Experience and judgment are required to obtain satisfactory results with this method. Experienced engineers will often simply make an assumption of the number of air changes per hour (ACH) that a building will experience, based on their appraisal of the building type, construction, and use. The range will usually be from 0.5 ACH (very low) to 2.0 ACH (very high). Modern office buildings may experience infiltration rates as low as 0.1 ACH. This approach is usually satisfactory for design load calculation but not recommended for the beginner. The infiltration rate is related to ACH and space volume as follows:
(6-4) where:
Q= infiltration rate, cfm or m3/s
ACH= number of air changes per hour, hr−1 V= gross space volume, ft3or m3
CT= constant, 60 for English units and 3600 for SI
Crack Method
Outdoor air infiltrates the indoor space through cracks around doors, windows, light- ing fixtures, and joints between walls and floor, and even through the building mate- rial itself. The amount depends on the total area of the cracks, the type of crack, and the pressure difference across the crack. The volume flow rate of infiltration may be calculated by
(6-5) where:
A= effective leakage area of the cracks
C= flow coefficient, which depends on the type of crack and the nature of the flow in the crack
∆P =outside − inside pressure difference, Po− Pi
n= exponent that depends on the nature of the flow in the crack, < 0.4 < n < 1.0. ˙
Q = AC P∆ n
˙ ( )( )/
Experimental data are required to use Eq. 6-5 directly; however, the relation is useful in understanding the problem. For example, Fig. 6-1 shows the leakage rate for some windows and doors as a function of the pressure difference and the type of crack. The curves clearly exhibit the behavior of Eq. 6-5.
The pressure difference of Eq. 6-5 results from three different effects:
(6-6) where:
∆Pw= pressure difference due to the wind ∆Ps= pressure difference due to the stack effect ∆Pp= difference due to building pressurization
Each of the pressure differences is taken as positive when it causes flow of air to the inside of the building.
The pressure difference due to the wind results from an increase or decrease in air velocity and is calculated by
(6-7a) where ∆Pwhas the unit of lbf/ft2when consistent English units are used or Pa for SI units. The velocity Vfis the velocity of the wind at the building boundary. Note that ∆Pw is positive when Vw > Vf, which gives an increase in pressure. The velocity Vf is not known or easily predictable; therefore, it is assumed equal to zero in this appli- cation and a pressure coefficient, defined by
(6-8) Cp = ∆Pw/∆Pwt ∆P g V V w c w f = ρ − 2 2 2 ( ) ∆P = ∆Pw +∆Ps+∆Pp
162
Chapter 6 Space Heating LoadFigure 6-1 Window and door infiltration characteristics. (Reprinted by permission, from ASHRAE Cooling and Heating Load Calculation Manual, 2nd ed., 1992.)
2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0 0 0.04 0.08 0.12 0.16 0.20 0.24 0.28 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0 K = 6.0 K = 2.0 K = 1.0 P, inches of water P, pascals ∆ ∆ Q /L , L/(s-m) ⋅ Q /L , cfm/ft ⋅ 0 25 50 70
is used to allow for the fact that Vf is not zero. The pressure difference ∆Pwt is the computed pressure difference when Vfis zero. The pressure coefficient may be posi- tive or negative. Finally, Eq. 6-7a may be written
(6-7b) The pressure coefficient depends on the shape and orientation of the building with respect to the wind. To satisfy conditions of flow continuity, the air velocity must increase as air flows around or over a building; therefore, the pressure coefficient will change from a positive to a negative value in going from the windward to the leeward side. The pressure coefficients will also depend on whether the wind approaches nor- mal to the side of the building or at an angle. Figure 6-2 gives average wall pressure coefficients for low-rise buildings. Buildings are classified as low-rise or high-rise, where high-rise is defined as having height greater than three times the crosswind width (H > 3W). The average roof pressure coefficient for a low-rise building with the roof inclined less than 20 degrees is approximately 0.5. Figures 6-3 and 6-4 give aver- age pressure coefficients for high-rise buildings. There is an increase in pressure coef- ficient with height; however, the variation is well within the approximations of the data in general.
The stack effect occurs when the air density differs between the inside and out- side of a building. On winter days, the lower outdoor temperature causes a higher pressure at ground level on the outside and consequent infiltration. Buoyancy of the warm inside air leads to upward flow, a higher inside pressure at the top of the build- ing, and exfiltration of air. In the summer, the process reverses with infiltration in the upper portion of the building and exfiltration in the lower part.
Considering only the stack effect, there is a level in the building where no pres- sure difference exists. This is defined as the neutral pressure level. Theoretically, the neutral pressure level will be at the midheight of the building if the cracks and other
∆P C g V w p c w = ρ 2 2
Figure 6-2 Variation of wall averaged pressure coefficients for a low-rise building. (Reprinted by
permission from ASHRAE Cooling and Heating Load Calculation Manual, 2nd ed., 1992.)
0.5 0 –0.5 –1.0 20° 40° 60° 80° 100° 120° 140° 160° Approximate bound to 90% of data L W Wind θ ,wind angle Cp
openings are distributed uniformly in the vertical direction. When larger openings pre- dominate in the lower portion of the building, the neutral pressure level will be low- ered. Similarly, the neutral pressure level will be raised by larger openings in the upper portion of the building. Normally the larger openings will occur in the lower part of
164
Chapter 6 Space Heating LoadFigure 6-4 Average roof pressure coefficients for a tall building. (Reprinted by permission from
ASHRAE Cooling and Heating Load Calculation Manual, 2nd ed., 1992.) 0.25
–0.25
–0.50
–0.75
Cp
,average roof pressure coefficient
0 0.50 0.75 W Wind L 20° 40° 60° 80° L/W=1 4 1 2 1
Figure 6-3 Wall averaged pressure coefficients for a tall building. (Reprinted by permission from ASHRAE Cooling and Heating Load Calculation Manual, 2nd ed., 1992.)
0.50 –0.25 –0.75 L W Wind C p
,average wall pressure coefficient
θ –0.50 0 0.25 0.75 20° 40° 60° 80° 100° 120° 140° 160° L/W =1 4 L/W = 1 L/W = 4
the building because of doors. The theoretical pressure difference with no internal sep- arations is given by
(6-9) where:
Po= outside pressure, psia or Pa
h= vertical distance, up or down, from neutral pressure level, ft or m To= outside temperature, R or K
Ti= inside temperature, R or K
Ra= gas constant for air, (ft-lbf)/(lbm-R) or J/(kg-K)
The floors in a conventional building offer resistance to vertical air flow. Furthermore, this resistance varies depending on how stairwells and elevator shafts are sealed. When the resistance can be assumed equal for each floor, a single correction, called the draft coefficient, can be used to relate the actual pressure difference ∆Psto the theoretical value ∆Pst:
(6-10) The flow of air from floor to floor causes a decrease in pressure at each floor; there- fore,∆Psis less than ∆Pst, and Cdis less than one. Using the draft coefficient, Eq. 6-9 becomes
(6-11) Figure 6-5 is a plot of Eq. 6-11 for an inside temperature of 75 F or 24 C, sea-level outside pressure, and winter temperatures; however, Fig. 6-5 can be used for summer stack effect with little loss in accuracy.
The draft coefficient depends on the tightness of the doors in the stairwells and elevator shafts. Values of Cdrange from 1.0 for buildings with no doors in the stair- wells to about 0.65–0.85 for modern office buildings.
Pressurization of the indoor space is accomplished by introducing more makeup air than exhaust air and depends on the design of the air distribution system rather than natural phenomena. The space may be depressurized by improper or maladjusted equipment, which is usually undesirable. For purposes of design, the designer must assume a value for ∆Pp, taking care to use a value that can actually be achieved in practice. Often the space is pressurized in an attempt to offset infiltration, especially with very tall buildings.