QUANTIFYING THE PERFORMANCE OF A TOP-DOWN NATURAL VENTILATION WINDCATCHER. Benjamin M. Jones a,b and Ray Kirby b, *

Transcription

1 QUANTFYNG TH PRFORMANC OF A TOP-DOWN NATURAL VNTLATON WNDCATCHR Benjamin M. Jones a,b and Ray Kirby b, * a Monodraght Ltd. Halifax Hose, Halifax Road, Cressex Bsiness Park High Wycombe, Bckinghamshire, HP 3S b School of ngineering and Design, Mechanical ngineering, Brnel University, Uxbridge, Middlesex, UB8 3PH, UK. ray.kirby@brnel.ac.k * Corresonding athor.

2 Address for corresondence: Dr. Ray Kirby, School of ngineering and Design, Mechanical ngineering, Brnel University, Uxbridge, Middlesex, UB8 3PH. mail: Tel: + (0) Fax: + (0)

3 Abstract stimating the erformance of a natral ventilation system is very imortant if one is to correctly size the system for a articlar alication. stimating the erformance of a Windcatcher is comlicated by the comlex flow atterns that occr dring the todown ventilation rocess. Methods for redicting Windcatcher erformance can crrently be searated into simlistic analytic methods sch as the enveloe flow model and the se of comlex and time consming nmerical methods sch as CFD. This article resents an alternative semi-emirical aroach in which a detailed analytic model makes se of exerimental data blished in the literatre for 500 mm sqare Windcatchers, in order to rovide a fast bt accrate estimate of Windcatcher erformance. nclded in the model are boyancy effects, the effect of changes in wind seed and direction, as well as the treatment of sealed and nsealed rooms. The semi-emirical redictions obtained are shown to comare well with measred data and CFD redictions, and air boyancy is shown only to be significant at relatively low flow velocities. n addition, a very simle algorithm is roosed for qantifying the air flow rates from a room indced by a Windcatcher in the absence of boyancy effects. Keywords: Natral Ventilation, Windcatcher, Analytic Model, Boyancy 3

4 . ntrodction A Windcatcher is a to-down, roof monted, omni-directional device sed for natrally ventilating bildings. The Windcatcher rotrdes ot from a roof and works by channelling air thogh a series of lovers into a room nder the action of wind ressre, and simltaneosly drawing air ot of the room by virte of a low ressre region created downstream of the Windcatcher. The Windcatcher concet has been arond for centries and is commonlace in the Middle ast [, ]. This concet has been alied commercially in the UK for at least 30 years, see for examle the review of Windcatchers and other related wind driven devices by Khan et al. [3]. The crosssection of the Windcatcher may be any shae, althogh it is imortant to try and maximise the ressre dros on the leeward side and so crrent commercial designs are either circlar or rectanglar. xerimental stdies have shown, however, that a Windcatcher of rectanglar cross-section oterforms other designs, see for examle Refs. [] and [5]. For a rectanglar Windcatcher, the cross-section is normally slit into for qadrants so that one or more qadrants act as sly dcts to a room and the remaining qadrants act as extract dcts. The key indicator of erformance for a Windcatcher is the rate at which fresh air is delivered into the room and the rate at which stale air is extracted. Accordingly, it is very imortant to be able to redict ventilation rates rior to choosing the aroriate size of a Windcatcher for a articlar bilding. This article addresses this isse by develoing a simle semi-emirical model sitable for estimating Windcatcher erformance as a fnction of wind velocity and cross-sectional area. Windcatcher is a rorietary rodct of Monodraght Ltd.

5 t is common to redict natral ventilation flow rates sing simle enveloe flow models, see for examle Refs. [6-0]. A major factor that inflences the erformance of a natral ventilation system is the losses incrred as the air asses throgh an oening. For enveloe flow models it is normally assmed that these losses can be modelled sing an eqivalent coefficient of discharge, and vales similar to those measred for orifice lates are commonly sed [6, 9]. However, a Windcatcher reresents a far more comlex oening than, say, a window and sch an aroach is nlikely to catre the tre erformance of a Windcatcher over a range of arameters. Therefore, in order to realise a more accrate nderstanding of the energy losses inside a Windcatcher it is necessary to stdy the air flow in more detail. xerimental and theoretical investigations into Windcatcher erformance have been reorted in the literatre, althogh data on Windcatchers is not as revalent as that seen for other tyes of natral ventilation. The measrement of Windcatcher erformance has generally been restricted to laboratory conditions and very few stdies have examined erformance in sit. For examle, lmalim and Awbi [5], Parker and Teekeram [], and lmlalim [] all sed a wind tnnel to measre the erformance of a sqare Windcatcher divided into for qadrants and connected to a sealed room; later, S et al. [3] erformed similar wind tnnel tests bt for circlar Windcatchers. Parker and Teekeram focssed on measring the average coefficient of ressre (C ) over each face of the Windcatcher for wind of normal incidence. lmalim [] also measred C vales, bt extended the stdy to wind incident at different angles in order to bild a more general ictre of a Windcatcher s erformance. The exerimental data reorted by lmalim [] is based on measrements taken sing only two ressre taings laced on the centre line of each Windcatcher face, which may introdce frther errors and is significantly fewer in nmber than the ressre taings sed by Parker and Teekeram []. Kirk and 5

6 Kolokotroni [] also measred the erformance of rectanglar Windcatchers, bt chose to measre the ventilation flow rates for mltile Windcatchers oerating in sit. Kirk and Kolokotroni measred the decay of tracer gas in order to estimate ventilation rates and for an office environment they observed a linear relationshi between extract volme flow rate and the incident wind velocity. A linear relationshi was also observed by Shea et al. [5], who measred a net flow ot of the Windcatcher indicating that there is air infiltration into the room to comensate for the mass shortfall. The vales measred for C clearly demonstrate the action of the Windcatcher in that those qadrants with ositive vales of C act as sly dcts, whereas those with negative vales act as extract dcts. This is also confirmed by observations taken sing smoke tests, see for examle the measrements of lmalim and Awbi [5]. To corroborate laboratory measrements, lmalim and Awbi [5] develoed a CFD model for both circlar and rectanglar Windcatchers, and for the windward qadrant nder normal incidence good agreement between redicted and measred C vales was observed for the rectanglar Windcatcher. However, a comarison between rediction and measrement for the leeward faces is less sccessfl, althogh this is, erhas, not srrising given the comlex and highly trblent natre of the air flow arond a tyical Windcatcher. Whilst the measred C vales are imortant in dictating the magnitde and direction of the flow velocities into and ot of a room, they do not on their own qantify the ventilation rates. Here, ventilation rates also deend on the losses within the Windcatcher, which mst be qantified before a comlete ictre of Windcatcher erformance can be realised. The ventilation rates for a 500 mm sqare Windcatcher were measred by lmalim and Awbi [5] nder controlled conditions in a wind tnnel. Later, lmalim [] sed CFD to redict ventilation rates in a sqare Windcatcher, althogh only 6

7 limited agreement with measred data is observed. Li and Mak [6] also sed CFD to examine the erformance of a 500 mm sqare Windcatcher and demonstrated good agreement with lmlaim and Awbi s [5] data, althogh this is limited to overall ventilation rates. Recently, Hghes and Ghani [7] sed CFD to calclate net flow rates throgh a 000 mm sqare Windcatcher, and by normalising their reslts they were able to obtain redictions that agreed to within 0% of those generated by lmalim []; see also an earlier CFD stdy by the same athors [8]. Whilst CFD models have been shown to be artially sccessfl in catring the erformance of a Windcatcher, the difficlty of sing CFD to generate redictions covering a wide range of arameters, as well as the time taken to generate and solve these models, means that CFD is not so sefl as an iterative design tool. Moreover, the very fnction of a Windcatcher deends on high levels of trblence and early bondary layer searation, an area that not srrisingly cases CFD roblems. Accordingly, it aears to be sensible to investigate an analytic aroach with a view to develoing simle algorithms based on the se of emirical data to estimate the losses de to trblence. To this end, lmalim [] sed a so-called exlicit model in order to estimate Windcatcher erformance and reresented the losses within the Windcatcher sing an eqivalent coefficient of discharge. This aroach is very similar to the enveloe flow model described by theridge [7], althogh good agreement with exeriment is observed only nder limited conditions. Moreover, the method ses two heristic constants that aear to bear very little relation to the Windcatcher itself and it is not clear why certain vales were chosen, nor how one shold go abot identifying these vales for different Windcatcher designs. Accordingly, there is a clear need for a simle analytic model from which Windcatcher erformance can be qickly and reliably estimated. This 7

8 article addresses this need by develoing an analytic model that exlicitly incldes exerimental data for the Windcatcher as art of the modelling methodology, as well as adding other henomena sch as boyancy. Here, exerimental data is sed to qantify the losses in the Windcatcher rather than sing CFD or heristic constants. Frthermore, the model is extended to address both sealed and nsealed rooms and will also deliver reslts for wind incident at two different angles, something that is omitted in the exlicit model of lmalim []. Accordingly, in Section that follows an analytic model is develoed based on conservation of energy and mass. xerimental data reorted in the literatre and obtained nder controlled laboratory conditions is then sed to identify aroriate C vales in Section 3; by comaring rediction and exeriment aroriate loss factors are also calclated and a semi-emirical model formlated. n Section the semi-emirical redictions are comared against other data available in the literatre and a very simle relationshi between Windcatcher ventilation rates, incident wind velocity and Windcatcher area is resented.. Analytic Model A Windcatcher is normally either rectanglar or circlar in cross-section, althogh a Windcatcher of rectanglar cross-section is known to significantly oterform one of circlar cross-section [5] and so the analysis that follows is restricted to rectanglar crosssections. The cross-section is assmed to be divided into for qadrants, where each qadrant contains lovers at the to and damers ls a grill at the bottom, see Fig.. The Windcatcher exeriences wind of velocity w incident at an angle of θ degrees, see Fig. 8

9 a. The Windcatcher has cross-sectional dimensions d d ; the length of the lover section is L and the length of the section from the lovers to the bottom is L. To model the erformance of a Windcatcher conservation of energy and mass are enforced sing a method similar to that reorted by theridge and Sandberg [6], and CBS [8]. n the analysis that follows, the wind is assmed to have zero angle of incidence ( θ = 0 ) as this will simlify the discssion; however, a vale of θ = 5 will be inclded in Section 3. For a qadrant that faces into the wind, flow will be from the otside into the room and here conservation of energy yields [6], in = ρ g z +, () w where and are the external and internal ressres, resectively, and in is the ressre dro over the Windcatcher qadrant (assming that all losses between the room and the srrondings are attribtable solely to the Windcatcher ). n addition, denotes the change in air density between the room and the srrondings, z denotes the height of the entrance to the Windcatcher from the room, relative to the lower srface of ρ the room, and w denotes the ressre generated by the wind. Similarly, for a qadrant in which air travels from the room to the srrondings, ot = + ρ g z, () w where ot is the ressre dro over the otlet qadrant. n general, the ressre generated by the action of the wind over the face of a Windcatcher qadrant may be 9

10 related to the velocity of the air flowing into or ot of the qadrant by se of the coefficient of ressre C, which is defined as [6] C =. (3) ρ w Here, is the difference between the static ressre on the face of the Windcatcher ( w ) and a reference ressre. Ths, for air flow from the srrondings into the room (an inlet qadrant) q. () may be re-written as [6] in = ρ w C gz ( ρ ρ ), () where ρ = ρ ρ and the reference ressre is assmed to be atmosheric. qation () also assmes that the air velocity in the room is negligible and changes in density cased by the variation of ressre with height may be neglected. Similarly, for an otlet qadrant ot = gz ( ρ ρ ) ρ wc. (5) The change in density that aears in qs. () and (5) is assmed here to be de solely to temeratre changes and, following theridge and Sandberg [6], and gz = wc R T T in ρ (6) 0

11 gz ρ C ot = w R. (7) T T Here T denotes temeratre and R is the secific gas constant for air. The ressre dros in and ot reresent the losses imarted by the Windcatcher and these losses may be exressed in a nmber of ways, for examle sing a standard loss coefficient (see CBS, [8]). However, the Windcatcher contains many different elements and it is desirable here to gain an areciation of how each element imacts on Windcatcher erformance and so the losses are exressed in terms of a loss coefficient K, where in general K in, ot in, ot =. (8) ρ This allows qs. (6) and (7) to be re-written to give and gz ρ K = wc R T T in in ρ (9) ρ ot K ot gz = wc R ρ T T. (0) Here, in and ot reresent the velocity inside the qadrant of an inlet and otlet dct, resectively, and ρ is an average vale for density over the length of the qadrant.

12 For = 0 θ, we may assme that one qadrant acts as an inlet [qadrant ()] and three qadrants act as an otlet, where qadrants () and (3) are assmed to be identical, see for examle the exerimental data of lmalim []. After re-arranging, conservation of energy for the inlet and otlet qadrants may be written as w T T R gz C K = ρ ρ, () w C T T R gz K ρ ρ + = () and w C T T R gz K ρ ρ + = (3) assming that the external temeratre is the same for each qadrant. To solve qs. ()-(3) it is necessary also to enforce mass continity, which will deend on the conditions assmed inside the room. Here, there are two limiting cases (i) a room in which air exchange with the srrondings is ermitted, and (ii) a room that is erfectly sealed. Both scenarios will be considered here, with a sealed room to be stdied first... Sealed room For a sealed room, mass continity for 0 = 0 θ in which air flows in throgh qadrant and ot throgh qadrants, 3 and, gives Q Q Q + =, ()

13 where Q is the volme flow rate inside the Windcatcher and qadrants () and (3) are assmed to be identical. Here, the density (and hence temeratre) of the air inside each qadrant is assmed to be eqal in order to be consistent with the average vales for density sed reviosly for the energy eqation. Writing q. (5) in terms of the velocity in each qadrant yields, = + (5) A A A where A is the area of a qadrant. qations ()-(3) and (5) form for simltaneos eqations that may be solved for the nknowns,, and vales for K and rovided one assigns C. The method sed to solve these eqations is described in the Aendix; the estimation of vales for K and C, based on a 500 mm sqare Windcatcher, is addressed in Section 3. Note that it is ossible for the flow to reverse if the boyancy force is greater than the ressre force de to the wind and nder these circmstances a steady state wold no longer exist. The conditions nder which this occrs deends on many arameters and it will be seen in the reslts that follow that flow reversal is not seen to occr for θ = 0... Unsealed room f air exchange between the room and the srrondings (other than throgh the Windcatcher ) is allowed then the analysis of the revios section simlifies considerably becase air exchange will set = 0. This allows qs. ()-(3) to be solved directly, noting that if the flow reverses in qadrant then Q = A + A + A and 3

14 gz[ T T ] C w gz =, when < T K[ + T T ] w. (6) C T Here, a steady state is maintained by air infiltration into the room..3. Wind incident at θ = 5 Vales of θ = 0 and θ = 5 reresent limiting cases for the incident wind and so θ = 5 is reviewed in this section. When the wind is incident at θ = 5 it is assmed to enter throgh qadrants and, and to extract throgh qadrants 3 and. The energy carried by the wind now slits eqally between the two inlet qadrants and so qs. ()-(3) are re-written to give and gz ρ,k, = ρwc R (7), T T ρ 3, K 3, gz = + wc 3, R ρ T T. (8) Here, the inlet qadrants and, and the otlet qadrants 3 and, are assmed to be identical. For a sealed room, mass continity yields Q =. (9) Q The symmetry that aears for θ = 5 allows qs. (7)-(9) to be solved analytically, giving w[ C C ] [ ] gl T T 3 = =. (0) [ + T T ][ K ( A A ) + K ]

15 Note that flow reversal will occr when w gl[ T T ] <. () [ C C ] Under these circmstances a steady state wold no longer exist and so these conditions are not considered in the following section. For an nsealed room, setting = 0 allows qs. (7) and (8) to be solved directly, noting that if the flow reverses in qadrant then Q = A + A and gz[ T T ] C w gz = = when < T w. () K[ + T T ] C T 3. Semi-emirical model The model develoed in the revios section will comte ventilation rates generated by a Windcatcher rovided one knows vales for C and K. The C vales are related to the design of the to section of the Windcatcher and the K vales to the losses inside the Windcatcher itself. The C vales are assmed here to deend only on wind direction, whereas the K vales are assmed to be indeendent of wind direction. Accordingly, it is referable to obtain these vales nder controlled conditions and Parker and Teekeram [] measred C vales for a 500 mm sqare Windcatcher in a wind tnnel, with a sealed room of volme 5.5 m 3. lmalim [] also sed a wind tnnel to measre C vales and this data was comared with CFD redictions. A comarison between the C 5

16 vales measred by Parker and Teekeram, and lmalim, are shown in Table, for θ = 0. Here, the C vales agree well for qadrant, althogh significant discreancies between rediction and measrement are observed for the other qadrants. The measred data does, however, agree reasonably well for the other qadrants (aart from a seemingly erroneos vale in lmalim s data for qadrant 3) and this data seems to be sfficiently consistent to rovide confidence when taking an average C vale for each qadrant. The only C data available for θ = 5 is reorted by lmalim [] for a 500 mm sqare Windcatcher. Here, lmalim comared measrements with redictions obtained sing CFD and reorted varying levels of agreement. n view of the discreancies between rediction and exeriment observed for θ = 5, it aears sensible here to follow the method sed for θ = 0 and to se only the measred data for estimating C vales. Moreover, lmalim s measred data is asymmetric and this is inconsistent with the geometry of the roblem and so for the calclations that follow an average vale for C is generated for the inlet and otlet qadrants. The vales sed here for C are smmarised in Table. After assigning vales for C it is necessary to identify aroriate vales for the loss coefficients. One cold, of corse, estimate these vales sing, for examle, standard vales blished by CBS [9]. This aroach is, however, likely to lead to errors and it is argably more consistent first to se exerimental data measred over the whole Windcatcher, before attemting to analyse individal comonents. The wind tnnel measrements of lmalim and Awbi [5], and also lmalim and Teekaram [0], rovide data for flow rates into and ot of a 500 mm sqare Windcatcher nder controlled 6

17 conditions. Accordingly, a semi-emirical model is develoed here by comaring the redictions obtained sing the model resented in the revios section with wind tnnel measrements, and sccessively altering vales of K ntil accetable agreement is fond. n this way, the emirical data obtained nder controlled conditions is being sed solely to identify the losses in the Windcatcher ; the K vales calclated for a 500 mm sqare Windcatcher are then assmed to be valid over a mch wider range of conditions alicable to real installations. The data measred by lmalim and Awbi [5] was obtained with a sealed room and is resented in Fig. for a Windcatcher with L = m and d = d 0.5 m =. Here, θ = 0 and the volme flow rate in each qadrant is lotted against incident wind seed for a Windcatcher in which the damer and grill have been omitted. For θ = 0 the C vales in Table are sed and vales for K, K and K are sccessively altered ntil accetable agreement between theory and exeriment is achieved for the gradient m, where w m = Q, assming that a straight line assing throgh the origin may be sed. The socalled semi emirical redictions are comared with lmalim and Awabi s data in Fig., with K = and K = K = 8. ; a comarison between measred and redicted vales for m are shown in Table 3. Here, it is evident that it is ossible to vary vales for K ntil very good agreement between rediction and measrement is obtained (error of less than 7%). The vale of K for the inlet qadrant aears to be lasible (for examle, a simle oening eqates to a vale of K =. 7 [5]), althogh one wold exect the Windcatcher to imart more resistance to flow than a simle oening and so a vale of K = 3.89 aears to be reasonable. The vale of K chosen for the otlet qadrants is, however, mch higher and the reasons for this are more ncertain. This vale of K does, 7

18 of corse, deend on the accracy of the exerimental measrements and it is ossible that exerimental errors may significantly affect the otlet K vales, see for examle the discssion on measrement errors by lmalim [0]. Alternatively, there may also be hysical reasons for increases in the otlet flow losses, for examle additional losses may occr in the otlet qadrants becase of the lower flow velocities in these qadrants, which are more rone to lie in the transition flow region. Moreover, increased losses may be attribtable to the flow into the room interfering with the exhast flow, which serves to increase the resistance exerienced by the flow leaving the room. The measrements taken by lmalim and Awbi [5] were obtained with a sealed room and it is reorted that more air flows into the room than flows ot; the reslts of Parker and Teekeram [], also for a sealed room, indicate the oosite effect. Clearly, in both stdies mass is not balanced, imlying mass transfer with the srrondings or, erhas more likely, errors in the exerimental measrements. The semi-emirical model develoed here mst balance mass and so it is interesting to view the effect this has on the redicted ressre in the room,. n Fig. 3, is lotted against w for the Windcatcher stdied in Fig. and is seen to be negative for all wind seeds so that the Windcatcher is drawing more air from the room than is being slied casing the ressre of the air in the room to dro, albeit only by a relatively small amont. The reslts resented in Fig. are for exerimental data measred in the absence of a damer and grill (see Fig. b). lmalim [] later obtained data for a 500 mm sqare Windcatcher that incldes both a damer and a grill and these reslts are resented in Fig.. A comarison between the exerimental data in Figs. and shows that the losses in qadrant increase by aroximately 8%, which is assmed here to be attribtable 8

19 solely to the damers and grill. Accordingly, the vales sed here for K are modified to inclde the damers and grill (the details of this modification is discssed in Section 3.), giving vales of K =. 59 and K = K = 9.. The semi-emirical redictions obtained sing these new vales are comared with lmalim s measred data in Fig.. Again, good agreement is observed for qadrants and (error of less than %), althogh for qadrant an over rediction of the flow rate is evident (error of %). 3.. dentification of Windcatcher loss factors The vales inferred for K in the revios section are for a 500 mm sqare Windcatcher as a whole and so do not rovide information on those losses attribtable to individal comonents of the Windcatcher aart from the estimation that the damers and grill contribte to 8% of overall losses. Here, the measrements of Parker and Teekeram [] are sefl since they isolate the losses in the to section of the Windcatcher (length L T in Fig. b). Parker and Teekeram measred a 500 mm sqare Windcatcher and sed a fan to blow air into and ot of the to section, which contains the lovers. Their data may readily be sed to find the loss coefficient for the to section and this gives vales of K =.5 for flow into the room, and K =. 3 for flow ot of the room. dentifying aroriate vales for other elements of the Windcatcher is rather more difficlt, as one mst rely on estimations based on standard vales. Here, estimated K vales are reorted in Table, assming that vales for the damer and grill make 8% of the overall losses. The frictional losses have been estimated from standard data for circlar dcts, and so a hydralic diameter (d H ) is sed for the (trianglar) qadrants. The additional losses in Table reresent a deartre from the standard losses in order to meet the overall vales of K identified earlier. Following the discssion otlined earlier these additional 9

20 losses are attribted to friction losses in the qadrant and to entrance losses for the otflow qadrants. Clearly, there is an element of gesswork involved in Table and more exerimental/modelling work is reqired to shed frther light on this data and also to investigate why it is necessary to assign higher vales of K to the otlet qadrants.. Reslts The semi-emirical model develoed in the revios section is now alied to different scenarios in order to investigate its accracy. For a 500 mm sqare Windcatcher identical to the one stdied by lmalim [], Li and Mak [6] generated CFD redictions for θ = 0, θ = 5, θ = 30 and θ = 5. Li and Mak qantified air flow rates into and ot of a sealed room and a comarison between their CFD redictions and those obtained sing the semi-emirical model is resented in Fig. 5 (with d = d 0.5 m and L = m ). = Here, good agreement is observed for θ = 0 (error of 3%), and for θ = 5 agreement is still accetable (error of %). Note here that the semi-emirical redictions for θ = 5 are obtained sing those K vales generated for θ = 0. lmalim and Teekeram [0] also examined the erformance of a 500 mm sqare Windcatcher with θ = 5, bt they obtained exerimental measrements and a comarison between this data and the semiemirical model is shown in Fig. 6. Some scattering and a lack of symmetry is evident in the exerimental data, althogh this is likely to be cased by exerimental error. The semi-emirical redictions do, however, deliver a relatively good fit for the exerimental data, with an error of 3.8% if one comares the gradient of the semi-emirical redictions with a gradient based on data regression of all of the exerimental data. 0

21 lmalim [] measred the inflence of density changes by lacing an electric heater in a (sealed) room and measring the effect this had on Windcatcher flow rates. lmalim generated a 0 temeratre difference between the room and the srrondings and in Fig. 7 the semi-emirical model is comared with lmalim s data for θ = 0 (with T = 0 C ). Here, good agreement with measred data is observed for qadrants and, in with an average error of 9% and % for qadrants and, resectively, althogh an over rediction is observed for qadrant (average error of 5%). t is noticeable, however, that the semi-emirical model redicts that the change in density has little inflence on the erformance of the Windcatcher. This is thoght to be becase the room is sealed and, in order to maintain mass continity, the ressre of the air dros in order to comensate for the temeratre change, rather than the air velocities within the Windcatcher changing. This effect can be observed in Fig. 8, where the ressre in the room is seen to dro as the temeratre difference increases. The redictions resented so far have been comared to data obtained nder controlled conditions for a sealed room; however, in real alications the Windcatcher is likely to be oerating in a room that allows air exchange (however small) with the srrondings, which may inclde adjoining rooms or srrondings external to the bilding. n Figs. 9 and 0 redictions are resented for flow rates in a nsealed room for a 500 mm sqare Windcatcher that is identical to the one sed in revios calclations (inclding a damer and grill). Here, data is resented with and withot a temeratre difference between the room and the srrondings, and a reversal of flow in qadrant is signified by a change in sign for the velocity. t can be seen that a temeratre change of 3 C (with

22 T in = 5 C ) only significantly alters Windcatcher erformance at low wind seeds, where a reversal of the flow in qadrant is observed. This effect is, however, more noticeable for θ = 5 and the flow in qadrant is seen to reverse at a higher wind velocity when comared to θ = 0. This is thoght to be becase the Windcatcher is less efficient at gathering the incident energy from the wind when θ = 5 and so the boyancy of the air is larger relative to the wind energy. t is interesting also to comare the otlet volme flow rates for the nsealed room with those fond reviosly for a sealed room. n Table 5, the gradient (m) of Q vs is comared for W θ = 0 and θ = 5. Here, it is evident that the reslts for the sealed and nsealed rooms are similar and that for θ = 0 the model is redicting that more air will flow ot of the room when the room is nsealed. When θ = 5 the air flow rate from the room clearly dros when comared to θ = 0, as one wold exect; however, it is seen that the sealed room now rodces the largest flow rate, which is the oosite to that seen for θ = 0. t is not clear here why this shold be the case when θ = 5. There is very little data in the literatre that qantifies the ventilation erformance of a Windcatcher working in sit. Clearly, accrately measring arameters sch as wind seed and air velocity inside Windcatcher qadrants resents a nmber of difficlties. Data has, however, been blished by Kirk and Kolokotroni [] for Windcatchers similar to those stdied here, bt oerating in an oen lan office environment. Kirk and Kolokotroni measred air exchange rates and blished a lot of the volme flow rate of the air exelled from the office verss wind seed, making this data sitable for comarison with the crrent stdy. The office stdied by Kirk and Kolokotroni contained for Windcatchers and data is reorted for the first floor of the office, which contained

23 two Windcatchers of dimensions. m sqare and two that were 0.6 m sqare, althogh Kirk and Kolokotroni note that only half of each Windcatcher serves the first floor, whilst the other half serves the grond floor. Accordingly, they roose that this arrangement effectively behaves as one. m sqare and one 0.6 m sqare Windcatcher serving the first floor. The accracy of this assmtion is debatable, bt their measred data does rovide an oortnity to review the accracy of the semi-emirical model nder what are far from idealised conditions, and also to examine the feasibility of extraolating a semi-emirical model based on 500 mm sqare Windcatcher data to other geometries. Accordingly, in Fig. the semi-emirical redictions are comared with Kirk and Kolokotroni s data assming a temeratre difference of 5 C between the room and the srrondings (with T in = 0 C ). The redictions in Fig. were obtained for a Windcatcher containing a damer and grill in an nsealed room, and by smming the volme flow rates calclated searately for a. m sqare and a 0.6 m sqare Windcatcher. t is evident in Fig. that the redictions for θ = 5 comare very well with exerimental measrements (an average error of %), althogh one may arge here that this level of agreement is somewhat fortitos and that the wind direction varied when the measrements were taken and so cannot be assmed to be exactly θ = 5. However, these reslts demonstrate that there is some romise in sing C and K vales determined for a 500 mm sqare Windcatcher to redict the erformance of Windcatchers of other dimensions. t shold be observed also that the theoretical model sed by Kirk and Kolokotroni that delivers good agreement with the exerimental data contains at least two heristic constants with little sorting jstification; moreover, there is no gide as to how transferable these constants are and how they shold be alied to different alications, therefore it is dobtfl that they reflect the tre hysics of the roblem. 3

24 Frthermore, given the exerimental errors likely to be resent in the semi-emirical model and the exerimental data, one cannot exect excellent agreement between rediction and measrement and so the semi-emirical model mst be treated only as an estimate of tre Windcatcher erformance. Nevertheless, the redictions obtained for θ = 0 and θ = 5 both lie within a reasonable distance of the exerimental data and it aears sensible here to treat these redictions as limiting cases, where θ = 0 reresents an estimate of otimm erformance and θ = 5 an estimate of a worst case erformance. n Section 3 the estimated losses in an otlet qadrant were seen to be significantly higher than those in the inlet qadrants. This is of some concern, esecially for an nsealed room. n Table 6, the gradient m is lotted for differing vales of K, and the effect this has on the redicted volme flow rates from an nsealed room (for a 500 mm sqare Windcatcher with damers and grill) is investigated. Here, it is evident that, as one redces the vale of K, the volme flow rate increases, as one wold exect. The lower limit chosen here is K, = K and the flow rates redicted at this limit are 0% higher than those seen when K 9.. This reresents a significant difference when the room, = is nsealed and so in the ftre more exerimental data is necessary in order to be confident of the vales estimated here for the otlet loss coefficients. n articlar it is imortant to investigate these vales nder real oerating conditions, as it may be ossible that the K vales sed here are ndly inflenced by those laboratory conditions nder which the measrements took lace, and that these do not reflect the tre behavior of the Windcatcher in sit.

25 Finally, the ltimate aim here is to deliver a simle method for estimating the ventilation rate delivered by a Windcatcher. f one neglects the effects of air boyancy, which has reviosly be shown to be significant only at low wind seeds, then it is obvios that a simle linear relationshi is redicted between the Windcatcher volme flow rate and the wind seed. This makes arametric stdies and the collasing of data into simle exressions very straightforward. Accordingly, the volme flow rates for a nmber of sqare Windcatchers of different dimensions, in which a damer and grill are resent for an nsealed room, have been comted for θ = 0 and θ = 5. From these calclations, the following simle exressions can be obtained: Q ot = 0.5 A w for θ = 0 (3) and Q ot = A w for θ = 5. () Here, Q ot is the volme flow rate of air removed by the Windcatcher from an nsealed room, A is the cross-sectional area of the whole Windcatcher (i.e. A + = A + A + A3 A ), and w boyancy effects and are for a Windcatcher of length is the incident wind seed. These eqations neglect L = m. According to the model sed here the effect of changing the length of the Windcatcher on the crves is small, for examle increasing the length of the Windcatcher to 0 m lowers the constant in q. (3) by only 5%; however, it shold be stressed here that the semi-emirical model is based on measrements taken for a relatively short Windcatcher and it is assmed that one may simly scale the frictional losses for longer dct length; the accracy of this assmtion remains to be tested for longer Windcatchers that, say, oerate over a nmber of floors. Frthermore, qs. (3) and () assme that the C and K vales 5

26 obtained for a 500 mm sqare Windcatcher may be alied to other geometries (throgh the area A). The validity of this assmtion was investigated in Fig., where good agreement was observed; however, it is also ossible to comare these exressions with the reslts of Hghes and Ghani, who sed CFD to redict the ventilation rates for a 000 mm sqare to-down ventilation device similar to the Windcatcher being stdied here. f a regression analysis is ndertaken for the linear region of Hghes and Ghani s CFD redictions for conter crrent flow, one obtains the exression Q ot = 0.6 w. For a 000 mm sqare Windcatcher, q. (3) gives Q ot = 0.5w, which is very close to the relationshi redicted by Hghes and Ghani and frther validates the semi-emirical exressions derived here. Ths, the semi-emirical model derived sing data for 500 mm sqare Windcatchers rovides good agreement with two stdies in which the geometry of the device is altered. This rovides confidence in the se of qs. (3) and () over a range of geometries, althogh it wold be sensible here to gather frther exerimental data for different geometries, referably nder controlled conditions, in order to frther establish the accracy of these eqations. Frthermore, it aears sensible to view qs. (3) and () as an estimation of the er and lower limits of Windcatcher erformance, recognising that they are derived from a semi-emirical model and that, by definition, these eqations will contain exerimental errors and so shold be treated only as an estimation of tre Windcatcher erformance. 6

27 5. Conclsions A semi-emirical model is develoed here that combines a simle analytic model with exerimental data reorted in the literatre. The model draws on data measred for the coefficient of ressre on each face of a 500 mm sqare Windcatcher, and then infers losses in each Windcatcher qadrant from measrements of ventilation rates. A semiemirical model is develoed here in the belief that this is the only ractical aroach to qickly and accrately estimating Windcatcher erformance, esecially in view of the highly trblent natre of the flow rond a tyical Windcatcher and the roblems this has been seen to case for nmerical models; however, this aroach means that any errors resent in the exerimental measrements will also aear in the model and so sch a model can only be as good as the exerimental data available. Moreover, the exerimental data tilised here was obtained nder laboratory conditions for a 500 mm sqare Windcatcher in a sealed room and so an assmtion inherent in this aroach is that this data may be extraolated to real, in sit, alications in which air transfer between the room and the srrondings is ermitted and different Windcatcher geometries are resent. The loss coefficients sed in the semi-emirical model allow very good agreement to be obtained between the model and exerimental data; however, the loss coefficient necessary to obtain good agreement for the extract dcts was mch higher than for the sly dct and it is not entirely clear why this shold be the case. t is ossible that increased frictional effects and interference effects between the sly and extract flows can exlain this increase, althogh frther exerimental investigation is reqired in order to be certain of the case. After assigning the emirical constants the model was comared against 7

28 other exerimental and theoretical data and good agreement is generally observed for different wind directions. Air boyancy was also analysed and here the effects of boyancy on the erformance of a Windcatcher were observed to be significant only at wind seeds below aroximately m/s for wind of normal incidence. When the wind changes direction the relative effect of the boyancy forces increases and for an angle of incident of 5 boyancy becomes significant at higher wind seeds, althogh this effect is still small above aroximately m/s. Accordingly, the reslts resented here aear to indicate that for temeratre differences of less than 0 C, the effects of boyancy may be neglected for wind seeds greater than abot m/s. The semi-emirical model was also validated against in sit measrements of Windcatcher erformance and here excellent agreement with measred data is observed, althogh this reqired certain assmtions abot wind direction, and the level of agreement is, robably, rather fortitos. The semi-emirical model has, however, been shown to erform well against a range of exerimental data and CFD redictions, and so offers the otential for se as a qick iterative design tool. To this end, a very simle exression for extract ventilation rates is roosed that, after neglecting boyancy effects, rovides a very qick estimate of Windcatcher erformance that reqires no comtational effort. Acknowledgement This research was carried ot with financial sort from the ngineering and Physical Sciences Concil (PSRC) and Monodraght Ltd. 8

29 9 Aendix qations ()-(3) and (5) can only be solved iteratively and it is common for this tye of roblem to sccessively change ntil q. (5) is satisfied. This method is, however, rather cmbersome and it is more efficient to se a recognised root finding techniqe, which will deliver a mch faster method that is easily atomated. Here, the Newton Rahson method is adoted and qs. ()-(3) and (5) are first combined to give ), ( b a A A f = (A) and ), ( b a A A f =. (A) The constants a and a are given by + = A A K K A A a (A3) and + = A A K K A A a. (A) The constants b and b are given by { } ] [ ) ( ] [ w T T gl C C A A T T K b + = (A5) and { } ] [ ) ( ] [ w T T gl C C A A T T K b + =. (A6) n general, T ] [ =, T ] [ f f = f and the Newton Rahson method gives

30 { } = { } [ J] { f}. (A7) Here, is an initial gess and is the new soltion fond after solving the right hand side of q. (A7). The Jacobian [J] is given by + A A A A + a [ J ] =. (A8) A A + A A This method reqires the identification of an initial gess for. When θ = 0 the velocities in qadrant are relatively small when comared to the other qadrants and so for an initial gess it aears sensible first to assme that 0, which gives = [ b 0]. On solving q. (A7) for and it is then straightforward to retrn to q. (5) to find, and q. (3) to find. For sbseqent calclations for different vales of w it is sensible to se vales for calclated for a revios (referably lower) vale of w as an initial gess. 30

31 References Beazley, Harverson M. Living with the Desert: Working Bildings of the ranian Platea, Orchid Press, Thailand 98. Montazeri H, Azizian R. xerimental stdy on natral ventilation erformance of one-side wind catcher. Bilding and nvironment 008; 3(): Khan N, S Y, Riffat SB. A review on wind driven ventilation techniqes. nergy and Bildings 008; 0(8): Gage SA, Graham JMR. Static slit dct roof ventilators. Bilding Research & nformation 000; 8(): lmalim AA, Awbi HB. Wind Tnnel and CFD nvestigation of the Performance of Windcatcher Ventilation Systems. nternational Jornal of Ventilation 00; (): theridge D, Sandberg M. Bilding Ventilation: Theory and Measrement, Wiley, UK theridge, D. Natral Ventilation throgh Large Oenings - Measrements at Model Scale and nveloe Flow Theory. nternational Jornal of Ventilation 00; (): CBS. Natral Ventilation in Non-Domestic Bildings AM0, Liddanet MW, A Gide to nergy fficient Ventilation, Air nfiltration and Ventilation Centre, Oscar Faber, Santamoris M, Asimakoolos D. Passive Cooling of Bildings, arthscan, 996. Parker J, Teekeram AJ. Design and Alication Gide for Roof Monted Natral Ventilation Systems. BSRA, UK 00. 3

32 lmalim AA. Dynamic modelling of a wind catcher/tower trret for natral ventilation. Bilding Services ngineering Research and Technology 006; 7(3): S Y, Riffat SB, Lin Y-L, Khan N. xerimental and CFD stdy of ventilation flow rate of a Monodraght windcatcher. nergy and Bildings 008: 0(6): 0-6. Kirk S, Kolokotroni M. Windcatchers in Modern UK Bildings: xerimental Stdy. nternational Jornal of Ventilation 00; 3(): Shea AD, Robertson AP, Aston W, Rideot NM. The erformance of a roof-monted natral ventilator. th nternational Conference on Wind ngineering. Texas Tech University, Lbbock, Texas, USA Li L, Mak CM. The assessment of the erformance of a Windcatcher system sing comtational flid dynamics. Bilding and nvironment 007; (3): Hghes BR, Ghani SAA. A nmerical investigation into the effect of windvent damers on oerating conditions. Bilding and nvironment 009; (): Hghes BR, Ghani SAA. nvestigation of a windvent assive ventilation device against crrent fresh air sly recommendations. nergy and Bildings 008: 0(9): CBS. Gide C lmalim AA, Teekaram AJ. Natral Ventilation Testing Carried ot for Monodraght Ltd., BSRA, UK 00. lmalim AA. ffect of damer and heat sorce on wind catcher natral ventilation erformance. nergy and Bildings 005; 38(8):

33 Figre a. Plan view of Windcatcher. Figre b. Side view of Windcatcher. 33

34 Figre. Comarison between semi-emirical redictions and the exerimental measrements of lmalim and Awbi [5] withot damers and grill for θ = 0. Qadrant,, rediction,, exeriment; qadrant,, rediction,, exeriment; qadrant, - -, rediction,, exeriment. 3

35 Figre 3. Predicted ressre in a sealed room withot damers and grill for θ = 0. 35

36 Figre. Comarison between semi-emirical redictions and the exerimental measrements of lmalim [] with damers and grill for θ = 0. Qadrant,, rediction,, exeriment; qadrant,, rediction,, exeriment; qadrant, - -, rediction,, exeriment. 36

37 Figre 5. Comarison between semi-emirical redictions and the CFD redictions of Li and Mak [6] for ventilation rates from a sealed room, withot damers and grill. θ = 0,, semi-emirical model,, CFD; θ = 5,, semi-emirical model,, CFD. 37

38 Figre 6. Comarison between semi-emirical redictions and the exerimental measrements of lmalim and Teekaram [0] for ventilation rates from a sealed room, withot damers and grill. θ = 5,, rediction, and, exeriment. 38

39 Figre 7. Comarison between semi-emirical redictions and the exerimental measrements of lmalim [] withot damers and grill for θ = 0. Labelled qadrants,, rediction T = 0 C,, rediction T = 0 C. xeriment:, qadrant ;, qadrant ;, qadrant. 39

40 Figre 8. Predicted ressre in nsealed room., T = 3 C, - -, T = 0 C. T = 0 C ;, 0

41 Figre 9. Predictions for nsealed room for θ = 0. Labelled qadrants,, rediction T = 0 C,, rediction T = 3 C.

42 Figre 0. Predictions for nsealed room for θ = 5. Labelled qadrants,, rediction T = 0 C,, rediction T = 3 C.

43 Figre. Comarison between semi emirical redictions and the exerimental measrements of Kirk and Kolokotroni [] for ventilation rates from an nsealed room, with damers and grill., rediction exeriment. θ = 0 ;, rediction θ = 5 ;, 3

44 Table. C vales for θ = 0. Qadrant xeriment. [] xeriment [] CFD. []

45 Table. C vales sed in semi-emirical model θ = 0 θ = 5 C C C C

46 Table 3. Gradient (m) of Q vs w. m m Qadrant Damer and grill omitted Damer and grill inclded xeriment rror xeriment rror Model Model [5] % [] %

47 Table. Loss coefficients for Windcatcher Section Sly K xtract K, To section.5.3 nlet Otlet.0.0 Dct K frict =0.06L/d H K frict =0.06L/d H Additional Loss Grill Damers Total.3 K K + frict frict 7

48 Qadrant Table 5. Predicted gradient (m) of Q vs w, damer and grill inclded. m nsealed m sealed θ = 0 θ = 5 θ = 0 θ =

49 Table 6. Sensitivity of redicted volme flow rate to vale of K, K Gradient, m K frict 7 + K frict K frict K frict K