These analytical results agree with data from the numerical simulations shown in Figures 7 and 8 (P. 207). In general, it can be observed from equation 11 that the rate of change of liquid fraction, dX/dt is directly proportional to the net thermal power into the receiver, ( /r]); however, inversely proportional to the PCM mass, m, and latent heat of fusion,X. Although the Brayton PCM has a higher positive rate dX/ dt in the sun period and a higher negative rate during eclipse than the Rankine PCM, the duration of the sun portion is greater than that of the eclipse period. Therefore, the Brayton PCM has a larger net gain of liquid fraction per orbit before reaching the steady periodic profile. The rate of change of the liquid fraction is related to the energy accumulation rate in the receiver. Combining equations 1 and 12 results in: Before reaching the steady periodic profile, the amount of stored energy per orbit for the Brayton system is: For the Organic Rankine cycle the amount of energy stored per orbit before reaching the steady periodic profile is: For the Rankine cycle (LiOH) the number of orbits required is:
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