slopes in each curve. By the end of the contingency orbit, all the latent energy has been extracted and the PCM is all solid, X=0. Minimum Required Liquid Fraction (Reserve Capacity) The minimum liquid fraction of the PCM normally occurs at the end of an eclipse period. The amount of excess receiver capacity at this time is determined by the contingency requirement of one half power for one complete orbit. The energy storage system must have a sufficient reserve capacity to meet this contingency demand if required. The minimum fraction of the stored energy which is its minimum liquid fraction is: The time t = 95 minutes corresponds to the end of a typical orbit and the beginning of the contingency orbit as illustrated in Figures 4 (bottom P. 205) and 5 (top P. 206). This would normally be the time at which the minimum liquid fraction would occur. At this point, X is equal to 0.537 for both the Brayton and Rankine systems. Therefore, because of the contingency requirement, the thermal energy storage system has about twice the amount of PCM that is necessary for normal operation in this case study. Results The computer simulation was used to compare the transient PCM behavior of the Brayton and the Organic Rankine power systems. Each power system was subjected to a typical 48 hour load profile as shown in Figure 6 (bottom P. 206), which was adjusted to have a 75 kW mean value. Although the minimum liquid fraction of the PCM was 0.537, it was initially assumed that the PCM was completely solid, X=0, for comparative purposes. Transient periodic responses in the liquid fraction are shown in Figures 7 and 8 for the Brayton and Rankine systems respectively. Steady periodic profiles are reached in the sixth orbit for the Brayton system and the eleventh orbit for the Rankine system. The following is an analytical derivation whose results were compared with those of the numerical approach. This discussion will initially focus on examining the different rates of change of the liquid fraction between LiOH for the Rankine and LiF/MgF2 for the Brayton systems. From equation 2 the rate of change of internal energy is:
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