Natural ventilation: a new method based on the Walton model applied to crossventilated buildings having two large external openings

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1 Natural ventilation: a new metod based on te Walton model applied to crossventilated buildings aving two large external openings Alain BASTIDE, Francis ALLARD 2 and Harry BOYER Laboratoire de Pysique du Bâtiment et des Systèmes, 40, Avenue de Soweto, 9740 Saint Pierre, Reunion Island, France 2 Laboratoire d'etude des Pénomènes de Transfert Appliqués, Avenue Micel CREPEAU, 7042 La Rocelle Cedex, France Abstract In order to provide comfort in a low energy consumption building, it is preferable to use natural ventilation rater tan HVAC systems. To acieve tis, engineers need tools tat predict te eat and mass transfers between te building's interior and exterior. Tis article presents a metod implemented in some building software, and te results are compared to CFD. Te results sow tat te knowledge model is not sufficiently well-described to identify all te pysical penomena and te relationsips between tem. A model is developed wic introduces a new building-dependent coefficient allowing te use of Walton's model, as extended by Roldan to large external openings, and wic better represents te turbulent penomena near large external openings. Te formulation of te mass flow rates is inversed to identify modeling problems. It appears tat te discarge coefficient is not te only or best parameter to obtain an indoor static pressure compatible wit CFD results, or to calculate more realistic mass flow rates. Key words: Natural ventilation, CFD, Walton model, large external opening, indoor pressure. Introduction Natural ventilation is usually used during summer or ot seasons; during te cold season buildings are closed to preserve energy. Te world energy context requires te prediction of bot te seasonal eat production and te seasonal cold production over one year to give a reliable estimation of energy expenditure, and to limit te CO 2 production of active systems. Tis article focuses on te mass transfers for natural ventilation and passive cooling during te summer season, by opening te building. To acieve a wellventilated and comfortable building, arcitects ougt to ave tools tat forecast and improve te energy consumption by a building, and te eat and mass transfers troug large external openings. Tese tools ave to integrate dynamic termo-aeraulic predictions (Boyer et al, 999) and various scenarios to cover te entire year in one simulation and to try and avoid te over-dimensioning of active air treatment systems. Our metodology is to use te simulation results of detailed models and to adapt tem to te discretization level generally in use in te termal study of buildings, in order to calculate te mass flow rate and eat transfer between termal zones. We cose te Walton model (Walton, 984) modified by Roldan (Roldan, 985 and Allard, 992) for large external openings, and compared te numerical results wit tose produced by te RNG k ε model (Yakot, 986). Walton proposes a metodology (Walton, 989) for studying te problem of a building wit an airflow network composed of infiltrations and large openings. Te Walton model (Walton, 989) is attractive for te following reasons : Te implementation is easy wen te dynamic simulation software include cracks; Te neutral axis is not required to calculate te mass transfer troug te opening and so te computational program's algoritm is less complex but efficient; Te number of constants to fix is reduced to one: te discarge coefficient for eac kind of opening. Te flow exponent is 0.5, wic corresponds to turbulent air flow. Te Walton model gives a good prediction of gravitational flows troug internal large openings in steady-state conditions (Bastide, 2004) compared to models based on neutral axis determination. Roldan (Roldan, 985) proposed to modify tis model for large openings placed on a facade. He added a term in te pressure calculation to take into account te external pressure, and to link it to te internal pressure. Te main difference between crack flow models and vertical large openings lies in te transformation of te kinetic energy into static pressure. In crack flow models, te mass flow rate is only governed by te

2 pressure difference and te main assumption is tat te kinetic energy is totally dissipated. For large opening models, streamlines cross te building. Te important consequence of tis is tat a large part of te kinetic energy is transported troug te building, witout transferring kinetic energy into static pressure. In tis article, te model defined by Walton (Walton, 984) and adapted by Roldan (Roldan, 985) is improved to take into account te pysics of te airflow tat goes troug a cross ventilated building. Te resulting model predicts te mass flow tat crosses te building wit good accuracy relative to CFD predictions. Te relative internal pressure of eac model is compared and discussed. 2. Numerical investigation and modeling of te mass flow rate troug large openings 2.. Turbulence modeling 2... Single zone building model Te computational domain is presented in Figure. All measurements are dimensionless. Te building model is at te center of te ground's surface. Te value of te parameter L is 7 meters. Figure 2: Te cross-ventilated building model and te orientation convention for eac facade (East and West) Introduction to CFD modeling Evola and Popov (Evola and Popov 2006) compare te CFD predictions of four turbulence models wit experimental observations. Te numerical results obtained using te RNG metod (Yakot, 986) sow good agreement wit te experimental data. Te discrepancy between te calculated and expected ventilation rates is under 0%. Te RNG model can be considered a useful tool for te study of airflow inside and around a building wen dealing wit wind-driven natural ventilation. Te Large Eddy Simulations (LES) model may be preferable for advanced fluid dynamics tat require iger precision Turbulence models Te air is treated as an incompressible fluid wit constant pysical properties. Te steady state equations of mass conservation and momentum are given below, applying te Reynolds decomposition in a tensorial form: U j x j =0 () Figure : Tree-dimensional pysical domain Te building model sown in Figure 2 is crossventilated. Two opposite openings are located at eigt H =m. Te areas of tese two identical openings are 5.6m 2. U x i U j = p i x j x i [ U j U i x i x j u ' ' i u j ] (2) Tese equations include te term, u ' ' i u j wic represents te Reynolds stresses. Tis term models turbulent penomena. Te quality of te results depends on te coice of te class of model, and tis depends on te set of equations used to solve te pysical problem. Te Reynolds stress terms were modeled wit te expression below, using te Boussinesq assumption of turbulent viscosity t. Tis approac assumes tat te turbulent Reynolds stresses are linked to te set of averaged flow properties: u ' i u ' j = t U i U j 2 x j x i 3 k ij (3) t =C k 2 (4) Tese equations introduce two terms k and tat are respectively te turbulent energy and te

3 turbulent energy dissipation rate. Two closure equations ave to be defined based on te transport of tese quantities. Several closure models ave been developed in recent decades to close te system of equations resulting from te Reynolds decomposition, suc as te k model (Launder and Spalding, 974) and te Boussinesq assumption. However, te Boussinesq assumption used by many turbulence models is not always efficient. Te concept of turbulent viscosity as been extended to try and model te anisotropy of turbulent flows. Quadratic and cubic models of turbulent viscosity ave been developed. Bastide (Bastide 2004) establised tat tis kind of model does not bring any significant improvement in flow predictions over a closed bluff body (Martinuzzi, 993, Rodi, 997 and Lakeal 997) compared to te RNG k model, but te results are better tan te standard k model. Vortex and reattacment zones are eiter nonexistent, under-predicted or over-predicted by te standard k model Te turbulence model of te renormalization group: RNG k Te two closure equations are widely implemented in computational fluid dynamics software. Te RNG k model presents a double advantage compared to all te RANS models. Te RNG k model is designed to predict fluid flow for ig and low Reynolds numbers, wereas te oter RANS models are designed for eiter ig or low Reynolds numbers. Tese two flow regimes are observed in an opened building, and so it appears necessary to apply a model suc as RNG k. Te two closure equations of te RNG k are given by te following expressions: k U j = x j x j [ t k k x j ] P k (5) U j = x j x j [ t x j ] C k P k C 2 2 k R (6) Te modification of te matematic structure compared wit te k model is located in te transport equation of te dissipation rate of turbulent kinetic energy. An new term R is added to reduce te influence of te term C k P k and to trim down te turbulent kinetic energy production for 0. Te production term P k is calculated from gradient products. wit =2 P k 2 k t Te constants introduced in tese equations ave been calculated matematically, unlike te traditional k models were tey are determined from various experiments for different flow structures and regimes. C C 2 C 0 k Table : RNG k model coefficients Boundary conditions and wall treatment Te boundary conditions are described in Figure. At te inlet, a log profile is set to model te atmosperic boundary layer. Te value of te velocity reference at a eigt of 0m above te ground is 2.96 m.s. Some simulations wic included a two layer turbulence model ardly improved te results for te mass flow rate, despite using muc calculation time. Te near wall cells are tus treated by a standard wall law using te assumption tat te walls are smoot for te building model and sligtly roug for te ground. Te wall law uses te following coefficient: E=9. Te rougness coefficient for te wall's log law is z 0 = Grid independence test Tree grids ave been defined to verify tat te observed results are grid-independent. Accurate results and a minimal number of cells were obtained at te end of te grid independence test. A grid of 4,000 cells was cosen to carry out all te numerical investigations Surface Pressure calculations P k = t U i U j x j x i C 3 R= k U i x j (7) (8)

4 Figure 3 : Windward and leeward surface pressure coefficients Te global pressure coefficient for different incident angles and for a facade is evaluated from CFD simulations. Te building model is closed and is sown in Figure 3. Te local surface pressure coefficients are calculated wit te following equation : location of te neutral axis, altoug te model developed by Walton does not use tis metodology. Tis model can be considered as an intermediary metod, somewere between te crack flow models and te classical models based on finding te neutral axis to predict te mass transfer tat goes troug internal large openings. C p =mean P surf z P 0 P dyn z 0 (9) C p is a dimensionless coefficient. It is te average surface pressure transformed into a relative pressure divided by te dynamic pressure predicted at eigt z 0. Tese coefficients are calculated from CFD predictions for a closed building. Figure 3 sows, as a function of some incident angles, te surface pressure coefficient evaluated for te windward and leeward facades excluding, in te calculation of te average, te edge pressures. Te pressure difference between tese two opposite facades is always positive. Te mass flow will ten be in a single direction Mass transfer troug large openings Te mass transfer calculation is performed for te N cells wic are distributed in te enclosure of te building or for te area considered in te enclosure. Te net mass flow at an opening is evaluated by : ṁ opening = in ṁ i. ṁ i is te mass flow rate tat goes troug one cell Mass transfer toug internal large openings Te termal beavior of buildings is a very complex problem. Different modes of eat and mass transfer appear in complex volumes and te interactions between different pysical penomena are significant. Detailed analysis, by CFD for example, of te airflow pattern troug te cracks is incompatible wit te computation of energy consumption over a eating and/or a cooling period. To study te global beavior of buildings, we need some simple and reliable models capable of correctly predicting indoor temperatures and air quality. Various models of eat and mass transfer airflow troug an internal building opening ave been based on te Bernoulli equation : see Allard and Utsumi (Allard, 992) or Walton (Walton, 984). Tese models adopt te following principal assumptions : te flow is considered laminar, te flow is steady state, air is a non-viscous fluid, and turbulence and flux constrictions are represented respectively by two coefficients: te discarge coefficient and te airflow exponent. Classical models developed to calculate eat and mass transfers troug large openings find te Figure 4 : Te locations of nodes ( M ) and pressure differences ( P ) respectively in and between termal zones Walton applied te metods of dimensional analysis Nu/Pr =C Gr/3 to te eat and mass transfers troug large openings. He concluded tat te airflow troug a large opening can be modeled by two small openings (Figure 4) placed at two special positions in a large opening. Tese positions are respectively located at 5/8 and 3/8 of te opening eigt. For non-zero termal gradients between two termal zones, te airflow between te top and te bottom of te openings is governed by te gradient of te ydrostatic pressures ( g z and T = 0 0 T ) at te openings. Te assumption is tat te density is uniform or linear in a termal zone and te air density in a termal zone is defined by its own air temperature. In te presence of a density difference between two linked termal zones, te airflow is bi-directional at an opening. Te net mass flow rate is defined below: ṁ=ṁ 5 /8 ṁ 3/8 (0) For eac small opening (i), te mass flow rate is given by te following expression: ṁ i = C d, i S 2 sign P i P i /2 () Te discarge coefficient in C d cluded in tis definition represents two effects. Te first effect is due to te friction between te air and te walls of te opening frame, and te intensity of tis friction depends on te fluid viscosity. Te second effect is due to te sape of te opening. Te value of te

5 discarge coefficient C d tends to one in te case of te opening area being almost equal to te wall area. Tis coefficient is valid for an air movement due to a termal difference. Walton obtained a discarge coefficient equal to for 0.78 an indoor opening separating two identical and closed termal zones. Flourentzou (Flourentzou et al, 998) evaluated a discarge coefficient close to 0.60 for an external large opening and for an in situ experiment in te absence of wind. In IEA Task 20 (Van der Mass, 992), an experiment in a closed cell test composed of two termal zones and a large opening between tem sowed tat te average vertical discarge coefficients depend on te flow structure at te opening. Te C d z vary between 0.0 and Wit regard to tis point, te C d z ave been observed to not ave locally constant values at te opening (Karava, 2004). Te value of te discarge coefficient is subject to a large degree of uncertainty. However, we need to define a set of constants tat are compatible wit te knowledge model and wit te space dimension. In te kind of model described ere, an average value of te discarge coefficient as to be fixed and adjusted on a case-by-case basis to well-represent te mass flow rate at an opening Application of te Walton model to large external openings Roldan (Roldan, 985 and Allard, 992) proposed to apply te Walton metod to large external openings. In te absence of wind, tis modeling applied to an external large opening is coerent wit te assumptions made by Walton. However, if te wind is present witin te building, te pressure field canges around and in te building, and so Roldan added a pressure term in te pressure difference to take account of te external pressure field to predict te pressure in te building. He proposed a modification to te discarge coefficient included in tis relation, in order to adjust te model to observations or to numerical predictions. Te Walton model of bi-directional airflow across an opening is given by te following expression: ṁ= C d S 2 sign P 5 8 P 5 8 /2 (2) C d S 2 sign P 3 8 P 3 8 /2 (3) Te pressure gradients are for two termal zones ZTH and ZTH2 : P 5 =P ZTH P ZTH2 g H [ ZTH ZTH2] (4) 3 P 3 ZTH P ZTH2 g H 8 8 [ ZTH ZTH2] (5) e unknown factors of te problem are te pressure P ZTH and P ZTH2 calculated by a iterative algoritm like Newton-Rapson metod. In tis article, tis model is compared to CFD predictions and a new approac is developed to optimize te Roldan model Influence of te external pressure distribution on mass flow rate Te pressure difference between te leeward and windward facades depends on te geometrical aspects of te building, te atmosperic boundary layer profile, te incident angle and te intensity of te reference velocity. Te velocity and pressure field around te building cange spatially. Te pressure field around a building is generally caracterized by regions of over-pressure on te windward facades, and under-pressure on te facades parallel to te air stream and on te leeward side. Wen te building is opened, te pressure difference induces a mass flow troug te building. Tis mass flow is dependent on te pressure difference field around te building Te streamline deformation near te building Oba et al (Oba, 200) give a correction to te incident angle. Te resulting angle incorporates te deformation of streamline tubes due to te upstream airflow complexity. Te form of te streamline tubes close to te external opening is investigated by Hul et al (Hul, 2005). Te streamlines do not follow te forward incident angle close to te wall, but depend on te form of te building, te sape and te configuration of te building openings and te incident angle. Te airflow direction troug te windward opening canges and te effective area 'seen' by te streamline tubes canges too. Oba et al (Oba, 200) propose correcting te incident A angle of te wind using te fraction A 0 were A= ṁ V p, A= Q V and wer V p e is te penetrating velocity and ṁ te mass flow rate. Te key point of tis metod exposed by Oba et al (Oba, 200) is to measure te velocity V p at te central position close to te inlet of te building and to suppose tat tis velocity represents te mean velocity at te inlet. Using numerical fluid dynamics, te effective area can be calculated from te discretization of te volume opening. Te effective area is given by te mean velocity : V = N i U i. Te new effective area is: A= i S i U i / N i U i. Te new expression for te effective area greatly increases te number of velocities and te accuracy of te mean velocity and te mass flow rate, wic improves te precision of te mean velocity value. But te results are too far from te results obtained by using te penetrating velocity located at te center of opening. Tis metodology based on te streamline pattern as not been included in te

6 model of mass flow rate formulated in tis article because te discarge coefficient is considered equal or practically equal for large openings and a new term is include in our system of equations Influence of te CFD modeling on predicted pressure distribution and mass flow rate predictions Results obtained by numerical simulations ave to be accurate for te two pysical quantities ṁ and. P Te mass flow and pressure differences are observed and used to define new knowledge models. Te turbulence modeling influences te quality of te CFD predictions. Evola and Popov (Evola and Popov 2006) sow tat te predictions and empirical values are close to te mean ventilation rate troug a cross-building. Te RNG model predicts te mass flow rate wit an error lower tan 0%, wereas te standard model over-predicts te mass flow rate (by more tan 5%). Te LES model as a relative error of 6.5% compared to experiments. Te expected mean pressure coefficients are under 0% for te windward and leeward faces. Te RNG k model seems to be a good compromise wit regard to te computational time and te quality of te predictions for tis kind of problem. Hu et al sow tat te structure of ventilating flow is better represented wit te SST k model tan wit LES (Wilcox, 998 and Menter, 994). Te pressure distribution on faces, te pressure extrema and te caracteristic lengts are analyzed by Endo et al (Endo, 2005). Tey conclude tat te SST k model is not accurate for tese tree quantities. RNG k is a good compromise between te RANS models for predicting mass flow rate and pressure distribution. Te mass flow rates troug te building are sown in Figure 3. Tree RANS turbulence models ave been employed : k, RNG k and SST k. Te mass flow rates for an incident angle in te range [30 90 ] are similar for te two models k and RNG k. Elsewere, te k results ave better residuals tan tose from te RNG k modeling. Te k standard model gives good agreement, but as Endo et al (Endo, 2005) found, te predicted pressure distribution is poor. Te mass flow is over-predicted, and te pressure distribution poorly placed by te SST k model. Tese results demonstrate tat te RNG k model seems to be effective in te specific case of mass flow modeling Te model proposed by Roldan : an adaptation of te Walton model for external large openings Roldan (Roldan, 985) proposed a modification of te matematical formulation of te pressure difference included in te Walton model. He included te static wind-induced pressure on a facade in te pressure difference. Figure 6 : Mass flow rate calculated by te detailled model (CFD) and by te model developed by Roldan Te pressure difference links te internal pressure and te external pressure on facade. Roldan suggested adjusting te discarge coefficient too. Preserving te mass flow model of equation, te mass balance of te termal zone is calculated assuming tat eac pressure model for eac node is as given in Table 2. Figure 5 : Mass flow rate troug te windward opening predicted from tree turbulence models.

7 Nodes Roldan modifications M 5 8, TZ P MTZ=P g [ H 5 8 ] M 5 8, out P Mout =P out g[ H 5 8 ] p V out H 5 8 M 3 8, TZ P MTZ=P g [ H 3 8 ] M 3 8, out P Mout =P out g[ H 3 8 ] p V out H 3 8 Table 2: nodes and teir corresponding models in Roldan's model, after te Walton model. Te model of pressure nodes mentioned above does not include te fact tat a part of te kinetic energy goes troug te building witout transferring a fraction of its energy into kinematic pressure. In te unknown pressure P, a static pressure and a dynamic pressure is calculated. But we do not know te fraction of tis dynamic pressure tat is converted into kinematic pressure or static pressure. Roldan (Roldan, 985) proposed adjusting te discarge coefficient to improve te model, but tis coefficient is generally used to take turbulence effects and flow constriction into account. An adaptation of tis model is tus needed. In Figure 6, we observe tat te results obtained by te Roldan (Roldan, 985) model are eiter 30% lower, or twice as large as te values tat result calculated using te CFD model. Te two sets of points are not omotetic, and so tis problem cannot be settled by adjusting a single discarge coefficient Inclusion of te predicted pysical parameters to modify and improve te Roldan model Introduction Airflow troug large openings involves a number of different pysical penomena, including steadystate gravitational flows, fluctuating flows resulting from wind turbulence, and re-circulation flows caused by boundary layer effects. Te complexity of tis problem as to be included in te knowledge model. Te Roldan (Roldan, 985) model adds to te Walton (Walton, 984) model te external pressure differences but te prediction of mass flow rate does not reproduce te CFD predictions. Te model presented by Roldan (Roldan, 985) is terefore modified to take all te effects mentioned into account. An artificial pressure is evaluated using te inversion of te knowledge model and included to predict te mass flow rate and te relative pressure in te building model Formulation of an artificial pressure difference by applying te inverse problem Te pressure difference P calculated from te external wind and external static pressure does not produce te expected predictions (Figures 7 and 8). Te model is not sufficiently detailed to suitably predict te mass excanges troug large external openings. We propose to inverse te problem and tus to create an artificial pressure difference P CFD in order to identify te modeling problems in Roldan's model. Te mass flow rate ṁ is given by CFD predictions. Te inverse pressure difference is given by te equation: 2 P CFD =sign ṁ CFD 2 ṁ CFD C d S (6) Figure 7 : East opening, pressure differences determined following te inverse problem for te two small openings using te Walton model and te pressure differences calculated wit te Roldan model

8 by te predicted indoor pressure in tis model tat includes a dynamic pressure. Figure 8 :West opening, pressure differences determined following te inverse problem for te two small openings using te Walton model and te pressure differences calculated wit te Roldan model P CFD results from a matematical construction tat depends on te mass flow rate predicted by te CFD model and depends on te discarge coefficient determined for a gravitational flow witout static pressure produced by te wind. Te slope formed (Figure 7) by te values of P CFD,East, top is steeper tan te values of P CFD, East, bottom. Tis difference is due to te sape of te atmosperic boundary layer and to a treedimensional recirculation present above te ground on te windward facade. Te airflow tus passes (Figure 7 and 8) mainly troug te opening at te top. Te same differences are observed for P Roldan but te pressure differences are not significant for an incident angle lying between 0 and 45. In te range [0,45 ] (Figure 7) te results are similar because te airflow pattern is modified by te building model. Below 45, te streamlines follow te building facade. Airflow enters te building wit a specific sape governed mainly by te pressure differences due to te air motion, wic is ortogonal to te natural air displacement troug a windward external large opening. In Figure 8, between 20 and 90 P CFD te are practically linear. For 90, te pressure differences are close to zero. Tere is no difference in beavior between te top and bottom of te leeward opening because te motion is mainly due to static pressure differences between te interior and te exterior. Te situation ere could be modeled as an airflow troug a large internal opening. However, te values determined by Roldan's model follow a parabolic sape (Figure 8). Tis is caused Modeling of te building pressure coefficient C B for eac small opening in te Walton sense Tanks to te pressure difference P CFD calculated above, a building pressure coefficient C B is defined. Tis coefficient models te part of kinetic energy tat crosses one small opening of an external large opening. Te matematical formulation, described below, results from allowing for te surface pressure of te facade ( C P ) and te mass flow rate troug P CFD. P CFD,top C B,top = 2 V 2 out H 3 8 C (7) p P CFD, bottom C B,bottom = 2 V 2 out H 5 8 C (8) p Tese non-dimensional coefficients are incorporated into te model developed by Roldan (Roldan, 985) to constitute a new model (Table 3) to predict te mass flow rate troug cross building models. Tis model can be easily included in classical energy building software like te crack models. Nodes M 5 8,TZ New formulation P MTZ =P g[ H 5 8 ] B, topv out H 5 8 M 5 8,out P Mout =P g [ H 5 8 ] p V out H 5 8 M 3 8,TZ P MTZ=P g [ H 3 8 ] B,bottomV out H 3 8 M 3 8,out P Mout =P g [ H 3 8 ] p V out H 3 8

9 Table 3: Te new formalisation of te pressures including te pressures deduced wit te inverse problem Equations 7 and 8 give, respectively, expressions for te building coefficient of te opening placed at te top and at te bottom of te opening. Figure 0: Mass flow rates calculated for eac knowledge model described above Figure 9 : Building coefficients C B for eac small opening in te Walton sense Te values of te mass flow rates for eac boundary condition of te numerical experiments and for eac small opening of tese coefficients are plotted in Figure 9. Following equations 7 and 8, te building pressure coefficients act on te pressure difference at openings. For te East external opening and te small opening placed on top, we notice tat te building pressure coefficients are muc iger tan te surface pressure on te leeward facade. Tese coefficients are tus present to increase te mass flow troug an external large opening. Te resulting model and tese outputs (Figure 0) sow tat te improvement of te knowledge model developed by Roldan (Roldan, 985) ave allowed te pysical penomena to be better represented. Te mass flow rate deduced by tis new formulation of pressure differences is close to te numerical experiments. Figure : Indoor kinematic pressure calculated for eac model Figure sows te pressure calculated for te models detailed in tis article. We note tat te kinematic pressure calculated by Roldan's model (Roldan, 985) differs greatly from te numerical experimental results. Te sape of te curve and te model detailed in Table sow tat te pressure determined by tis model includes a dynamic pressure. Tis dynamic pressure skews te problem because te pressure P defined by Walton (Walton, 984), wic partially crosses te building is static, and not dynamic. Te pressure model developed by Roldan cannot be implemented to evaluate pressures in buildings. A major implication is tat if te Roldan model is employed to analyze eat and mass transfers in a

10 complex building or multizone building ten eat transfers, mass transfers and termal comfort will be poorly predicted. On te oter and, in te absence of wind te Walton model will correctly calculate eat and mass transfers. 3. Conclusion Mass flow rate predictions troug large external openings deduced from te Walton-Roldan model differ greatly from CFD results. Te knowledge model developed by Roldan proposes to include te surface pressure induced by wind in te pressure difference between te interior and te exterior. He explains tat it is ten necessary to set te discarge coefficient for eac incident angle. However, te indoor pressure calculated by tis metod includes a dynamic pressure tat corresponds to te kinetic energy tat crosses te building witout transferring all tis former energy into kinematic pressure. Te problem could not be understood as a crack-flow. Building coefficients are ten introduced to take into account tis kinetic energy tat passes troug, and to improve te model implemented by Roldan. Energy present in te stream tube developed at te windward opening can now partly go troug te building and transfer a part of its energy into potential energy troug kinematic pressure. Results of tese modifications sow tat indoor pressures are close to te numerical experimental results, mass flows are better predicted and discarge coefficients are not canged. Te discarge coefficient is kept to te value defined for a modeling problem witout wind. Te indoor pressure evaluated by solving te mass balance is now kinematic, and not a dynamic pressure plus a static pressure. Tis model can now be coupled to a crack-flow model tat needs a static pressure. 4. References Boyer H., Lauret A. P., Adelard L. and Mara T. A.: (999). Building ventilation: a pressure airflow model computer generation and elements of validation. Energy and Buildings, Volume 29, Issue 3, Pages Walton G.N.: (984). A computer algoritm for predicting infiltration and inter-room airflows, ASHRAE Transactions, 90:, Roldan A.: (985). Etude termique et aéraulique des enveloppes de bâtiment. Influence des couplages intérieurs et du multizonage P.D. Tesis, INSA Lyon, France Allard F., and Y. Utsumi: (992). Air Flow troug Large Openings, Energy and Buildings, 8, Walton G.N.: (989). Airflow network models for element-based building airflow modeling,. ASHRAE Transactions 95:2, pp Bastide A.: (2004). Etude de la ventilation naturelle a l'aide de la mécanique des fluides numérique dans les bâtiments a grandes ouvertures; Application au confort termique et à l'amélioration de modèles aérauliques nodaux. PD Tesis. La Réunion, Indian Ocean, France. Yakot, V., and Orszag, S.A.: (986). Renormalization group analysis of turbulence I: Basic teory, J. Scientific Computing,, pp. 5.b Launder, B.E., and Spalding, D.B.: (974). Te numerical computation of turbulent flows, Comp. Met. in Appl. Mec. and Eng., 3, pp Martinuzzi R. and Tropea C.: (993). Te flow around surface-mounted prismatic obstacle placed in a fully developed cannel flow. Journal of Fluid Engineering, 5 :85-92, 993. Rodi W.: (997). Comparison of LES and RANS calculations of te flow around bluff bodies. Journal of Wind Engineering and Industrial Aerodynamics, 69-7 : Lakeal D. and Rodi W.: (997). Calculation of te flow past a surface-mounted cube wit two-layer turbulence models. Journal of Wind Engineering and Industrial Aerodynamics, : Evola G. and Popov V.: (2006). Computational analysis of wind driven natural ventilation in buildings, Energy and Buildings, Volume 38, Issue 5, Pages Flourentzou F., Van der Maas J. and Roulet C.-A. : (998). Natural ventilation for passive cooling: measurement of discarge coefficients, Energy and Buildings, Volume 27, Issue 3, Pages Van der Mass J.: (992). IEA-ECB Annex 20 Tecnical Report: Air Flow troug Large Openings in Buildings, International Energy Agency. Karava P., Statopoulos T. and Atienitis A.K: (2004). Wind Driven Flow Troug Openings A Review of Discarge Coefficients, International Journal of Ventilation, Volume: 3, Issue: 3, Pages: Oba M., Irie K. and Kurabuci T.: (200). Study on airflow caracteristics inside and outside a crossventilation model, and ventilation flow rates using wind tunnel experiments. Journal of Wind Engineering and Industrial Aerodynamics, Volume 89, Issues 4-5, Pages Hul C.H., Kurabuci T., Oba M.: (2005). Numerical Study of Cross-Ventilation Using Two-Equation RANS Turbulence Models, International Journal of Ventilation, Volume: 4, Issue: 2, pp Wilcox D.C.: (998). Turbulence Modeling for CFD", 2nd edition, DCW Industries, Inc. Menter F.R.: (994). "Two-equation eddy-viscosity

11 turbulence modeling for engineering applications", AIAA Journal 32(8) pp Endo T., Kurabuci T., Isii M., Komamura K., Maruta E. and Sawaci T.: (2005). Study on te Numerical Predictive Accuracy of Wind Pressure Distribution and Air Flow Caracteristics : Optimization of Turbulence Models for Practical Use. International Journal of Ventilation, Volume: 4, Issue: 3, pp: