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For a P-IHX, with sodium on the tube side, the heat transfer coefficient is given by ððĒðð,ðĄðĒðð = 6.3 + 0.0167ð ð0.85ðð0.93 Eqn. 4-28 for upward flow of sodium in tubes [Mills, 1995]. For S-CO2 flow on the tube side, Kim et al. [2008] have modified the Jackson and Fewster correlation for supercritical pressures in smooth tubes. Given that the operating pressure of S-IHXs will be much higher than the critical pressure of 7.377 MPa, the correlation can be used to produce a Nusselt number that applies to the entire heat exchanger once the Reynolds and Prandtl numbers are obtained from average properties at the inlet and outlet. Kim et al. [2008] determine the S-CO2 Nusselt number to be ððĒ = 0.0182ð ð0.824 ðð0.515 ððĪððð 0.299 Eqn. 4-29 ðððĒðð For enhanced tubes, the Ravigurarajan and Bergles correlation is used to determine the heat transfer coefficient [Ravigurarajan and Bergles, 1996]. The enhancements consist of spiral ribs on the interior of the tubes. Pressure drops are increased, but the heat transfer can be vastly improved, saving a great deal in terms of the size of the heat exchanger. The Ravigurarajan and Bergles correlations for heat transfer and pressure drop are excluded here due to their length, but they can be found in Appendix D. In all designs discussed hence, enhanced tubes are assumed to be used for CO2 only. The experiments used to develop enhanced tube correlations were conducted with air and single-phase water, so other fluids are assumed to be outside the range of validity of their correlations. With the average heat transfer coefficients determined for the two fluids, the overall heat transfer coefficient can be calculated. For sodium-sodium heat exchangers, single-wall tubes are appropriate, but to ensure a leak detection capability and increase the robustness of S-IHXs, double-walled tubes are assumed to be required in a sodium-CO2 or a sodium-water heat exchanger. The work of Kubo et al. [1997] produced results for the effective thermal conductivity of a 9Cr-1Mo double-walled steam generator tube. Using this data, and a thermal conductivity of 9Cr-1Mo steel of 27.9 W/mK [Williams et al., 1984] the value of the effective gap conductivity was determined to be 293.0 mW/mK. This value for effective helium gap conductivity has been used in SoSaT so that the user may define a double-walled tube of any wall thickness and any material. It should be noted that the experiments of Kubo et al. were conducted for a beginning of life (BOL) gap thicknesses of 3 Ξm and the end of life (EOL) gap thickness was measured to be ~7 Ξm. Comparison of the calculated value of gap conductivity with the conductivity of helium at 400 oC and 0.90 MPa, the 94PDF Image | Supercritical Carbon Dioxide Cycle Analysis
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