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Effect of Fluid Capacitance The models in this chapter were developed specifically with thermal energy storage systems in mind. However, much of the existing simulation capability was developed to evaluate gas-solid packed-bed heat transfer performance. In these gas-solid models the fluid thermal capacitance is often neglected. A numerical model that neglects fluid capacitance is presented here in order to quantify the impact of making this assumption with packed-bed thermal storage systems where the fluids have much higher thermal capacitances. The finite-difference equations are developed explicitly from the fluid energy balance shown in Figure 6.9 by neglecting the thermal capacitance term. For convenience, the temperature nodes are defined at the axial nodal interfaces. The fluid energy balance is then: 115 T =T − hAnode ⎛Tf ,(i,t) +Tf ,(i+1,t) −T ⎞ f , ( i + 1 , t ) f , ( i , t ) m& C ⎜ 2 s , ( i , t ) ⎟ ff⎝⎠ And the solid energy balance becomes: T =T +hAnode∆t⎛Tf,(i,t) +Tf,(i+1,t) −T ⎞ s,(i,t+∆t) s,(i,t) m C ⎜ 2 s,(i,t) ⎟ ss⎝ ⎠ [6.3.39] [6.3.40] Figure 6.17 shows the simplified explicit model (equations [6.3.26] and [6.3.27]) converging on the no-capacitance model (equations [6.3.39] and [6.3.40]) for a storage system where R (capacitance ratio)~0, demonstrating that for systems where the fluid capacitance truly is negligible, these two models are equivalent. This model will be used in section 6.3.4 to compare predicted performance in systems where fluid capacitance is not negligible, as is expected in thermal-storage systems.PDF Image | Organic Rankine Cycle Solar-Thermal Powerplants
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