THE DISCHARGE COEFFICIENT OF A CENTRE- PIVOT ROOF WINDOW

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1 THE DISCHARGE COEFFICIENT OF A CENTRE- PIVOT ROOF WINDOW Ahsan Iqbal 1, Alireza Afshari 1, P.V.Neilsen 2 and P. Heiselberg 2 1 Danish Building Researh Institute Aalborg University Dr Neergaards Vej Hørsholm, Denmark *Corresponding author: ahi@sbi.aau.dk 2 Indoor Environmental Engineering Aalborg University Sohngaardsholmsvej 57, 9000 Aalborg, Denmark ABSTRACT Auray in estimation of airflow through windows is the key parameter for modelling and designing of naturally ventilated buildings. The flow through windows is usually desribed by the orifie flow plate equation. This equation involves the disharge oeffiient. In pratie, often a onstant value of disharge oeffiient is used. The onstant value of disharge oeffiient leads to deeptive airflow estimation in the ases of entre-pivot roof windows. The objet of this paper is to study and evaluate the disharge oeffiient of the entre pivot roof window. Fous is given on unidiretional flows i.e. inflow and outflow. CFD tehniques are used to predit the airflow through the modelled window. Analytial orifie flow equation is used to alulate the disharge oeffiient. Results are ompared with experimental results. It is onluded that the single value of the disharge oeffiient leads to ambiguous estimation of airflow rates. The disharge oeffiient dereases with inrease in flap opening area. The disharge oeffiient also depends upon the flow diretion KEYWORDS Centre-pivot roof window, disharge oeffiient, CFD INTRODUCTION The amount of air entering through natural ventilation (or in hybrid systems) is extremely diffiult to predit aurately as airflow depends on unknown wind and buoyant effets. In pratie, the orifie flow equation is used to ompute the airflow through the intentional openings and windows. The disharge oeffiient (CD) in this equation is usually taken as onstant. The onstant value of the disharge oeffiient is valid only for onstant opening areas [8], [4]. Hene, the use of onstant value of CD for operable windows leads to deeptive results. The exatness of the CD an have a signifiant impat on the ability of a mathematial model to predit the airflow rates [4], [6]. There is a need of evaluation of CD of operable (i.e. with flap) windows. Operable windows are broadly used in residential buildings for ventilation. Sientifi literature on façade windows is somehow available. However, the literature on roof windows (espeially enter-pivot roof window) is not muh disussed. This paper fouses on the disharge oeffiient of a enterpivot roof window. Airflow rate through the opening is the integral of veloity over the opening area i.e. [10]. In pratie it is diffiult to do this integration. Therefore an alternate way has to be adopted. The airflow passet through the opening aquires the shape of a jet [3]. Therefore the volume flowrate at the vena ontrata of the jet is the atual volume flow rate through the opening. Veloity (v ) in the vena ontrata is defined in terms of a theoratial (fritionless flow) veloity (v th ) and the veloity oeffiient (C v ). The area (A ) of vena ontrata is defined q vda

2 in term of the opening area (A) and the ontration oeffiient (C ). The veloity in the vena ontrata is onstant therefore the flow rate (q ) in vena ontrata is: q A v C C Av v th The theoratial veloity (v th ) is mainly due to pressure differene (ΔP) and the produt of C and C v is alled the disharge oeffiient (CD). P v th C C C 2 and D v The C and C v are mostly disussed in literature but in pratie, espeially with operable windows, they are exteremly diffiult to estimate. Therefore, the disharge oeffiient is usually used to define the flow. From above mentioned orelations, the airflow through an opening is defined as: 2 P (1) Q CDA This is generally referred as orifie flow plate equation. A olossal literature is available for estimation of CD. However, a onstant values of CD is predominantly used in pratie. These onstant values are derived from the data used to estimate the flowrate in pipes [8]. Bot et. al. performed [7] a full sale measurements of flowrate through one side mounted asement windows (façade window). The authours defines the resistane oeffiient/frition fator in terms of aspet ratio of the window and opening angle. The resistane oeffiient(ζ) is a oeffiient that defines the pressure drop due to frition in the opening and flow. Theoratially, it is 1 i 2. The authours use the ross setional opening area, and from the Pfr v 2 results of their researh it an be onluded that the overall disharge oeffiient of the top hinged window inreases with the inrease in opening angle. P. Heiselberg et. al. [8] uses the minimum opening area to estimate the disharge oeffiient of a façade window with movable flap. Experimental results showed that the disharge oeffiient is not onstant for different flap opening angles. The authours onlude that the value of disharge oeffiient is approahing to 1 with the derease in flap opening angle (orresponding to minimum opening area). Only for large opening angles the value of 0.6 an be used as a disharge oeffiient of a window with movable flap. Andersen [2],[3] disussed theoretially, frition and ontration oeffiients of openings with movable flaps. The authour use artifiial as well as pure resistane oeffiients along with artifiial and real opening angle to alulate the ontration oeffiient. The authour onlude that (for entrally hinged flap) the ontration oeffiient dereases with inrease in the flap opening angle. Furthermore, the resistane oeffiient (both artifiial and theoratial) inreases with the inrease in flap opening angle. The real opening angle is dependent on aspet ratio of the window. Therefore, the ontration oeffiient, and onsequently the disharge oeffiient, is also dependent on the aspet ratio of the window. For sharp edged openings, the disharge oeffiient is about 0.61 [2], [3]. Hult et. al. [4] determines the disharge oeffiient of the façade window using CFD. The authours onlude that the disharge oeffient of a façade window is reliant upon aspet ratio and window opening angle. However, for larger opening angle it approahes to the ommonly used value of 0.6. Aording to their researh, the CFD results suggest that the atual flow through a top-pivoted window may be as muh as twie the flow predited by EnergyPlus software. i The definition is from theoratial books and from (ANDERSEN 1996)

3 METHODS CFD tehniques was used to test the dependene of disharge oeffiient (CD) on the flap opening angle(α). The CFD domain was defined in suh a way that on right side of the domain the outflow through the window ould be examined, and the inflow through the window ould be examined from the left side of the domain. For reduing the proessing time, only half part of the window was examined by using symmetri boundary ondition. Height and width of the domain was seleted in suh a way that the size of the domain had no influene on the loal veloities and the pressure distribution around the window. The model room was defined as shown in Figure 2. InVent was the opening in the model room with the window and OutVent was the opening without any window. Both InVent and OutVent were on the roof with slope/pith of 45 o. The window and flap geometry were kept simple beause the details of window (minor bends on flap) has insubstantial affet on overall disharge oeffiient [1]. The polyhedral meshing sheme was used with 8 prism layers mesher at the boundaries. The base size was 1 m. The prism layers were 8% of the base ell size. The surfae growth rate was 1.3. Allowable skewness for ells was 85 o. Several parts of the domain had ustomised surfae mesh size to ensure proper mesh quality. The Inlet was the veloity-inlet, the Outlet was the pressure-outlet. The domain top, left and the right boundaries were symmetri boundaries and all other boundaries were walls with no slip onditions. Physis: A body interats with the surrounding fluid through pressure and shear stress, and the resultant fore in the diretion of stream is the drag fore. The drag oeffiient Df is used to define the drag fore when the detailed information about pressure and shear stress is not known i.e. it is a ratio between the drag fore and the wind pressure fore [10]. The minimum number of ells was seleted in suh a way that by inrease in the number of ells, there is no effet on the Df of the model room. This means that the further derease in ell sizes had no effet on the loal veloity and the pressure distribution around the building. The Two layer realizable k-ε turbulent model was used to ompute the airflow and its physial behaviour [6]. The working fluid was inompressible ideal gas. The flow was 3D steady state. Flow and energy were both modelled using the segregated approah. The seond-order upwind disretisation sheme was used for both flow and energy. Under relaxation fators for veloity, pressure and energy were 0.7, 0.3 and 0.9 respetively. Inlet ondition (Inlet -Figure 1) for the turbulent kineti energy (ko =1.5(TiUo) 2 ) and the dissipation rate (εo=ko1.5/lo) were aording to Nielsen [9] reommendations. Where, Ti is the turbulene intensity and was taken as 4% with inlet temperature of 293K. Uo is inlet veloity in {m/s}. lo{m} is length sale and was taken as one-tenth of the height of the inlet. The inlet veloity was seleted in suh a way that for eah simulation the airflow through the window was fully developed turbulent flow. The CD value for fully developed turbulent flow does not vary with Reynolds number [6]. The equation (1) was used to find out the CD for the window (Figure 4). The flowrate at InVent (Figure 2) was estimated by the flowrate at the OutVent (Figure 2). The flow Q{m 3 /s} at OutVent was alulated by integration of veloity over the area of OutVent i.e. the fae area of the ells at the interfae (OutVent and external region) times the perpendiular omponent of the veloity i.e. Inlet Inflow Model Outlet Outflow Model Symmetry boundary ondition Figure 1 CFD Domain OutVent InVent Figure 2 Model room with InVent and OutVent

4 n 1 Q Ai vi i1 m i (2) Figure 3 Outside pressure (average) Bidiretional FAN Where, Ai{m 2 } is the fae area of ell at the interfae and vi{m/s} is the perpendiular (to Ai) omponent of the veloity. The airflow rate an also be alulated by the mass flow rate divided by the density as shown in Equation ( 2 ). The density ρ is onstant i.e. 1.2 kg/m 3, m i is mass flow rate in kg/s. Pressure differene: To measure the pressure differene (ΔP) aross the InVent one probe was measuring the pressure inside the room (in the entre of the room). The outside pressure was an area weighted average of outside pressure at the InVent opening as shown in Figure 3. Opening area: The CD was also dependent on the opening area. Therefore it was evaluated for two different opening areas. One was the minimum opening area (Amin). The minimum opening area is shown in Figure 5. The sum of two minimum opening areas is the total minimum opening area (see Figure 5). For flap opening angles of 50 o and greater, the minimum opening area is the sum of two fae ross setions of the window. Another way to define the opening area is the gross fae area (Afae) of the opening i.e x 1.4. On-site measurements: On-site measurements were performed in the Energy Flex House (EFH) of the Tehnologial Institute of Denmark (Copenhagen). The house was equiped with the VELUX entrepivot roof window. Blower door test, for infiltration/exfiltration, were perform before the measurements. Only outflow measurements were ompared in this study, beause this study is mainly foused on CFD, and measurements were performed only for validation purpose. The flow through the window was the sum of fan flow and infiltration/exfiltration. Figure 5 shows the shemati diagram of the measurements setup. The disharge oeffiient was alulated by using equation (1) and minimum opening area. The outside pressure was the area weighted average pressure around the window. Inside pressure was the average inside pressure of the house. The entrepivot roof window in the EFH was fully automati and it was not possible to open the window more than 17 o. Therefore, disharge oeffiient only for very small (α<17 o ) opening angles was measured. RESULTS Minimum opening area Figure 4 Centre-pivot roof window and minimum opening areas Centre-pivot roof window Figure 5 Shemati Figure 1 diagram of on-site measurements Figure 7 illustrate the disharge oeffiients (CD,min) of a entre-pivot roof window when minimum opening area is used in equation (1). The CFD results for CD,min of inflow through the window (flow from outside to inside) is represented by the blue line. The CFD results for CD,min of outflow (flow from inside to the outside) is represented by the red line. The green line is CD,min that is obtained by the on-site measurements. As mentioned earlier, it was not possible to

5 measure (onsite) the disharge oeffiient for angles greater than 17 o. Therefore, measurement data is available only for 17 o, 14 o, 9.3 o and 4.6 o. It should be noted that the minimum opening area is taken from the manufaturer atalogue. On the ontrary, with available omputing power for CFD alulations, it was very time onsuming to go below 15 o of opening angle. That s why the CFD simulation was performed only for 15 o, 25 o, 35 o, 45 o, 50 o and 90 o. It should be noted that the minimum opening areas were alulated through the CAD drawings. Figure 6 illustrate the disharge oeffiients (CD,fae) when the gross fae opening area is used in equation (1). The blue line shows the CD,fae, obtained from CFD alulations, when flow is direted inward. Whereas, the redline is the CD,fae (CFD result) when flow is direted outward. Figure 7 Disharge oeffiient of the entre-pivot roof window using minimum opening area DISCUSSION From Figure 7, apperantly there is a differene between the CD,min values evaluated by the measurements and by the CFD. One of the reason is ideal versus real ondition. However, the trend of derease in CD,min is almost the same. Figure 6 Disharge oeffiient of the window using fae area Ergo, the problem might also be in alulation of the minimum opening area. Therefore, another quantity, CD x A (so alled effetive area) of both, measurements and the CFD are ompared. This omparision is shown in Figure 8. The differene in measurements and the CFD results are now minimum. The CFD results are in sound aordanewith the measurements at the angle of 15 o and around. The onurrene, of CFD and the measurements, at low opening angles are taken as benhmark for higher opening angles. Hene, the realizable k-ε turbulent model predits the flow (aross the window) in a good agreement with the measurements. The CD,min urve represents the hange in the disharge oeffiient due to (mainly) flow effet. Whereas, the CD,fae urve represents the hange in the disharge oeffiient due to both flow and area effets. The C D,min (as shown in Figure 7) dereases with the ertain pattern until it reahes to 50 o of the flap opening. At this point the Amin shifted from the position shown in Figure 4 to the fae ross setional area. Then the pattern of Figure 8 Comparison of CFD results with On-site experimental results

6 derease in CD,min also hanges. This hange in CD,min is due to the hange in Amin and due to the fat that pressure field on the roof surfae (losed to the window) is disturbed. In the aseof inflow through the window, the flow in eah setion of the window is not evenly distributed, exept for very small opening angles. Flow in the lower setion is muh higher then in the upper setion. At the angle of 90 o there is no flow in the upper setion of the window. In the ase of outflow through the window, the flow in eah setion of the window is somewhat evenly distributed. Therefore, the CD,min inflow is higher than the CD,min values of outflow. This phenomenon negates the assumption of stagination ondition at the inlet in determination of CD. However, the slope/trend of the outflow urve is same as of inflow urve. After 50 o of flap opening, the slope of outflow beome lower than the inflow. Therefore, the CD,min at 90 o of flap opening of outflow diretion was higher value than that of inflow diretion. The reason for differene in CD,fae urves (for inflow and outflow diretion) is also the same. For more onrete onlusion, the results have to be evaluated for several openings with different aspet ratios. However, these results are only subjeted to the partiular window type and for natural ventilation aused by wind effet. CONCLUSION It is onluded that the k-ε turbulent model predits the flow in sound agreement with the measurements. It is also onluded that in the orifie flow plate equation, the disharge oeffiient is not a onstant quantity. The CD,min dereases with flap opening angles. The trend of derease in CD,min hanges after 50 o of flap opening angle. Likewise, the disharge oeffiient also depends upon the flow diretion. The CD,min is higher for inflow and the CD,min is lower for outflow. For higher opening angles (e.g. higher than 65 o ) the riteria is swapped. ACKNOWLEDGEMENTS This paper is based on researh onduted in a PhD projet, whih is a part of the Strategi Researh Center for Zero energy Buildings at Aalborg University and finaned by Velux A/S, Aalborg University and The Danish Counil for Strategi Researh (DSF), the Programme Commission for Sustainable Energy and Environment. Furthermore, the authors gratefully aknowledge the assistane of Tehnologial Institute of Denmark during measurements in Energy Flex House. REFERENCES [1] Computational fluid dynamis in ventilation design REHVA guidebook no International Journal of Ventilation(- 3): [2] ANDERSEN, K. (2002). Frition and ontration by ventilation openings with movable flaps. Room Vent 2002 (8th International Conferene on Air Distribution in Rooms), Copenhagen.. [3] ANDERSEN, K. (1996). Inlet and outlet oeffiients - A theoretial analysis. ROOMVENT, 5th International Conferene on Air Distribution in Rooms, Yokohama. [4] E. Hult, G. Iaarion and M. Frisher, Using CFD simulation to improve the modeling of window disharge oeffiients, in SimBuild, Madison, [5] Chiu Y, Etheridge DW. External flow effets on the disharge oeffiients of two types of ventilation opening. J Wind Eng Ind Aerodyn ;95(4): [6] A. Iqbal, A. Afshari, P. V. Nielsen and P. K. Heiselberg, Numerial preditions of the disharge oeffiient of a window with, in Healthy Buildings, Brisbane, [7] de Jong, T., & Bot, G. P. A. (1992). Flow harateristis of one-side-mounted windows. Energy and Buildings, 19(2), [8] Heiselberg P, Svidt K, Nielsen PV. Charateristis of airflow from open windows. Build Environ ;36(7): [9] P. V. Nielsen, Speifiation of a two-dimentional test ase, International energy ageny, energy onservation in buildings and omunity systems, p. Annes 20: Airflow pattern withing buildings, [10] Munson, B. R., Young, D., & Okiishi, T. (1999). Fundamentals of fluid mehanis John Wiley & Sons.