_ 2.97 X 10 X 31 X 9.1 X 106 X 1.637 X 0.76 X 0.251 4.5 + 2.97

0.175

From Eq. (11.88), pcpb2Qg _ 2200 X 910 X 0.42 X 1.05 X 109 _ , A_„ _T

Y = Sb + 0.047Sw = 13.02 + 0.047 X 1.052 = 37 34 qd 0.350 .

P = [1 - exp(—0.144Y)]0 53 = [1 - exp(—0.144 X 37.34)]053 = 0.998

From Eq. (11.91a), f = min{Pf + 0.88(1 - P)[1 - exp(-1.26f ], 1} = min{0.998 X 0.175 + 0.88(1 - 0.998)[1 - exp(-1.26 X 0.175)], 1} = min{0.175,1} = 0.175

Finally, from Eq. (11.92), Qaux = (1 - f)(Lm + Lw) = (1 - 0.175)(15.82 + 2.08) = 14.77GJ

11.4.3 Active Collection with Passive Storage Systems

The third type of system analyzed with the unutilizability method concerns active air or liquid collector systems used to heat a building that utilize the building structure for storage. The advantages of such a system are the control of heat collection with the solar collector; the elimination of separate storage, which reduces the cost and complexity of the system; and the relative simplicity of the system. The disadvantages include the large temperature swings of the building, which are inevitable when the building provides the storage, and the limits of the solar energy that can be given to the building in order not to exceed the allowable temperature swing. The method of estimation, developed by Evans and Klein (1984), is similar to that of Monsen et al. (1981) for direct gain passive systems, outlined in Section 11.4.1. In this system, two critical radiation levels are specified: one for the collector system and one for the building. As in previous systems, the limits on performance are required by considering the two extreme cases, i.e., the infinite and zero capacitance buildings. As before, the performance of real buildings is determined on correlations based on simulations.

As indicated in Section 11.2.3, the output of an active collector can be expressed with Eq. (11.43). For a month output, it becomes

where $c = monthly average utilizability associated with solar energy collection.

The critical radiation level used to determine $c is similar to Eq. (11.41), given by

where T = monthly average inlet temperature, the building temperature during collection (°C).

It should be noted that, in both limiting cases of zero and infinite capacitance, Ti is constant. For real cases, this temperature is higher than the minimum building temperature and varies slightly, but this does not affect XQu too much. For a building with infinite storage capacity, the monthly energy balance is

For the zero capacitance building, energy has to be dumped if solar input exceeds the load. The intensity of radiation incident on the collector that is adequate to meet the building load without dumping is called the dumping critical radiation level, given on a monthly average basis by j = (UA)h(Tb - Ta) + AcFrUl(Ti - Ta) (n.9fi)

where

(UA)h = overall loss coefficient-area product of the building (W/K). Tb = average building base temperature (°C). T = average building interior temperature (°C).

Therefore, for the zero capacitance building, a radiation level above jtc,c is necessary for collection to take place and Jtcd for the collector to meet the building load without dumping on a monthly basis. Energy greater than jtc,d is dumped, estimated by

where $d = monthly average utilizability, in fact unutilizability, based on Jtcd.

So, for the zero capacitance building, the energy supplied from the collector system that is useful in meeting the load is the difference between the total energy collected and the energy dumped, given by

The monthly auxiliary energy required for the zero capacitance building is then

The limits of auxiliary energy requirements are given by Eqs. (11.95) and (11.99), and the auxiliary of a real building with finite capacitance can be obtained by correlations of the solar fraction, f, with two dimensionless coefficients, the solar-load ratio, X, and the storage-dump ratio, Y, given by x = AFéN (11.100)

v CbATb _CbNATb (11101)

AFRS*d Qd

Finally, the correlation of the monthly solar fraction, f, with monthly collection utilizability, $c, and the monthly dumping utilizability, $d, is given by f = PX$c + (1 - P)(3.082 - 3.142$„)[1 - exp(-0.329X)] (11.102a)

The parameter is the zero capacitance building unutilizability resulting from energy loss from the collectors (1 - $c) and the energy loss from dumping, $d. It should be noted that the correlation for f is very similar to Eq. (11.71) for direct gain systems, for which /tc, c = 0 and $c = 1. It then follows that X and Y are the same as in Eqs. (11.66) and (11.70).

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