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Study on pressure-equalization of curtain wall systems
Journal of Wind Engineering and Industrial Aerodynamics 73 (1998) 251—266
Study on pressure-equalization of curtain wall systems Edmund C.C. Choi*, Zhihong Wang School of CSE, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore Received 16 May 1996; accepted 22 September 1997
Abstract In recent years, aluminium-curtain-wall systems are often used in southeast Asia. Many of these curtain-wall systems can be classified as a two-barrier system with a front-panel (the rainscreen) and the back-panel (the air barrier). The back-panels of such systems are usually thin and flexible. Compared with the brick or brick-veneer rainscreen walls, where the backpanels are very rigid, the pressure-equalization characteristics are expected to be quite different. To improve on the understanding of the behaviour of such systems and to evaluate design parameters, full-scale measurements were carried out. A numerical model which takes into account the flexibility of the back-panel has been developed for the prediction of cavity pressure in curtain walls. The results based on this model show good agreement with those obtained from full-scale experiments. ( 1998 Elsevier Science B.V. All rights reserved.
Nomenclature A a, b b-p k $ l % n , n@ 0 0 P ! P # P % p-e » » 0 X a, b a 1
venting area side length of rectangular back panel back panel discharge coefficient effective length of opening undamped resonant frequency atmospheric pressure cavity pressure external pressure pressure equalization cavity volume initial cavity volume movement of air constants in back panel stiffness function effective length coefficient
* Corresponding author. 0167-6105/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 7 - 6 1 0 5 ( 9 7 ) 0 0 2 9 0 - 0
252
*» d o,o # %
E.C.C. Choi, Z. Wang/J. Wind Eng. Ind. Aerodyn. 73 (1998) 251—266
volume change deflection at centre of back panel air density
1. Introduction Many curtain walls, built in southeast Asia make use of the pressure equalization or rainscreen method as a means to eliminate or reduce rain penetration. Essentially, the two-barrier system consists of two leaves of wall: a rainscreen as the outer leaf and the air barrier (back-panel) as the inner leaf. The two leaves are separated by a cavity that is vented to the outsides by openings on the rainscreen. With pressure equalization, i.e., the cavity having the same pressure as the external pressure, rain water will not be forced to penetrate the rainscreen. Normally, the cavity is compartmentalized to prevent air movement over zones with large pressure gradients. Since the introduction of the rainscreen wall system over 20 years ago, studies on the pressure-equalization performance of such wall systems have been carried out [1,2]. Many of the investigations are on brick-veneer or double-brick walls. For such systems the volume of the internal cavity is usually large and both the rainscreen and the air barrier are very rigid. It is also common that the air barrier is not 100% air tight but with leakage paths into the inside of the building. Some studies on pressure equalization of rigid wall systems are reported, see e.g. Refs. [3,4]. The back-panels of curtain walls are normally made of thin flexible steel sheets, the internal volume of the cavity will change under the action of cavity pressure. The construction of the back-panels is also usually quite air tight. This will have a strong influence on the pressure-equalization process and the performance of the curtain wall. Experimental and theoretical investigations on the behaviour of curtain wall with flexible backpanel are needed to obtain design parameters and to have a better understanding of its performance characteristics. The pressure inside the cavities of a curtain wall generated by wind action is influenced by the external pressure, fluctuation frequency, vent hole area, volume of cavity and back-panel stiffness. The wind force is a random process which can be represented by a large number of sinusoidal processes with different frequencies and amplitudes. The present study first looks at the response of curtain wall subjected to sinusoidal external pressure fluctuations and secondly the effect due to random pressure fluctuations is investigated.
2. Full-scale measurements 2.1. Description of specimen The experimental study involves the investigation of the performance of two curtain-wall systems constructed by P.D. Manufacturing International Pte Ltd. The
E.C.C. Choi, Z. Wang/J. Wind Eng. Ind. Aerodyn. 73 (1998) 251—266
Fig. 1. (a) Front elevation of (a) CW I (b) CW II.
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first test specimen (CW I) consists of two bays of width 1.2 m. Each bay is 3 m high and is divided into three vertical compartments as shown in Fig. 1a. The middle compartment with a height of 1.19 m is the larger one and is selected for pressure-equalization (p-e) investigation. The front-panels of the middle compartments are different for the two bays, one is 3 mm thick aluminium and the other is 8.76 mm laminated glass. The back-panels (b-p) are made of 1 mm thick galvanized steel sheets. The internal cavity volume is 0.0699 m3 and there are weep holes venting to the outside. Two sizes of weep hole area can be configured, 0.0003 or 0.0012 m2. The second test specimen (CW II) consists of three bays of width 1.414 m each. There are three vertical compartments in each bay with the top and bottom compartments having heights of 2.65 m (Fig. 1b) and these are selected for p-e study. The front-panels are 6 mm thick reflective glass and the back-panels are 1 mm thick galvanized steel sheeting. The volume of the internal cavity is 0.2476 m3 with a weep hole area of 0.0006 m2. A schematic diagram showing a section of CW II and the components of a twobarrier system (the front- and back-panels, internal cavity and vent hole) is given in Fig. 2.
2.2. Experimental set-up The specimens were mounted facing inwards, in a test chamber, such that the exterior face of the curtain wall was subjected to the sinusoidal pressure fluctuation generated in the chamber. The interior face of the curtain wall was exposed to atmospheric pressure. Pressure taping points were connected to various locations in the cavity as well as to the exterior face so as to monitor the internal cavity and external pressures. Testing of the two curtain walls was carried out using static pressure as well as dynamic (near) sinusoidal pressure fluctuations. The frequency, mean and amplitude of pressure fluctuation were varied in the experiment. Besides testing the specimens with (near) sinusoidal pressure fluctuations in the pressure chamber, the specimens were also tested using random wind generated by an aeroplane engine. The specimens were mounted facing outwards such that the external face is directed towards the engine exposing to the random wind generated by the engine. The wind speed, external pressure and internal cavity pressure were monitored during the experiment. Due to difficulties in the setting up of the engine, random wind test was only carried out on CW I. Results of the experimental study showing the time-wise and frequency-wise plots of the cavity and external pressures are given in Section 4. Further details of the experimental results are described in Ref. [5].
2.3. Flexibility of back-panel One of the major differences between an aluminium curtain wall p-e system and a brick-veneer p-e system is the flexibility of the back-panel. This can significantly
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Fig. 2. Schematic diagram of a two-barrier system.
change the response characteristic of the internal cavity pressure. Thus, it is important to obtain the load—deflection characteristics of the b-p of the curtain wall. Fig. 3 shows the stiffness function of the b-p of CW I obtained from static pressure test. It is noteworthy that the deflection (d) at the centre of the panel versus cavity pressure (P ) # curve is highly nonlinear which is quite typical for curtain-wall systems. There shows a highly flexible region near the zero pressure that is due to the popping action of a thin plate. The two branches (positive and negative cavity pressure) of the curve can be fitted well by the exponential functions d"aPb. The two parameters a and #
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Fig. 3. Stiffness function of back-panel.
b obtained in metric units (d in m, P in kPa) are as follows: # d"aPb, # a"0.0100, b"0.714 if P '0, (1) # a"0.0178, b"0.324 if P (0. # These flexibility equations are needed for the theoretical analysis of the p-e system. Air leakage of the back-panel was also investigated. Standard air-permeability test was carried out on the whole specimen. At a pressure of 75 Pa, the amount of air leaking through the curtain wall (including the mullions, transoms and joints) was measured to be 0.033 m3/h/m2. This shows that the leakage is very small and the back-panel can be considered to be airtight.
3. Theory In response to the exterior pressure changes, a “plug” of air moves in and out through an opening from an exterior location just outside the opening, “e”, to an interior location in the cavity just inside the opening, “c”. The differential equation governing the motion of this mass of air can be described in one-dimensional form as 1 P P l X$ # DXQ DXQ # #" %, (2) % 2k2 o o $ # % where X is the movement of the “plug” of air, l is the effective length of opening which % can be expressed as a JA (A is venting area through rainscreen), k "0.65 is the $ l discharge coefficient and o is the density of air. The effective length coefficient a can be l taken to be Jp/4 [6]. Eq. (2) is derived for incompressible flow. The absolute value of
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the velocity is needed to take care of the reversing flows. It is noted that the terms X, P and P are time dependent and in the subsequent derivations, the other terms », % # *», d are also time dependent. If it is assumed that there are no back-panel leakages, conservation of mass requires that the rate of mass influx through the opening must equal the rate of change of the mass of air inside i.e. d o + A XQ " (o »), (3) % k k dt # k where A is the kth venting area, and » is the cavity volume and is a constant when the k front- and back-panels are both rigid. When the b-p is flexible, the change in the cavity volume due to the deformation of the panel has to be considered. The cavity volume » can then be expressed as follows: »"» #*», (4) 0 where » is the initial volume and *» is the volume change. 0 Based on the isothermal process assumption (P/o"const.), Eq. (3) can be written as d o + A XQ " (o ») % k k dt # k d*» o dP d*» do " ! # (» #*»)#o , (5) " # (» #*»)#o 0 # dt 0 # dt P dt dt ! where P is the atmospheric pressure and equals to 1.013]105 Pa. ! To simplify the problem, all the venting areas are assumed to lump into one opening with a total venting area of A and with an external pressure P at the 34 % opening. The change in air density is also very small for the practical problem and the term can be neglected. Substituting Eq. (5) into Eq. (2), the following expression is obtained:
K
K
o l (» #*») (» #*») ol o !% 0 0 P$ # ! % *»Q PQ # ! PQ #*»Q # A P # 2k2A2 # A P P 34 ! $ 34 ! 34 ! (» #*») ol 0 ] PQ #*»Q #P # ! % *»$ "P , (6) # # A % P 34 ! where o is the atmospheric air density. ! The change in cavity volume can be calculated from the deformation of the b-p as follows:
A
*»"(4/p2)abd,
B
(7)
where a and b are the lengths of the sides of a rectangular b-p and d is the deflection at the centre of the panel. The factor 4/p2 is derived for the assumption of a rectangular parabolic deflected shape. From the experimental study described in the earlier section, d is expressed in terms of the pressure P as given in Eq. (1). #
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The first and second derivative of the increment or decrement of cavity volume with respect to time can be derived as follows: 4 4 *»Q " abdQ " ababPb~1PQ , # # n2 n2
(8)
4 4 *»$ " abd$ " abab[(b!1)Pb~2PQ 2#Pb~1P$ ]. # # # # n2 n2
(9)
Substituting Eq. (8) and (9) into Eq. (6), the time-varying cavity pressure P can be # solved using the Runge—Kutta method. For a rigid b-p, the cavity volume change is negligible. By setting the time derivatives of the volume to be zero in Eq. (6), the above equations are equivalent to those given in Ref. [3], which gives the following relationship between P and P : % #
K KA B
ol» » o ! % 0 P$ # ! 0 PQ A P # 2k2A2 P # 34 ! $ 34 !
» 0 PQ #P "P . # % P # !
(10)
The undamped resonant frequency for Eq. (10) is 1 u n " 0" 0 2p 2p
S
A P 34 ! . ol» !% 0
(11)
For the case where the b-p is flexible, the expression for the natural frequency is
S S
1 n@ " 0 2p "n 0
A P 34 ! ol» !% 0
S
1 1#*»/» #4ababP Pb~1/(p2» ) 0 0 ! #
1 . 1#(4aba/(p2» ))(Pb#bP Pb~1) 0 # ! #
(12)
4. Results and discussion In the following section, results of tests carried out with different amplitudes and frequencies of external pressure fluctuations are presented. Results of the sinusoidal pressure test and the random pressure test are given. Predictions using theoretical models with rigid and flexible back-panels are also presented and compared with the measured values. 4.1. Sinusoidal exterior pressure fluctuations Using the numerical model with parameter (b-p stiffness, panel geometry, etc.) measured from the curtain wall, the internal pressures corresponding to the applied external pressure can be predicted. Responses for both rigid and flexible b-p
E.C.C. Choi, Z. Wang/J. Wind Eng. Ind. Aerodyn. 73 (1998) 251—266
259
Fig. 4. Time history of cavity pressure.
assumptions are calculated and compared with the performance of the actual curtain wall. Time histories of the cavity pressure (P ) for different weep hole sizes, frequencies # and amplitudes of external pressure fluctuations were obtained. Before performing the actual experiment, it was decided that a calibration study must first be carried out. This is because a detailed examination of the curtain wall reviewed that there were many unintentional openings (e.g. slot holes for screws not properly sealed up) on the rain screen other than the weep holes. The calibration was carried out with all the weep holes blocked up and the specimen subjected to the sinusoidal external pressure. The dynamic component of the cavity pressure, P , is # shown in Fig. 4. It is observed that P is not stationary but fluctuates with P . Using # % Eq. (6) and adjusting the area A , a good match between the predicted and measured 34 values can be obtained. This gives an estimation of the area of these unintentional openings (initial venting area) WP1. WP1 is estimated to be about one-ninth of the actual weep hole area. The predicted values are also shown in the same figure. With the same value of A , predictions using the rigid b-p assumption (Eq. (10)) are also 34 shown in Fig. 4. The rigid b-p assumption very much over estimates the cavity pressure. Experiments were then carried out with weep hole areas of 0.0003 m2 (WP2) and 0.0012 m2 (WP3). The measured and predicted values of the cavity pressure are shown in Figs. 5 and 6, respectively. In calculating the theoretical values, A is set equal to 34 the sum of WP1 and the actual weep hole area. It can be seen that the flexible b-p assumption produces much better predictions than the rigid b-p assumption. Further tests were carried out at different frequencies, different mean pressures and different amplitudes of pressure fluctuations. Results of these tests are similar to those in Figs. 5 and 6 where the flexible b-p model consistently gives better predictions as shown in Table 1. For CW II, no unintentional openings were found and A was taken to be 34 the actual weep hole area.
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Fig. 5. Time history of cavity pressure.
Fig. 6. Time history of cavity pressure.
The flexible b-p model, Eq. (6), is shown to predict the cavity pressure very well for different conditions. The results using the rigid b-p assumption, however, differ greatly from the measured values for the smaller venting areas. Thus, Eq. (10) does not seem to reflect the performance of curtain wall with thin metal b-p. Using the numerical model, several parametric runs were carried out to study the sensitivity of the pressure ratio (P /P ) to weep hole size, fluctuation frequency and b-p # % stiffness. Fig. 7 shows the effect of frequency of external pressure fluctuation on the pressure ratio. Predictions calculated using the flexible b-p and the rigid b-p models are presented. For the flexible b-p, there shows a trend of decreasing P with increase in # frequency of pressure fluctuation. The higher the frequency, the lower is the internal pressure. For frequencies of five or more cycle per second, the internal pressure is less
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E.C.C. Choi, Z. Wang/J. Wind Eng. Ind. Aerodyn. 73 (1998) 251—266 Table 1 Pressure amplitude ratios (P /P ) # % Freq (Hz)
P (Pa) %
CW I
CW II
WP1
0.30 0.45 0.81 0.33 0.46 0.64 1.07 0.49 0.64 0.82 0.124 0.132 0.133 0.136 0.156 0.164 0.195 0.20 0.23 0.25
400 400 250 400 400 300 250 200 330 250 350 200 300 500 350 350 300 250 250 200
WP2
M
F
R
0.37 0.28 0.22
0.45 0.30 0.21
1.0 0.95 0.96
WP3
M
F
R
0.98 0.93 0.85 0.67
0.98 0.92 0.84 0.63
1.0 0.95 0.99 0.97
M
F
R
1.0 0.96 0.88
1.0 0.97 0.92
1.0 1.0 1.0
M
F
R
0.72 0.75 0.71 0.71 0.74 0.67 0.66 0.61 0.56 0.57
0.74 0.81 0.80 0.73 0.76 0.69 0.70 0.69 0.54 0.61
0.93 0.98 0.99 0.95 0.92 0.98 0.98 0.99 0.99 0.95
Note: M — measured; F — Flexible back panel model; R — Rigid back panel model.
Fig. 7. Pressure ratio versus fluctuation frequency (A /» "0.0193 m~1). 34 0
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Fig. 8. Pressure ratio versus external pressure.
Fig. 9. Pressure ratio versus vent factor.
than 30% of the external pressure. This is not so for the rigid b-p; there seems to be very little change in the internal pressure with increasing frequency. The cavity pressure is also dependent on the stiffness of the back-panel which is a function of pressure. The dependence of the pressure ratio on the external pressure is demonstrated in Fig. 8, in which the mean external pressure PM is varied but % with the amplitude of external pressure fluctuation fixed at 300 Pa. As shown in the chart, a higher mean pressure induces a higher stiffness resulting in a higher P value. # In the previous section, the pressure amplitude ratio P /P is shown to be dependent # % to a great extent on the venting area. A closer examination of Eq. (6) shows that the
E.C.C. Choi, Z. Wang/J. Wind Eng. Ind. Aerodyn. 73 (1998) 251—266
263
Fig. 10. Pressure ratio versus fluctuation frequency.
controlling factor should be the venting area to cavity volume ratio A /» , which is 34 0 termed the vent factor. This factor is an important parameter for the design of curtain wall. Fig. 9 shows the effect of the vent factor on the pressure ratio for different frequency of external pressure. For small values of the vent factor, the internal pressure of the curtain wall with a flexible b-p is significantly lower than the corresponding value for the rigid b-p. To achieve good pressure equalization (i.e. to have P /P close to unity) a large vent factor of more than 0.035 m~1 is required for # % frequency of 1 Hz or less. The value is also dependent on other factors such as value of the mean pressure. Fluctuating exterior pressures cause fluctuating flows through the venting holes of a rainscreen. As air flows through these holes, the drag on the air suppresses the fluctuations and causes damping. The damping of flow through venting area increases with the decreasing of weep hole size. Variation of P /P ratio with fluctuation # % frequency for a vent factor of 0.0193 m~1 has been described in Fig. 7. In Fig. 10, the curves are extended to higher frequencies. It can be seen that the damping for the system is very large (especially for the flexible b-p) and the curves decrease very fast with increasing frequency. To investigate the effect on systems with smaller damping (i.e. a larger value of the vent-factor), similar curves for a vent factor of 0.193 m~1 are also plotted in the same figure. These curves show the resonance response of the cavity pressure with a peak at the natural frequency. This peak is specially prominent for the rigid b-p model. Whereas for the flexible b-p model, the peak is much smaller and it occurs at a much lower frequency. The theoretical values of the natural frequency calculated using Eqs. (11) and (12) for the rigid b-p and flexible b-p are 57.8 and 10.9 Hz, respectively. At the same frequency, for both models, the cavity pressure is larger than values of the previous curves where the vent factor is smaller.
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Fig. 11. Spectrum of external pressure.
Fig. 12. Spectra of cavity pressure.
4.2. Random exterior pressure fluctuations Due to the limitation of the machine, tests for (near) sinusoidal pressure fluctuations could only be carried out at the low-frequency range (less than 1.2 Hz). Although the theoretical flexible b-p model was used to extend the predictions into the higherfrequency range, it is interesting to verify such predictions. To investigate the behaviour of the p-e system at high frequencies, tests using an aeroplane engine wind generator was carried out.
E.C.C. Choi, Z. Wang/J. Wind Eng. Ind. Aerodyn. 73 (1998) 251—266
265
Fig. 13. Spectra of cavity pressure.
The spectrum of the external pressure is shown in Fig. 11. It gives the frequencywise distribution of the pressure fluctuation. The spectra of the calculated cavity pressure using Eqs. (6) and (10) corresponding to the measured external pressure are given in Figs. 12 and 13, respectively. Spectrum of the measured cavity pressure fluctuation is also presented. The prediction using the flexible b-p model agrees fairly well with the measured data over the entire frequency range as shown in Fig. 12. However, Fig. 13 shows that the rigid b-p assumption over estimates the cavity pressure. It is obvious that the flexible b-p model represents the performance of the curtain wall better than the rigid b-p assumption.
5. Conclusions Results of full-scale measurements of pressure-equalization performance of curtain walls are reported in the present paper. The back-panels of these curtain walls are shown to be very flexible and the flexibility of the back-panel is observed to affect strongly the pressure-equalization performance of the curtain wall. A theoretical model taking into account the back-panel flexibility is established. The results show that the flexible b-p model (Eq. (6)) gives much more accurate predictions than Eq. (10) which was derived for brick-type rainscreen where the back-panels are rigid. Eq. (10) overestimates the fluctuation of cavity pressure for curtain walls, especially for the smaller vent factors (A /» ) and in the higher34 0 frequency range. Sensitivity studies using the two models indicated that the pressure-equalization performance of metal curtain walls can be very different from that of the rainscreen walls with rigid back-panels. The difference is not just the result of geometry differences (e.g. differences in cavity volume and weep hole size). Material property which directly affects the back-panel stiffness is an important factor governing pressureequalization performance.
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The effect of the flexibility of the back-panel is to slow down the increase of the cavity pressure. Thus, for the same size of vent area and cavity volume, the cavity pressure of curtain walls will be lower than that of rainscreen walls with rigid back-panels (at the same frequency of pressure fluctuation). Furthermore, since the stiffness of the back-panel is highly nonlinear, the mean value of the external pressure will also affect the amplitude of the cavity-pressure fluctuation. Results of the flexible b-p model indicate that the vent factor is a crucial factor governing the pressure-equalization performance of the curtain wall. As shown in Fig. 9, the cavity pressure dropped very fast with decreasing vent hole size when the vent factor is small. For gusts with a gust period of one or more seconds, a vent factor of 0.035 m~1 is needed for 100% pressure equalization. For the two curtain walls tested, the vent factor for CW 1 with WP3 weep hole configuration is 0.019 m~1. This gives 80% pressure equalization for the 1 s gust. The vent factor for CW II is 0.0022 m~1 which corresponds to about 20% pressure equalization for the 1 s gust. This means that the configuration of CW II will not be able to utilise the pressureequalization principle as a means for controlling water leakage. Result of the sensitivity study also shows that the flexibility of the back-panel shifts the position of the resonance of the cavity pressure to a lower frequency and also reduces the magnitude of the resonance peak as compared to those of a rigid back-panel rainscreen wall.
Acknowledgements The study reported in the present paper is part of a joint research programme of Nanyang Technological University and P.D. Manufacturing International Pte Ltd. The curtain wall specimen and the testing chamber were provided by P.D. Manufacturing.
References [1] P.A. Irwin, G.D. Schuyler, M.A. Wawzonek, A wind tunnel investigation of rainscreen wall systems, MH Report 483-01021, National Research Council, Canada, 1984. [2] J.M. Xie, G.D. Schuyler, H.R. Resar, Prediction of net pressure on pressure equalized cavities, J. Wind. Eng. Ind. Aerodyn. 41—44 (1992) 2449—2460. [3] D.R. Inculet, A.G. Davenport, Pressure-equalized rainscreens: a study in the frequency domain, J. Wind. Eng. Ind. Aerodyn. 53 (1994) 63—87. [4] D.R. Inculet, Pressure-equalization of rainscreen cladding, M.E.Sc. Thesis, Faculty of Engineering Science, The University of Western Ontario, April 1990. [5] E.C.C. Choi, Z.H. Wang, Full scale measurements of pressure-equalization in curtain wall systems, 5th National Workshop on Wind Engineering, Tanunda, Australia, February 1996. [6] J.D. Holmes, Mean and fluctuating internal pressures induced by wind, Proc. 5th Int. Conf. on Wind Engineering, Fort Collins, CO, July 1979.
Study on pressure-equalization of curtain wall systems Edmund C.C. Choi*, Zhihong Wang School of CSE, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore Received 16 May 1996; accepted 22 September 1997
Abstract In recent years, aluminium-curtain-wall systems are often used in southeast Asia. Many of these curtain-wall systems can be classified as a two-barrier system with a front-panel (the rainscreen) and the back-panel (the air barrier). The back-panels of such systems are usually thin and flexible. Compared with the brick or brick-veneer rainscreen walls, where the backpanels are very rigid, the pressure-equalization characteristics are expected to be quite different. To improve on the understanding of the behaviour of such systems and to evaluate design parameters, full-scale measurements were carried out. A numerical model which takes into account the flexibility of the back-panel has been developed for the prediction of cavity pressure in curtain walls. The results based on this model show good agreement with those obtained from full-scale experiments. ( 1998 Elsevier Science B.V. All rights reserved.
Nomenclature A a, b b-p k $ l % n , n@ 0 0 P ! P # P % p-e » » 0 X a, b a 1
venting area side length of rectangular back panel back panel discharge coefficient effective length of opening undamped resonant frequency atmospheric pressure cavity pressure external pressure pressure equalization cavity volume initial cavity volume movement of air constants in back panel stiffness function effective length coefficient
* Corresponding author. 0167-6105/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 7 - 6 1 0 5 ( 9 7 ) 0 0 2 9 0 - 0
252
*» d o,o # %
E.C.C. Choi, Z. Wang/J. Wind Eng. Ind. Aerodyn. 73 (1998) 251—266
volume change deflection at centre of back panel air density
1. Introduction Many curtain walls, built in southeast Asia make use of the pressure equalization or rainscreen method as a means to eliminate or reduce rain penetration. Essentially, the two-barrier system consists of two leaves of wall: a rainscreen as the outer leaf and the air barrier (back-panel) as the inner leaf. The two leaves are separated by a cavity that is vented to the outsides by openings on the rainscreen. With pressure equalization, i.e., the cavity having the same pressure as the external pressure, rain water will not be forced to penetrate the rainscreen. Normally, the cavity is compartmentalized to prevent air movement over zones with large pressure gradients. Since the introduction of the rainscreen wall system over 20 years ago, studies on the pressure-equalization performance of such wall systems have been carried out [1,2]. Many of the investigations are on brick-veneer or double-brick walls. For such systems the volume of the internal cavity is usually large and both the rainscreen and the air barrier are very rigid. It is also common that the air barrier is not 100% air tight but with leakage paths into the inside of the building. Some studies on pressure equalization of rigid wall systems are reported, see e.g. Refs. [3,4]. The back-panels of curtain walls are normally made of thin flexible steel sheets, the internal volume of the cavity will change under the action of cavity pressure. The construction of the back-panels is also usually quite air tight. This will have a strong influence on the pressure-equalization process and the performance of the curtain wall. Experimental and theoretical investigations on the behaviour of curtain wall with flexible backpanel are needed to obtain design parameters and to have a better understanding of its performance characteristics. The pressure inside the cavities of a curtain wall generated by wind action is influenced by the external pressure, fluctuation frequency, vent hole area, volume of cavity and back-panel stiffness. The wind force is a random process which can be represented by a large number of sinusoidal processes with different frequencies and amplitudes. The present study first looks at the response of curtain wall subjected to sinusoidal external pressure fluctuations and secondly the effect due to random pressure fluctuations is investigated.
2. Full-scale measurements 2.1. Description of specimen The experimental study involves the investigation of the performance of two curtain-wall systems constructed by P.D. Manufacturing International Pte Ltd. The
E.C.C. Choi, Z. Wang/J. Wind Eng. Ind. Aerodyn. 73 (1998) 251—266
Fig. 1. (a) Front elevation of (a) CW I (b) CW II.
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first test specimen (CW I) consists of two bays of width 1.2 m. Each bay is 3 m high and is divided into three vertical compartments as shown in Fig. 1a. The middle compartment with a height of 1.19 m is the larger one and is selected for pressure-equalization (p-e) investigation. The front-panels of the middle compartments are different for the two bays, one is 3 mm thick aluminium and the other is 8.76 mm laminated glass. The back-panels (b-p) are made of 1 mm thick galvanized steel sheets. The internal cavity volume is 0.0699 m3 and there are weep holes venting to the outside. Two sizes of weep hole area can be configured, 0.0003 or 0.0012 m2. The second test specimen (CW II) consists of three bays of width 1.414 m each. There are three vertical compartments in each bay with the top and bottom compartments having heights of 2.65 m (Fig. 1b) and these are selected for p-e study. The front-panels are 6 mm thick reflective glass and the back-panels are 1 mm thick galvanized steel sheeting. The volume of the internal cavity is 0.2476 m3 with a weep hole area of 0.0006 m2. A schematic diagram showing a section of CW II and the components of a twobarrier system (the front- and back-panels, internal cavity and vent hole) is given in Fig. 2.
2.2. Experimental set-up The specimens were mounted facing inwards, in a test chamber, such that the exterior face of the curtain wall was subjected to the sinusoidal pressure fluctuation generated in the chamber. The interior face of the curtain wall was exposed to atmospheric pressure. Pressure taping points were connected to various locations in the cavity as well as to the exterior face so as to monitor the internal cavity and external pressures. Testing of the two curtain walls was carried out using static pressure as well as dynamic (near) sinusoidal pressure fluctuations. The frequency, mean and amplitude of pressure fluctuation were varied in the experiment. Besides testing the specimens with (near) sinusoidal pressure fluctuations in the pressure chamber, the specimens were also tested using random wind generated by an aeroplane engine. The specimens were mounted facing outwards such that the external face is directed towards the engine exposing to the random wind generated by the engine. The wind speed, external pressure and internal cavity pressure were monitored during the experiment. Due to difficulties in the setting up of the engine, random wind test was only carried out on CW I. Results of the experimental study showing the time-wise and frequency-wise plots of the cavity and external pressures are given in Section 4. Further details of the experimental results are described in Ref. [5].
2.3. Flexibility of back-panel One of the major differences between an aluminium curtain wall p-e system and a brick-veneer p-e system is the flexibility of the back-panel. This can significantly
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Fig. 2. Schematic diagram of a two-barrier system.
change the response characteristic of the internal cavity pressure. Thus, it is important to obtain the load—deflection characteristics of the b-p of the curtain wall. Fig. 3 shows the stiffness function of the b-p of CW I obtained from static pressure test. It is noteworthy that the deflection (d) at the centre of the panel versus cavity pressure (P ) # curve is highly nonlinear which is quite typical for curtain-wall systems. There shows a highly flexible region near the zero pressure that is due to the popping action of a thin plate. The two branches (positive and negative cavity pressure) of the curve can be fitted well by the exponential functions d"aPb. The two parameters a and #
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Fig. 3. Stiffness function of back-panel.
b obtained in metric units (d in m, P in kPa) are as follows: # d"aPb, # a"0.0100, b"0.714 if P '0, (1) # a"0.0178, b"0.324 if P (0. # These flexibility equations are needed for the theoretical analysis of the p-e system. Air leakage of the back-panel was also investigated. Standard air-permeability test was carried out on the whole specimen. At a pressure of 75 Pa, the amount of air leaking through the curtain wall (including the mullions, transoms and joints) was measured to be 0.033 m3/h/m2. This shows that the leakage is very small and the back-panel can be considered to be airtight.
3. Theory In response to the exterior pressure changes, a “plug” of air moves in and out through an opening from an exterior location just outside the opening, “e”, to an interior location in the cavity just inside the opening, “c”. The differential equation governing the motion of this mass of air can be described in one-dimensional form as 1 P P l X$ # DXQ DXQ # #" %, (2) % 2k2 o o $ # % where X is the movement of the “plug” of air, l is the effective length of opening which % can be expressed as a JA (A is venting area through rainscreen), k "0.65 is the $ l discharge coefficient and o is the density of air. The effective length coefficient a can be l taken to be Jp/4 [6]. Eq. (2) is derived for incompressible flow. The absolute value of
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the velocity is needed to take care of the reversing flows. It is noted that the terms X, P and P are time dependent and in the subsequent derivations, the other terms », % # *», d are also time dependent. If it is assumed that there are no back-panel leakages, conservation of mass requires that the rate of mass influx through the opening must equal the rate of change of the mass of air inside i.e. d o + A XQ " (o »), (3) % k k dt # k where A is the kth venting area, and » is the cavity volume and is a constant when the k front- and back-panels are both rigid. When the b-p is flexible, the change in the cavity volume due to the deformation of the panel has to be considered. The cavity volume » can then be expressed as follows: »"» #*», (4) 0 where » is the initial volume and *» is the volume change. 0 Based on the isothermal process assumption (P/o"const.), Eq. (3) can be written as d o + A XQ " (o ») % k k dt # k d*» o dP d*» do " ! # (» #*»)#o , (5) " # (» #*»)#o 0 # dt 0 # dt P dt dt ! where P is the atmospheric pressure and equals to 1.013]105 Pa. ! To simplify the problem, all the venting areas are assumed to lump into one opening with a total venting area of A and with an external pressure P at the 34 % opening. The change in air density is also very small for the practical problem and the term can be neglected. Substituting Eq. (5) into Eq. (2), the following expression is obtained:
K
K
o l (» #*») (» #*») ol o !% 0 0 P$ # ! % *»Q PQ # ! PQ #*»Q # A P # 2k2A2 # A P P 34 ! $ 34 ! 34 ! (» #*») ol 0 ] PQ #*»Q #P # ! % *»$ "P , (6) # # A % P 34 ! where o is the atmospheric air density. ! The change in cavity volume can be calculated from the deformation of the b-p as follows:
A
*»"(4/p2)abd,
B
(7)
where a and b are the lengths of the sides of a rectangular b-p and d is the deflection at the centre of the panel. The factor 4/p2 is derived for the assumption of a rectangular parabolic deflected shape. From the experimental study described in the earlier section, d is expressed in terms of the pressure P as given in Eq. (1). #
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The first and second derivative of the increment or decrement of cavity volume with respect to time can be derived as follows: 4 4 *»Q " abdQ " ababPb~1PQ , # # n2 n2
(8)
4 4 *»$ " abd$ " abab[(b!1)Pb~2PQ 2#Pb~1P$ ]. # # # # n2 n2
(9)
Substituting Eq. (8) and (9) into Eq. (6), the time-varying cavity pressure P can be # solved using the Runge—Kutta method. For a rigid b-p, the cavity volume change is negligible. By setting the time derivatives of the volume to be zero in Eq. (6), the above equations are equivalent to those given in Ref. [3], which gives the following relationship between P and P : % #
K KA B
ol» » o ! % 0 P$ # ! 0 PQ A P # 2k2A2 P # 34 ! $ 34 !
» 0 PQ #P "P . # % P # !
(10)
The undamped resonant frequency for Eq. (10) is 1 u n " 0" 0 2p 2p
S
A P 34 ! . ol» !% 0
(11)
For the case where the b-p is flexible, the expression for the natural frequency is
S S
1 n@ " 0 2p "n 0
A P 34 ! ol» !% 0
S
1 1#*»/» #4ababP Pb~1/(p2» ) 0 0 ! #
1 . 1#(4aba/(p2» ))(Pb#bP Pb~1) 0 # ! #
(12)
4. Results and discussion In the following section, results of tests carried out with different amplitudes and frequencies of external pressure fluctuations are presented. Results of the sinusoidal pressure test and the random pressure test are given. Predictions using theoretical models with rigid and flexible back-panels are also presented and compared with the measured values. 4.1. Sinusoidal exterior pressure fluctuations Using the numerical model with parameter (b-p stiffness, panel geometry, etc.) measured from the curtain wall, the internal pressures corresponding to the applied external pressure can be predicted. Responses for both rigid and flexible b-p
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Fig. 4. Time history of cavity pressure.
assumptions are calculated and compared with the performance of the actual curtain wall. Time histories of the cavity pressure (P ) for different weep hole sizes, frequencies # and amplitudes of external pressure fluctuations were obtained. Before performing the actual experiment, it was decided that a calibration study must first be carried out. This is because a detailed examination of the curtain wall reviewed that there were many unintentional openings (e.g. slot holes for screws not properly sealed up) on the rain screen other than the weep holes. The calibration was carried out with all the weep holes blocked up and the specimen subjected to the sinusoidal external pressure. The dynamic component of the cavity pressure, P , is # shown in Fig. 4. It is observed that P is not stationary but fluctuates with P . Using # % Eq. (6) and adjusting the area A , a good match between the predicted and measured 34 values can be obtained. This gives an estimation of the area of these unintentional openings (initial venting area) WP1. WP1 is estimated to be about one-ninth of the actual weep hole area. The predicted values are also shown in the same figure. With the same value of A , predictions using the rigid b-p assumption (Eq. (10)) are also 34 shown in Fig. 4. The rigid b-p assumption very much over estimates the cavity pressure. Experiments were then carried out with weep hole areas of 0.0003 m2 (WP2) and 0.0012 m2 (WP3). The measured and predicted values of the cavity pressure are shown in Figs. 5 and 6, respectively. In calculating the theoretical values, A is set equal to 34 the sum of WP1 and the actual weep hole area. It can be seen that the flexible b-p assumption produces much better predictions than the rigid b-p assumption. Further tests were carried out at different frequencies, different mean pressures and different amplitudes of pressure fluctuations. Results of these tests are similar to those in Figs. 5 and 6 where the flexible b-p model consistently gives better predictions as shown in Table 1. For CW II, no unintentional openings were found and A was taken to be 34 the actual weep hole area.
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Fig. 5. Time history of cavity pressure.
Fig. 6. Time history of cavity pressure.
The flexible b-p model, Eq. (6), is shown to predict the cavity pressure very well for different conditions. The results using the rigid b-p assumption, however, differ greatly from the measured values for the smaller venting areas. Thus, Eq. (10) does not seem to reflect the performance of curtain wall with thin metal b-p. Using the numerical model, several parametric runs were carried out to study the sensitivity of the pressure ratio (P /P ) to weep hole size, fluctuation frequency and b-p # % stiffness. Fig. 7 shows the effect of frequency of external pressure fluctuation on the pressure ratio. Predictions calculated using the flexible b-p and the rigid b-p models are presented. For the flexible b-p, there shows a trend of decreasing P with increase in # frequency of pressure fluctuation. The higher the frequency, the lower is the internal pressure. For frequencies of five or more cycle per second, the internal pressure is less
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E.C.C. Choi, Z. Wang/J. Wind Eng. Ind. Aerodyn. 73 (1998) 251—266 Table 1 Pressure amplitude ratios (P /P ) # % Freq (Hz)
P (Pa) %
CW I
CW II
WP1
0.30 0.45 0.81 0.33 0.46 0.64 1.07 0.49 0.64 0.82 0.124 0.132 0.133 0.136 0.156 0.164 0.195 0.20 0.23 0.25
400 400 250 400 400 300 250 200 330 250 350 200 300 500 350 350 300 250 250 200
WP2
M
F
R
0.37 0.28 0.22
0.45 0.30 0.21
1.0 0.95 0.96
WP3
M
F
R
0.98 0.93 0.85 0.67
0.98 0.92 0.84 0.63
1.0 0.95 0.99 0.97
M
F
R
1.0 0.96 0.88
1.0 0.97 0.92
1.0 1.0 1.0
M
F
R
0.72 0.75 0.71 0.71 0.74 0.67 0.66 0.61 0.56 0.57
0.74 0.81 0.80 0.73 0.76 0.69 0.70 0.69 0.54 0.61
0.93 0.98 0.99 0.95 0.92 0.98 0.98 0.99 0.99 0.95
Note: M — measured; F — Flexible back panel model; R — Rigid back panel model.
Fig. 7. Pressure ratio versus fluctuation frequency (A /» "0.0193 m~1). 34 0
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Fig. 8. Pressure ratio versus external pressure.
Fig. 9. Pressure ratio versus vent factor.
than 30% of the external pressure. This is not so for the rigid b-p; there seems to be very little change in the internal pressure with increasing frequency. The cavity pressure is also dependent on the stiffness of the back-panel which is a function of pressure. The dependence of the pressure ratio on the external pressure is demonstrated in Fig. 8, in which the mean external pressure PM is varied but % with the amplitude of external pressure fluctuation fixed at 300 Pa. As shown in the chart, a higher mean pressure induces a higher stiffness resulting in a higher P value. # In the previous section, the pressure amplitude ratio P /P is shown to be dependent # % to a great extent on the venting area. A closer examination of Eq. (6) shows that the
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263
Fig. 10. Pressure ratio versus fluctuation frequency.
controlling factor should be the venting area to cavity volume ratio A /» , which is 34 0 termed the vent factor. This factor is an important parameter for the design of curtain wall. Fig. 9 shows the effect of the vent factor on the pressure ratio for different frequency of external pressure. For small values of the vent factor, the internal pressure of the curtain wall with a flexible b-p is significantly lower than the corresponding value for the rigid b-p. To achieve good pressure equalization (i.e. to have P /P close to unity) a large vent factor of more than 0.035 m~1 is required for # % frequency of 1 Hz or less. The value is also dependent on other factors such as value of the mean pressure. Fluctuating exterior pressures cause fluctuating flows through the venting holes of a rainscreen. As air flows through these holes, the drag on the air suppresses the fluctuations and causes damping. The damping of flow through venting area increases with the decreasing of weep hole size. Variation of P /P ratio with fluctuation # % frequency for a vent factor of 0.0193 m~1 has been described in Fig. 7. In Fig. 10, the curves are extended to higher frequencies. It can be seen that the damping for the system is very large (especially for the flexible b-p) and the curves decrease very fast with increasing frequency. To investigate the effect on systems with smaller damping (i.e. a larger value of the vent-factor), similar curves for a vent factor of 0.193 m~1 are also plotted in the same figure. These curves show the resonance response of the cavity pressure with a peak at the natural frequency. This peak is specially prominent for the rigid b-p model. Whereas for the flexible b-p model, the peak is much smaller and it occurs at a much lower frequency. The theoretical values of the natural frequency calculated using Eqs. (11) and (12) for the rigid b-p and flexible b-p are 57.8 and 10.9 Hz, respectively. At the same frequency, for both models, the cavity pressure is larger than values of the previous curves where the vent factor is smaller.
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Fig. 11. Spectrum of external pressure.
Fig. 12. Spectra of cavity pressure.
4.2. Random exterior pressure fluctuations Due to the limitation of the machine, tests for (near) sinusoidal pressure fluctuations could only be carried out at the low-frequency range (less than 1.2 Hz). Although the theoretical flexible b-p model was used to extend the predictions into the higherfrequency range, it is interesting to verify such predictions. To investigate the behaviour of the p-e system at high frequencies, tests using an aeroplane engine wind generator was carried out.
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265
Fig. 13. Spectra of cavity pressure.
The spectrum of the external pressure is shown in Fig. 11. It gives the frequencywise distribution of the pressure fluctuation. The spectra of the calculated cavity pressure using Eqs. (6) and (10) corresponding to the measured external pressure are given in Figs. 12 and 13, respectively. Spectrum of the measured cavity pressure fluctuation is also presented. The prediction using the flexible b-p model agrees fairly well with the measured data over the entire frequency range as shown in Fig. 12. However, Fig. 13 shows that the rigid b-p assumption over estimates the cavity pressure. It is obvious that the flexible b-p model represents the performance of the curtain wall better than the rigid b-p assumption.
5. Conclusions Results of full-scale measurements of pressure-equalization performance of curtain walls are reported in the present paper. The back-panels of these curtain walls are shown to be very flexible and the flexibility of the back-panel is observed to affect strongly the pressure-equalization performance of the curtain wall. A theoretical model taking into account the back-panel flexibility is established. The results show that the flexible b-p model (Eq. (6)) gives much more accurate predictions than Eq. (10) which was derived for brick-type rainscreen where the back-panels are rigid. Eq. (10) overestimates the fluctuation of cavity pressure for curtain walls, especially for the smaller vent factors (A /» ) and in the higher34 0 frequency range. Sensitivity studies using the two models indicated that the pressure-equalization performance of metal curtain walls can be very different from that of the rainscreen walls with rigid back-panels. The difference is not just the result of geometry differences (e.g. differences in cavity volume and weep hole size). Material property which directly affects the back-panel stiffness is an important factor governing pressureequalization performance.
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The effect of the flexibility of the back-panel is to slow down the increase of the cavity pressure. Thus, for the same size of vent area and cavity volume, the cavity pressure of curtain walls will be lower than that of rainscreen walls with rigid back-panels (at the same frequency of pressure fluctuation). Furthermore, since the stiffness of the back-panel is highly nonlinear, the mean value of the external pressure will also affect the amplitude of the cavity-pressure fluctuation. Results of the flexible b-p model indicate that the vent factor is a crucial factor governing the pressure-equalization performance of the curtain wall. As shown in Fig. 9, the cavity pressure dropped very fast with decreasing vent hole size when the vent factor is small. For gusts with a gust period of one or more seconds, a vent factor of 0.035 m~1 is needed for 100% pressure equalization. For the two curtain walls tested, the vent factor for CW 1 with WP3 weep hole configuration is 0.019 m~1. This gives 80% pressure equalization for the 1 s gust. The vent factor for CW II is 0.0022 m~1 which corresponds to about 20% pressure equalization for the 1 s gust. This means that the configuration of CW II will not be able to utilise the pressureequalization principle as a means for controlling water leakage. Result of the sensitivity study also shows that the flexibility of the back-panel shifts the position of the resonance of the cavity pressure to a lower frequency and also reduces the magnitude of the resonance peak as compared to those of a rigid back-panel rainscreen wall.
Acknowledgements The study reported in the present paper is part of a joint research programme of Nanyang Technological University and P.D. Manufacturing International Pte Ltd. The curtain wall specimen and the testing chamber were provided by P.D. Manufacturing.
References [1] P.A. Irwin, G.D. Schuyler, M.A. Wawzonek, A wind tunnel investigation of rainscreen wall systems, MH Report 483-01021, National Research Council, Canada, 1984. [2] J.M. Xie, G.D. Schuyler, H.R. Resar, Prediction of net pressure on pressure equalized cavities, J. Wind. Eng. Ind. Aerodyn. 41—44 (1992) 2449—2460. [3] D.R. Inculet, A.G. Davenport, Pressure-equalized rainscreens: a study in the frequency domain, J. Wind. Eng. Ind. Aerodyn. 53 (1994) 63—87. [4] D.R. Inculet, Pressure-equalization of rainscreen cladding, M.E.Sc. Thesis, Faculty of Engineering Science, The University of Western Ontario, April 1990. [5] E.C.C. Choi, Z.H. Wang, Full scale measurements of pressure-equalization in curtain wall systems, 5th National Workshop on Wind Engineering, Tanunda, Australia, February 1996. [6] J.D. Holmes, Mean and fluctuating internal pressures induced by wind, Proc. 5th Int. Conf. on Wind Engineering, Fort Collins, CO, July 1979.