a given wall orientation totalled over te worst spell likely to occur in any tree-year period. A spell is defined as a period during wic WD occurs, and tat is preceded and followed by at least 96 ours wit airfield ourly index ((2/9)U 10 8/9 cosθ) smaller tan or equal 3

4 to zero. Using at least 10 (and preferably 20 or 30) years of ourly values of wind speed, wind direction and orizontal rainfall intensity, separate airfield indices are calculated for te given wall orientation and for eac spell of WD: IS ' = U10.. cosθ 9 (6) were I S is expressed in L/m². Te summation is again taken over all ours in te spell wen cosθ is positive. Te airfield spell index I S is ten obtained as te maximum value of I S likely to occur once every tree years Wall indices and correction factors Te wall annual index (I WA ) and te wall spell index (I WS ) are calculated by multiplying te airfield indices wit four correction factors: te rougness coefficient C, te topograpy coefficient C T, te obstruction factor O and te wall factor W: I WA = I C C O W ; I = I C C O W (7) A T WS S T Te rougness coefficient C takes into account te cange of mean wind speed at te site due to te eigt above te ground and te upstream rougness of te terrain. It is given by: z C (z) = K ln for z z min z (8) 0 C (z) = C (z ) for z < z (9) min min were z is te eigt above ground, K te terrain factor, z 0 te aerodynamic rougness lengt and z min a minimum eigt. Values of K, z 0 and z min as a function of te terrain category are given in Table 1. It is noted in te Standard Draft tat if a cange of upstream rougness occurs witin 1 km, te smootest upstream terrain category must be used. Note tat te smootest terrain category provides te largest C value. Te topograpy coefficient C T takes into account te increase of mean wind speed over isolated ills and escarpments. It is applied wen te wind approaces te slope of te ill or te escarpment and wen te building is located at more tan alf way up te slope of a ill or witin 1.5 times te eigt of te cliff from te base of a cliff. It ranges between 1.0 for upstream slopes wit less tan 5% inclination to a peak value of 1.6 for buildings situated at te crest of steep cliffs or escarpments. Te obstruction factor O takes into account te selter of te wall by te nearest obstacle, wic is at least as ig as te wall, along te line of sigt from te wall. Te line of sigt is defined as te orizontal view away from te wall, over a sector spanning about 25 eiter side of te normal to te wall. Te obstruction factor is given in Table 2. It is indicated in te Standard Draft tat te obstruction factor may vary significantly at different points along a long wall, and tat, if te layout of te built environment is likely to funnel wind towards te wall, te obstruction factor sould be taken equal to one, irrespective of te presence of obstructions. Finally, te wall factor W is defined as te ratio of te quantity of water itting a wall to te quantity passing troug an equivalent unobstructed space, i.e. te ratio of WD on te building to free-field WD. Note tat tis is not te airfield free WD, but te free-field WD at te building location, after taking into account te correction factors C, C T and O. Te wall factor is a means to account for te type of te wall (eigt, roof overang) and te variation of WD across its surface. Te wall factors made available in te ISO Standard are sown in Fig Discussion Te ISO Standard itself does not explicitly use te terms WD relationsip and WD coefficient. However, combining Eqs. (5-6) and (7), and comparing tem wit Eq. (4), sows tat te ISO model is actually a form of te WD relationsip in wic te ratio 2/9 corresponds to Lacy s free-field WD coefficient 0.222, in wic te exponent 8/9 corresponds to Lacy s exponent 0.88, and in wic te WD coefficient is given by: α 2 = C CT O W (10) 9 Inserting into Eq. (10) into Eq. (4) yields: 4

5 wdr = C C T O W U10 cosθ (11) 9 Altoug te Standard strictly only guides te calculation of te average annual amount of WD and te amount of WD in te worst likely spell in a tree-year period, Eq. (11) could teoretically also be used to determine WD intensities or amounts for any spell witin a year. Note tat tis is done implicitly witin te ISO Standard procedure to determine te annual and spell indices. Te ISO model as been used in tis way in building pysics researc to provide boundary conditions for HAM (eat-air-moisture) analysis of building components. Te ISO Standard correctly provides several warnings concerning its applicability and reliability [14], wic are mentioned ere: (1) Te metod primarily applies to climates similar to te UK; (2) In all cases, especially in mountainous areas, direct WD measurements sould be made werever possible; (3) ain penetration around edges of doors and windows or similar cracks in building facades depends on sorter periods of eavy rain and strong winds; (4) Te ISO model is not applicable to mountainous areas wit seer cliffs or deep gorges; (5) It is not applicable in areas were more tan 25% of te annual rainfall comes from severe convective storms, i.e. eavy precipitation in te form of sowers or tunderstorms generally lasting less tan one our; (6) It is also not applicable in areas and for periods wen a significant proportion of precipitation is made up of snow or ail; (7) As to te proximity of meteorological stations, te ISO Standard notes tat it will be necessary to decide ow representative te values calculated at a meteorological station are for a building at a distant location. Note tat te tird and fift warning correspond to te findings by Blocken and Carmeliet [21,35], wo indicated tat using ourly data, especially for convective rains, can lead to (very) large underestimation errors in te calculated WD amounts, due to neglecting te sub-ourly co-occurrence of wind and rain. Also note tat te Standard does not specify te criteria to determine weter a climate is similar to tat of te UK. It also does not provide a quantitative measure for te significant proportion of snow or ail in precipitation. Comparing Eq. (1) wit Eqs. (2) and (3) sows tat te free-field WD coefficient is teoretically and approximately equal to te inverse of te raindrop terminal velocity of fall. Eq. (3) terefore implies tat an average spell could be considered as composed of all similar-sized drops wit approximately V t = (1/0.222) m/s = 4.5 m/s, corresponding to a raindrop diameter of 1.2 mm. Tis is a realistic value for spells of ligt to moderate intensity ( 1 mm/) [36]. Tis implies tat for oter spells (e.g., < 0.5 mm/ and > 5 mm/), tis freefield WD coefficient value migt need adjustment, wic is not taken into account in te ISO model. As opposed to many early publications on te WD relationsip, te ISO Standard clearly specifies te wind speed measurement eigt (10 m) and te reference conditions (airfield). To determine te wall factor, te ISO Standard only provides te information in Fig. 1. Note tat it contains mainly information for low-rise buildings. Tis is most likely due to te fact tat te Standard Draft was written wit masonry walls in mind [4], and tat it was developed primarily from te UK perspective, and later from te European perspective. Te ISO Standard assumes tat te wall factors, and terefore te WD exposure, are te same across te widt of te facade, altoug many WD measurements in te past ave sown tat te WD intensity increases from te middle of te facade to te sides [4]. Te Standard provides no comment on tis assumption. Wile te rougness coefficient C is related to te neutral logaritmic mean wind speed profile in te atmosperic boundary layer, te values of te obstruction factor seem to ave been cosen quite arbitrarily. ecent CFD simulations ave sown tat upstream obstructions can also increase, rater tan only decrease, WD exposure [37]. However, we also note tat te information in te ISO Standard as been obtained from onsite measurements at te facades of different buildings, tat suc measurements are difficult and timeconsuming, and tat te available information as been converted into a quite compreensive WD calculation model tat takes into account many of te influencing parameters of WD. In fact, te ISO model is te most compreensive semi-empirical model known to te autors. In addition, it sould be noted tat at te time of te introduction of te correction factors, te Britis Standards Institution [32] explicitly recognized tat using tese four empirical factors constituted an important simplification of reality, but tat tis was necessary to avoid complicating te standard too muc. 4. Te semi-empirical model by Straube and Burnett 4.1. Model description Te model by Straube [15] and Straube and Burnett [16] also starts from Eq. (1), in wic tey introduce te Driving ain Function DF as te inverse of te raindrop terminal velocity of fall: wdr 1 = U = DF U (12) V t 5

6 Note tat Straube and Burnett omit te orizontal rainfall intensity exponent 0.88 (see Eq. 3). Te DF is equal to te free-field WD coefficient as defined in Eq. (2). Straube and Burnett recommend calculating it from te equation by Dingle and Lee [38] for te terminal velocity: V t ( d) d d² d³ 9.20 m/s = (13) were d is te raindrop diameter. Concerning te coice of d, tey suggest te median diameter from te raindrop spectrum by Best [36]: n d p F(d) 1 exp =, a = A (14) a were F(d) is te fraction of liquid water in te air wit raindrops of diameter less tan d, and A, n, p are parameters, te experimentally determined averages of wic are 1.30, 2.25 and 0.232, respectively. From Eq. (14), te following equation for te median raindrop diameter can be obtained: d = (15) Eqs. (12-15) indicate tat te DF or free-field WD coefficient suggested by Straube and Burnett is a function of raindrop terminal velocity of fall, raindrop-size distribution and orizontal rainfall intensity. Tis is based on te work by Coi [39], wo demonstrated analytically tat te DF is a function of bot te raindrop-size distribution and te raindrop terminal velocity of fall, bot of wic are linked to. Straube and Burnett found tat te DF ranges from 0.20 to 0.25 s/m for average conditions wic corresponds to Lacy s average value of s/m (see Eq. 3) but tat it varies considerably for different rainfall intensities and rain storm types, from more tan 0.5 s/m for drizzle to 0.1 s/m for intense cloudbursts. Te model by Straube and Burnett for WD on building facades is given by: wdr = DF AF. U(z) cosθ (16) were AF, te ain Admittance Factor, is introduced to convert te free-field WD intensity to te WD intensity on te building facade. Based on teir own WD measurements (bot free-field WD and WD on te walls of a test building) and on a literature review, Straube and Burnett provided values of te AF in grapical form for tree types of building geometries (Fig. 2). Tey claimed tat tese contours and values are relatively building-scale independent [16]. Te increase of WD intensity wit eigt is partly taken into account by te presence of te power law function U(z) in Eq. (16), and partly by te AF values temselves Discussion Te WD coefficient α as been defined as in Eq. (4). Comparing wit Eq. (16) sows tat tis coefficient in te SB model is given by: α U(z) 0.12 = DF. AF. (17) U 10 Taking into account te power-law relationsip U(z) = U 10 (z/10) β yields: α β z 0.12 = DF. AF. (18) 10 were β is te power-law exponent of te mean wind speed profile. Straube [15] and Straube and Burnett [16] explicitly suggested te use of teir model in combination wit ourly or 15-minute weater data to provide te WD boundary condition in HAM models. However, tey also provided some specific comments on te reliability of teir model. Tey mentioned tat te AF values were obtained from averaging measurements over several rain events or even years, and tat te real AF during a spell is likely to sow a significant variability wit wind speed, orizontal rainfall intensity and raindrop-size distribution. Tey also indicate tat te literature contains only a few references to simultaneous measurements of free-field WD and WD on buildings. As tis is required to determine te AF, it justifies wy te SB model only provides AF patterns for tree types of buildings. Note owever tat teir statement on building- 6

7 scale independence of te AF, given in [16], suggests applicability of tese patterns for a wider range of building facade configurations. No specific information on te function U(z) is provided, apart from its powerlaw distribution. Finally, note tat, in different publications on te SB model [15,16,40], sligtly different names are used for te DF and AF. Te DF is called driving rain factor or driving rain function, and te AF is called rain admittance factor or rain admittance function. 5. CFD model 5.1. Background Starting from 1974, different efforts were made to gain increased insigt in te complex interaction between wind, rain and buildings. Sandberg [41] calculated te movements of raindrops around a building based on a flow pattern obtained by wind tunnel modelling. Similar calculations were performed by oter autors [42-45]. Souster [46] studied raindrop trajectories based on computed flow patterns around 2D buildings, introducing Computational Fluid Dynamics (CFD) in te area. Te break-troug for numerical WD researc was te pioneering work of Coi in te first alf of te 90ies Model description Te numerical model developed by Coi [17-19] consists of four steps. Tis model was extended in te time domain by Blocken and Carmeliet [20,21], adding a fift step. As opposed to te two semi-empirical models outlined in te previous sections, tis numerical model as been quite extensively described in te literature. Terefore, only te salient features of te model are described. Te model is based on te definition of two quantities, wic ave sometimes been given different names by different autors. Here, te names specific catc ratio and catc ratio are used. Te specific catc ratio η d is related to te raindrop diameter d, and te catc ratio η is related to te entire spectrum of raindrop diameters: wdr (d) η d (d) = ; (d) wdr η = (19) were wdr (d) and (d) are te specific WD intensity on te building and te specific unobstructed orizontal rainfall intensity for raindrops wit diameter d. wdr and respectively refer to te same quantities but integrated over all raindrop diameters. Te five steps of te model are: (1) Te wind-flow pattern around te building is calculated using CFD (steady ANS, often combined wit a version of te k-ε turbulence model). (2) aindrop trajectories are obtained by injecting raindrops of different sizes in te calculated wind-flow pattern and by solving teir equations of motion (Lagrangian particle tracking). (3) Te specific catc ratio (η d ) is calculated based on te raindrop trajectories. Te calculation is performed for a number of zones on te building facade (e.g. zone A f in Fig. 3). For eac zone, te same procedure is employed. In te steady-state wind-flow pattern tus neglecting te turbulent dispersion of raindrops raindrop trajectories of diameter d ending on te corner points of te zone form a steady stream tube (Fig. 3). Conservation of mass for te raindrops in te stream tube allows η d to be expressed in terms of areas: (d) η (d) = d A (d) wdr = (20) (d) A f were A f is te area of te zone on te building facade were η d is to be determined and A (d) is te area of te orizontal plane bounded by te injection positions of te raindrops of diameter d ending on te corner points of A f. (4) Te catc ratio (η) is calculated from η d and from te orizontal raindrop-size distribution. Often, te size distribution by Best [36] is adopted. (5) Wen te four previous steps are executed for several combinations of reference wind speed U 10, wind direction ϕ 10 and orizontal rainfall intensity, te obtained data can be used to construct catc-ratio carts for different zones (positions) at te building facade. Eac cart provides te catc ratio η as a function of U 10 and, for a given position on te building facade and a given ϕ 10 (Fig. 4). Experimental data records of U 10, ϕ 10 and (10-minute values) can ten be combined wit tese catc-ratio carts to determine te corresponding spatial and temporal distribution of WD on te building facade. Using 10-minute data rater tan ourly data as been sown to be very important, especially for convective rain [21,35]. 7

8 Many applications of te first four steps of te CFD model were performed by Coi [17-19,47,48], Hangan [49], van Mook [12], and oters, illustrating te detailed and complex spatial distribution of WD across various types of building facades. Applications of te five steps of tis model for real rain events ave been performed by Blocken and Carmeliet [5,20,50,51], Tang and Davidson [52], Abuku et al. [53] and Briggen et al. [54]. As an illustration of a typical result of te 5-step model, Fig. 5 sows contours of te ratio of accumulated WD to accumulated orizontal rainfall at te end of a rain event, on te sout-west facade of a test building wit a sloped-roof module and a flat-roof module [51] Discussion Comparing Eq. (19) wit Eq. (4) sows tat te WD coefficient in tis model is given by: α 0.12 η = (21) U cosθ 10 were η is te catc ratio from CFD simulation(s) wit incidence angle θ, corresponding to te wind direction ϕ 10. Te first four steps of te model, listed above, allow determining te spatial distribution of WD on buildings under steady-state conditions of wind and rain, i.e. for fixed, static values of U 10, ϕ 10 and. Validation studies of te steady-state simulation tecnique were performed by e.g. Hangan [49] and van Mook [12]. Te extension of tis tecnique in te time domain (fift step) allows te numerical determination of bot te spatial and temporal distribution of WD on buildings. Validation studies for different buildings and for different rain events ave indicated tat tis extended numerical metod can provide quite accurate predictions of te WD amount and deposition pattern on building facades [5,20,50-54]. Previous studies ave clearly sown te power and potential of te CFD model, not only to gain more insigt in te interaction between wind, rain and buildings, but also to actually determine te intensity of WD on building facades. In spite of its large potential, te model also as some specific limitations, as summarized in [4]. Tese include te need for grid-sensitivity analysis and model validation, te fact tat turbulent dispersion is generally neglected and te assumption of a certain raindrop-size distribution. 6. Comparison of te models 6.1. Comparison in terms of implemented influencing parameters Seven basic parameters can be distinguised tat determine te WD intensity tat impinges at a certain position on a building facade: (1) building geometry; (2) position at te building facade; (3) environment topograpy, (4) wind speed, (5) wind direction, (6) orizontal rainfall intensity and (7) raindrop-size distribution. Environment topograpy refers to terrain rougness, irregularities suc as ills and escarpments, and surrounding buildings and trees. Wind speed refers to bot mean wind speed and turbulent fluctuations, and as suc includes turbulent dispersion. Table 3 provides a summary of te implementation of eac of tese parameters in te tree models. Tis is discussed below Building geometry and position at te facade Te ISO model only provides information for six typical building facade configurations, and te SB model only for tree, altoug tis model also points to building-scale independence of AF values. In CFD, all types of building configurations can be implemented. Concerning position at te facade; te ISO model provides wall factors W at discrete positions across te facade (Fig. 1) and te SB model provides AF contours, wit minimum and maximum values (Fig. 2). Note tat te parameters W and AF are bot defined as te ratio of te WD intensity on te facade to te free-field WD intensity, but tat tey are considerably different at some facade positions (compare Fig. 1 wit Fig. 2). For example, at te top edge and te side edges for ig-rise buildings, te differences between W and AF can attain more tan a factor 2. In CFD, WD can be determined at all positions of a facade. Te size of A f (Fig. 3), to be specified by te user, determines te spatial resolution at te facade Environment topograpy and variation of wind speed wit eigt Te ISO model provides correction factors for most features of environment topograpy, wile te SB model can only take into account terrain rougness by te exponent of te power law U(z) in Eq. (16). Terefore, te SB model is strictly only applicable for isolated buildings or at least buildings wit no direct surroundings. All features of terrain topograpy can teoretically be included in CFD: ills and valleys [55-57], oter buildings [37,58] and trees [59,60]. Te variation of wind speed wit eigt is taken into account in all tree models. In te ISO model, a correction factor (rougness coefficient) is applied for tis purpose, wic is based on te logaritmic law (Eqs. 8

9 8-9). In te SB model, te wind speed in Eq. (16) is a power law expression: U(z) = U 10 (z/10) β. In CFD, te variation of wind speed wit eigt is imposed as a boundary condition at te inlet plane, and tese inlet profiles sould be sustained in te computational domain by appropriate ground-rougness specifications [61-65]. We compare te ISO and SB approac for variation wit eigt. For eac ISO terrain category (Table 1), te corresponding power-law exponent β can be determined by fitting te power law to te log law wit parameter z 0 from Table 1, at te standard eigt of 10 m (Fig. 6). Tis yields: β = 0.125, 0.16, 0.22 and 0.3 for terrain category I, II, III and IV, respectively. Fig. 7 compares te differences between te ISO and te SB approac for te four terrain categories. Some important observations are made: (1) Apart from te lowest 4 m, te ISO and SB values are almost identical for terrain category II. (2) In te ISO model, te overall value of C decreases wit increasing terrain category, wereas tis is opposite for U/U 10 in te SB model; (3) In te ISO model, te lower part of C is constant, but smaller tan one. In te SB model, suc feature is not implemented, and te lower part of U/U 10 goes to zero, implying tat te WD intensity is zero at te bottom of te facade. Tis owever is not te case, as sown by previous studies of WD [4]. Te first two observations can be explained as follows. Te reference wind speed U 10 in te ISO model (Eqs. 5-6, 11) is te wind speed tat would occur at 10 m eigt in te middle of an airfield, at te geograpical location of te building: U 10,airfield. Fig. 7 sows tat te correction factor C is equal to one at 10 m eigt for terrain category II, wic implies tat te airfield situation corresponds to tis category. Wen te building is in reality located on a terrain wit iger rougness, te local wind speed U 10,real will be lower tan te corresponding value U 10,airfield, and vice versa wen te building is located on smooter terrain. Tis is indicated by te variation of C wit terrain category in Fig. 7. C (Eqs. 8-9) is actually a transformation model for wind speed based on te logaritmic form of te mean wind speed profile. In te SB model on te oter and, no transformation model is implemented. Instead, te implementation of U(z) as power law in Eq. (16) implies tat U 10 is a local reference wind speed, at 10 m eigt in te same terrain category as te building location. Fig. 7 indeed sows tat U/U 10 = 1 in all terrain categories at 10 m eigt. Tis means tat te SB model in its present form sould only be applied wit wind speed data corresponding to te terrain category of te building location. Alternatively, te SB model sould be extended to include a wind speed transformation model, or suc a transformation model sould be applied to te transfer/convert te meteorological data to te building site, prior to applying te SB model Wind-flow pattern around building and turbulent dispersion Te particular WD distribution on te building, due to te complex wind-flow pattern around it, is taken into account by W (ISO model) and AF (SB model), bot of wic are mainly based on on-site WD measurements. In CFD, te full interaction between wind and building is included. Turbulent dispersion of raindrops is not explicitly considered in any of te models. It is implicitly included in te ISO and SB models because W and AF are based on measurements, in wic, to some extent, turbulent dispersion was present. Altoug CFD can model turbulent dispersion [66], tis can not be done wit te CFD model based on Lagrangian particle tracking and steady stream tubes (Fig. 3). Te reason is tat raindrop trajectories influenced by turbulent dispersion are not capable of forming tubes of steady raindrop streams. Based on previous studies in wic CFD results were compared wit full-scale WD measurements [20,50,51,53,54], it is expected tat te effect of turbulent dispersion is small for low-rise buildings, wile it can be quite large for te lower part of ig-rise buildings. For a ig-rise tower building, CFD simulations of WD witout turbulent dispersion sowed good agreement wit measurements at te top of te facade, but large underestimations (up to more tan a factor 2) for te lower facade parts [54]. Tis was attributed to neglecting te turbulent dispersion of raindrops. Near te lower part of te facade, te calculated raindrop trajectories are almost parallel to te facade, and do not always intersect wit te surface, as sown in [54]. Turbulent dispersion in te streamwise direction can cause tese raindrops to deviate from teir mean trajectory and to it te facade anyway. For tis reason, more rain will it tese lower facade parts wen turbulent dispersion is included Wind direction, orizontal rainfall intensity and raindrop-size distribution Wind direction in bot te ISO and SB model is taken into account by te cosine projection, wile in CFD, simulations wit different wind directions can be made. Using te CFD model, Blocken and Carmeliet [28] sowed tat te cosine projection is strictly not valid, altoug Janssen et al. [67] indicated tat errors averaged over a rain event wit te wind direction on average perpendicular to te facade can remain limited. Horizontal rainfall intensity appears in eac of te model equations (Eqs. 5, 6, 11, 16, 19). In addition, it is also included in te SB model wen calculating te DF (Eq ). A comparison of te influence of between te models can be made by focusing on te expressions for te WD coefficient α: Eq. 10, 18 and 21. In te ISO model, α is independent of. On te oter and for te SB model, α is a function of Te WD coefficient α varies from 0.58 to 1.74 for values of ranging from 0.01 to 100 mm/. In te CFD model, 9

10 α is a more complex function of, as te catc ratio η itself is a function of, and tis function depends on te position at te facade [35]. Te orizontal rainfall intensity also influences te raindrop-size distribution. Te ISO model does not consider raindrop-size distributions explicitly, altoug tey are implicitly present in te wall factors, wic are based on measurements during wic different raindrop-size distributions occurred. Te SB model takes raindrop-size distributions into account bot explicitly (DF median diameter) and implicitly (AF based on measurements). In CFD, any type of raindrop-size distribution can be taken into account in detail. However, since suc measurements are generally not available, usually empirical drop-size distribution equations are used, in wic is a parameter Comparison in terms of calculation cost and accuracy Important differences between semi-empirical and CFD models are te calculation cost, in terms of time and storage, and te potential accuracy [4]. Te ISO and SB model are easy-to-use and can be applied reasonably quickly, at te expense of lower resolution and generally lower accuracy. CFD simulations of WD based on Lagrangian particle tracking are time-consuming, because raindrop trajectories for eac raindrop diameter d ave to be calculated in wind-flow patterns wit different reference wind speeds and wind directions. On te oter and, it is clear tat CFD can provide muc more detailed information as illustrated, for example, by comparing te information provided in Figs. 1, 2 and 5,. If CFD is carefully applied, results from validation studies ave sown tat suc information can be in good agreement wit experimental data [20,50-54]. Altoug te steady stream-tube model (CFD-ST) will be less accurate tan a model tat includes turbulent dispersion in a proper way (CFD-TD), te former is generally preferred over te latter. One of te main reasons is calculation cost. Application of te CFD-ST model is already very time-consuming. Wit tis model, calculating te specific catc ratio for a certain drop diameter and at a certain facade position requires calculating only tree raindrop trajectories tat form a stream tube ending near tis facade position. However, as steady stream tubes do not exist wen turbulent dispersion is included (CFD-TD model), te specific catc ratio in suc case sould be determined by releasing a large number of drops, and counting te number of drops tat impinge at a certain facade position. Te specific catc ratio is ten te ratio of te number of impinged drops (at tat position) versus te number of injected drops from a certain reference position. For every facade position, many raindrop trajectories are needed to acieve results tat are independent of te injection positions and te number of injections, wic are cosen by te user. In sort, te sopistication and efficiency of te CFD-ST model is lost wen turbulent dispersion is included. In addition, accurately modelling turbulent dispersion requires accurate information on te turbulence field. Given te deficiencies of te k-ε family of turbulence models, second moment closure but possibly LES (Large Eddy Simulation) or ybrid LES/UANS (Unsteady ANS) will be required. esorting to suc transient wind-flow pattern calculations will drastically increase computation times. Te Lagrangian approac is te natural approac for dealing wit particle motion. In tis approac, individual particles are tracked as tey move troug te computational domain. Tis approac is sometimes also referred to as te non-continuum approac, because particle pase is dealt wit in a discrete way. As an alternative to te Lagrangian approac, te Eulerian approac can be considered [68,69,70]. In tis approac, te particle pase is treated as a continuum, and its caracteristics are obtained by solving te partial differential equations for particle continuity and particle momentum in a given coordinate system. Tis approac is also referred to as te continuum or two-fluid approac [69]. Often, a Boussinesq approximation is used to relate te turbulent particle flux to te average particle concentration gradients in te particle pase equations. Lot [68], Sirolkar et al. [69] and Zang and Cen [70] describe advantages and disadvantages of bot approaces. Some of tese are briefly mentioned below, from te viewpoint of WD modelling. Some of te main advantages of te Lagrangian approac are tat it generally does not rely on gradient diffusion approximations, and it can elegantly take into account inertia effects, crossing trajectory effects and temporal and cross-correlations in te turbulence velocity [69]. A disadvantage is te difficulty in estimating te appropriate time and lengt scale of te turbulence [69]. Lagrangian modelling for WD will generally also be significantly more time-consuming tan Eulerian modelling. Advantages of te Eulerian approac are tat te particle pase can be treated wit te same discretisation and numerical tecniques as te continuum (fluid) pase. Tis is beneficial for including two-way coupling effects. It can also strongly reduce te computational cost. Disadvantages can be te gradient diffusion approximation and numerical diffusion [68,69]. To te knowledge of te autors, Eulerian modelling as not yet been applied for WD. 7. Summary and conclusions Tis paper as presented a detailed overview of tree calculation models for wind-driven rain (WD) on buildings and a comparison of tese models based on model teory. Tese models are te semi-empirical model in te ISO Standard (ISO model), te semi-empirical model by Straube and Burnett (SB model) and te CFD 10

11 model by Coi, extended by Blocken and Carmeliet (CFD model). First, te istorical and teoretical background, as well as te capabilities and limitations of eac model ave been described. Next, te models ave been compared in terms of ow te influencing parameters of WD are implemented, and in terms of calculation cost and accuracy. Te following conclusions are made: (1) Altoug tey are bot based on te WD relationsip, te ISO model and SB model are quite different: a. Te ISO model uses a constant free-field WD coefficient (0.222 s/m), wereas in te SB model te DF is a strong function of orizontal rainfall intensity, wic is closer to reality. b. Te ISO model includes a transformation model to convert te wind speed at a standard meteorological station (airfield) to te building site. Te SB model lacks suc a transformation model. Te reference wind speed U 10 in te ISO model corresponds to terrain category II (airfield), wile U 10 in te SB model corresponds to te local terrain rougness (i.e. at te location of te building). Tis means tat not just any meteorological data can be used as input to eac of tese models, and appropriate conversions need to be made. c. Te ISO model provides correction factors to take into account te effect of topograpic features suc as ills and valleys, and surrounding obstacles suc as buildings and trees. Te SB model does not provide suc factors. d. Te ISO wall factor W and te SB rain admittance function AF ave te same definition, but teir values in bot models are considerably different for some facade positions. For example, at te top edge and te side edges for ig-rise buildings, te differences between W and AF can be more tan a factor 2. Te two models can terefore provide very different results. e. Te ISO model provides a single result, wile te SB model provides a minimum and maximum limit for te WD intensity, resulting from te minimum and maximum limit for te AF. f. In te ISO model, te WD coefficient α is independent of, wile in te SB model it is a function of (2) Te CFD model inerently exibits a considerably stronger implementation of te influencing parameters of WD on buildings tan te two semi-empirical models, and is terefore potentially more accurate, at te expense of increased model complexity and calculation cost. Te ISO model is te most compreensive semi-empirical model known to te autors; it provides a more pronounced implementation of te influencing parameters tan te SB model. (3) Te CFD model is too complex and too costly for widespread practical use. It can owever be used to evaluate te two semi-empirical models and to improve teir performance. (4) It sould be noted tat te two semi-empirical models are witout any doubt considered very valuable. Tese models provide a strong and necessary basis for furter model development, wic can be guided by among oters validated CFD simulations. (5) Te detailed overview and te comparison in tis paper provide te basis for future comparison studies. and for future improvements of te two semi-empirical models. Te future comparison studies will include application of te tree calculation models to calculate WD for a range of idealized and real building configurations. Acknowledgements Te autors are grateful to te European Committee for Standardization (CEN) for te permission to reproduce Fig. 1. Notation A f area of a zone on te building facade (m²) A area of a orizontal surface at a certain eigt in te upstream undisturbed flow (m²) a annum (per annum = per year) a, A, n, p parameters in raindrop-size distribution equation C rougness coefficient C T topograpy coefficient d raindrop diameter (mm) d median raindrop diameter (mm) f (d) probability-density function of raindrop size falling troug a orizontal plane (m -1 ) I A airfield annual index (L/m²a) I S airfield spell index (L/m²) I S airfield index for a given spell (L/m²) I WA wall annual index (L/m²a) I WS wall spell index (L/m²) K terrain factor N number of years of available data 11

12 O wdr S S wdr U U 10 V t W z z 0 z min α β ε η d η θ κ ϕ 10 BSI CEN CFD DF ISO AF ANS SB VLIET WD obstruction factor orizontal rainfall intensity, i.e. troug a orizontal plane (L/m² or mm/) wind-driven rain intensity (L/m² or mm/) orizontal rainfall amount, i.e. troug a orizontal plane (L/m² or mm) wind-driven rain amount (L/m² or mm) streamwise orizontal component of te mean wind-velocity vector (m/s) reference wind speed at 10 m eigt in te upstream undisturbed flow (m/s) raindrop terminal velocity of fall (m/s) wall factor eigt above ground (m) aerodynamic rougness lengt (m) minimum eigt (m) wind-driven rain coefficient power-law exponent of mean wind speed profile turbulence dissipation rate (m²/s³) specific catc ratio catc ratio angle between te wind direction and te normal to te facade/wall ( from nort) free-field wind-driven rain coefficient wind direction at 10 m eigt in te upstream undisturbed flow (degrees from nort) Britis Standards Institution European Committee for Standardisation Computational Fluid Dynamics Driving ain Function International Organization for Standardization ain Admittance Factor eynolds-averaged Navier-Stokes Straube and Burnett Flemis Impulse Programme for Energy Tecnology Wind-Driven ain eferences [1] Sanders C. Heat, air and moisture transfer in insulated envelope parts: Environmental conditions. International Energy Agency, Annex 24. Final report, volume 2. Acco, Leuven, [2] Dalglies WA, Surry D. BLWT, CFD and HAM modelling vs. te real world: Bridging te gaps wit fullscale measurements. Journal of Wind Engineering and Industrial Aerodynamics 2003; 91(12-15): [3] Tang W, Davidson CI, Finger S, Vance K. Erosion of limestone building surfaces caused by wind-driven rain. 1. Field measurements. Atmosperic Environment 2004; 38(33): [4] Blocken B, Carmeliet J. A review on wind-driven rain researc in building science. Journal of Wind Engineering and Industrial Aerodynamics 2004; 92(13): [5] Blocken B, oels S, Carmeliet J. A combined CFD-HAM approac for wind-driven rain on building facades. Journal of Wind Engineering and Industrial Aerodynamics 2007; 95(7): [6] Janssen H, Blocken B, Carmeliet J. Conservative modelling of te moisture and eat transfer in building components under atmosperic excitation. International Journal of Heat and Mass Transfer 2007; 50(5-6): [7] Abuku M, Janssen H, Poesen J, oels S. Impact, absorption and evaporation of raindrops on building facades. Building and Environment 2009; 44(1): [8] Lacasse MA. IC studies on te control of rain penetration in exterior wood-frame walls. Solplan eview 2004; 14, January 2004, pp [9] Bitsuamlak GT, Cowdury AG, Sambare D. Application of a full-scale testing facility for assessing wind driven rain intrusion. Building and Environment 2009; 44(12): [10] Masters FJ, Gurley K, Prevatt DO. Full-scale simulation of turbulent wind-driven rain effects on fenestration and wall systems. 3 rd International Symposium on Wind Effects on Buildings and Urban Environment, Marc 4-5, 2008, Tokyo, Japan. 12

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14 [39] Coi ECC. Caracteristics of te co-occurrence of wind and rain and te driving-rain index. Journal of Wind Engineering and Industrial Aerodynamics 1994; 53: [40] Straube JF, Burnett EFP. Driving rain and masonry veneer, ASTM Symposium on Water Leakage Troug Building Facades, Orlando, Marc , Special Tecnical Publication, ASTM STP 1314, Piladelpia, 1997, pp [41] Sandberg PI. Driving rain distribution over an infinitely long ig building: computerized Calculations. 2 nd Int. CIB/ILEM Symp. on Moisture Problems in Buildings. otterdam, Te Neterlands, September 1974, Paper 1-1-2, [42] odgers GG, Poots G, Page JK, Pickering WM. Teoretical predictions of rain drop impaction on a slab type building. Building Science 1974; 9: [43] Beijer O. Concrete walls and weatering. ILEM/ASTM/CIB Symp. on Evaluation of te Performance of External Vertical Surfaces of Buildings, vol. 1, Otaniemi, Espoo, Finland, August and September 1 2, 1977, pp [44] odgers GG. Teoretical studies of te interaction of wind flow wit precipitation elements in determining te deposition of rain, snow and ice on buildings and structures. Sixt Course Airflow and Building Design, Seffield University, [45] Hilaire J, Savina H. Pluie battante sur une facade d immeuble (in Frenc), EN-CLI 88.5, CSTB, Nantes, [46] Souster C. A teoretical approac to predicting snow loads and driving rain deposition on buildings, P.D. Tesis, University of Seffield, UK, [47] Coi ECC. Wind-driven rain on building faces and te driving-rain index. Journal of Wind Engineering and Industrial Aerodynamics 1999; 79: [48] Coi ECC. Variation of wind-driven rain intensity wit building orientation. Journal of Arcitectural Engineering 2000; 6(4): [49] Hangan H. Wind-driven rain studies. A C-FD-E approac. Journal of Wind Engineering and Industrial Aerodynamics 1999; 81: [50] Blocken B, Carmeliet J. Te influence of te wind-blocking effect by a building on its wind-driven rain exposure. Journal of Wind Engineering and Industrial Aerodynamics 2006; 94(2): [51] Blocken B, Carmeliet J. Validation of CFD simulations of wind-driven rain on a low-rise building facade. Building and Environment 2007; 42(7): [52] Tang W, Davidson CI. Erosion of limestone building surfaces caused by wind-driven rain. 2. Numerical modelling. Atmosperic Environment 2004; 38(33): [53] Abuku M, Blocken B, Nore K, Tue JV, Carmeliet J, oels S. On te validity of numerical wind-driven rain simulation on a rectangular low-rise building under various oblique winds. Building and Environment 2009; 44(3): [54] Briggen PM, Blocken B, Scellen HL. Wind-driven rain on te facade of a monumental tower: numerical simulation, full-scale validation and sensitivity analysis. Building and Environment 2009; 44(8), [55] Coi ECC. Modeling of wind-driven rain and its soil detacment effect on ill slopes. Journal of Wind Engineering and Industrial Aerodynamics 2002; 90: [56] Blocken B, Carmeliet J, Poesen J. Numerical simulation of te wind-driven rainfall distribution over smallscale topograpy in space and time. Journal of Hydrology 2005; 315(1-4): [57] Blocken B, Poesen J, Carmeliet J. Impact of wind on te spatial distribution of rain over micro-scale topograpy numerical modelling and experimental verification. Hydrological Processes 2006; 20(2): [58] Karagiozis A, Hadjisopocleous G, Cao S. Wind-driven rain distributions on two buildings. Journal of Wind Engineering and Industrial Aerodynamics 1997; 67&68: [59] Melese Endalew A, Hertog M, Delele MA, Baetens K, Persoons T, Baelmans M, amon, H, Nicolai BM, Verboven P. CFD modelling and wind tunnel validation of airflow troug plant canopies using 3D canopy arcitecture. International Journal of Heat and Fluid Flow 2009; 30(2): [60] Melese Endalew A, Hertog M, Gebreslasie Gebreiwot M, Baelmans M, amon H, Nicolai BM, Verboven P. Modelling airflow witin model plant canopies using an integrated approac. Computers and Electronics in Agriculture 2009; 66(1): [61] icards PJ, Hoxey P. Appropriate boundary conditions for computational wind engineering models using te k-ε turbulence model. Journal of Wind Engineering and Industrial Aerodynamics 1993; 46&47: [62] Blocken B, Statopoulos T, Carmeliet J. CFD simulation of te atmosperic boundary layer: wall function problems. Atmosperic Environment 2007; 41(2):

15 [63] Blocken B, Carmeliet J, Statopoulos T. CFD evaluation of te wind speed conditions in passages between buildings effect of wall-function rougness modifications on te atmosperic boundary layer flow. Journal of Wind Engineering and Industrial Aerodynamics 2007; 95(9-11): [64] Franke J, Hellsten A, Sclünzen H, Carissimo B. Best practice guideline for te CFD simulation of flows in te urban environment. COST Action 732: Quality Assurance and Improvement of Microscale Meteorological Models, [65] Gorlé C, van Beeck J, ambaud P, Van Tendeloo G. CFD modelling of small particle dispersion: te influence of te turbulence kinetic energy in te atmosperic boundary layer. Atmosperic Environment 2009; 43(3) [66] Coi ECC. Numerical modeling of gust effect on wind-driven rain. Journal of Wind Engineering and Industrial Aerodynamics 1997; 72: [67] Janssen H, Blocken B, oels S, Carmeliet J. Wind-driven rain as a boundary condition for HAM simulations: analysis of simplified modelling approaces. Building and Environment 2007; 42(4): [68] Lot E. Numerical approaces for motion of dispersed particles, droplets, and bubbles. Progress in Energy and Combustion Science 2000; 26: [69] Sirolkar JS, Coimbra CFM, McQuay MQ. Fundamental aspects of modeling turbulent particle dispersion in dilute flows. Progress in Energy and Combustion Science 1996; 22(4): [70] Zang Z, Cen Q. Comparison of te Eulerian and Lagrangian metods for predicting particle transport in enclosed spaces. Atmosperic Environment 41(25):

16 Fig. 1. Wall factors (W) in te 2009 ISO Standard ( ISO 2009, reproduced wit permission). 16

17 (a) (b) (c) < to to 0.50 < 0.35 Fig. 2. ain admittance factors (AF) as provided by Straube [15] and Straube and Burnett [16]: (a) Low-rise building wit H/W << 1; (b) Tall building (> 10 m) wit H/W >> 1; (c) Low-rise building wit sloped roof and roof overang. (d ) A(d) wdr (d) (d) A f Fig. 3. Metod to determine te specific catc ratio in te CFD model by Coi. Stream tube bounded by two trajectories of raindrops wit diameter d. Te specific catc ratio η d for zone A f and for raindrops wit diameter d is determined based on conservation of mass for te raindrops in te stream tube. 17

18 catc ratio (-) η ref. wind speed ref. wind speed U 10 (m/s) U 10 (m/s) or. rainfall intensity (mm/r) or. rainfall intensity (mm/r) Fig. 4. Typical example of a catc-ratio cart or η-cart tat presents te catc ratio η as a function of reference wind speed U 10 and orizontal rainfall intensity, for a given position on te building facade and for a given wind direction [50]. roof overang lengt 0.44 m 0.44 m 0.41 m 0 m 0.32 m Fig. 5. CFD results for distribution of te ratio S wdr /S (accumulated wind-driven rain to accumulated orizontal rainfall) across te sout-west facade of te VLIET test building at te end of a rain event [51]. Black areas indicate regions seltered from rain by roof overang. 18