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Organic Rankine Cycle Solar-Thermal Powerplants

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Organic Rankine Cycle Solar-Thermal Powerplants ( organic-rankine-cycle-solar-thermal-powerplants )

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106 Figure 6.10 shows the numerical grid that is used for this explicit scheme and all other numerical models discussed in these sections. Note that both fluid and solid temperature nodes are located at the center of the numerical control volumes. Temperature node location was chosen to simplify expression of the fluid-solid heat transfer term. The only coupling effect between the two governing energy equations is the convective heat transfer term. Figure 6.10: Numerical grid used for finite-difference numerical modeling techniques Explicitly approximating the differential fluid energy balance in Figure 6.6 using a linear relation yields the following nodal energy balance: m& C ⎛Tf ,(i−1,t) +Tf ,(i,t) ⎞=m& C ⎛Tf ,(i,t) +Tf ,(i+1,t) ⎞+hA (T −T s,(i,t) ) ⎟ f f⎜ 2 ⎝⎠⎝⎠ f f⎜ 2 ρ A(1−ε)∆xC [6.3.20] [6.3.21] [6.3.22] ⎟ node f,(i,t) f (Tf,(i,t+∆t) −Tf,(i,t)) Tf ,(i,t) =Tfluid,(node,time) Likewise the solid energy balance becomes: ρ A∆xC (T −T )=hA ∆t(T s c s s,(i,t+∆t) s,(i,t) node −T ) s,(i,t) + f c ∆t where f ,(i,t) To accommodate the nodal locations chosen in Figure 6.10 the average fluid temperature between nodes is the basis for calculating the convective energy transport across the nodal boundary during a given timestep. Discretized in this way the equations are explicit in both time and space. Simplified explicit formulation

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