A theoretical framework is developed to determine the so-called thermal state-of-charge in solar heat receivers employing encapsulated phase change materials that undergo cyclic melting and freezing, and results are presented for the solar heat receiver component of NASA John H. Glenn Research Center at Lewis Field's Ground Test Demonstration System. The concepts of available power, virtual source temperature, and minimum gas available power are used as the bases for determining the state-of-charge. The state-of-charge is characterized in the subcooled, two-phase, and superheat regimes as well as startup, transition, and balanced-orbit modes. Baseline conjugate and primary state-of-charge curves are generated based on a priori known baseline system operating conditions through measurable parameters. Results indicate that for the baseline primary state-of-charge curve in balanced-orbit mode, there is a 33% energy margin (from the minimum state-of-charge line) at sunrise that indicates safe operation of the solar dynamic system; at sunset, the primary state-of-charge reaches 76%. Results for parametric changes indicate that the state-of-charge in the sensible regimes is completely reversed in the latent regime.
NomenclatureA = area c = speci c heat of solid or liquid phase change material (PCM) c p = working uid speci c heat at constant pressure D ap = aperture diameter D cav = active cavity diameter F = geometric view factor h = enthalpy per unit mass h sf = PCM latent heat of fusion M = total number of axial nodes along tube or total PCM mass Çm = working uid mass ow rate N = total number of tubes in receiver P = working uid pressure Ç Q = heat transfer rate R = speci c gas constant Ç S gen = entropy generation rate Ste = modi ed Stefan number s, S = speci c, total entropy T = temperature T ap = effective aperture or virtual source temperature T m = PCM melt temperature T 0 = environmental dead state temperature t = time u, U = speci c, total internal energy V = total volume Ç W = rate of work transfer z = axial location Propulsion Of ce, Analysis and Management Branch. b 1 = rst conjugate state-of-charge (SOC) function b 2 = second conjugate SOC function c = ratio of speci c heats e = thermal capacitance ratio q = density r = Stefan-Boltzmann constant s cyc = total orbit period s off = eclipse period s on = sun period U = primary SOC function v j = j th tube mass fraction Subscripts ap = aperture av = average in = tube inlet losses = losses through shell and aperture max = maximum min = minimum out = tube outlet rcvr = receiver