wind-driven rain as a boundary condition for ham simulations: analysis of simplified modelling...

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Building and Environment 42 (2007) 1555–1567

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Wind-driven rain as a boundary condition for HAM simulations:Analysis of simplified modelling approaches

Hans Janssena,�, Bert Blockenb, Staf Roelsc, Jan Carmelietb,c,1

aTechnical University of Denmark, Department of Civil Engineering, Brovej-Building 118, 2800 Kgs. Lyngby, DenmarkbBuilding Physics and Systems, Technische Universiteit Eindhoven, P.O. box 513, 5600 MB Eindhoven, The Netherlands

cLaboratory of Building Physics, Department of Civil Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 40, 3001 Leuven, Belgium

Abstract

While the numerical simulation of moisture transfer inside building components is currently undergoing standardisation, the modelling

of the atmospheric boundary conditions has received far less attention.

This article analyses the modelling of the wind-driven-rain load on building facades by partial simplification of a complex CFD-based

method along the lines of the European Standard method. The results indicate that the directional dependence of the wind-driven-rain

coefficient is not of substantial importance. A constant wind-driven-rain coefficient appears to be an oversimplification though: the full

variability with the perpendicular wind speed and horizontal rain intensity should be preserved, where feasible, for improved estimations

of the moisture transfer in building components.

In the concluding section, it is moreover shown that the dependence of the surface moisture transfer coefficient on wind speed has an

equally important influence on the moisture transfer in building components.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: HAM; Wind-driven rain; Driving rain; Evaporation; Surface moisture transfer coefficient

1. Introduction

Knowledge of the hygric behaviour of building compo-nents is of serious importance for different building physicsissues. Insight into a building component’s hygric beha-viour is evidently needed when analysing durabilityproblems of existing components, or when assessing theexpected performances of newly developed components.The moisture transfer inside building components alsoaffects the interior climate though, and hence plays a rolein interior air quality and energy performance. Themoisture transfer inside the building components moreoverdetermines the moisture regime at the exterior surface, andthus influences esthetical appearance, by playing a part insoiling phenomena and algae formation.

e front matter r 2006 Elsevier Ltd. All rights reserved.

ildenv.2006.10.001

ing author. Tel.: +3216 32 13 45; fax: +3216 32 19 80.

ess: [email protected] (H. Janssen).

ulty of Building and Architecture, Building Physics Group,

ersity, Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The

Until recently, the Glaser method was accepted as thestandard [1] calculation tool for such evaluation of buildingcomponents’ hygric behaviour, but its restrictions—sta-tionary, no liquid transfer, no air transfer—make it onlyrarely reliably applicable. Presently, application of hygro-thermal simulation programmes for the evaluation [2,3] oroptimisation [4,5] of the hygric performance of buildingcomponents is becoming general practice.Currently, numerical simulation of moisture transfer in

building components is undergoing standardisation [6], towhich a quality assessment methodology was recentlyadded [7]. Both are restricted though to moisture and heattransfer inside permeable building components, and do notthoroughly discuss the atmospheric boundary conditions.The dependability of hygrothermal simulations underatmospheric excitation cannot be guaranteed, however,without an accurate modelling of these phenomena. Thisarticle concentrates on the atmospheric moisture load,presumed the largest and most important uncertainty.The ensuing study reveals that wind-driven rain is the

main moisture source for permeable building facades and

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ARTICLE IN PRESSH. Janssen et al. / Building and Environment 42 (2007) 1555–15671556

investigates the required level of detail in implementationsof wind-driven rain as a boundary condition in hygro-thermal simulations. This study focuses on the long-term‘moisture response’ of building facades, which isrepresented by the variation of average and surfacemoisture contents over the course of a year. The yearlywind-driven rain and evaporative drying amounts are,however, also incorporated in the comparison. Other‘shorter-term’ wind-driven rain-related phenomena, suchas run off and water penetration, are discussed onlysecondarily.

This analysis, based on hygrothermal simulations ofbuilding components, piecewise simplifies a complexCFD-based formulation [8] for wind-driven rain alongthe concepts of the European Standard on wind-drivenrain [9], in order to evaluate the acceptability of thediffering features of both approaches. More specifically,this article investigates the significance of the dependencyof the wind-driven-rain coefficients on rain intensity,wind speed and wind direction. In the final paragraph,the resulting conclusions are put into a larger perspective,by sketching the effect of the surface moisturetransfer coefficients on evaporative drying, the primarymoisture removal mechanism for permeable buildingfacades.

2. Numerical simulation of moisture and heat transfer in

building components

All results presented in this article are achieved bynumerical solution of the standard partial differentialequations for coupled moisture and heat transfer in porousbuilding materials, combined with the complete formula-tions for the atmospheric hygrothermal boundary condi-tions. Air transfer and the consequent advective transfer ofmoisture and heat are not included in this analysis. Furtherdetails on the numerical simulation model can be found in[10]. In this article, the formulations for the atmosphericmoisture load are concisely repeated.

2.1. Atmospheric moisture load

As long as the building facade’s exterior surface does notreach capillary saturation, the moisture exchange with theatmosphere ges comprises wind-driven rain Rwdr andvapour exchange Ee (all in kg/m2s):

ges ¼ Rwdr þ Ee: (1)

In this numerical model, wind-driven rain is calculatedfrom the wind-driven-rain index, the product of referencewind speed U (m/s)—at 10m height in theupstream undisturbed flow—and horizontal rainfall intensityRh (kg/m2s)—through a horizontal plane—by use of thewind-driven-rain coefficient a (s/m) [11]:

Rwdr ¼ aURh. (2)

All arriving wind-driven rain is assumed to be retained by thesurface, splash-off is thus neglected. When the exteriorsurface reaches capillary saturation though, the moistureflow supplied to the surface may exceed the possible inflowinto the component: the excess is assumed to be discardedfrom the system as runoff.Evaporative exchange Ee is described by:

Ee ¼ hm;eðpv;e � pv;esÞ, (3)

where hm,e is the surface moisture transfer coefficient (s/m),and pv,e and pv,es are the air and surface vapour pressure(both in Pa), respectively.

2.2. Wind-driven-rain coefficients

All wind-driven-rain coefficients used in this study areadapted from the CFD simulations in [12]. The numericalmethodology to obtain these coefficients was validated bycomparison with full-scale measurements by Blocken andCarmeliet [8].Blocken and Carmeliet applied a three-step approach to

compute the wind-driven-rain coefficients:

1.
Steady-state wind flow pattern
The steady-state wind flow patterns around the build-ings are simulated with CFD, for wind speeds from 0 to10m/s and for deviations between wind direction y andthe surface normal j (both in degrees from north) of 01,221, 451 and 671. The Reynolds averaged Navier–Stokesequations and continuity equation are solved applyingthe control volume method (with commercial codeFluent 5.4). Closure is obtained by the use of realizablek–e turbulence model. Results are numerical values forwind speeds, pressure and the turbulence quantities atthe centre of each volume.

2.
Raindrop trajectories
With the obtained wind flow patterns, raindrop trajec-tories are calculated for raindrop diameters from 0.5 to6mm. Rain drops are injected from a horizontal planelocated in the upstream-undisturbed wind flow, high abovethe ground: its location must allow injected raindrops toreach the terminal fall velocity (vertical) and wind velocity(horizontal) before entering the flow pattern disturbed bythe presence of the building and its surroundings.

3.
Specific and integrated catch ratio, and wind-driven-rain
coefficient

Comparison of the horizontal rain drop density with thedensity of wind-driven dropsarriving at the buildingfacade defines the specific (for a rain-drop diameter d)catch ratio’s Zd,y ¼ Rwdr,d/Rh,d. The global catch ratio Zy( ¼ Rwdr/Rh) is obtained by integration over the rain-drop spectrum. Division of Zy by wind speed U yields thewind-driven rain coefficient ay.

The resulting ay(Rh,U,y–j) relations are depicted in Fig. 1,for the left top corner and centre of a cubic(10� 10� 10m3) building’s facade. It is apparent that ay

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Fig. 1. Wind-driven-rain coefficient ay (Rh,U, y–j) (Rh and Rwdr in kg/m2 h) for the left top corner (a, c, e, g) and centre (b, d, f, h) of a cubic

(10� 10� 10m3) building’s facade, as a function of rainfall intensity Rh wind speed U, and wind direction deviation y–j.

H. Janssen et al. / Building and Environment 42 (2007) 1555–1567 1557

depends on the location on the facade, the deviationbetween wind direction and surface normal, the wind speedand the horizontal rain intensity. Whereas ay may bepractically independent of Rh and U for the top corner, it

varies substantially at the centre of the facade. Blocken andCarmeliet [8,12,13] state that, in reality, wind-driven-raincoefficients vary substantially with Rh, U and y–j for mostlocations on most buildings.


2.3. Surface moisture transfer coefficients

The surface moisture transfer coefficients applied in thesimulations are calculated from the wind speed and winddirection [14], presuming conformity between the thermaland hygric boundary layer near the surface (Lewisanalogy):

hm;e ¼ 7:7� 10�9ð1:7V loc þ 5:1Þ,

V loc ¼ 1:8U þ 0:2 ðwindwardÞ,

V loc ¼ 0:4U þ 1:7 ðleewardÞ, ð4Þ

where Vloc is the local wind speed near—at a distance of0.3m [14]—the facade (m/s), which is deduced from thereference wind speed U at 10m height in the upstreamundisturbed flow. Several relations between wind speed andsurface transfer coefficient were compared in [10]: curve (4)was shown to lie centrally between all other relations. Thisarticle will reveal however that further research on thisspecific topic is essential.

2.4. Calculation objects and climate data

All simulations are performed for a ceramic brick outerleaf and a mineral rendering, assumed located once at theleft top corner, and once at the centre of a facade of a cubic(10� 10� 10m3) building, orientated once south-west,once north-east.

Only the outer layer (outer leaf/rendering) of the facadesis simulated: the underlying insulation layer constitutes ahygric and thermal break, leaving the hygric and thermalcapacity of the inner leaf negligible for this analysis.Insulation and inner leaf are thus modelled with surfacetransfer coefficients of 10�10 s/m and 0.7W/m2K, con-sidering a nearly vapour tight, insulated structure. Theceramic brick outer leaf is 9 cm thick, the mineral renderingconsists of a 1.05 cm top and a 0.95 cm base layer.Capillary absorption coefficients and capillary moisture

0%

4%

8%0

30

60

90

120

150

180

210

240

270

300

330

(a)

EssenBremer

Fig. 2. Directional roses for average wind speed (m/s) (a) and norm

contents are: 0.15 kg/m2s1/2 and 157 kg/m3 (ceramicbrick), 0.02 kg/m2s1/2 and 231 kg/m3 (rendering baselayer), 0.06 kg/m2s1/2 and 126 kg/m3 (rendering toplayer). Two-year intervals are simulated, from whichthe first is assumed transitional: only the secondsimulated year is retained for analysis here, as themoisture responses have then reached their steady-period-ical state.Hourly design reference year climate values for Essen

and Bremerhaven (Germany) are obtained from [15]. Fig. 2illustrates the average wind speed and the normalisedyearly amounts of wind-driven-rain index along the windrose. The latter was obtained by summing all hourlydirectional wind-driven-rain indices URh per 301 interval,and dividing this by the sum over all wind directions. It isapparent that both wind and wind-driven rain arrivepredominantly from the south-west quadrant. The interiortemperature and relative humidity are maintained at 20 1Cand 50%, as this investigation does not go into interiorclimate influences.Use of hourly climate data, instead of 10-min data, in

simulations of vapour transfer in building components wasanalysed by Geving [16]: no noteworthy differences weredemonstrated. A similarly comprehensive investigation ofliquid transfer is still lacking.Blocken and Carmeliet [17] state that 10-min data for

rain intensity and wind speed are most appropriate foraccurate estimations of the wind-driven rain load. Theyalso point out that only weighted hourly averages of rainintensity and wind speed preserve this accurate wind-driven-rain estimation whereas ordinary arithmeticaverages tend to yield underestimations. When suchweighted hourly averages are applied though, the influenceof applying hourly instead of 10-min climate data isinsubstantial when assessing longer-term moisture re-sponses of building components. For this investigation,however, the available hourly climate data are assumedsufficiently accurate.

0%

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150

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300

330haven

alised wind-driven-rain index (b) for Essen and Bremerhaven.

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Table 1

Division of atmospheric moisture loads (kg/m2 yr) for Essen: exemplary simulations

Brick SW corner SW centre NE corner NE centre

Supply Impinging wind-driven rain 439.5 127.0 83.9 21.2

Vapour supply during rain 0.9 0.9 0.1 0.2

Vapour supply during no rain 2.0 2.9 4.9 6.0

Removal Surface moisture runoff 139.7 1.6 4.1 0.0

Evaporation during rain 66.7 45.3 11.2 4.9

Evaporation during no rain 235.6 83.6 73.5 20.8

Rendering SW corner SW centre NE corner NE centre








3. Relative importance of the different parts in the

atmospheric moisture load

Introductorily, the relative significances of the differentphenomena in the atmospheric moisture load are analysed.Table 1 shows the breakdown of the yearly atmosphericmoisture loads for the different configurations fromsimulations with the Essen climate: distinction is madebetween supply sources (impinging wind-driven rain,vapour supply during ‘rain’, and vapour supply during‘no rain’) and the removal mechanisms (surface moisturerunoff, evaporation during ‘rain’ and evaporation during‘no rain’).

The SW orientation appears as most exposed, due to theleading SW–W wind-driven-rain direction in the Essenclimate (Fig. 2). Table 1 also indicates the sheltered natureof the facade’s centre (Fig. 1): far less impinging wind-driven rain is observed. Wind-driven rain forms theprimary supply mechanism: vapour supply only has a(very) secondary impact, even for less exposed orientationsand locations.

Evaporation forms the main removal mechanism,assisted by runoff for very exposed locations and orienta-tions. Part of the evaporation occurs during the rain spells,thus reducing the amount of moisture supplied to thebuilding facade. It is noticed that the rendering yields morerunoff due to its smaller hygric sorptivity and capacity.

Moisture runoff is assumed to disappear from thesystem: Table 1 reveals though that runoff may form animportant moisture source for underlying locations. A firststep towards the combined simulation of moisture transferin building materials and film flow runoff is documentedin [18].

Similar proportions are found for the Bremerhavenclimate and for different insulation levels (results notshown). It is easily concluded that reliable simulations ofmoisture transfer in permeable building facades necessitate

a correct modelling of wind-driven rain and of evaporativedrying. This article primarily focuses on the implementa-tion of wind-driven rain, but in a final paragraph alsodiscusses the evaporative drying, to put the findings onwind-driven rain in a larger perspective.

4. Moisture response sensitivity to wind–driven rain-

modelling

In the prior simulations, wind-driven rain was deter-mined from the wind-driven-rain index with the CFD-based wind-driven-rain coefficients ay, which depend onhorizontal rain intensity, wind speed and wind direction[8,12,13]:

Rwdr ¼ ayðRh;U ; y� jÞURh. (5)

Accurate modelling of wind-driven rain must hence bebased on representative data for Rh, U and y, and thewhole ay(Rh,U,y–j) relationship. The issue of representa-tive data is not discussed in this paper: this topic is tackledin [17]. This study presumes hourly climate data assufficiently accurate, and focuses on the ay(Rh,U,y–j)dependence.

The use of
1. the projected wind-driven-rain index U cos(y�j) �Rh
combined with wind-driven-rain coefficients for perpen-dicular wind a? only:

Rwdr ¼ a?ðRh;U cosðy� jÞÞU cosðy� jÞRh

¼ a?ðRh;U0ÞU 0Rh, ð6Þ

where U0 is the normally projected wind speed (m/s);and

2.
one constant—Rh and U0 independent—value for a?is computationally attractive however, and both simpli-fications are conceptually implied in prEN 15927-3 [9],


the European Standard on the calculation of wind-driven-rain load. Their acceptability when assessingmoisture responses of building facades has, however,not been examined yet.

4.1. Directional dependence of wind-driven-rain coefficient a

In the prior exemplary simulations, directional ay wereused when calculating wind-driven rain. As such ay wereavailable only for discrete deviations y–j (01, 22.51, 451,67.51), intermediary directions were projected on thenearest existing ay-direction. It is assumed that suchsmall-angle projections do not disturb the analysis. Thedirectional dependence of wind-driven rain can be simpli-fied though: by projecting the wind speed U on the normalto the facade, combined with a? for perpendicular wind(Eq. (6)), a simplification commonly applied in hygro-thermal simulation models [15,19].

CFD results from Blocken and Carmeliet [13] indicate,however, that such projection might give rise to seriouserrors. Fig. 3 shows the distributions of the wind-driven-rain coefficient (Rh: 1 kg/m

2h, U: 10m/s) over the facadefor the directional and projection approach. The leftcolumn depicts the directional ay, while the right columncontains the equivalent normally projected a, equal toa? cos(y–j). It is clear that both approaches deviatesignificantly, particularly for larger y–j. The effect on themoisture response of building facades has, however, notbeen investigated yet.

The exemplary simulations, using directional ay, arecomplemented by simulations applying the normal projec-tion. Results for Essen SW centre are brought togethergraphically in Fig. 4: the facades’ moisture responses areexemplified by the variations of surface and averagemoisture contents in the outer leaf/rendering over a year.These are only depicted, however, for a winter month, sincethe low wind-driven rain and extensive drying yield onlyminor moisture content variations in the summer. Thealphanumerical results for the yearly moisture loads arecollected in Table 2.

While Fig. 3 indicates serious deviations betweendirectional and normally projected wind-driven-rain coeffi-cients, even for the centre of the facade, these are notobserved in the moisture responses of the building facades.A further analysis of separate wind-driven-rain eventsindicates that the largest share of the wind-driven rain onthe facade stems from wind directions closest to thenormal: 65% of the yearly impinging wind-driven-rainamount on Essen SW centre arrives from wind directionsjy–jjo301, for which projection errors are smallest(Fig. 3). For Bremerhaven SW centre, this is 76%.

This observation can also be deduced from Fig. 1, themagnitude of ay declines with increasing deviation betweenwind direction and surface normal. The large y–j, whichyield the largest projection errors (Fig. 3), do notcontribute substantially to the total wind-driven-rain

amount, and can thus not largely affect the moistureresponses.This conclusion slightly deteriorates though for facades

orientated parallel to the main wind-driven-rain direction,for which an important share of wind-driven rain arrivesfrom shearing directions. These are the 150–1801 and300–3301 orientations for the Essen and Bremerhavenclimates (Fig. 2). Analysis of these (and other) orientationsshows that even then the deviations remain limited for themost exposed locations (the two top corners, Figs. 1 and 3)on the facades: the yearly wind-driven-rain loads in thedirectional and the projection approach deviate generallyjust up to a few percents, with an exceptional peak to 10%.The least exposed centre location yields a similar conclu-sion: deviations remain limited. Larger differences areobserved at mid-height of the lateral sides, where Blockenand Carmeliet [13] also noted the largest errors: thedeviation in yearly wind-driven-rain loads may peak upto 20%, but is generally lower.When interpreting these differences, a few nuances

should be kept in mind. All these total differences inyearly wind-driven-rain load are the accumulation of smalldifferences built up progressively over the year: they arenot the result of massively wrong estimations at a limitednumber of points in time. Such facades with orientationsparallel to the main wind-driven-rain direction, moreover,receive only half (or less) the amounts of wind-driven rainon the more heavily exposed SW facades. The locations forwhich the largest deviations are obtained (mid-height oflateral sides), furthermore catch only half the amounts ofwind-driven rain of their respective top corners. Whilerelative deviations up to 20% are obtained, the corre-sponding absolute deviations can hence be consideredminor. On the other hand, the analysis has solely beenperformed for two European climates (Essen and Bremer-haven). The wind-driven-rain roses (Fig. 2b) point outthough that especially Bremerhaven yields a stronglyorientated wind-driven-rain load, which is apt to createlarge deviations between the directional and projectionapproach.While fundamentally not valid [13], it is concluded that

when modelling wind-driven rain as a boundary conditionin hygrothermal simulations of building components, theprojection approach is acceptable: wind-driven-rain calcu-lations with the projected wind speed and the wind-driven-rain coefficient for perpendicular wind can be assumedsufficiently accurate. An exception has to be made forclimates where the largest part of the wind-driven rainarrives from a very narrow slice of the wind rose: in thatcase the directional dependence of the wind-driven-raincoefficients cannot be neglected. For the remainder of thisarticle however, normal projection is applied whendetermining wind-driven-rain coefficients.The deviations obtained in this study and in [13], both

investigating the influence of the projection approach onwind-driven rain, largely differ in order of magnitude. Anexplanation can be found in their different approaches.

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0.04

0.06

0.080.100.10

0.08

0.06

0.04

0.12

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0.08

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0.120.14 0.12

0.08

0.06

(a) (b)

(c) (d)

(e) (f)

0.10

0.05

0.02

0.03

0.040.04

0.03

0.01

0.02

- =

22˚

- =

45˚

- =

67˚

directional

Fig. 3. Comparison of directional (a, c, e) and normally projected (b, d, f) a, for Rh ¼ 1 kg/m2h and U ¼ 10m=s along wind direction y [13].


Blocken and Carmeliet study separate rain events with aspecific Rh, U and y–j, and the largest deviations are foundfor large y–j. This study on the other hand compares long-term moisture responses (average and surface moisturecontents over a year), accumulating the effects of separaterain events. For most locations on facades with mostorientations, the rain events with small y–j always yield afair share of the total wind-driven-rain load, due to theirproportionally larger wind-driven-rain coefficients (Fig. 1).

As the directional–projection deviations are smallest(Fig. 3) for such small y–j, the global deviation betweenthe directional and projection approach remains limited.

4.2. Rh and U dependence of wind-driven-rain coefficient a

In all prior simulations, Rh and U0 dependent a? wereused. The wind-driven-rain coefficient is, however, gen-erally implemented as a constant [15,19] for computational

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50

50

100

150

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ave

rage

moi

stur

e co

nten

t (kg

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directional alfanormal projection

directional alfanormal projection

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335 345 355 365

time (days)

surf

ace

moi

stur

e co

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t (kg

/m³)

335 345 355 365

time (days)

ceramic brick mineral rendering

50

(a) (b)

(c) (d)

Fig. 4. Average (a, b) and surface (c, d) moisture contents of the ceramic brick (a, c) and rendering (b, d) for SW centre in December under Essen climate:

directional dependence.

Table 2

Atmospheric moisture loads (kg/m2yr) for Essen SW centre: directional

dependence

Brick Directional a Normal

projection

Supply Impinging wind-driven rain 127.0 131.2

Vapour supply during rain 0.9 0.9

Vapour supply during no

rain

2.9 2.9

Removal Surface moisture runoff 1.6 3.1

Evaporation during rain 45.3 45.6

Evaporation during no rain 83.6 86.0

H. Janssen et al. / Building and Environment 42 (2007) 1555–15671562

ease. prEN 15927-3 implies that a Rh and U0 independenta? can be applied when assessing ‘the moisture content ofmasonry’.

A first possible proposal for such constant value is thearithmetic average of all hourly a?; this is, however, notrecommendable as the numerous small wind-driven-rainevents over a year govern such value (0.029 and 0.048 s/mfor Essen and Bremerhaven SW centre respectively). It is,therefore, not retained for further study. A secondpotential expression for the constant a?, denoted as a?,

is based on the yearly wind-driven-rain load:

a?;year ¼

P8760j¼1 Rwdr;j

P8760j¼1 U 0j � Rh;j

. (7)

This leads to 0.048 and 0.069 s/m for Essen andBremerhaven SW centre, respectively. The Rwdr-weightedaverage of all hourly a? forms the third proposal:

a?;weig ¼

P8760j¼1 Rwdr;ja?;jP8760

j¼1 Rwdr;j

, (8)

hence giving the largest weight to the most ‘productive’wind-driven-rain events, resulting in 0.056 and 0.075 s/m.The weighted averaging process is not entirely equivalentwith a linear regression through all hourly (U0Rh, Rwdr)couples a?;fit, leading to 0.059 and 0.081 s/m.Fig. 5 gives a graphical comparison of the proposed

values for Essen. It is clear that a?;year will underestimatealmost all large wind-driven-rain events, whereas these willbe better represented when using a?;weigh or a?;fit. Allproposed a? values, however, tend to overestimate thesmaller wind-driven-rain events. Complementary simula-tions with the three retained proposals for a? are carriedout: results are brought together in Fig. 6 and Table 3.

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0.0

0.5

1.0

1.5

Win

d-dr

iven

rai

n (k

g/m

²h)

= 0.048 (year)

= 0.056 (weig)

= 0.059 (fit)

Essen SW centre hourly events

0.00

0.02

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0.10

0 5 10 15 20

Wind-driven-rain index (m/s.kg/m²h)

Win

d-dr

iven

-rai

n co

effic

ient

α (

s/m

)

= 0.048 (year)

= 0.056 (weig)

= 0.059 (fit)

Essen SW centre hourly

(a)

(b)

Fig. 5. Comparison of different constant a? values with variable a? for Essen SW centre, for the wind-driven-rain relation (6) (a) and the hourly a?values (b).


The use of a?;weigh or a?;fit affects the moisture responseof the ceramic brick outer leaf, but its effect is not ruinous:a fair agreement is obtained (Fig. 6). The total yearly wind-driven-rain loads are overestimated, however (Table 3).The rendering does not allow such distinct conclusions, dueto the disturbing influence of runoff. These overestimationsoccur mainly for the small wind-driven rain events ofsummer (Fig. 5) when extensive drying prevents accumula-tion of deviations: the summer moisture responses are notsubstantially affected. It is noted that the overestimationsof wind-driven rain hence also affect the estimatedevaporative drying amounts (Table 3). Fig. 6 and Table 3

indicate that a?;weigh gives a slightly better agreement thana?;fit.The use of a?;year, on the other hand, gives rise to clearly

deviating moisture responses for the ceramic brick (Fig. 6).While leading to the expected total yearly wind-driven-rainload (Table 3), the temporal distribution is not predictedwell: further analysis of the separate wind-driven-rainevents shows that this specific a? value underestimates thelarge wind-driven-rain events of winter (Fig. 5).At first sight, it can be concluded that use of a constant

a? is acceptable for hygrothermal simulations ofbuilding components. The examples above do, however,

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alfa variablealfa constant (year)alfa constant (weig)alfa constant (fit)

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surf

ace

moi

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335 345 355 365

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ceramic brick mineral rendering

(b)(a)

(d)(c)

Fig. 6. Average (a, b) and surface (c, d) moisture contents of the ceramic brick (a, c) and rendering (b, d) for SW centre in December under Essen climate:

variable versus constant a?.

Table 3

Atmospheric moisture loads (kg/m2yr) for Essen SW centre: variable vs

constant a?

Brick a variable a?;year a?;weig a?;fit








demonstrate that different values are suitable for simulat-ing the hourly varying moisture response or the total yearlywind-driven-rain load. The values do, furthermore, dependon climate: all three coefficients differed for Essen andBremerhaven, due to differing concurrence of wind andrain at those locations. Note that such climatic dependencyis not incorporated in the European Standard. It is finallyremarked that a determination of a?;weigh and a?;fitimplicitly requires the knowledge of the full a?(Rh,U

0)dependence. The only reconciliation of these observationsis to recommend the use of the complete a?(Rh,U

0) relationin hygrothermal simulations, and not reduce the wind-driven-rain coefficients to one constant value.

To avoid complex and time-consuming CFD simulationsbefore any hygrothermal simulation a proposal of Blocken[11] is reiterated here: the compilation of a wind-driven-rain catalogue, where the full a?(Rh,U

0) relations fordifferent buildings and building configurations could bebrought together, and be made available to the buildingphysics community.

4.3. Modelling of wind-driven rain: conclusions

It has been verified that calculations of wind-driven rainbased on projected wind speed and perpendicular wind-driven-rain coefficient can be assumed sufficiently accuratefor hygrothermal simulations of building components,when concentrating on the long-term moisture responsesof the facade. While the projection approach is fundamen-tally not valid [13], it has been shown that, for mostlocations on facades with most orientations, the deviationsare not significant. An exception has to be made forclimates with a very narrow wind-driven rain rose, wherethe directional dependence of the wind-driven-rain coeffi-cient cannot be neglected.It has also been shown that use of the constant a?;weigh or

a?;fit does not substantially affect the hourly varyingmoisture responses. These values do, however, unavoidablydiffer from a?;year, are not independent of climate, and

ARTICLE IN PRESSH. Janssen et al. / Building and Environment 42 (2007) 1555–1567 1565

implicitly require knowledge of the complete a?(Rh,U0)

relation for their estimation. For all these reasons,implementation of the variability of a? with Rh and U0 isrecommended in hygrothermal simulations of buildingcomponents.

5. Moisture response sensitivity to modelling of evaporative

drying

Wind-driven rain forms the key moisture supply sourcefor permeable building facades, with only a (very)secondary role for vapour supply, for the locationsconsidered in this study. The main removal role, on theother hand, is taken up by evaporative drying: theconvective water vapour transport from the surface tothe air. The evaporative drying modelling is only tenta-tively discussed here, to put the findings on wind-drivenrain in a larger perspective.

The major uncertainty when modelling evaporativedrying is the surface moisture transfer coefficient hm,e. Inall prior simulations, hm,e was calculated from the windspeed and wind direction (4). Surface moisture transfercoefficients are though usually implemented as a constant,and various values are found in the literature. To exemplifythe sensitivity of the moisture responses to hm,e, threefurther simulations are added to the variable hm,e simula-tion. In the first, hm,e is considered a constant and equal to

0

50

100

150

200

aver

age

moi

stur

e co

nten

t (kg

/m³)

hm variablehm constanthm doubledhm halved

0

50

100

150

200

0 10 20 30

time (days)

surf

ace

moi

stur

e co

nten

t (kg

/m³)

ceramic brick

(a)

(c)

Fig. 7. Average (a, b) and surface (c, d) moisture contents of the ceramic brick

sensitivity to hm,e.

9.6� 10�8 s/m, the average (windward & leeward) value forthe yearly averaged wind speed (3.1m/s) for Essen.Hagentoft et al. [7] typically use 20.0� 10�8 s/m, whereas[6] suggests 4.7� 10�8 s/m, respectively, nearly double andhalf our value. In the second and third simulation, thus,hm,e is doubled and halved, respectively. Results arebrought together in Fig. 7 and Table 4. Moisture responsesare now illustrated for the drier January, whereas thewetter December was used for the wind-driven rain graphs.Fig. 7 and Table 4 suggest that both hm,e’s order of

magnitude and its variations with U are crucial whenmodelling evaporative drying: the moisture responses arefairly different. It can be observed that mainly evaporationduring rain is affected by changes of the surface moisturetransfer coefficient, which is partially compensated bychanging runoff amounts. The deviations in moistureresponses would thus be even larger for an outer layerwith such sorptivity and capacity that no compensatingrunoff would occur.Given the wet state of the outer layer, hm,e forms the

primary resistance for evaporative drying. Changes in hm,e,

hence, considerably affect the moisture responses. It mustbe noted that the observed differences are of similarmagnitude as those in the analysis of the wind-driven-rainimplementation. The correct modelling of surface moisturetransfer coefficients—including their variation with windspeed—hence is equally important. The knowledge of the

0 10 20 30

time (days)

mineral rendering

(b)

(d)

(a, c) and rendering (b, d) for SW centre in January under Essen climate:

ARTICLE IN PRESS

Table 4

Atmospheric moisture loads (kg/m2yr) for Essen SW centre: hm,e sensitivity

Brick Variable hm,e Constant hm,e Doubled hm,e Halved hm,e








spatial and temporal variation of the surface transfercoefficient is, however, scarce. If reliable simulations ofmoisture transfer in building components are desired, moreresearch on this topic is required. CFD, shown to be apowerful tool for the estimation of wind-driven rain, mayalso form a potent instrument here.

6. Conclusions

In this article, the sensitivity of hygrothermal simulationsof building facades to the level of detail in modelling thewind-driven rain has been analysed. For the locationsinvestigated here (Essen and Bremerhaven), wind-drivenrain appears to be the main moisture supply for permeablefacades, while evaporative drying appears to be theprimary loss mechanism. The study mainly focused onthe correct modelling of the wind-driven rain.

The modelling results indicate that for most locations onfacades with most orientations in most climates, thedirectional dependence of the wind-driven-rain coefficientis not of substantial importance when assessing the long-term moisture response of permeable building components.The directional ay(Rh,U, y–j) can be replaced bya?(Rh,U

0), to be used in combination with the projectedwind-driven-rain index U cos(y–j) �Rh.

The use of a constant a?, on the other hand, appears tobe an oversimplification. Implementation of the wholea?(Rh,U

0) relation is recommended where feasible. Toavoid complex and time-consuming CFD-simulationsbefore any hygrothermal simulation, the idea of a wind-driven-rain catalogue was reiterated.

In a final paragraph, it has been shown that the moistureresponses of building facades are as sensitive to themodelling of evaporative drying, specifically the surfacemoisture transfer coefficient. Whereas reliable predictionmethods exist for a?(Rh,U

0), these are lacking for thehm,e(U,y–j) dependence. Further research on this topic ishence encouraged.

Acknowledgements

The results presented in this paper have been obtainedwithin the frame of the SBO IWT 03175 project ‘Structuraldamage due to dynamic excitations: a multi-disciplinaryapproach’, funded by ‘IWT Vlaanderen’, the Institute for

the Promotion of Innovation by Science and Technology inFlanders. The second author was a postdoctoral fellow ofthe FWO-Flanders (Research Fund Flanders). This finan-cial support is gratefully acknowledged.

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wind-driven rain as a boundary condition for ham simulations: analysis of simplified modelling...

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