The UWO contribution to the NIST aerodynamic database for wind loads on low buildings: Part 3. Internal pressures

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Journal of Wind Engineering and Industrial Aerodynamics 95 (2007) 755–779 www.elsevier.com/locate/jweia

The UWO contribution to the NIST aerodynamic database for wind loads on low buildings: Part 3. Internal pressures Jeong Hee Oh, Gregory A. Kopp, Diana R. Inculet Alan G. Davenport Wind Engineering Group, Boundary Layer Wind Tunnel Laboratory, University of Western Ontario, London, Ont., Canada N6A 5B9 Received 18 March 2005; received in revised form 2 January 2007; accepted 25 January 2007 Available online 23 March 2007

Abstract Wind tunnel tests of generic low buildings have been conducted at the University of Western Ontario for contribution to the National Institute on Standards and Technology (NIST) aerodynamic database. Part 1 provided the archiving format and basic aerodynamic data. In Part 2, the data of external pressures were compared with existing wind load provisions for low buildings. This paper, Part 3, deals with an investigation of wind-induced internal pressures of low-rise buildings with realistic dominant opening and leakage scenarios. Data from one building model with four different opening sizes were compared with numerical simulations. The existing theory, using the unsteady orifice discharge equation, works well for the building models used in this study, given the external pressures near the openings, irrespective of shifts of wind direction and upstream terrain. Numerical simulations can capture the temporal variations of the internal pressure fluctuations, as well as mean values. The internal pressure fluctuations for the building with leakage (nominally sealed building) are attenuated as they pass through the openings, while mean values are consistent with spatially averaged external pressures. Internal pressure resonance occurs for the dominant opening (3.3% open ratio) with building leakage. Effects of oblique wind angles on internal pressure dynamics are not significant, at least for the openings in the centre of wall, as is the case herein. Peak internal pressures occur for a wind direction normal to the wall with a dominant opening. Measured internal

Corresponding author. Tel.: +1 519 661 3338; fax: +1 519 661 3339.

E-mail address: [email protected] (G.A. Kopp). 0167-6105/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jweia.2007.01.007

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pressure coefficients are compared with current wind load provisions. Some peak values were found to exceed the recommended design values for the dominant windward wall opening cases. r 2007 Elsevier Ltd. All rights reserved. Keywords: Internal pressure; Wind loads; Helmholtz resonance; Building codes

1. Introduction Internal pressures arise in buildings through leakage or openings in response to windinduced external pressures. They play a significant role in the design of structures and cladding, air infiltration systems (Davenport and Surry, 1984), as well as in controlling the migration of water through the building envelope (Inculet, 1990). Experimental research has indicated that internal pressures depend on several factors (Holmes, 1979; Vickery, 1986; Liu and Saathoff, 1982; Womble et al., 1995) including: the external pressure distributions near the openings, the geometry of the openings, vents, or leakage, the fluid properties (density, viscosity), the internal volume, the wind direction, the turbulence in the upstream boundary layer, the flexibility of the building ‘‘skin’’ and structure (Vickery and Bloxham, 1992; Vickery, 1994; Vickery and Georgiou, 1991; Sharma and Richards, 1997), and the compartmentalization within the building (Saathoff and Liu, 1983; Sharma, 2003). There has been significant work done regarding internal pressures (Holmes, 1979; Vickery, 1986, 1994; Liu and Saathoff, 1982; Womble et al., 1995; Vickery and Bloxham, 1992; Vickery and Georgiou, 1991; Sharma and Richards, 1997; Saathoff and Liu, 1983; Sharma, 2003; Irminger and Nokkentved, 1930; Liu, 1975; Shaw, 1981; Bloxham and Vickery, 1989; Pearce and Sykes, 1999; Ho et al., 2004; Liu and Rhee, 1986; Vickery and Karakatsanis, 1987; Stathopoulos et al., 1979; Ginger, 2000; Yeatts and Mehta, 1993; Sharma and Richards, 2003), the experimental studies being summarized in Table 1 and discussed further below. Irminger and Nokkentved (1930) in Denmark measured the internal pressure on small building models with various geometries of building shapes and openings in 1930. They introduced the flow rate equation to account for the air passing into and out of the openings. Liu (1975) investigated the validity of the equations to predict the mean internal pressure and found agreement between the measured and predicted internal pressures. As a result of pressurization tests of air-tightness of supermarkets and shopping malls, Shaw (1981) established a more general model of flow rate to express air leakage data. Holmes (1979) reported that a building with a single dominant opening behaves like a Helmholtz resonator and internal pressure fluctuations are due to compressibility effects of the fluid (i.e., air). This phenomenon can be modelled with an equation of motion for a ‘‘slug’’ of air moving in and out of the opening. Holmes introduced the method of internal volume scaling to maintain similarity in model scale experiments. This scaling parameter for the internal pressure dynamics has been applied in the experimental studies by Bloxham and Vickery (1989), Womble et al. (1995), Pearce and Sykes (1999), and Ho et al. (2004). Bloxham and Vickery (1989) reported from their investigation of background porosity effects that this effect is of little significance if the open (leakage) area is less than 10% of the dominant opening area. The nature of wind-induced Helmholtz oscillation of internal pressures was also studied by Liu and Rhee (1986). Adopting Holmes’ Helmholtz resonator equation, and comparing with their experimental results, they reported a

Table 1 Summary of previous experimental research on internal pressure Year

Building geometry

Scale

Opening ratio (%)

Terrain

Wind angle

Vol. scaling

Code comparison

Theoretical development

Irminger and Nokkentved (1930) Liu (1975)

1930

40  70  (50) mm3

N/A

0.03, 0.4, 2.8, 5.4

N/A

Normal

No

None

Flow rate

1975

152  152  (304) mm3

N/A

0.02–1.4

N/A

Normal

No

None

Continuity equation Helmholtz oscillation volume scaling

3

1979

Domestic structure

1/50

0.35, 1.8, 5.4, 10.8, 21.6

Open

Normal

No

None

Stathopoulos et al. (1979)

1979

244  381  (38) mm3

1/250

2.5, 5, 10, 20, 50 0.5, 3.0 (leakage)

Open/suburban

0–901

No

ANSI A58.1 NBCC

Shaw (1981) Liu and Rhee (1986) Vickery and Karakatsanis (1987) Bloxham and Vickery (1989) Yeatts and Mehta (1993) Womble et al. (1995) Woods and Blackmore (1995) Pearce and Sykes (1999) Sharma (2003) Sharma and Richards (2003)

1981 1986

97  152  (38) mm3 Commercial structure 140  140  (290) mm3

Full N/A

N/A 0.25, 1.0, 2.2, 4

N/A Iu ¼ 0.01, 0.1

N/A Normal

No No

None None

1987

Domestic structure

1/100

5, 12, 21, 46, 47, 71a

Smooth

0–3601

No

None

1989

300  150  (90) mm3

N/A

Yes

None

9.1  13.7  (4.0) m3

Full

Smooth/ suburban Open

Normal

1993

0.25, 0.5, 1.0, 1.6, 1.8 1, 2, 5

0–3601

Full

ASCE 7-88

N/A

1, 4, 9, 16, 25

Urban

0–1801

No

None

1/50

0–100

Open

0–3601

Yes

None

N/A

2.5

Open

0–1801

Yes

None

2003 2003

182  274  (80) mm 182  274  (80) mm3

1/50 1/50

5.4 2.7, 5.3, 5.4

Open Open

0–3601 0–3601

No No

None AS/ NZS1170.2:2002

Ho et al. (2004)

2003

381  244  (122) mm3

1/100

0.1(leakage), 0.3, 3.3

Open/suburban

0–1801

Yes

None

1995

100  100  (100) mm

1995

182  274  (80) mm

3

1999

F300  (75) mm2

3

3

Envelope flexibility Eddy dynamics for oblique winds

757

(): Eaves height, F: diameter of cylinder, and N/A: not applicable. a Porosity ratio.

Flow rate Helmholtz oscillation Flow rate, discharge equation Transient behavior

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Holmes (1979)

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relatively larger discharge coefficient (k ¼ 0.88, Holmes suggested 0.6), which is a significant factor in determining the internal pressures. Vickery and Karakatsanis (1987) also established discharge coefficients from their wind tunnel and pressurization tests, obtaining discharge coefficients as a function of Reynolds numbers. After Vickery (1986) considered the effect of the flexibility of the building ‘‘skin’’ on internal pressure fluctuations, Pearce and Sykes (1999) examined the internal pressure dynamics for a flexible building with a single dominant opening in a wind tunnel experiment. They reported that both the Helmholtz frequency and the magnitude of the resonant peak decrease when the roof flexibility increases. Ginger (2000) has also applied a modified internal volume and verified Vickery’s theory with his experimental results. Previous research has tended to focus on investigating the behaviour of the fluctuating internal pressure for a building with a single dominant opening, or on estimating mean internal pressures for a nominally sealed, but leaky, building. There have been few studies for buildings with both dominant openings and leakage. Although the category of the building with a single dominant opening is usually critical for design, the correct assessment of internal pressure behaviour for buildings with realistic openings, and leakage, is essential. Experiments performed with such realistic openings and leakage are examined herein. In addition, the theoretical equations for internal pressures based on the Helmholtz resonator model or the Bernoulli equation, have not often been solved to obtain time series of internal pressures. With the advent of the database assisted design, estimation of internal pressure time series based on the external pressure distributions is important, given the significant role internal pressures can play in the overall loading. This paper is Part 3 in a series of papers documenting the University of Western Ontario’s (UWO) contribution to the aerodynamic database for low-rise buildings sponsored by the United States’ National Institute on Standards and Technology (NIST). Part 1 (Ho et al., 2004) provides a detailed description of the experiments, while Part 2 (St. Pierre et al., 2005) provides a detailed comparison of the external pressure data with the wind load provisions in several building codes. It is important to note that internal pressures were not measured in all cases because of the challenges involved with those measurements. Thus, users of the database would either have to neglect internal pressures or make some assumption about them. The present paper seeks to address this point. Thus, there are two main objectives in the current paper: (i) to determine how accurately mean and fluctuating internal pressure time histories can be predicted based on the external pressures measured on the wind tunnel models when there is both a dominant opening and leakage present, and (ii) to examine a greater range of leakage area to dominant opening area ratios than has been previously studied.

2. Experimental details Aerodynamic data from six low-rise building models were obtained at UWO since 2000 in support of an initiative by Texas Tech University and NIST, as reported in Part 1. The model design and wind tunnel experiments were conducted by Dr. T.C.E. Ho. The current study examines only the data from models, which contain openings in the wall to generate internal pressures. Only the relevant information to make the paper complete is presented here; many other details pertaining to the experimental work are given in Ho et al. (2004) and St. Pierre et al. (2005).

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The model building used in this research, shown in Fig. 1, has equivalent full-scale dimensions of 38.1 m  24.4 m with a roof slope of 1:12 and a maximum eaves height of 12.2 m. The model, constructed of acrylic at a scale of 1:100, could be slid through the tunnel floor to change the eaves height. Fig. 1(b) shows an exploded view of the model building and the locations of the 665 external pressure taps. Internal pressures were measured at two locations within the model. The openings in the model were of two types. Uniform background leakage was provided by 80 small holes of 1.6 mm diameter (model scale). These were distributed on the long (25 on each) and short (15 on each) walls of the model. Two cases of dominant openings were constructed to capture the behaviour of internal pressures which depends on the opening size for a given building: a ‘‘large’’ opening for which the external pressure fluctuations will be transmitted to the internal pressures, a ‘‘small’’ opening for which some of the external pressure fluctuations will be attenuated and affected by the presence of background leakage. A rectangular opening (81.3 mm  19.1 mm in model scale), representing 3.3% of its single wall area is used for the larger opening. Two other circular openings (diameters of 14.3 and 8.97 mm) are used for the smaller openings. It should be emphasized that only one dominant opening was open at a time, while the openings for the background leakage were always open. The two circular openings were used with different eave heights so that each represents 0.3% of its single wall area. The total area of the background leakage was 7.1% of the area of the larger opening but was 70% of the open area for the smaller opening. Table 2 lists the details of the openings. The internal volume was scaled in the experiments in order to maintain the similarity of the dynamic response of the volume at model scale to that in full scale. It is critical for obtaining the correct natural frequency for Helmholtz resonators. This scaling requires that V o;m ¼ V o;f

ðLm =Lf Þ3 , ðU H;m =U H;f Þ2

(1)

where L is a characteristic length, Vo is the volume, UH is the mean roof height wind speed, and the subscripts m and f are for model and full scale, respectively. A velocity scale (UH,m/UH,f) of 1:4 was used in this study. In order to achieve this, a sealed volume chamber was installed, fit to the bottom of the model so that the internal volume was increased. Applying (1) to the current model, a total internal volume of 0.18 m3 is required for the 12.2 m high building (and 0.081 m3 for the 4.8 m high building). Fig. 2 illustrates the chamber attached to the building model underneath the wind tunnel floor. Measurements were made for two upstream terrain conditions: an open country and a suburban exposure. Roughness lengths of 0.03 and 0.3 m have been used for the definition of open and suburban terrains, respectively. The pressure signals from all taps were sampled at 500 Hz for 100 s, essentially simultaneously. The data were digitally low-pass filtered at 200 Hz. Measurements were obtained for 37 wind angles ranging from 1801 to 3601 in 51 increments. The wind direction of 2701 is normal to the dominant openings in the windward wall and is the main focus of the work presented herein. All measured pressures were referenced to the dynamic pressures (1/2rU2ref) at an upper reference height in the wind tunnel. These were then converted to a roof height reference by multiplying them with conversion factors found in Part 1 (Ho et al., 2004). A nominal wind tunnel

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a

b

38.13m

24.40m

Wind direction

0.90m ∅

8.14m

4.88m 5.49m 9.76m 12.20m

Side Wall

Building Heights

1.43m ∅

1.91m

Fig. 1. (a) Photograph of the building model and (b) an exploded view of the pressure tap layout and dominant openings (from Ho et al. (2004)).

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Table 2 Geometry and ratio of dominant openings and leakage Description of opening

Dominant opening

‘‘Large’’ opening ‘‘Small’ opening

Distributed leakage (80 holes)

Rectangle (door) Large circle (window) Small circle (window)

Dimension (mm) (model scale)

Opening ratioa(%)

Porosity ratiob(%)

Eaves height (m)

81.3  19.1 d ¼ 14.3

3.3 0.3

7.1 68.9

12.2 12.2

d ¼ 8.97

0.3

70.0

4.88c

d ¼ 1.6

0.1

N/A

12.2

a Ratio of the opening area to the single wall area (for leakage case, ratio of the whole leakage area to the entire wall area). b Ratio of the background leakage area to the dominant opening area. c Height was adjusted for the small circular opening case by sliding the model through the wind tunnel floor.

Fig. 2. Photograph of the sealed internal volume chamber underneath the wind tunnel floor, attached to the building model. (Photograph courtesy of Dr. T.C.E. Ho).

speed of 13.7 m/s at upper reference height was used. All data were stored on CD-ROMs for processing and public distribution. The readers are referred to Ho et al. (2004) for details.

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3. Theory 3.1. Continuity equation The equation of mass conservation (the continuity equation (CE)) is given by X dr Qj r ¼ V o dt

(2)

for flow through multiple openings P into or out of a common internal volume, where Qj is the flow rate through opening j, Qj is the sum of volume flow rates into the building, Vo is the internal volume, and r is the fluid density (Holmes, 1979; White, 2003). For either steady or incompressible flow, this leads to X

Qj ¼ 0.

(3)

3.2. Single discharge equation For unsteady fluid flow along a streamline, the Bernoulli equation is Z 2 Z 2 qU 1 ds þ r dp þ rðU 22  U 21 Þ þ rgðz2  z1 Þ ¼ 0, qt 2 1 1

(4)

where U is the flow velocity, p is the pressure in moving fluid, g is the gravitational acceleration, and z is the altitude. This form of the Bernoulli equation requires several assumptions: (1) incompressible flow, (2) no shaft work, (3) isothermal flow, and (4) frictionless flow. Assumptions 1, 2 and 3 are acceptable for flow through an orifice (White, 2003), but assumption 4 is quite limiting, especially for flow in ducts. This is usually handled by adding loss terms to (4) for frictional, entrance, exit, expansion, contraction and other types of losses. Since these losses are normally proportional to the velocity squared (except for friction), adding the loss coefficient CL in the third (kinetic energy) term of (4) and neglecting the fourth term (i.e. Dz ¼ 0), the Bernoulli equation becomes rl e

dU rU 2 þ CL ¼ pe  pi , dt 2

(5)

where le is the effective length of an ‘‘air slug’’, and pe and pi are the external and internal pressure, respectively (Saathoff and Liu, 1983). This is the discharge equation for the unsteady flow through an orifice. Then assuming that the flow acts like a Helmholtz resonator, from the well-established theory in acoustics, one can assume that the ‘‘slug’’ of air, of length le, moves in and out of the opening (Holmes, 1979). If x is the distance the slug of air moves, then (5) becomes r _ xj _ ¼ pe  p i , (6) rl e x€ þ C L xj 2 where x_ is the velocity in the opening (i.e., x_ ¼ U ¼ dx=dt) and x€ is the second time derivative of x (Vickery, 1986). The first term represents an inertial effect of the air slug (rle) and the second term characterizes a damping effect related to energy losses when flow passes through the opening.

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For steady and incompressible flow (dU/dt ¼ 0), rearranging (5) leads to the flow rate Q through an opening: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2jpj  pi j Qj ¼ ka , r

(7)

where k ¼ (I/CL)1/2 is the discharge coefficient. This can be made more general as  1=2 2 Qj ¼ ka jpj  pi jn , r

(8)

where n is the flow exponent ranging from 0.5 to 1.0. These equations require further comment. For steady flow through an orifice plate, the effect of Reynolds number is handled by varying k (e.g., Potter and Wiggert, 2002) and a value of n ¼ 1/2 is used whether the flow is laminar or turbulent. However, as an opening becomes smaller, the role of the wall thickness increases so that for very small openings, the physical behaviour is more like a pipe flow than an orifice flow. Thus, in the limit of long openings, it is essential to consider the effect of solid wall shear stresses. The pressure drop due to the friction can be expressed by Dp ¼ 4tw

lo l o rU 2 ¼f , d d 2

(9)

which is well known as the pipe-friction equation where d is the opening diameter, lo is the opening length, and tw is the wall shear stress. The dimensionless parameter f is the Darcy friction factor, and for laminar flow equals 64/Re (note that Re is Reynolds number, Ud/n). For fully developed turbulent flow, f also depends on the relative roughness of the surface but is often assumed to be a constant for a given pipe. Thus for turbulent flow, n ¼ 0.5 for both friction and orifice effects, while for laminar flow, there are differences, since (9) can be re-arranged to show that n ¼ 1 for laminar friction losses. Note that ASHRAE (2001) recommends an intermediate value of n ¼ 0.65 for leakage in full-scale structures. Since our model scale experiments have well-defined ‘‘leakage’’ openings of small diameter pipes with lo/d ratios of order 10, we have decided to include both the orifice-type and frictiontype of loss coefficients in the equations as they may both be important. In full-scale, where the geometries of leakage openings are ill-defined, the approach of ASHRAE makes more sense. Thus, for the current experiments, (6) has been modified to be  1=n   1 r 1=2n 32ml o _ xj _ ð1=nÞ1 þ 2 x_ ¼ pe  pi , r‘e x€ þ xj k 2 d

(10)

so that both friction and the remaining (minor) losses are accounted for explicitly. The variables pe, pi and x are functions of time, g is the ratio of specific heats (of air), pffiffiffiffiffiffi ffi po is the static pressure, a is the opening area, k is the discharge coefficient ð¼ 1= C L Þ, and m is the dynamic viscosity of air. Further details on k and n are discussed in Section 5.2. Note that for the current study, the flow through the leakage holes is laminar (but unsteady) with the Reynolds numbers being less than 400 (calculated from the experimental data).

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3.3. Multiple discharge equations For unsteady flow through multiple openings or leaks in the building envelope, Vickery (1986) suggested using (6) simultaneously for each opening. Since there are multiple openings and, therefore, slugs of air, a separate equation in x is used for each opening: 9  1=n   r 1=2n 32ml o ð1=nÞ1 > _ _ _ j j r‘e1 x€ 1 þ k11 > þ ¼ p  p x x x 1 1 1 2 1 i > 2 d > > >  1=n   > = 1=2n r 32ml o ð1=nÞ1 1 _ _ _ j j r‘e2 x€ 2 þ k2 þ ¼ p  p x x x 2 2 2 2 2 i 2 , (11) d > > ... > >  1=n   > > r 1=2n ; r‘em x€ m þ 1 x_ m jx_ m jð1=nÞ1 þ 32ml2 o x_ m ¼ pm  pi > km

2

d

where m is the number of openings of the building envelope, and pm is the external pressure at opening m. In the simultaneous equations, there are m+1 unknowns (pi, x1, x2yxm) while the number of discharge equations is m. Hence, an additional equation (the CE) is required to solve them: rða1 x1 þ a2 x2 þ . . . þ am xm Þ ¼

rV o p, gPo i

(12)

where Q ¼ ax_ and the pressure–density relationship is assumed to be governed by an isentropic process.

4. Experimental results Fig. 3 depicts the basic statistics (mean, root-mean-square (rms), maxima and minima) of the measured internal pressures versus wind direction for the open exposure. For the dominant openings with background leakage presented in Fig. 3(a), the maxima vary most significantly with wind angle, being largest for a normal wind (2701) and smallest when the opening is on a side wall (relative to the wind direction). The minima show the same trend, having negative values for wind parallel to the opening (3601). The mean values also decline with wind angle from 2701 to 3601, becoming negative for wind angles between 3451 and 3601. The standard deviation or rms of the fluctuations1 also decreases, as is clearly evident from the spectra presented in Fig. 4. In contrast to the cases with dominant openings plus leakage, the case with only leakage, shown in Fig. 3(b), exhibits no significant variation with wind direction and the magnitudes are small. The maximum coefficient for any wind direction is 0.1 (compared to 2.2 for the dominant opening). In addition, the mean value is negative, consistent with mean suctions occurring on the side and leeward walls and positive pressures only on the windward face. (From the practical or design perspective, it is the maximum values which are important since they add with the peak roof suctions to significantly increase the overall uplift experienced by the roof systems if and when the peak internal and external pressures are correlated (Holmes, 1979).) 1

We will use the abbreviation rms to denote the standard deviation or root-mean-square of the fluctuations throughout.

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2.5 mean rms maxima minima

2

Cpi

1.5 1 0.5 0 -0.5 -1 270

280

290

300

310

320

330

340

350

360

Wind Direction

2.5 mean rms maxima minima

2 1.5

Cpi

1 0.5 0 -0.5 -1 270

280

290

300

310 320 Wind Direction

330

340

350

360

90 θ 180

360 270

Fig. 3. Basic statistics of the measured internal pressures for (a) the ‘‘large’’ opening (3.3%) plus background leakage and (b) only background leakage (opening ratio of 0.1%), in the open exposure.

Fig. 4 shows the spectra of the internal pressure fluctuations corresponding to the statistics in Fig. 3 for the large opening (3.3%). Several observations can be made. First, there is a resonant peak around 23 Hz for most wind angles, but it is strongest for the normal wind direction (2701). There are only slight changes in the resonant frequency with wind angle. Second, differences in the rms values tend to correspond to frequencies below the resonant frequency. The largest maxima and rms values observed for the normal wind

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Power Spectral Density (s (f))

10-1

270 : normal wind direction 285

270 285 300 315 330 345 360

10-2 10-3 10-4

300 315 330 360 345

10-5 10-6 100

101

102 f (Hz) 90 θ 180

360 270

Fig. 4. Spectra of the internal pressure fluctuations for the ‘‘large’’ opening (3.3%) plus background leakage in the open exposure (UH ¼ 9.0 m/s).

direction are due to both of these factors, that is, the strongest resonance and greatest energy at low frequencies. Third, the change in the slope of the spectra at 50 Hz is due to electronic noise (from the pressure scanners) as the signal strength is extremely weak by this point, being four orders of magnitude lower (note that this is not due to tubing response, since this is flat to about 100 Hz, Ho et al. (2004)). Statistics and spectra for the suburban exposure show a similar trend as for the open exposure. Further plots can be found in Oh (2004).

5. Numerical simulations 5.1. Numerical method Eqs. (11) and (12) represent the set of simultaneous equations to compute the internal pressures, given the external pressures at the openings together with some empirically determined coefficients. Thus, the problem to be solved is the solution of 81 (80 leakage holes and one dominant opening) simultaneous, non-linear ordinary differential equations. To solve these differential equations, a backward differencing, iterative method was adopted (Oh, 2004). When all 81 equations are solved, we will call this the multiple discharge equations (MDE). When a single equation is solved (e.g., Eq. (10)), we will refer to this as the single discharge equation (SDE). The steady continuity equation, Eq. (3), will be referred to as CE.

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5.2. Loss coefficients, effective lengths and flow exponents In the discharge equation, there are three empirically determined coefficients: the loss coefficient, CL (or discharge coefficient, k), the effective length, le, and the flow exponent, n. The loss coefficient varies primarily with time, the opening geometry and the approaching wind direction due to the exterior pressure field, which is defined as a function of Reynolds number and the orifice length to diameter ratio (lo/d) (Chaplin et al., 2000). The effective length, le, varies with shape and length of the opening (Holmes, 2001; Vickery, 1991). Also, the flow exponent, n, depends on the flow and opening details (Shaw, 1981). The coefficients reported in the literature have been suggested by either pressurization tests (Vickery and Karakatsanis, 1987; ASHRAE, 2001) or numerical simulations (Holmes, 1979; Ginger, 2000; Sharma and Richards, 2003). Herein, the coefficients were determined by solving the equations numerically and fitting the best coefficients to match the data for a single configurationpand ffiffiffiffiffiffiffi wind angle. In particular, the best value of the discharge coefficient, k (where k ¼ 1= C L ) of 0.38 (CL ¼ 6.9) was found for the leakage case. For dominant openings we used k ¼ 0.63 (CL ¼ 2.5), as this is the commonly used value in the literature. Table 3 shows these discharge coefficients together with those that have been used in previous studies. The reader is referred to Oh (2004) for more details, where the sensitivity to the coefficients can be observed. Holmes, Liu et al. and Vickery have used the loss coefficients in the range 2.5–2.8, while Sharma and Richards suggested a new concept associated with the opening length–area ratio (CL ¼ 1.5, 1.2). Ginger found much larger values (CL ¼ 8.2, 45) for 2% and 5% dominant openings. pffiffiffi There have been two effective lengths, le, usedpin ffiffiffi the literature, where l e ¼ l o þ 0:89 a (Vickery, 1986; Liu and Saathoff, 1982) and 0:89 a (Holmes, 1979; Ginger, 2000), lo is the opening length (wall thickness pof ffiffiffi model), and a is the opening area. In the current work, it was found that l e ¼ l o þ 0:89 a was slightly better and was used for all calculations shown herein (Oh, 2004).

Table 3 Discharge coefficients (k) and loss coefficients (CL) used in previous studies along with those from the current study

Previous studies

Author

k

CL

Comments

Holmes (1979)

0.6 (0.15)

2.8 (45)

Under steady flow conditions Under highly fluctuation and reversed flow conditions

0.6

2.8

0.63 1.0 0.6 0.63 0.35 0.15

2.5 1.5 1.2 2.5 8.2 45

pffiffiffiffiffiffiffiffi For long opening ðI o 4 a=pÞ pffiffiffiffiffiffiffiffi For thin opening ðI o o a=pÞ To calculate Helmholtz frequency For a 2% opening For a 5% opening

0.63 0.38

2.5 4.1

For 3.3% and 0.3% openings For 0.1% leakage

Liu and Saathoff (1982) Vickery (1986) Sharma and Richards (2003) Ginger (2000)

Static coefficient chosen in this study

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As mentioned by Shaw (1981), it is thought that the flow exponent n ¼ 0.5 is not appropriate for leakage in buildings and for long thin openings. In our study of the background leakage case, several flow exponents were evaluated with the MDE. We found excellent agreement between the experiment and simulation for n ¼ 0.7 and used this value for openings considered to be leakage. The reader is referred to Oh (2004) for details pertaining to the sensitivity of this choice. This is close to the value recommended in (ASHRAE, 2001). An exponent n ¼ 0.5 was used for the dominant openings, which is appropriate for orifice flows (Potter and Wiggert, 2002). 5.3. Comparison between experiments and numerical predictions 5.3.1. Building with a dominant opening and leakage As implied by Fig. 3, a single windward opening is the worst situation for the extremes of fluctuating internal pressures. Holmes (1979) pointed out that ‘‘small density changes are maintained by the small mass flows through the opening so that the internal pressures respond almost instantaneously to the external fluctuations’’. This is confirmed by the segment of time series indicating that the internal pressure coefficients track the external pressures depicted in Fig. 5(a). The peaks of the internal pressure coefficients which are higher than the external pressures in Fig. 5(a) indicate that the inertial term in (11) is significant, while the damping effects are much smaller for the current 3.3% opening size. For much larger openings, with more significant resonance, the inertial term would play a larger role; for the smaller openings characteristic of leakage, the damping term which is inversely proportional to the open area, a2, is significant. The experimental and numerical time histories in Fig. 5(a) show that the numerical method is able to capture the temporal variations of the internal pressure with good accuracy when either the SDE or MDE are used. Indeed, there is little difference between the solutions with and without the background leakage included, indicating that the leakage is not playing a significant role in determining the internal pressures for this case. This is consistent with the results of Bloxham and Vickery (1989) who suggested that the leakage only becomes important when the background porosity exceeds about 10% of the main opening area. Fig. 5(b) illustrates the spectra of the internal and external pressure fluctuations corresponding to the time series in Fig. 5(a). There are only small differences in the rms between the experimental and predicted internal pressures. This confirms how well the theory works to simulate the pressure fluctuations. A resonant peak appears between 22 and 23 Hz on all internal pressures but not the external pressures. In fact, the external pressure slightly ‘‘bumps up’’ around the resonant frequency indicating that the measured external pressure near the opening is also affected by the resonance of the internal volume. This measured Helmholtz frequency is an excellent match with the predicted value of 23 Hz from Holmes’ equation (Holmes, 1979) (see also Liu and Saathoff (1982); Vickery (1986)): sffiffiffiffiffiffiffiffiffiffiffiffi 1 gPo a fH ¼ . (13) 2p rl e V o Holmes examined the effects of opening size and found that the height of the peaks and the resonant frequency decrease as the dominant opening becomes smaller. The implication is that the smaller the opening area, the higher the effect of the damping term in the Eq. (11).

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2.5 Cpi(exp) Cpi(MDE) Cpi(SDE) Cpe(exp)

2

Cp

1.5

1

0.5

0 6800

6900

7000

7100

7200

7300

7400

7500

Data Point

Power Spectral Density (s (f))

100 Cpi(exp) Cpi(MDE) Cpi(SDE) Cpe(exp)

10-1

10-2

10-3

10-4

10-5 10-1

100

101

102

f (Hz)

Fig. 5. (a) Time series of internal pressure coefficients and (b) spectra of the internal pressure for the ‘‘large’’ opening (3.3%) plus background leakage for a wind angle of 2701 and the open exposure (each data point has 0.002 s. UH ¼ 9.0 m/s).

Since the value of a3/2/Vo ¼ 3.4  104 for the current case is relatively small (Holmes, 1979), the resonant effects are small. Fig. 6 shows time series and spectra of the internal pressure coefficients for the smaller opening (0.3%) plus background leakage. Since both the two circular openings show similar behaviour, only the results of the larger circular case are presented herein. For the numerical computations, the same numerical values (k ¼ 0.63, n ¼ 0.5) as those for the large opening (3.3%) case were used except for the opening area and location. Time histories for the small opening (0.3%) also show that the numerical solutions obtained with the MDE can predict the fluctuations of the internal pressure accurately.

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1.2

Cpi(exp) Cpi(MDE) Cpi(SDE)

1

Cp

0.8 0.6 0.4 0.2 0 6800

6900

7000

7100

7200

7300

7400

7500

Data Point

Power Spectral Density (s (f))

10-1

Cpi(exp) Cpi(MDE) Cpi(SDE)

10-2 10-3 10-4 10-5 10-6 10-7 10-1

Uref=9.0m/sec

100

101

102

f (Hz)

Fig. 6. (a) Time series of internal pressure coefficients and (b) spectra of the internal pressure the ‘‘small’’ opening (0.3%) plus background leakage for a wind angle of 2701 and the open exposure (each data point has 0.002 s. UH ¼ 9.0 m/s).

Unlike the 3.3% opening case, the SDE method (i.e., ignoring the background leakage) predicts much higher values of the fluctuating internal pressures, indicating that the background leakage is playing an important role in determining the internal pressures for this 0.3% opening size. This makes sense because the open leakage area is about 70% of the dominant opening area, as shown in Table 2. It is clearly seen from the spectra in Fig. 6(b) that the spectral density predicted by the MDE is much closer to the experiments than that by the SDE indicating that the background leakage attenuates total fluctuating energy of the internal pressures when a porosity ratio reaches 70%, and showing the superiority of the MDE where the leakage

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effects are considered. The spectra do not show Helmholtz resonant peaks for this 0.3% circular opening. 5.3.2. Background leakage (nominally sealed building) All nominally sealed buildings have air leakage. However, background leakage by itself leads to smaller magnitudes of internal pressures than when a dominant opening is present, as indicated by Fig. 3. In this case, the inertial (first) term in (11) is much smaller than for a dominant opening while the damping (second) term (which is similar to the unsteady term in the CE) is dominant. Two approaches were used to simulate the internal pressure fluctuations, namely the CE assuming incompressible or steady flow, or Eq. (11) applied to the 80 openings that make up the distributed leakage case. Fig. 7(a) illustrates a segment of the internal pressure fluctuations predicted by the CE and the MDE approach, along with the experimental measurements. It is clear that the MDE approach is superior since the resulting time series tracks the actual time series quite accurately. Results from the CE, on the other hand, fluctuate about the actual time series, indicating there is too much energy content at higher frequencies (see also the spectra in Fig. 7(b)). This is attributed to compressibility effects, which are neglected under the incompressible form of the CE. Note that the small mean offset between all of the signals could be due to numerical errors, but given the small signals, is more likely due to experimental uncertainty (the external pressure coefficients are much larger and the error is proportional to the full range of the instruments). To better understand the role of leakage, it is useful to compare the external pressure fluctuations at the centre of each wall with the internal pressures. This is done in Fig. 7(b), which illustrates the dramatic damping effect the small holes have on the external fluctuations as they pass through the openings. Clearly, the fluctuating internal pressures are of much smaller magnitude than the external pressures, indicating that external fluctuating energies are attenuated by the leakage over all frequencies. 5.3.3. Summary comparison Fig. 8 provides a summary comparison of the predicted and the measured internal pressure statistics. Data for only the 3.3% (rectangular) opening in the open country terrain are presented here for the seven wind directions examined. Recall that 2701 is a wind direction normal to the dominant opening and 3601 is parallel to it. The X- and Y-axes show internal pressure coefficients for the experimental and predicted results, respectively. The solid, straight lines in the figures are for a line whose slope is unity, such that if predictions were identical to the experiments, all data would fall on this line. The dotted lines represent a linear regression from the seven data points for comparison. It is clearly seen that for the case of the 3.3% opening plus background leakage, the mean, rms, maxima and minima are all placed closely to the matching line, indicating that the internal pressure signals are predicted very well by the MDE for all seven wind angles. It is also observed from the figure that all values are larger for the normal wind (2701) than for any other oblique winds, at least for the openings in the centre of wall, as is the case here. (Sharma and Richards have shown that Helmholtz resonance is higher for oblique winds than for the normal winds in their study with the opening near the corner of the wall (Sharma and Richards, 2003)).

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0.05 Cpi(exp) Cpi(MDE) Cpi(CE)

0

Cp

-0.05 -0.1 -0.15 -0.2 -0.25 5800

6000

6200

6400

6600

6800

7000

7200

7400

DataPoint

100 Power Spectral Density (s (f))

Cpe(windward & side walls) 10-1 Cpe(leeward wall) 10-2 10-3 10-4 10-5

Cpi(CE)

-6

Cpi(exp)

10

Cpi(MDE) 10-7 10-1

100

101

102

f (Hz)

Fig. 7. (a) Time series of internal pressure coefficients and (b) spectra of the external and internal pressures for the background leakage (opening ratio of 0.1%) for a wind angle of 2701 and the open exposure (each data point has 0.002 s. UH ¼ 9.0 m/s).

5.4. Evaluation of suburban exposure The suburban exposure is defined by a roughness length of 0.3 m, which leads to a turbulence intensity of 0.28 at roof height. To obtain the numerical results, the same empirical coefficients were used except for the smaller mean roof height wind speed, UH. Numerical simulation by the MDE can predict temporal variations of the internal pressure very well irrespective of changes of the exposure. There are similarities between the two exposures in terms of the trends of statistics (mean, rms, maxima, and minima), the wind azimuth effects, opening ratio dependence, background leakage effects, the occurrence of resonance. However, the magnitude of the internal pressures is altered.

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270 285 300 315 330 345 360

0.35 PREDICTION

0.8 PREDICTION

0.4

270 285 300 315 330 345 360

1

0.6 0.4 Slope= 0.97

0.2

Intercept= -0.03

0

0.3 0.25 0.2 0.15 0.1

-0.2

Slope=0.85 Intercept=0.03

0.05 -0.2

0

0.2

0.4

Cpi (mean)

0.6

0.8

1

773

1.2

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Cpi (rms) EXPERIMENT

EXPERIMENT

3 270 285 300 315 330 345 360

2

0 PREDICTION

PREDICTION

2.5

270 285 300 315 330 345 360

0.2

1.5 Slope=0.92 Intercept=0.07

1

-0.2 -0.4 -0.6

Slope=1.00 Intercept=0.04

-0.8

0.5

-1 0 0

0.5

1

Cpi (maxima)

1.5

2

2.5

EXPERIMENT

3

-1

-0.8 -0.6 -0.4 -0.2 Cpi (minima)

0

0.2

EXPERIMENT 90

θ 180

360 270

Fig. 8. (a) MEAN, (b) RMS, (c) MAXIMA, and (d) MINIMA of internal pressure coefficients measured and predicted by the MDE for the ‘‘large’’ opening (3.3%) plus background leakage for 7 wind angles in the open exposure. (A least squares regression yielded the slope and intercept values for the best straight line through the experimental data in each plot.)

Fig. 9 illustrates the dependence of the internal pressure fluctuation on the upstream terrain roughness (turbulence intensity) for the opening ratios of 0.1% (leakage), 0.3%, and 3.3% for the normal wind direction. The figure also contains the full-scale field measurement results for the four opening ratios (leakage, 1%, 2%, and 5%) at Texas Tech

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MEAN

0.8 0.6

Cpi

0.4 0.2 0 -0.2

0

1

2 3 Opening Ratio (%)

4

5

4

5

4

5

RMS

0.5 0.4

Cpi

0.3 0.2 0.1 0

0

1

2 3 Opening Ratio (%) PEAK

3 2.5

Cpi

2 1.5 1 0.5 0 -0.5

0

1

2 3 Opening Ratio (%)

Suburban exposure (Iu = 0.28), Open exposure (Iu = 0.20), Open exposure used in field experiments at Texas Tech University [23] Fig. 9. Dependence of the measured internal pressure coefficients on the exposure (turbulence intensity) for four opening ratios for a normal wind.

University (Yeatts and Mehta, 1993). It is observed that the statistics of internal pressures measured in the suburban exposure show that the mean, rms, and peak increase with the larger turbulence intensity. The rms and peak values for the test with the open country

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terrain are lower than those obtained from the TTU field measurements. The mean, rms and peak Cpi vary significantly with the opening ratio of less than 1%. 6. Comparison with current wind load standards The measured internal pressure coefficients are compared with four wind load provisions: the ASCE 7-02 (1998), the NBCC (1995), the AS/NZS (2002) and the Eurocode (2004). Pressure coefficients for wind tunnel data have been transformed to correspond to the ASCE 7-02, using the method adopted in Part 2 (St. Pierre et al., 2005). The equation used to determine the equivalent ASCE values (GCpi)eq from the wind tunnel data was ðGC pi Þeq ¼

1=2rU 2H 2 1=2rU 10 m;3 sec gust K zt K h K d I

C pi ¼ F WT C pi ,

(14)

where U10 m,3 secgust is the 3-s gust wind speed obtained at a height of 10 m in an open country terrain, Kzt is the topographic factor of 1.0, Kd is the wind directionality factor of 1.0, Kh is the velocity pressure exposure factor of (1.04, 0.86) and (0.76, 0.70) for open exposure (12.2, 4.88 m eave heights) and suburban exposure (12.2, 4.88 m eave heights), respectively, I is the importance factor of 1.0, and FWT is the pressure conversion factor between wind tunnel data and ASCE. The design pressure coefficients were converted from NBCC (1995), to equivalent ASCE values using ðGC pi Þeq ¼

1=2rU 210 m;meanhrly C e 1=2rU 210 m;3

gust K zt K h K d I

C pi C g ¼ F NBCC C pi C g ,

(15)

where U10 m,meanhrly is the hourly mean wind velocity obtained at a height of 10 m in an open country terrain, Ce is the exposure factor of (1.06, 0.90) for open exposure (12.2, 4.88 m eave heights), CpiCg is the combined gust internal pressure coefficient, and FNBCC is the pressure conversion factor between NBCC and ASCE. The equivalent pressure coefficients, (GCpi)eq, from the AS/NZS (2002) were defined as ðGC pi Þeq ¼

1=2rU 210 m;3

gust ðM d M z;cat M s M t Þ 2 1=2rU 10 m;3 gust K zt K h K d I

2

kc

C p;i ¼ F AS=NZS C p;i ,

(16)

where Md is the directionality multiplier of 1.0, Mz,cat is the terrain/height multiplier of (1.03, 0.97) and (0.83, 0.83) for open exposure (12.2, 4.88 m eave heights) and suburban exposure (12.2, 4.88 m eave heights), Ms is the shielding multiplier of 1.0, Mt is the topographic multiplier of 1.0, Kc is the combination factor of 1.0, and FAS/NZS is the pressure conversion factor between AS/NZS and ASCE. The equivalent pressure coefficients, (GCpi)eq, from the Eurocode (2004) were defined as ðGC pi Þeq ¼

1=2rU 210 m;10 min C e ðzÞ 1=2rU 210 m;3

gust K zt K h K d I

C pi ¼ F EURO C pi ,

(17)

where U10 m,10 min is the 10 min-mean wind velocity obtained at a height of 10 m in a terrain of zo ¼ 0.05 m, Ce(Z) is the exposure factor of (2.5, 1.9) and (1.85, 1.3) for open exposure (12.2, 4.88 m eave heights) and suburban exposure (12.2, 4.88 m eave heights), respectively,

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and FEURO is the pressure conversion factor between Eurocode and ASCE. Further details regarding the coefficient conversion technique can be found in St. Pierre et al. (2005). The internal pressure coefficients GCpi in the ASCE 7-02 are classified as 70.55 for partially enclosed buildings and 70.18 for enclosed buildings. The cases of a dominant opening with leakage were considered as a partially enclosed building, and the case of leakage only was regarded as an enclosed building. The internal pressure coefficients CpiCg in the NBCC are arranged into three categories as 0.3 for buildings with small uniformly distributed openings (accumulating to less than 0.1% of total surface area), 70.7 for buildings with non-uniformly distributed small openings, and 71.4 for building with large or significant openings. The rectangular opening and leakage cases correspond to the CpiCg of 71.4 and 0.3, respectively. The two circular opening cases are considered to fall into the category with 70.7. The internal pressure coefficients Cp,i in the AS/NZS are classified with opening conditions such as (1) the opening location against wind direction, (2) the leakage-distributed condition and (3) the ratio of dominant opening to total open area of background faces. When applying the AS/NZS code to the test model building, the internal pressures Cp,i is 0.7 for the rectangular dominant opening (windward wall), 0.35 for the circular opening (windward wall), and 0.3 for the leakage case (all walls equally permeable). The internal pressure Cpi in the Eurocode is written depending on the size and distribution of the openings in the building envelope. According to the Eurocode, the test building internal pressure Cpi with the rectangular dominant opening would be 0.65, the circular opening 0.25 and the leakage case 0.18. The corresponding ASCE-equivalent internal pressure coefficients (GCpi)eq are listed in Table 4. The table gives a summary of the comparison of the measured internal pressure coefficients to the building codes. It is observed that for the largest opening case with an open area ratio of 3.3%, the measured peak (GCpi)eq considerably exceeds the recommended design ranges from the standards (approximately 180% in ASCE7-02, 130% in NBCC and AS/NZS, 120% in Eurocode). For both the circular opening cases with an open area ratio of 0.3%, the measured peak values are slightly beyond the design values from the Eurocode. However, for the leakage only case, all the standards are conservative. Comparing the values between both the circular opens, the equivalent Table 4 Comparison of the measured internal pressure coefficients to the Building Codes of ASCE 7-02, NBCC (1995), Eurocode (2004), AS/NZS 1170,2:2002 Eaves height (m)

Wind tunnel peak (GCpi)eq

ASCE 7-02 (GCpi)

NBCC (1995) (GCpi)eq

AS/NZS (2002) (GCpi)eq

Eurocode (2004) (GCpi)eq

12.2 12.2 4.88 12.2

1.01 0.38 0.33 0.14

0.55 0.55 0.55 0.18

0.74 0.37 0.38 0.16

0.84 0.42 0.45 0.36

0.81 0.31 0.28 0.22

Suburban exposure 3.3% (RECT) 12.2 0.3% (L.CIR.) 12.2 0.3% (S.CIR.) 4.88 0.1% (LEAK) 12.2

0.96 0.41 0.28 0.09

0.55 0.55 0.55 0.18

N/A N/A N/A N/A

0.75 0.37 0.41 0.32

0.82 0.31 0.24 0.23

Open ratio

Open exposure 3.3% (RECT) 0.3% (L.CIR.) 0.3% (S.CIR.) 0.1% (LEAK)

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internal pressure coefficients of NBCC and AS/NZS for the small circular open (4.88 m of eaves height) are larger than the ones for the large circular open (12.2 m of eaves height) even though the same values are applied to both the circular open cases in the codes as mentioned above. This implies that the height-related multipliers (e.g., kh in ASCE, Ce in NBCC, Mz,cat in AS/NZS and Ce(z) in Eurocode) are not identical in the codes. For instance, kh,4.88 m/kh,12.2 m in ASCE is 0.83 (0.86/1.04) and M2z,cat,4.88 m/M2z,cat,12.2 m in AS/ NZS is 0.89 (0.972/1.032). This results in the 7% (0.89/0.83) higher value in the equivalent internal pressure coefficient of AS/NZS for the small circular open. 7. Conclusions Wind-induced internal pressures in a low-rise building were examined using the NIST aerodynamic database with realistic dominant opening and leakage scenarios. The main objectives of this study were (i) to determine how accurately mean and fluctuating internal pressures can be predicted from measured external pressures, and (ii) to examine a greater range of leakage area to dominant opening area ratios, than has been previously studied. The research further developed the unsteady orifice discharge equation to predict the internal pressure time histories. For this, 81 equations, one for each opening, were solved. The following conclusions can be drawn: 1. Numerical simulation using MDE can capture the temporal variations of the internal pressure with the selected empirical coefficients of the discharge coefficient (k), the effective length (le), and the flow exponent (n). 2. While a SDE produces much higher rms internal pressure fluctuations, MDE can predict relatively accurate rms values for buildings with high leakage to opening ratios (e.g., in the current study, a ratio of 70% for the circular opening with background leakage cases). 3. For buildings with leakage only, external pressure fluctuations are dramatically attenuated by the damping effect of the flow through small holes, indicating that the damping terms in the discharge equations are significant and the friction term is necessary. The damping is related, in part, to compressibility effects, and also to flow losses. 4. For the buildings with a single centrally located dominant opening plus leakage, Helmholtz resonance occurs and can be predicted well with theory. 5. For the large buildings considered here with a single dominant opening near the centre of the wall, and including leakage, peak internal pressures occur for a wind direction normal to the wall having the dominant opening. 6. The rms (standard deviation) and peak internal pressure coefficients are higher in the suburban terrain than in the open-country terrain for all opening cases. 7. Peak internal pressure coefficients measured in the wind tunnel exceed the design values from the design standards of ASCE 7-02, NBCC, AS/NZS and Eurocode for the case of a dominant opening with leakage with an open area ratio of 3.3% and leakage of 7% of the dominant opening area. It is encouraging that computational models for internal pressures can be used for simulation with high accuracy. Nevertheless, the models presented here have been evaluated for a single internal volume, rigid structure, and only an opening in the centre of

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the wall. The applicability of the discharge equations for buildings with separated internal volume, flexible envelope, and various opening locations needs to be studied. Eventually, the equations should be verified together with field experiments of internal pressures to clarify conversion of the model-scale to a full-scale building. Acknowledgements The experimental data was obtained with financial support from the US National Institute of Standards and Technology (NIST) and Texas Tech University. The authors are indebted to Dr. T.C.E. Ho and Prof. D. Surry who designed the experiments and provided many hours of valuable discussions. Student support was provided by the Institute for Catastrophic Loss Reduction (ICLR) and NSERC, through the CRD program. G.A. Kopp also gratefully acknowledges the support provided by the Canada Research Chairs Program. References ASCE STANDARD, 1998. Minimum Design Loads for Buildings and Other Structures. ASCE7-02, New York. ASHRAE, 2001. ASHRAE Handbook: Fundamentals, SI ed. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc, pp. 26.1–26.32 (Chapter 26). Bloxham, C., Vickery, B.J., 1989. An experimental investigation of internal pressure dynamics with a dominant front wall opening. University of Western Ontario, Faculty of Engineering and Science, Report No. BLWTLSS46-1989, November 1989. Canadian Commission for Building and Fire Codes, NRC User’s guide—NBC, 1995. Structural Commentaries (Part 4), National Research Council of Canada, Ottawa, 1996. Chaplin, G.C., Randall, J.R., Baker, C.J., 2000. The turbulent ventilation of a single opening enclosure. J. Wind Eng. Ind. Aerodyn. 85, 145–161. Davenport, A.G., Surry, D., 1984. The estimation of internal pressures due to wind with application to cladding pressures and infiltration. In: Proceedings of the Wind Pressure Workshop, March 21–22, Brussels, Belgium, 1984. European Committee for Standardization/Technical committee (CEN/TC 250), 2004. ‘‘Eurocode 1: Actions on structures—General actions—Part 1–4: Wind actions. prEN 1991-1-4, CEN TC 250. Ginger, J.D., 2000. Internal pressures and cladding net wind loads on full-scale low-rise building. J. Struct. Eng. 126 (Part 4), 538–543. Ho, T.C.E., Surry, D., Morrish, D., Kopp, G.A., 2004. The UWO contribution to the NIST aerodynamic database for wind loads on low buildings: Part 1. Archiving format and basic aerodynamic data. J. Wind Eng. Ind. Aerodyn. 193, 1–30. Holmes, J.D., 1979. Mean and fluctuating internal pressure induced by wind. In: Proceedings of the Fifth International Conference on Wind Engineering, Colorado State University, pp. 435–450. Holmes, J.D., 2001. Wind Loading of Structures. Spon Press, pp. 128–138 (Chapter 6). Inculet, D.R., 1990. Pressure-equalization of rain screen cladding. Masters Thesis in Civil and Environmental Engineering, University of Western Ontario. Irminger, J.O.V., Nokkentved, C., 1930. Wind pressure on buildings. Experimental Researches First Series, Ingenior Videnskabelige Skrifter A Nr 23. Liu, H., 1975. Wind pressure inside buildings. In: Proceedings of the Third US National Conference on Wind Engineering, pIII-3-1, Fort Collins, Colorado, June 1975. Liu, H., Rhee, K.H., 1986. Helmholtz oscillation in building models. J. Wind Eng. Ind. Aerodyn. 24, 95–115. Liu, H., Saathoff, P.J., 1982. Internal pressure and building safety. ASCE J. Struct. Div. 108, 2223–2234. Oh, J.H., 2004. Wind-induced internal pressures on low-rise buildings. Masters Thesis in Civil and Environmental Engineering, University of Western Ontario. Pearce, W., Sykes, D.M., 1999. Wind tunnel measurements of cavity pressure dynamics in a low-rise flexible roofed building. J. Wind Eng. Ind. Aerodyn. 82, 27–48. Potter, M.C., Wiggert, D.C., 2002. Mechanics of Fluids, third ed. Brooks/Cole, Pacific Grove, CA, USA.

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