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Assumption Relaxation The assumptions made in the formulation of equations [6.3.2] and [6.3.3], as well as the subsequent analytical solution place some limitations on simulation accuracy using the Schumann equations. Of principle concern are material and transport property variation and the assumption of infinite solid conductivity. Properties can vary dramatically with temperature and the solid materials under consideration have relatively low conductivity indicating the likely presence of significant temperature gradients within solid particles. Variable properties are readily managed in the context of the numerical solutions that will be used to solve the governing equations. The treatment of the solid as a lumped capacitance (infinite conductivity) requires more consideration. The solid materials (quartzite rock, silica sand, etc...) under consideration for powerplant thermal storage possess relatively low thermal conductivities, calling into question the universal validity of the lumped-capacitance assumption. Jeffreson [1972] proposes a heat transfer coefficient correction factor that accounts for temperature gradients within solid particles without adding dimensions to the computational domain. Jeffreson’s correction factor is formulated in terms of the Biot number, shown below: hcorrected = 1 [6.3.11] h 1 + Bi / 5 The Biot number is a ratio of convective heat transfer with the fluid and conduction within the solid. As the Biot number becomes large convective heat transfer from fluid to solid dominates conduction within the solid, indicating significant temperature gradients within the solid. The Jeffreson factor estimates the degradation of fluid-solid overall heat transfer coefficient resulting from these temperature gradients. A more advanced correction factor that includes both the Biot and Fourier numbers is proposed by Engelbrecht, et al [2006]. 99PDF Image | Organic Rankine Cycle Solar-Thermal Powerplants
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