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and the process is iterated until the sodium outlet temperature converges. This outlet temperature is necessary for determining the fluid properties (and then the heat transfer coefficient) of sodium at the bottom of the shell, where the first node of the heat transfer calculation lies. The calculation will proceed upward in nodes of 1 cm length. The critical heat flux is determined for each node from interpolation of Groeneveldβs 2006 CHF Lookup table [Groeneveld, 2007], which requires tube diameter, mass flow rate, pressure, and quality as inputs. This calculation occurs at each node because many of these parameters will change at each node. The sodium heat transfer coefficient is calculated based on properties obtained from the outlet temperature and the Westinghouse correlation for liquid-metal, counterflow heat transfer in a tube bundle. ππ’ = 4 + 0.33 π/π 3.8 + π πππ/100 0.86 + 0.16 π/π 5.0 Eqn. 4-31 Based on conditions on the tube side, an appropriate heat transfer correlation will be chosen. When the water is still subcooled, the Dittus-Boelter correlation is used. The code identifies subcooled water by the wall temperature and the bulk fluid temperature. ππ»2π = 0.023π π0.8ππ0.4π/π Eqn. 4-32 and friction factors are given by the Blasius or McAdams correlation, according to the Reynolds number. π = 0.316π πβ0.25 , π΅πππ ππ’π ππππππππππ: π π < 30,000 0.184π πβ0.20 , πππ΄ππππ ππππππππ‘πππ: π π β₯ 30,000 Eqn. 4-33 The code assumes that, until saturation, all heat transfer to the water manifests as a temperature rise. This is valid on a bulk fluid basis, and since the total length of pipe is more interesting than the details of the flow, the assumption is used in SoSaT. Therefore, the temperature increase of the subcooled fluid is given by βπππ’ππ = ππ Eqn. 4-34 ππ»2πππ where dq represents the heat transferred in the node. The fluid reaches subcooled boiling when the wall temperature reaches a minimum value above the saturation temperature. This point is termed the onset of nucleate boiling. The temperature above which the wall must rise is given by 97PDF Image | Supercritical Carbon Dioxide Cycle Analysis
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