Pebble bed storage size correction
For the development of the /chart of Figure 11.6, a standard storage capacity of 0.25 cubic meters of pebbles per square meter of collector area was considered, which corresponds to 350 kJ/m2°C for typical void fractions and rock properties. Although the performance of airbased systems is not as sensitive to the storage capacity as in liquidbased systems, other storage capacities can be used by modifying the factor X by a storage size correction factor, Xc/X, as given by (Klein et al., 1977):
Mb,a
X where
Mb, a = actual pebble storage capacity per square meter of collector area (m3/m2). Mb, s = standard storage capacity per square meter of collector area = 0.25 m3/m2.
Equation (11.18) is applied in the range of 0.5 < (Mb,a/Mb,s) < 4.0 or 0.125 < Mb a < 1.0. The storage correction factor can also be determined from Figure 11.7 directly, obtained by plotting Eq. (11.18) for this range.
s 
Mbs = 0.25 m3/m2  
\  
\  
FIGURE 11.7 Storage size correction factor for airbased systems.
FIGURE 11.7 Storage size correction factor for airbased systems.
AIR FLow RATE correction
Airbased heating systems must also be corrected for the flow rate. An increased air flow rate tends to increase system performance by improving FR, but it tends to decrease performance by reducing the pebble bed thermal stratification. The standard collector flow rate is 10 L/s of air per square meter of collector area. The performance of systems having other collector flow rates can be estimated by using appropriate values of FR and Y, then modifying the value of X by a collector air flow rate correction factor, Xc/X, to account for the degree of stratification in the pebble bed (Klein et al., 1977):
x0.28
where ma = actual collector flow rate per square meter of collector area (L/sm2). ms = standard collector flow rate per square meter of collector area = 10 L/sm2.
Equation (11.19) is applied in the range of 0.5 < (ma/ms) < 2.0 or 5 < rna < 20. The air flow rate correction factor can also be determined from Figure 11.8 directly, obtained by plotting Eq. (11.19) for this range.
Air systems ms = 10 L/sm2  
/  
z  
z  
/ 
FIGURE 11.8 Correction factor for air flow rate to account for stratification in pebble bed. ma/ms Example 11.7If the air system of Example 11.6 uses a flow rate equal to 17 L/sm2, estimate the solar fraction for the month of January. At the new flow rate, the performance parameters of the collector are FRUL = 3.03 W/m2°C, Fr(to) = 0.54. Solution
