Multi-objective optimization and evaluation of supercritical CO₂ Brayton cycle for nuclear power generation

Abstract

The supercritical CO₂ Brayton cycle is considered a promising energy conversion system for Generation IV reactors for its simple layout, compact structure, and high cycle efficiency. Mathematical models of four Brayton cycle layouts are developed in this study for different reactors to reduce the cost and increase the thermohydraulic performance of nuclear power generation to promote the commercialization of nuclear energy. Parametric analysis, multi-objective optimizations, and four decision-making methods are applied to obtain each Brayton scheme’s optimal thermohydraulic and economic indexes. Results show that for the same design thermal power scale of reactors, the higher the core’s exit temperature, the better the Brayton cycle’s thermo-economic performance. Among the four-cycle layouts, the recompression cycle (RC) has the best overall performance, followed by the simple recuperation cycle (SR) and the intercooling cycle (IC), and the worst is the reheating cycle (RH). However, RH has the lowest total cost of investment (C_tot) of $1619.85 million, and IC has the lowest levelized cost of energy (LCOE) of 0.012 $/(kWh). The nuclear Brayton cycle system’s overall performance has been improved due to optimization. The performance of the molten salt reactor combined with the intercooling cycle (MSR-IC) scheme has the greatest improvement, with the net output power (W_net), thermal efficiency η_t, and exergy efficiency (η_e) improved by 8.58%, 8.58%, and 11.21%, respectively. The performance of the lead-cooled fast reactor combined with the simple recuperation cycle scheme was optimized to increase C_tot by 27.78%. In comparison, the internal rate of return (IRR) increased by only 7.8%, which is not friendly to investors with limited funds. For the nuclear Brayton cycle, the molten salt reactor combined with the recompression cycle scheme should receive priority, and the gas-cooled fast reactor combined with the reheating cycle scheme should be considered carefully.

Appendix: Nusselt number and friction factor calculation

For the semi-circular straight channel PCHE, the Nussle number is calculated by the Gnielinski correlation [44]. The Nussle number in Eq. (13) is calculated by Eqs. (A1)–(A3).

$${{Nu}} = 4.089\,\left( {{{Re}} < 2300} \right)$$

(A1)

$${{Nu}} = 4.089 + \frac{{{{Nu}}_{{{{Re}} = 5000}} - 4.089}}{5000 - 2300}\left( {{{Re}} - 2300} \right)\,\,\left( {2300 \leqslant {{Re}} < 5000} \right)$$

(A2)

$${{Nu}} = \frac{{\left( {f_{{\text{d}}} /8} \right)\left( {{{Re}} - 1000} \right){{Pr}}}}{{1 + 12.7\left( {{{Pr}}^{2/3} - 1} \right)\sqrt {f_{{\text{d}}} /8} }}\,\,\left( {{{Re}} \geqslant 5000} \right)$$

(A3)

$$f_{{\text{d}}} = \left( {\frac{1}{{1.8\log_{10} \left( {{{Re}}} \right) - 1.5}}} \right)^{2}$$

(A4)

The friction factor (f) used for the Darcy–Weisbach equation [Eq. (16)] depends on the relative roughness of the channels [Eq. (A5)] and the Reynolds number. The Reynolds number from laminar to turbulent flow is calculated by Eqs. (A6)–(A9).

$$\delta = \frac{\varepsilon }{d}$$

(A5)

$${{Re}}_{0} = \left\{ {\begin{array}{*{20}c} {2000,} & {\delta < 0.007} \\ {754\exp \left( {0.0065/\delta } \right),} & {\delta \ge 0.007} \\ \end{array} } \right.$$

(A6)

$${{Re}}_{1} = \left\{ {\begin{array}{*{20}c} {2000,} & {\delta < 0.007} \\ {1160\left( {1/\delta } \right)^{0.11} ,} & {\delta \ge 0.007} \\ \end{array} } \right.$$

(A7)

$${{Re}}_{2} = 2090\left( {1/\delta } \right)^{0.0635}$$

(A8)

$${{Re}}_{3} = 441.19\delta^{ - 1.1772}$$

(A9)

The friction factor (f) in Eq. (16) is calculated by Eq. (35) [45].

$$f = \frac{64}{{Re}}\,\,(Re < Re_{0} )$$

(A10)

$$f = \left\{ {\begin{array}{*{20}c} {0.032 + 3.895 \times 10^{ - 7} \left( {{{Re}} - 2000} \right),} & {\delta_{{\text{rel }}} < 0.007} \\ {4.4{{Re}}^{ - 0.595} \exp \left( { - 0.00275/\delta_{{\text{rel }}} } \right),} & {\delta_{{\text{rel }}} \ge 0.007} \\ \end{array} } \right.\,\,\,\left( {{{Re}}_{\text{0}} < {{Re}} < {{Re}}_{\text{1}} } \right)$$

(A11)

When Re₁ > Re > Re₂, the f is obtained from Eq. (A12), where f₁ is obtained from the formula given by Idelchik [46], as shown in Eq. (A13). The Colebrook–White correlation [44] is used to calculate f_i, and f_n is calculated by iteration. When the error between f_i and f_n is less than 0.01, it can be assumed that f_i = f_n. Eqs. (A16)–(A19) use the same calculation method.

$$f = \left( {f_{2} - f_{1} } \right)\exp \left\{ { - \left[ {0.0017\left( {{{Re}}_{2} - {{Re}}} \right)} \right]^{2} } \right\} + f_{1}$$

(A12)

$$f_{1} = \left\{ {\begin{array}{*{20}c} {0.032,} & {\delta < 0.007} \\ {0.075 - \left( {\frac{0.0109}{{\delta_{ \, } 0.286}}} \right),} & {\delta \ge 0.007} \\ \end{array} } \right.$$

(A13)

$$f_{i} = 0.11\left( {\delta + 68/{{Re}}_{2} } \right)^{0.25}$$

(A14)

$$f_{n} = \left[ {\frac{1}{{2\log_{10} \left( {\frac{2.51}{{{{Re}}_{2} \sqrt {f_{{\text{i}}} } }} + \frac{\delta }{3.7}} \right)}}} \right]^{2}$$

(A15)

When ${{Re}}_{2} < {{Re}} < {{Re}}_{3}$

$$f_{i} = 0.11\left( {\delta + 68/{{Re}}_{2} } \right)^{0.25}$$

(A16)

$$f_{n} = \left[ {\frac{1}{{2\log_{10} \left( {\frac{2.51}{{{{Re}}\sqrt f_{i} }} + \frac{\delta }{3.7}} \right)}}} \right]^{2}$$

(A17)

When ${{Re}} > {{Re}}_{3}$

$$f_{i} = 0.11\left( {\delta + 68/{{Re}}_{3} } \right)^{0.25}$$

(A18)

$$f_{n} = \left[ {\frac{1}{{2\log_{10} \left( {\frac{2.51}{{{{Re}}_{3} \sqrt {f_{i} } }} + \frac{\delta }{3.7}} \right)}}} \right]^{2}$$

(A19)

For more information on the above equations, it is recommended to refer to the references cited in Appendix.