Energy and Buildings 40 (2008) 1666–1681

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Energy and Buildings

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Natural cross-ventilation in buildings: Building-scale experiments, numericalsimulation and thermal comfort evaluation

G.M. Stavrakakis a, M.K. Koukou b, M.Gr. Vrachopoulos b, N.C. Markatos a,*a Computational Fluid Dynamics Unit, School of Chemical Engineering, National Technical University of Athens, Iroon Polytechniou 9, GR-15780 Athens, Greeceb Environmental Research Laboratory, Department of Mechanical Engineering, Technological Educational Institution of Halkida, Psachna GR-34400, Greece

A R T I C L E I N F O

Article history:

Received 29 November 2007

Received in revised form 8 February 2008

Accepted 19 February 2008

Keywords:

Natural ventilation

Cross-ventilation

Turbulence

Buoyancy

CFD

Thermal comfort

A B S T R A C T

The constantly increasing energy consumption due to the use of mechanical ventilation contributes to

atmospheric pollution and global warming. An alternative method to overcome this problem is natural

ventilation. The proper design of natural ventilation must be based on detailed understanding of airflow

within enclosed spaces, governed by pressure differences due to wind and buoyancy forces. In the present

study, natural cross-ventilation with openings at non-symmetrical locations is examined experimentally

in a test chamber and numerically using advanced computational fluid dynamics techniques. The

experimental part consisted of temperature and velocity measurements at strategically selected

locations in the chamber, during noon and afternoon hours of typical summer days. External weather

conditions were recorded by a weather station at the chamber’s site. The computational part of the study

consisted of the steady-state application of three Reynolds-Averaged Navier-Stokes (RANS) models

modified to account for both wind and buoyancy effects: the standard k–e, the RNG k–e and the so-called

‘‘realizable’’ k–e models. Two computational domains were used, corresponding to each recorded wind

incidence angle. It is concluded that all turbulence models applied agree relatively well with the

experimental measurements. The indoor thermal environment was also studied using two thermal

comfort models found in literature for the estimation of thermal comfort under high-temperature

experimental conditions.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

Mechanical ventilation in buildings is common practicenowadays, due to the need to provide thermal comfort and goodindoor air quality in enclosed spaces. The energy consumptionrelated to the operation of heating, ventilating and air-condition-ing (HVAC) systems is considerable. According to recentlypublished data, nearly 68% of the total energy used in serviceand residential buildings is attributable to HVAC systems [1]. Onthe other hand, natural ventilation replaces indoor air with freshoutdoor air without any energy consumption, and it also helps toovercome common health problems related to insufficientmaintenance of mechanical ventilation systems. Typically, theenergy cost of a naturally ventilated building is 40% less than thatof an air-conditioned building [2,3]. From a design’s point of view,it is noticeable that modern building designers make imaginativeuse of glass and space to create well-lit and attractive interiors [4].However, these buildings are usually characterised by tightness

* Corresponding author. Tel.: +30 210772 3126; fax: +30 210772 3228.

E-mail addresses: gstavr@mail.ntua.gr, N.Markatos@ntua.gr (N.C. Markatos).

0378-7788/$ – see front matter � 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.enbuild.2008.02.022

and highly glazed facades, often with poor shading. This, combinedwith extra heat gains from the electric lighting and officeequipment, such as computers and photocopiers, increase theoverheating risk that is finally leading to a significant degradationof indoor thermal comfort [5]. This problem is challenging forengineers who must design optimum ventilation systems giventhe above constraints of improvident application of HVAC systems.Natural ventilation uses the freely available resources of wind andsolar energy and could represent an optimum ventilationtechnique. Although, these resources are free, they are verydifficult to control [4]. The challenge is to provide the appropriatecontrol mechanisms to establish the required indoor air quality(IAQ). To achieve this, it is necessary to understand the physics ofnatural ventilation.

The air movement in a naturally ventilated building is a result ofpressure differences produced by wind and buoyancy forces [4,6].The most common models to predict the performance of naturallyventilated buildings are network, zonal and field (computationalfluid dynamics, CFD) models. Network models are used for theairflow rate prediction through the openings of a building. Thiskind of models can predict the airflow rates adequately but havethe disadvantage of not predicting the airflow field inside the

Fig. 1. (a) Experimental chamber and (b) geometrical details.

G.M. Stavrakakis et al. / Energy and Buildings 40 (2008) 1666–1681 1667

building, thus they produce little information about pollutanttransport and local thermal discomfort. When experimental datado not exist, network models could be used for validation ofimplemented CFD models, such as in reference [7]. On the otherhand, zonal modelling may predict both the airflow rates and airdistribution with relatively high accuracy, especially whentemperature variations are concerned. However, applications ofthese models in cases of mixed convection in indoor spacesshowed that zonal models did not provide satisfactory predictionsfor velocity distribution concerning indoor airflow [8]. In this lastinvestigation, CFD and zonal models were compared with availableexperimental data. The main conclusion was that zonal modellingunder-predicted velocity distribution compared to the CFD modelwhich provided higher accuracy concerning the airflow field andthus gave a better prediction of the recirculation region. The sameconclusion may be found in reference [9], where isothermal indoorairflow is investigated. This work shows that airflow predictions inlarge spaces are substantially more accurate when obtained by aCFD model, even with coarse grids, than that obtained by variouszonal models. Finally, for complicated flow fields the specificationof ‘‘zones’’ is at best speculative. For this reason, field modelling isconsidered to be a more accurate method to deal with the problemof natural cross ventilation. Especially when the airflow isrepresented by strong streamline curvature, due to wind forces,CFD modelling is considered as the most suitable tool for reliableairflow simulation. The more accurate the information of anyrecirculation region the more advanced the knowledge about localthermal discomfort (especially due to air draughts) and pollutantdistribution; for example, the possibility of pollutant confinementin certain regions of the indoor space.

Natural ventilation has been widely investigated by manyresearchers. Jiang et al. [10] presented an extensive experimentaland computational study (LES, large eddy simulation) of naturalventilation, driven only by wind forces for simple geometriesrepresenting cross-ventilation and single-sided ventilation con-figurations. In order to reduce the computational cost, Evola andPopov [11] applied Reynolds Averaged Navier-Stokes (RANS)models, the standard and the RNG k–emodels, for the experimentalset up described in reference [10], and also obtained reasonableaccuracy for the velocity distribution inside the building model andalso for the ventilation flow rates. In most cases, research for windforces effects on natural cross-ventilation is focused on windtunnel experiments for symmetric building-like models, and isoften associated with advanced turbulence models such as LES[11–15]. These investigations provide useful information about theair movement inside buildings, but the geometrical symmetry andthe controlled conditions in wind tunnels mean that the flow takesplace under idealized conditions. Building-scale experimentalresults of the wind effect for a single-sided ventilation case werepresented by Dascalaki et al. [16]. A validated LES model for thiscase may also be found in reference [15]. Buoyancy-driven single-sided natural ventilation has also been studied widely for theassessment of any heat gain by internal heat sources in enclosedspaces [17,18]. Experimental measurements and numericalanalysis of this type of natural ventilation may be found inreference [17], where an LES model is validated with experimentaldata for a simple geometry. In case of problems with more complexgeometries, for which the demand of computational resources ishigh, RANS modelling may produce reasonably accurate results[18,2]. The first application of such models was back in 1983 byMarkatos [19]. A case of combining wind and buoyancy forces waspresented by Chen [20], for the discussion of the potential of CFD inorder to design buildings that take advantage of the wind, withinternal heat gains taken into account. Thermal comfort providedby natural ventilation has also been studied in reference [21]. The

main conclusion was that indoor thermal comfort in summer canbe improved by appropriately controlling window opening, inaccordance with the temporal variations of indoor and outdoorclimatic conditions.

The objective of the present study is to investigate the potentialof RANS modelling in natural cross-ventilation for an experimentalchamber with two openings (doors) at non-symmetrical locations.The research focuses on the numerical analysis of indoor airflowusing CFD techniques and the validation of the numericalpredictions with the experimental results. Both wind and buoy-ancy forces were taken into account to obtain results for velocityand temperature distributions. The numerical results werevalidated with the experimental measurements for two typicalsummer days. The reliability of the mathematical models appliedwas also investigated using two different computational domains,according to the wind incidence angle and also accounting forinternal–external flow effects. Finally, thermal conditions of thechamber were examined by integrating two additional mathema-tical models, found in literature [22–26], standing for thermalcomfort.

2. Method of analysis

2.1. General

In the present study, natural cross-ventilation is examinedexperimentally and numerically. The experiments took place in achamber, also presented in reference [27], that was built, amongothers, for indoor air quality examination purposes and consistedof a roof covered with roman tiles and a radiant barrier reflectiveinsulation system (Fig. 1, Section 2.2 for further details). Two doorsare located at the north and south facing walls and the room isventilated through these openings. A small internal partition of1 m height is also located adjacent to the north wall. As far as windforces are concerned, both doors were kept wide open (cross-ventilation) to ensure relatively large pressure differences. Thereflective insulation of the side walls causes temperaturedifferences between internal and external surfaces of the walls.This creates temperature difference among internal wall surfaces

Fig. 2. Arrangement of probes for: (a) case A and (b) case B.

G.M. Stavrakakis et al. / Energy and Buildings 40 (2008) 1666–16811668

and incoming outdoor thermal masses and consequently genera-tion of buoyancy forces. The above-mentioned arrangement of thebuilding establishes an internal air movement governed by bothwind and buoyancy forces.

Referring to the numerical simulation, a mathematical modelwas developed for the prediction of indoor air movement, withinthe general framework provided by a commercial CFD code(FLUENT 6.3.26). The model is based on three high Reynoldsnumber RANS turbulence models, modified for buoyancy effects,that were tested following the procedure reported in reference[28]. Boundary conditions were provided by measurementsaccomplished for internal flow by thermo-couples or for externalflow by a weather station. The simulated airflow was examined interms of two different computational domains, due to various windincidence angles, and finally the temperature and velocitydistributions were the outcome of the solution procedure.

Thermal comfort predictions in the occupied zone were alsoincluded using two models found in literature, assessing local andglobal (general) discomfort. The first one, used for local discomfortassessment, is the well-known PMV/PPD model [22–24], extendedto account for non-air-conditioned buildings in warm climates[25]. The factors predicted mean vote (PMV), predicted percentagedissatisfied (PPD) and percentage dissatisfied (PD) represent aquantification of thermal dissatisfaction of occupants underseveral activity levels and clothing, with respect to air tempera-ture, air velocity, turbulence, wall temperatures and relativehumidity. The second thermal comfort model, used for globaldiscomfort assessment, is the so-called ‘‘adaptive model’’ ofthermal comfort in naturally ventilated buildings found inreferences [26] and [29], where it is presented as an optionalmodel. It is based on an extensive field study by de Dear et al. [30]and determines a range of indoor comfort temperatures thatcorrespond to a percentage of thermal acceptability, as a functionof the mean monthly outdoor temperature. Details for both modelsare given in Section 2.3 below.

2.2. Experimental equipment, methodology and results

The test room is of dimensions 6 m � 4 m � 5.5 m (Fig. 1a andb). The side walls are a two series brick construction with a bubblematerial lamination among layers of aluminum foil placed in the20 mm gap of the brick layers. The total wall thickness consists of90 mm brick, 10 mm air gap, 1 or 2 mm reflective insulation,10 mm air gap and 90 mm brick. The walls can be coated internallyand externally resulting to a total width ranging from 200 to240 mm (including a 20 mm thickness of the wall sheathing-plaster on each side). The experimental measurements referring tovelocity and temperature, obtained at various locations of the testroom were selected according to regulations found in reference[24]. The schedule of the experiments included 3 h total samplingperiod for two typical summer days and the time-intervalsampling between consecutive measurements was 60 s. Underthose imposed conditions, there were simultaneous recordings oftemperature and velocity at the middle of the inlet door A1 or A2(being south or north doors, respectively, according to wind datataken by a weather station), at positions B1, B2, C1, C2, C3 and oftemperature at point D (middle of the room) (Fig. 2a). That was forthe first day’s arrangement (case A). For the second day’sexperimental arrangement (case B), the sampling points weredifferent and measurements were obtained as follows: velocityand temperature at A1 or A2, B1, B2, B3, C1, C2, C3 (Fig. 2b). Forboth experiments, temperatures at the middle of the internalsurface of each wall were also recorded. The exact location,measured flow property at each sampling point and which doorplays the role of inlet are given in Table 1. Temperature and

(one-dimensional) velocity measurements in the test room wereobtained using the KIMO thermo-anemometer multi-probes VT200F [31] with accuracy of �3% for readings of 0–3 m/s and �2% forreading of 0.1 8C.

Temperature of internal wall surfaces of the walls wasmeasured using UTECO thermo-couples DIN 43732, connectedto a data logging system [32] for the collection of the experimentalresults.

Sample experimental results obtained (also presented inreference [33]), for example, for case A, referring to velocity andtemperature at the selected locations and the temperature of thebuilding walls are presented in Figs. 3 and 4, respectively.

Bi-directional flow may occur through the openings due tobuoyancy forces. In this case, information about the infiltrating airmay be lost by placing the air speed sensor at the middle of theinlet door. Thus, it is important to investigate this possibility underthe current experimental conditions for both cases. The measuredtemperature differences between indoor and outdoor airflowswere 1.9 and 1.0 8C for cases A and B (see Table 2; Fig. 3),respectively. According to the above temperature differences, thecomparison of the importance of wind and buoyancy forces isobtained using the Archimedes number as follows [15]:

Ar ¼ Grashof

Reynolds2¼ bgH3

DT

U2D2(1)

where b = 1/Tref is the thermal expansion coefficient, Tref thereference temperature taken as Tref ¼ ðToutdoor þ Twalls averageÞ=2,

g = 9.81 m/s2 the gravitational force, DT ¼ 1:9 �C for case A

1:0 �C for case B

� �, U

the wind speed at the building height. Its value is taken by thepower-law profile of the incoming wind using Eq. (3). H is theheight of the inlet door and D is the chamber’s depth equal to 4 m(see Fig. 1b).

Table 1x, y, z coordinates of experimental locations

Case A A1 A2 (inlet) B1 B2 C1 C2 C3 D

Coordinates (x, y, z) 5.25, 0, 1.1 0.75, 4, 1.1 4.7, 0.7, 0.5 4.7, 0.7, 1.25 1.8, 1.6, 0.77 1.8, 1.6, 1.4 1.8, 1.6, 1.93 3, 2, 2.75

Temperature O X X X X X X X

Velocity O X X X X X X O

Case B A1 (inlet) A2 B1 B2 B3 C1 C2 C3

Coordinates (x, y, z) 5.25, 0, 1.1 0.75, 4, 1.1 3, 2, 0.2 3, 2, 2 3, 2, 3 0.7, 2, 0.5 0.7, 2, 1 0.7, 2, 2

Temperature X O X X X X X X

Velocity X O X X X X X X

Symbols: X for measured property, O for non-measured property.

G.M. Stavrakakis et al. / Energy and Buildings 40 (2008) 1666–1681 1669

Using the above data, Eq. (1) gives an Ar number equal to 0.02and 0.0029 for cases A and B, respectively. Thus, because of Ar� 1for both cases, natural convection due to the buoyancy effect ismuch smaller than forced convection due to the wind effect.Furthermore, the chamber is free of internal thermal sources andalso, even though the height at which wind speed is recorded isrelatively low (7.5 m), the chamber is built in a rural environmentfree of thermal sources. All the above advocate that the airflowinside and outside the chamber is wind dominant. However, thebuoyancy effect is not neglected in the CFD model due to thepresence of experimental results for temperature, used for furtherverification of the numerical results.

Under the action of the wind, and taking into account that bothopenings have the same dimensions and also that the internalspace has no obstacles except the small partition, the air flows inthrough the one opening leading to high pressures at this area. Thepressure at the opposite door is lower and due to this pressuredifference between the two doors, the air is finally leaving thechamber through the opposite door. According to the aboveanalysis, the flow through the openings is not bi-directional (if itwere it would have been predicted by the CFD model, which isdescribed below, as, for example, in reference [2]). Thus, thevelocity at the middle of the opening is representative of the airentering the chamber.

Fig. 3. Typical experimental results for velocity and temperature, case A.

2.3. Mathematical modelling

2.3.1. The governing equations

Natural ventilation is a phenomenon of random nature due tothe constant changes of external weather conditions. Thus, anymathematical model applied for the prediction of naturalventilation should include the dynamic nature of the externalconditions. In applying a CFD method one should ideally use atime-dependent approach, which, however, would require knowl-edge of the time-dependent variations of the boundary conditionsused. This technique would provide very detailed and usefulinformation about natural ventilation but it requires excessivecomputational resources for practical applications. An engineer’sapproach to overcome such technical restrictions is the steady-state assumption, as most phenomena take place at almost steady-state conditions over long periods of time. Furthermore, duringday-time cycles in real buildings, temperature changes occur butthe steady-state assumption is considered to be valid over longperiods, because the time needed for the development of theairflow pattern is short compared to the duration of the day-timecycle and the values of the time constants of the massive buildingelements required for passive ventilation. Thus, in order torecognize potential time-averaged values of temperatures andvelocities, two temporal sub-domains were chosen, representativeof minimum fluctuations of monitored flow properties for noonand afternoon hours of cases A and B, respectively. The selectedtime periods were 13:00–13:30 h (case A) and 19:00–19:30 h (caseB). In any case, the mathematical model developed is general andmay be applied to both steady-state and transient problems, asrequired.

The ensemble-averaged values of the external wind wereselected for time periods not exceeding the recommended timeperiod limit of 30 min, as found in reference [34] for fieldmeasurements. Following this, the selected 30 min time periods ofthe experimental cases studied were identified according to – as

Fig. 4. Temperature at the middle of the internal surface of each wall, case A.

Table 2Experimental conditions

External conditions

Cases Inflow planes (Fig. 5) Relative humidity (%) Outdoor temperature (K) Wind speed at 7.5 m (m/s) Incidence angle (u)

Case A A1, A2 19.2 308.90 1.48 358Case B B1 24.8 305.50 2.85 908

Internal conditions

Cases Tnorth wall Tsouth wall Twest wall Teast wall

Case A 300.9 303.0 301.4 302.0

Case B 302.0 302.1 302.0 302.1

Fig. 5. Computational domains for each case: A1 and A2, inflow boundaries for case

A; B1, inflow boundary for case B.

G.M. Stavrakakis et al. / Energy and Buildings 40 (2008) 1666–16811670

stable as possible – recordings of external and internal conditionsprovided by the weather station and the hot-wires, respectively. Asimilar technique can also be found in reference [35]. Significantinformation is provided by the steady-state solution concerningthe effects of the prevailing ensemble-averaged values of winds ofany building’s site on the internal structure of the flow. Since CFD isbased on mean representative wind data, it could lead to optimaldesigns even in the pre-construction phase of a building, with theexternal ‘‘fluid mechanics’’ taken into account.

The mathematical model applies numerical techniques to solvethe Navier-Stokes (N-S), continuity and energy equations for 3D,turbulent fluid flow. All the governing conservation equations, forsteady-state conditions, can be written in the following generalform [36]:

divðr~u’� G’grad’Þ ¼ S’ (2)

where w is the dependent variable, i.e. 1 for mass continuity, ~u forvelocity, T for temperature, Ci for the concentration of variouschemical species i, Gw the ‘‘effective’’ exchange coefficient ofvariable w and Sw is the source/sink term of variable w [36]. Thetransferred quantity w also stands for turbulence dependentvariables, here k the kinetic energy of turbulence and e the eddydissipation rate. In this study, three RANS models were applied, thestandard k–e, the RNG k–e [37] and the so-called ‘‘realizable’’ k–e[38] model, all modified to account for buoyancy effects due todensity differences [28]. All models treat flow effects close to wallsusing standard wall functions [39,40]. The assumptions made for theproblem were: (a) single phase, steady-state flow for a Newtonianfluid and (b) heat transfer at the walls by either conduction orradiation was neglected due to the already measured internal-wall-surface temperature and the use of reflective insulation.

The CFD code used for the numerical simulations employs astandard finite-volume method and a body-fitted structured grid[41], which is adopted to account for two different computationaldomains, corresponding to 358 (grid A) and 908 (grid B) windincidence angle for cases A and B, respectively (Section 2.3.2 forfurther details). The first-order upwind discretization scheme andthe SIMPLE solution algorithm for handling pressure were used[42]. Simulations were performed on a Windows PC with one2.4 GHz CPUs and 1 GB of RAM and required approximately 36 and24 h for the optimum grids A and B, respectively.

2.3.2. Computational domains and spatial discretization

As mentioned earlier, two grid methodologies were applied forthe simulation according to the wind incidence angle. The mainpurpose was to simulate the air movement in the chamber as aresult of the interaction among internal and external flow effects,within reasonable computational resources. The problem followsthe general theoretical aspects of the flow around a bluff body.Consequently, specific techniques found in literature [43,44] wereapplied concerning the computational domain. Thus, in case of

vertical wind direction (case B) the computational domain, forwhich grid B was constructed, had a downstream length of 10H (H:chamber’s height), an upstream length of 5H, a lateral length of 5H

on both sides of the chamber and a height of 18.2H, in order toimpose, as inflow boundary conditions, the appropriate velocityand turbulence distribution, corresponding to the atmosphericboundary layer. In case of non-vertical wind direction (case A), twoinflow boundaries are needed to account for the incoming wind. Inorder to capture the reattachment point downwind to the chambercorrectly, two outflow boundaries were imposed being thedownwind faces of the flow domain. This leads to a computationaldomain, resulting to grid A, which consisted of 10H length amongthe chamber’s external walls and all lateral boundaries with thehigh boundary being at the same height as in the case of verticalwind direction. The computational domains constructed for eachexperimental case and the corresponding inlet door are presentedin Fig. 5.

Since grid A is simply a result of dimensional expansion of grid Bin regions where no flow obstructions occur, a grid-independencystudy was only performed for grid B. The optimum mesh producedfor grid B led to the optimum grid A with additional meshing in theextra regions of the computational domain in the case of non-vertical flow direction. Spatial discretization of the flow domainwas examined by repeating runs for grids with continuouslyincreased grid-nodes density. A comparison for the verticalvelocity distribution at the middle of the test room, obtainedusing various grids is presented in Fig. 6.

The solution obtained using each grid was also examined forother independent variables at various physical locations of thedomain and, as demonstrated in Fig. 6, a grid-independent solutionwas achieved using a grid consisting of 636,456 hexahedral cellsfor grid B and, consequently, a grid of 730,488 hexahedral cells forgrid A, corresponding to experimental cases B and A, respectively.

Fig. 6. Velocity distribution with height at the middle of the test room for various

grids (case of grid B).

G.M. Stavrakakis et al. / Energy and Buildings 40 (2008) 1666–1681 1671

The optimum discretization for both grids A and B is presented inFig. 7. The selection of a structured grid, instead of a moreconvenient unstructured was due to more accurate results thatmay be obtained, at least for the case of the flow around a bluffbody, using a structured grid, as found in reference [45].

The grids used were highly non-uniform characterised by highgrid-nodes density near solid surfaces. The minimum cell size

Fig. 7. Optimum mesh for both grids A and B: (a) three-dimensional meshing, (b) longitu

near each wall was 0.05 m, leading to y+ values less than 150 inorder to apply properly ‘‘wall-function’’ boundary conditions[39,46].

2.3.3. Boundary conditions and special sources

For some of the imposed boundary conditions measured datarepresenting external and internal conditions have been used,while the rest are set according to well-known practices[2,11,21]. For the selected time periods (Section 2.2) ofexperimental monitoring, time-averaged values were producedreferring to outdoor temperature, relative humidity, wind speedand direction at 7.5 m from the ground, as provided by a weatherstation. At the interior, wall temperatures were measured at themiddle of each internal wall surface. The measured boundaryvalues are summarized in Table 2. According to these measuredflow variables, the boundary conditions were categorized asfollows:

(1) S

dina

olid planes: No-slip, no-penetration condition for momentumand fixed temperatures.

(2) S

ymmetry planes: Zero normal velocity and zero normalgradients of all variables.

(3) O

utflow planes: Zero diffusion flux for all variables and overallmass balance correction [47].

l meshing, (c) partition’s height plane meshing and (d) traverse plane meshing.

G.M. Stavrakakis et al. / Energy and Buildings 40 (2008) 1666–16811672

(4) I

nflow planes: Specified external temperature and moisturemass fraction as given by the weather station. Modifiedequations of the atmospheric boundary layer [48] wereused to account also for incidence angles other thanvertical:

u ¼ urefz

h

� �1=7

(3)

v ¼ vrefz

h

� �1=7

(4)

kinflow ¼u2�ffiffiffiffiffiffiCm

p 1� z

h

� �2

(5)

einflow ¼C3=4

m k3=2

l(6)

where u, v, kinflow, einflow are the inflow velocity and turbulenceproperties; uref ¼ velrefsin u and vref ¼ velrefcos u, h = 300 m. u standsfor wind incidence angle. If u = 908 then Eqs. (3)–(6) were imposedonly at the upwind boundary (plane B1, see Fig. 5). If u < 908 thenEqs. (3)–(6) were imposed at the upwind (west) and at the onelateral (north) boundary (planes A1 and A2, see Fig. 5). u* is thefriction velocity, u� ¼

ffiffiffiffiffiffiffiffiffiffiffitw=r

p. tw is the shear stress and tw ¼

f rvel2ref=2 is the density of the mixture of air and moisture. f is thefriction coefficient f ¼ 0:045ðvelrefh=vÞ�1=4. v is the kinematicviscosity of air. velref is the wind velocity at 100 m provided by the

Fig. 8. Numerical results for 1/7 and 1/6 power-law inlet profiles for: (a) incoming wind v

C3 experimental locations (case B, u = 908).

recorded velocity and the calculated one (Eq. (3)) at 7.5 and at300 m, respectively, by the weather station using Eq. (3). l is themixing length, l = min[kz, 0.085h]. k = 0.41 stands for the VonKarman constant and Cm = 0.09.

The main difference of the ‘‘realizable’’ k–e model against theother two models is that it is based on the dynamic equation forfluctuating vorticity. This leads to a Cm value expressed as functionof vorticity and not just as a fixed value [38]. However, the imposedCm at the inflow boundaries is considered acceptable as theincoming flow is simulated as a flat boundary layer, for whichexperiments have shown that Cm � 0.09 in the inertial sublayer[38].

The experimental chamber is built in a flat rural environment(Psachna area, Evia, Greece) surrounded by low-rise trees and low-rise residences at a sufficiently away distance. Thus, any externaldisturbance of the incoming wind is assumed to be eliminated andthe flow is re-established at its form of the atmospheric boundarylayer equations. Therefore, for full-scale 3D modelling, a stand-alone rural-type chamber is assumed. The exponent of the power-law for a surface terrain that represents a flat rural site is taken as1/7 (Eqs. (3) and (4)). Two additional runs have been performed forthe investigation of the terrain’s roughness impact on thenumerical results, using the standard k–e model. For this reason,1/7 and 1/6 power-law profiles were applied, corresponding to flatand typical rural environment, respectively [49]. The resultsobtained are presented, for example, along the vertical direction ofC1, C2 and C3 experimental locations, in Fig. 8. It is observed thatno significant differences occur and thus both profiles could be

elocity, (b) x-velocity and (c) temperature along the vertical direction of C1, C2 and

G.M. Stavrakakis et al. / Energy and Buildings 40 (2008) 1666–1681 1673

used to predict natural ventilation of the chamber with the sameaccuracy.

2.3.4. Water vapour transportation modelling

The basic assumption of moisture transport modelling is thatair is considered as a mixture of dry air and water vapour. Watervapour represents a scalar transported by the airflow (dry air:carrier gas), according to the general Eq. (2), that becomes:

divðr~uYH2O þ~JH2OÞ ¼ SH2O (7)

where YH2O is the water vapour mass fraction in the mixture,~JH2O

the diffusion flux and SH2O is the source (water vapour production)imposed as a fixed mass fraction at the inflow boundary as afunction of the measured relative humidity, temperature andvapour pressure at the chamber’s site.

The diffusion flux, ~JH2O, can be written as:

~JH2O ¼ � rDH2O;m þmt

Sct

� �rYH2O � DT;H2O

rT

T(8)

where DH2O;m is the mass diffusion coefficient for water vapour in themixture and DT;H2O is the thermal diffusion coefficient. The first onefound in literature [50] with respect to the reference temperature(defined as an averaged value among internal and external tempera-ture), while the second one was calculated using the kinetic-theorymethod [47]. As far as the other factors are concerned, Sct is theturbulence Schmidt number and mt is the turbulence viscosity.

Referring to the physical properties of the mixture, they wereimposed using the ideal gas law for an incompressible flow fordensity, the ideal gas mixing law for both thermal conductivity andviscosity, while the heat capacity is expressed as a mass-fraction-average of moisture and air’s heat capacities [47]. The abovemethods use constant values of the species properties at thereference temperature.

2.3.5. Thermal comfort modelling

For thermal comfort evaluation, under the already describedextreme summer experimental conditions, the extended PMVmodel was firstly implemented in the mathematical CFD model.The extended PMV model for non-air-conditioned buildings isbased on the inclusion of the expectancy factor, e, which isassumed to depend on the duration of the warm weather over theyear and whether non-air-conditioned buildings can be comparedwith many others in the region that are air-conditioned. Forexample, if the weather is warm all year or most of the year andthere are no or few other air-conditioned buildings, e may be 0.5,while it may be 0.7 if there are many other buildings with air-conditioning. In regions with only brief periods of warm weatherduring the summer, the expectancy factor may be 0.9–1. Anothercritical factor which contributes to the reported differencebetween the calculated PMV and actual thermal sensation innon-air-conditioned buildings is the estimated activity. People,unconsciously, tend to slow down their activity and thus theyadapt to the warm environment by decreasing their metabolic rate.It has been found that the metabolic rate is reduced by 6.7% forevery scale unit of PMV above neutral. Further details of theextended PMV can be found in reference [25]. The numericalprocedure includes the calculation of the traditional PMV (for air-conditioned spaces) and the reduction of the metabolic rate by 6.7%,using linear interpolation techniques to account for intermediatevalues of PMV in the intervals {0,1}, {1,2}, {2,3} (Eq. (16)). After that,the PMV is recalculated and the emerged value is multiplied by theexpectancy factor, e. PMV ranges from �3 to +3 for cold and hotsensations, respectively, with mid values representing intermediatethermal perception states. On the other hand, this factor can beexpressed in terms of dissatisfied occupants’ percentage using the

PPD factor. As far as discomfort due to air draughts is concerned, itcan be quantified with respect to local air velocity, temperature andturbulence intensity using the PD factor. The algebraic expressionsof this integrated model are as follows.

2.3.5.1. PMV for natural ventilation.

PMVtrad ¼ ½0:303expð�0:036MÞ þ 0:028L (9)

where PMVtrad is the traditional PMV (for HVAC), M the metabolicrate (W/m2), applied for standing sedentary activity in the presentstudy [24] and L is the thermal load on the body expressed asfollows:

L ¼ internal heat production

� heat loss to the actual environment

L ¼ M �W � f3:96� 10�8 f cl½ðTcl þ 273Þ4 � ðTr þ 273Þ4

þ f clhcðTcl � TÞ þ 3:05� 10�3½5733� 6:99ðM �WÞ

� pv þ 0:42ðM �W � 58:15Þ þ 1:7� 10�5Mð5867

� pvÞ þ 0:0014Mð34� TÞg (10)

where W stands for active work or shivering (W/m2) and fcl is thegarment insulation factor (1 clo = 0.155 m2 K/W) expressed as:

f cl ¼1:05þ 0:645Icl; Icl0:0781þ 1:29Icl; Icl <0:078

� �(11)

The term Icl stands for the resistance to sensible heat transferprovided by a clothing ensemble (clo) and its value was taken fortypical clothing insulation under summer conditions (0.5 clo). TheTcl (8C) term is defined as the cloth temperature and is determinedbelow as:

Tcl ¼ 35:7� 0:028ðM �WÞ � Iclf3:96

� 10�8 f cl½ðTcl þ 273Þ4 � ðTr þ 273Þ4 þ f clhcðTcl � TÞg (12)

In Eqs. (10) and (12), T (8C) is the calculated local airtemperature by the CFD model, hc is the heat-transfer coefficientbetween the cloth and air (W/m2 K) and Tr (8C) is the mean radianttemperature (Eq. (14)). The heat-transfer coefficient is given by:

hc ¼ 2:38ðTcl � TÞ0:25 for 2:38ðTcl � TÞ0:2512:1u0:5

12:1u0:5 for 2:38ðTcl � TÞ0:25 <12:1u0:5

� �(13)

where u is the local velocity calculated by the CFD model.The mean radiant temperature is computed for an averaged

wall temperature, since there were no significant differencesbetween wall temperatures during the experiments, i.e.:

Tr ¼X4

i¼1

TiF p�i (14)

where Ti is the temperature value at the i wall and Fp�i stands forthe radiation shape factor from face p of a grid cell to the visibleroom surface i.

The water vapour pressure, which participates in Eq. (10), wascalculated using the following equation:

pv ¼PYH2O=ð1� YH2OÞ

0:622þ YH2O=ð1� YH2OÞ(15)

where P is the local absolute pressure calculated by the CFD model.The PMV is then recalculated using Eqs. (9)–(15) with a reduced

metabolic rate (Mred) according to Eq. (16) below:

Mred ¼�0:067M � PMVtrad þM; PMVtrad 2 ½0;1�0:067M � PMVtrad þ 1:004M; PMVtrad 2 ð1;2�0:067M � PMVtrad þ 1:013M; PMVtrad 2 ð2;3

8<:

9=; (16)

G.M. Stavrakakis et al. / Energy and Buildings 40 (2008) 1666–16811674

Consequently, PMV for natural ventilation (PMVNV) is deter-mined as follows:

PMVNV ¼ e½0:303expð�0:036MredÞ þ 0:028L (17)

where e is the expectancy factor (e = 0.7 for Athens [25]).

2.3.5.2. PPD and PD. Finally, the factors PPD and PD are computedas follows:

PPD

PPDð%Þ ¼ 100� 95exp½�0:03353ðPMVNVÞ4

� 0:2179ðPMVNVÞ2 (18)

PD

PDð%Þ ¼ ð34� TÞðu� 0:05Þ0:62ð3:14þ 0:37uTuÞ (19)

for u < 0.05, use u = 0.05 m/s and for PD > 100%, use PD = 100%,

where Tu is the turbulence intensity Tu(%) = 100(2k)0.5/u.

The adaptive comfort standard has a mean comfort zone bandof 5 K for 90% acceptance, and another of 7 K for 80% acceptance,

Fig. 9. Numerical results by various wind velocities at 7.5 m height for: (a) incoming

experimental locations C1, C2 and C3 (case B, u = 908).

both centered around the optimum comfort temperature calcu-lated as follows [26,29]:

Topt:comf: ¼ 0:31Ta;outdoor þ 17:8 ð�CÞ (20)

where Topt.comf. is the optimum indoor temperature for thermalneutrality and Ta,outdoor is the mean monthly outdoor temperature.The adaptive model can be applied within a mean outdoortemperature range from 10 to 33 8C and thus it cannot provideinformation for more severe weather conditions, such as thosedescribed in case A. On the other hand, the PMV model [25] isacceptable for all conditions. According to this restriction boththermal comfort models were applied for case B. For case A, onlythe extended PMV is used since the recorded outdoor temperature(35.9 8C) was out of the range of the adaptive model’s applicability.

3. Results and discussion

3.1. Airflow patterns

Due to the dynamic nature of the external wind, speed anddirection, the specification of the incoming wind’s boundaryconditions is highly uncertain. Thus, any mathematical approach

wind velocity, (b) x-velocity and (c) temperature along the vertical direction of

G.M. Stavrakakis et al. / Energy and Buildings 40 (2008) 1666–1681 1675

requires a parametric study to quantify the effect of boundaryconditions (bc’s) on the interior results. For this reason, suchsensitivity study was performed concerning vertical incidenceangle of the incoming wind (case B), using the standard k–e model.This study produced results obtained for different wind speedsmeasured at 7.5 m height, corresponding to possible fluctuatingrecordings by the weather station. A �10% fluctuation factor to themean value of 2.85 m/s is applied to investigate the response of thenumerical results. According to this, recorded wind speeds of 2.565,2.7075, 2.85, 2.9925 and 3.135 m/s were used. The corresponding bcvelocity profiles of the incoming wind are presented in Fig. 9(a), fittedby the power-law equation (Eq. (3)). Runs were performed usingthese profiles restarting the CFD program by the solution obtained foru7.5m = 2.8 m/s to accelerate convergence. The numerical resultsalong the vertical direction of C1, C2 and C3 experimental locationsare presented in Fig. 9(b) and (c) for the x-component of velocity andfor temperature, respectively. It is observed that the solution is littlesensitive to a 10% variation of external wind speeds. Specifically, the

Fig. 10. Impact of the incoming wind’s incidence angle on the: (a) incoming wind x-velocit

direction of experimental locations B1 and B2 (case A, u = 358).

maximum divergence among the numerical results obtained for2.85 m/s wind speed with those obtained for the other wind speeds isranging from 0.5% to 4% and 0.16% to 0.3% for x-velocity andtemperature, respectively.

The previous analysis verifies the assumption of using just onemean wind-speed value as a time-averaged value and thus makesthe steady-state assumption to be valid, at least for practicalengineering purposes. Furthermore, the solution is not substan-tially affected by the turbulence distributions at the inletboundaries as presented in reference [33]. In this last investigation,the problem was solved using the equations of atmosphericboundary layer for the extended domain and also for a limited,between the two doors, domain applying a uniform velocity at theinlet door. No significant qualitative difference was observedamong the two approaches with the first one, adopted in thepresent study, leading to more accurate results.

The problem is also solved for different wind incidence angles,using the standard k–e model, to evaluate the sensitivity of the

y, (b) incoming wind y-velocity, (c) x-velocity and (d) temperature along the vertical

Fig. 11. Experimental and numerical results for: (a) x-velocity (case A, u = 358), (b) temperature (case A, u = 358), (c) x-velocity (case B, u = 908) and (d) temperature (case B, u = 908).

G.M. Stavrakakis et al. / Energy and Buildings 40 (2008) 1666–16811676

results to this parameter. The mean recorded value of the windspeed for the case A is 1.48 m/s (Table 2). Three incidence angleswere tested numerically: 308, 358 and 408 corresponding to atime-averaged value of 358, used for comparisons with the

Fig. 12. Velocity vectors at partition’s height for case A:

experimental results. In Fig. 10(a) and (b), the velocitycomponents of the incoming wind (Eqs. (3) and (4)) thatrepresent the tested wind directions are presented. The impact ofthe incoming wind’s incidence angle on the x-velocity and

(a) standard k–e; (b) realizable k–e and (c) RNG k–e.

G.M. Stavrakakis et al. / Energy and Buildings 40 (2008) 1666–1681 1677

temperature is presented in Fig. 10(c) and (d) along the verticaldirection of experimental locations B1 and B2. It is seen that theresults are little sensitive to a �15% change of the mean incidenceangle.

It should be emphasized that the usefulness of the developedmodel lies in the fact that the same uncertainty in the results existsfor all designs that may be studied. In other words, although theerror in predicting a variable may be small or large it is going to bealso the same for all alternative designs considered. Thus, therelative change to the results introduced by a design change will becertainly predicted correctly.

Results obtained by both experimental measurements andnumerical predictions are presented in Fig. 11. Absolute values ofx-velocities are used for validation, i.e. absolute values of velocitiespresented in Figs. 9(b) and 10(c) at each experimental location, asonly one-dimensional velocity magnitude measurements wereperformed.

There are significant points to be noted resulting from thecomparison among experimental and numerical results. First of all,it can be noticed that for case A, which represents noon hours with358 incidence angle, the discrepancy for temperature at the inletdoor (A2) was only 0.8% using the standard k–e model, beingslightly higher using the other two models but in any case notexceeding 1.5% when applying the RNG model. Low differenceswere also obtained referring to the middle location of the chamber(point D), especially by the RNG k–e model for which the calculatedminimum error was only 0.9%. As far as any other location isconcerned, it is observed that the discrepancy for temperature is alittle higher and obtains its maximum value at the location B2,approximately 4.1% using the RNG model, which represents thelower discrepancy among all the applied models. This difference

Fig. 13. Velocity vectors at partition’s height for case B:

may be partly due to experimental errors but it may also occurbecause of the possibility of air infiltration through the oppositedoor (A1, Fig. 2a), considered as outlet in the mathematical model,due to random direction variations, since B2 was placed next to theoutlet door. That is why the error at location B1, which was placed atthe same vertical direction, was also high. Specifically, it was around4% using the RNG model, which presents the lower discrepancyvalue compared to the other models. Referring to the rest of theexperimental locations, the difference varied from 2% to 4% for allmodels, while the ‘‘realizable’’ model was found to lead to slightlyhigher differences. The x-velocity discrepancies were higher butcould be considered acceptable because of the inevitable uncer-tainties during the experiments, due to uncontrolled weatherconditions such as external wind speed and turbulence. Particularly,the predicted inlet x-velocity (point A2, Fig. 2a) differed frommeasurements about 11–12% using the standard and the ‘‘realiz-able’’ models, respectively, being much lower using the RNG model(around 2%). On the contrary, the standard k–e model provided abetter solution at B1 and B2 (close to the outlet door) with thediscrepancy being 16% and 9.5%, respectively. However, using the‘‘realizable’’ model, a better prediction was obtained for thelocations in front of the inlet door (C1, C2, C3), i.e. the discrepancyat the location C1 was approximately 8% rather than 25% and 18%using the other two models. Much lower discrepancies can beobserved concerning experimental case B which represents theafternoon hours. For example, the difference of the computed x-velocity decreased and it was about the same for all models leadingto an adequate prediction, i.e. the discrepancy at the inlet (A1), B3,C1 and C2 does not exceed 6%. The same conclusion may be statedfor the temperature prediction with all models performing wellenough, compared to the experimental results.

(a) standard k–e; (b) realizable k–e and (c) RNG k–e.

G.M. Stavrakakis et al. / Energy and Buildings 40 (2008) 1666–16811678

It is obvious that at the afternoon hours the proposed modelsperformed better for both velocity and temperature predictions.This may be due to the omission of heat conduction inside the wallsand of solar radiation. According to the assumptions used, theimposed boundary conditions at internal wall surfaces were theexperimental results at just one point of each wall, so in reality amean value of temperature applied at each wall, rather than adistribution of temperature (which would be an outcome of thesolution procedure if conduction had been taken into considera-tion). Furthermore, solar radiation may have a significant impacton the physical phenomenon, especially during the noon hours,thus providing a different temperature distribution than thatcalculated when this mechanism is neglected. Other errors couldbe due to the possibility of air infiltration through smallexperimental building cracks and also due to the existence ofsmall obstacles such as packets used for the equipment storage.

Finally, it may be concluded that all models used for thenumerical simulation are satisfactory, giving qualitatively similarperformance, for both experimental arrangements, while giving

Fig. 14. Experimental case A: (a) velocity magnitude (m/s), (b) temperature distr

also acceptable quantitative predictions in the sense of relativedesigns. Due to the existing uncertainties depending on theconstant variation of the external weather conditions, theproposed approach is considered sufficient enough to representnatural cross-ventilation.

The distributions of velocity magnitude vectors, obtained by allmodels for each case studied, are presented in Figs. 12 and 13. Itcan be noticed that all models lead to almost identical internal flowbehaviour and, at least qualitatively, the recirculations occur at thesame place. On the contrary, interesting differences may beobserved for the external flow. The main difference is that thestandard k–e leads to larger vortices downwind of the test chambercompared to the vortices calculated by the other two models.Especially the ‘‘realizable’’ model leads to the smallest vortices atthis particular area of the flow. However, since there were noexperimental data at this area, these differences serve just for airmovement evaluation purposes. Furthermore, the area of impor-tance is mainly the internal flow domain, as indoor air qualityissues are investigated in the present study.

ibution (K), (c) iso-relative humidity (%), (d) iso-PMVNV and (e) iso-PPD (%).

Fig. 15. Experimental case B: (a) velocity magnitude (m/s), (b) temperature distribution (K), (c) iso-relative humidity (%), (d) iso-PMVNV, (e) iso-PPD (%) and (f) iso-PD (%).

Fig. 16. Temperature variation at the middle of the chamber.

G.M. Stavrakakis et al. / Energy and Buildings 40 (2008) 1666–1681 1679

3.2. Thermal comfort study

Thermal comfort was examined under the experimentalconditions which correspond to summer days and consequentlyto high temperatures. Space restrictions dictate that only resultsobtained by the RNG k–e model are presented, as this modelpresents the best agreement with experiments especially fortemperature for both cases studied. For example, in case A, the‘‘realizable’’ model led to the highest temperature differences at allexperimental locations (see Fig. 11b) and thus it leads to under-prediction of occupant’s thermal perception. The standard k–ecould also be chosen due to similar discrepancies with those of theRNG. However, because of the better formulation validity of thelatter for flows that include strong streamline curvature andvortices [37], like in the present one, it has been selected forpresentation. It should be emphasized that thermal comfort couldequally well be studied using the other two models, because of theflexibility of the computer program developed for the presentwork, which calculates thermal comfort parameters, and iscompatible with any available flow distribution.

The distributions of local velocity, relative humidity, tempera-ture, PMVNV and PPD, for both experimental cases, are presented inFigs. 14 and 15 at the traverse plane of the chamber. Referring to theexperimental case A (Fig. 14), it can be observed that the tem-perature difference at all vertical sites that represent occupied zonesdoes not exceed 3 8C (threshold value for thermal comfort [24]).

G.M. Stavrakakis et al. / Energy and Buildings 40 (2008) 1666–16811680

In Fig. 16, for example, the maximum temperature at the middlevertical direction of the chamber is 307.1 K, while its minimumvalue is 305.8 K, even though the external temperature was 7 8Cabove the initial wall temperatures.

As far as relative humidity is concerned, it is observed that theinternal values are higher than the external, due to thetemperature decrease inside the chamber and the small pressuredifferences between the calculated local pressure and the externalatmospheric pressure. The PMVNV values reveal an unacceptableinternal thermal environment due to high external temperatures.Specifically, this factor ranges from a mean value of 1.9 in the bulkflow to 2.91 near the inlet-door area, representing warm and hotsensations in the occupied zone, respectively. This is also obvioususing the PPD factor which received high values especially near thepartition (65%) and in front of the inlet door (87%). Consequently, incase of both doors being open, the reflective insulation applied forthe walls is not enough for the establishment of the desiredthermal comfort conditions, due to the strong thermal loadentering the room by the external hot air masses. In case ofmoderate external temperatures, PPD could be minimized due tosufficient mixing, provided by the non-symmetrical locations ofthe openings. The same conclusions are valid for the experimentalcase B (Fig. 15). The maximum PPD is calculated 76.1% and is nowobserved near the partition (Fig. 15e), rather than near the southwall as in case A (Fig. 14e). This is due to the change of winddirection that leads to hot air infiltration through the east door. Themean value of PPD in the occupied zone is around 62% and 55% forcases A and B, respectively, corresponding to 38% and 45%acceptability of the indoor conditions. For both cases, internalwall temperatures are similar. While the infiltrating air’stemperature is reduced by 3.4 8C from case A to case B, thecorresponding PPD reduced by approximately 7% in the occupiedzone. Thus, indoor thermal environment was slightly improvedduring the afternoon hours (case B) but still remains unacceptable.This is not surprising as the infiltrating outdoor air enters thechamber at a vertical incidence angle and thus provides maximumthermal load. Since the recommended PPD values for an acceptableindoor environment are below 20% (80% acceptability) [26], thecurrent indoor environment is prohibitive for both cases studied.This is also true, using the adaptive model for case B concerningglobal thermal comfort assessment. The optimum indoor tem-perature for thermal comfort is calculated 27.875 8C, using Eq. (20),by setting the external temperature as the mean value of the30 min measurements. Thus, the maximum indoor temperaturefor 80% acceptability should be 31.375 8C, while the averagetemperature predicted by the CFD model is approximately 31.8 8C(Fig. 15b). This means that indoor environment is again predictedout of the optimum temperature range. Referring to local thermalcomfort using the adaptive model, the same conclusion is true,especially near the partition. Due to high temperatures of theinfiltrating air at this area, predicted temperature is at least 1 8Chigher than the optimum one for 80% acceptability. However,temperature differences at all vertical directions are below thethreshold value, as in case A (see Fig. 16). It is meaningful, for thiscase, to investigate also the local PD factor, standing for airdraughts occurring when temperatures are lower than the value ofhuman thermal neutrality (34 8C) under sedentary activity. It isobserved that, even though the indoor thermal conditions could beconsidered unacceptable in terms of thermal perception (PMVNV/PPD, adaptive), the draught sensation of any occupant remained atlow acceptable values (<20%) [24] in the bulk flow (see Fig. 15f).This was due to the low indoor velocities, especially in therecirculation zones, and also to low turbulence intensity. However,PD can exceed recommended values in front of an inlet doorbecause of the dominant maximum velocity of the internal

domain, while it can obtain relatively high values near thepartition, due to high velocity gradients that occur there.

4. Conclusions

An experimental method has been developed to determine theairflow pattern and indoor thermal environment in case of naturalcross-ventilation. Two experimental arrangements were examinedfor noon and afternoon hours under hot summer- and moderatewind-conditions. Furthermore, a mathematical model was devel-oped and applied to study the indoor environment computation-ally, using finite-volume techniques and three high-ReynoldsRANS models. Steady-state simulations were performed incorpor-ating – as stable as possible – measurements for some of theboundary conditions applied. A sensitivity study was performedconcerning the impact of the terrain’s roughness and also of thefluctuating recorded wind speeds and incidence angles on thenumerical results. It was found that no significant differencesoccurred for flat- and typical-rural’s terrain roughness. A similarobservation is true referring to a �10% fluctuating wind speed and a�15% fluctuating incidence angle. The numerical predictionsobtained by all turbulence models were generally in acceptableagreement with the experimental measurements; and, thus, theyprovide an ‘‘image’’ of the airflow which may represent naturalventilation as a result of prevailing wind effects. The RNG k–e modelperformed relatively better, especially for temperature predictionsand it was chosen and used further for thermal comfort estimationpurposes, under both measured experimental conditions. For thisreason, the extended PMV model was implemented in the CFD modelusing the expectancy factor and the reduction of the metabolic rateaccording to a linear interpolation technique. The adaptive model fornatural ventilation was also used for additional thermal comfortestimation purposes. It is concluded that the indoor thermalenvironment considered is unsatisfactory in terms of thermalperception using either model (for case B), as for both cases studiedthermal acceptability was calculated below the recommended 80%,referring to both local and global assessment. However, due to thenon-symmetrical locations of the openings, natural cross-ventilationcan provide well-mixed conditions, leading to low temperaturedifferences in the occupied zone and minimize local air draughts,even in regions close to internal obstacles which may representfurnishings or any building equipment. Finally, it is concluded thatreliable predictions may be obtained using numerical simulations,within relatively modest computer resources.

Acknowledgments

This research work was co-funded by the European Social Fund(75%) and National resources (25%) through the OperationalProgram for Educational and Vocational Training II (EPEAEK II)‘‘Archimedes II’’.

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