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In optimizing the recompression cycle, CYCLES III treats the IHX very simply, requiring a pressure drop, power rating, and turbine inlet temperature as the only inputs related to the IHX. Mass flow rate is scaled with the power as π = π 3000 ππ/π Eqn. 4-5 600 ππ where Q is the thermal power input in the IHX. This scaling of mass flow rate with power has been a feature of the CYCLES code since its original version. The only PCHE type that needs to be modeled within CYCLES III is the gas-to-gas recuperator because CYCLES III only requires pressure drop, power, and temperature for the IHX. Therefore, the existing codes proved sufficient for optimizing the S-CO2 balance of plant. In order to model the heat exchangers of the entire system, the PCHE modeling capabilities required expansion and a shell-and-tube code needed to be written. 4.4.1 The Shell-and-Tube Code SoSaT In order to size shell-and-tube heat exchangers, a Fortran code called SoSaT (Sodium Shell and Tube) was written. The code has the capability to size sodium-sodium, sodium-CO2, or sodium-water heat exchangers. The code can perform calculations for single phase, boiling, or supercritical water. For sodium-sodium and sodium-CO2 heat exchangers, the method of the number of transfer units (NTU) is used. NTU is an expression of the heat exchanger effectiveness relative to the overall heat transfer coefficient and fluid heat capacities [Shah, 2003]. The relationships between heat transfer coefficient, NTU and effectiveness are summarized as follows: ππ΄ β1 = 1 1 +πππ ππ,π/ππ,π + 1 Eqn.4-6 πΏ πππ,πππ‘π’ππ 2πππ‘π’ππ πππ,ππππ where UA is the product of the overall heat transfer coefficient and the heat transfer area. The number of transfer units is based on the overall heat transfer coefficient and the mass flow rates and heat capacities of the two fluids. πππ = ππ΄/ππΌπ(πΆ1, πΆ2) Eqn. 4-7 where C1 and C2 are the products of mass flow rate and heat capacity for each fluid. The effectiveness is related to NTU by 91PDF Image | Supercritical Carbon Dioxide Cycle Analysis
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