1. Introduction
With the emphasis on environmental issues and carbon emission reduction, countries around the world are working to reduce the proportion of coal-fired cogeneration and actively develop new types of clean energy [
1]. As a form of energy with low pollution, low cost and controllability, nuclear energy is receiving widespread attention to meet the needs of low-carbon energy conservation [
2]. In order to achieve the sustainable development and improve the safety, reliability and economic competitiveness of nuclear energy, the Generation IV International Forum (GIF), organized by the US Department of Energy (DOE), is a collaboration with 12 other countries which has proposed six advanced Generation IV reactors after discussion and verification [
3]. Among the six most potential advanced reactor types, the lead-cooled fast reactor (LFR) has drawn much attention due to its unique advantages, including high safety, high fuel utilization, excellent neutron physical, thermal-hydraulic characteristics and economic efficiency [
4,
5,
6]. The lead-cooled fast reactor (LFR) adopts liquid lead or liquid lead-bismuth eutectic (LBE) as a core coolant. Due to higher core outlet temperature of the lead-based reactor (usually above 500 °C), the traditional steam Rankine cycle cannot meet the demand of a high power generation rate under high-temperature operation conditions [
4]. The supercritical carbon dioxide (SCO
2) power cycles have been put forward as a promising candidate with the main advantages of being high thermal efficiencies, a simple and compact physical footprint and good operational flexibility [
7,
8,
9]. Consequently, lead-cooled fast reactors coupled with a supercritical CO
2 power cycle are considered a highly competitive option and the most promising power conversion system for the miniaturization and modularization of advanced nuclear reactors.
As critical energy conversion equipment links the primary and secondary circuit in LFR, the primary heat exchanger (HE) is an important equipment which transfers heat from the core to the secondary heat transport system. When liquid lead and SCO
2 are employed as the working fluid in the primary heat exchanger (HE), the fluid flow and heat transfer characteristics are quite different from conventional coolants such as water and air. On the one hand, heavy metal fluids usually result in great loss of momentum and significant frictional pressure drop [
10]. Moreover, high viscosity also means an extremely low Prandtl number (much lower than 1), which makes the flow more likely to show laminar flow characteristics and a thermal boundary layer which will be much thicker than the flow boundary layer, which means that the role of molecular heat conduction in the entire heat transfer process is more significant. As a result, a considerable part of heat transfer correlations concluded from the conventional coolants such as water are no longer applicable to liquid metals [
3,
11]. On the other hand, the supercritical carbon dioxide (SCO
2) power cycle utilizes the characteristics of SCO
2 near the quasi-critical region and realizes the efficient and compact design of the secondary loop, which makes SCO
2 a better choice of coolant [
12,
13]. The pressure of a secondary loop is usually higher than 20 MPa, and the temperature of the primary circuit using lead as coolant normally exceeds 500 °C which is limited by the high melting point of lead. The safety and convenient maintenance of HE under long-term operation is a crucial problem under such high-temperature and high-pressure conditions. In addition, as the key energy conversion device, the heat transfer efficiency of the primary heat exchanger determines the inlet temperature of the turbine and further influences the overall efficiency of the nuclear energy system. Meanwhile, the pressure loss of the fluids through the HE is also an important issue and should be considered since the total pressure loss has a significant impact on flow distribution and heat transfer performance. Therefore, it is crucially important to optimize the flow and heat transfer characteristics of lead-SCO
2 in the primary heat exchanger.
With a mature theory, sufficient experimental studies and extensive industrial application experience, the shell-and-tube heat exchanger (STHE) has been widely used in different fields [
14,
15]. Moreover, the shell-and-tube heat exchanger is a considerable choice of HE among the existing reactors including LFR [
16,
17]. Consequently, STHE is an available type of HE with liquid lead and SCO
2 as a working medium. In response to the dramatic changes in the physical properties of SCO
2 with temperature, the subsection model is used to simulate the variation in physical properties in the design of SCO
2 [
18]. Some heat transfer enhancement methods used for the conventional fluids such as conventional segmental baffles may not be suitable choices, because this will lead to vast dead zones and increase the risk of liquid metal solidification [
10]. Straight tube HE is recommended for the safety and miniaturization of the system design of LFR [
19].
In addition to the design of a heat exchanger, the optimization of its performance is another important work. In recent years, the emergence of various intelligent optimization algorithms provides a powerful tool for the optimization of a heat exchanger. In the past decade, the genetic algorithm is definitely a competitive intelligent algorithm. It is widely used in the optimization of various thermal equipment and systems [
20,
21] and compared with other algorithms [
22,
23].
In the optimization process of the genetic algorithm, there is commonly single or multi-objective functions to evaluate the optimization results. Some researchers focus on the efficiency, pressure drop, heat transfer area and other thermodynamic parameters of HE [
24], whilst others consider the cost and economy of HE [
25], and some researchers take the entropy generation and exergy based on the second law of thermodynamics as the objective function. Furthermore, many researchers ensure comprehensive consideration on the design of HE through the combination of different perspectives [
26,
27]. Maida et al. [
28] took the ecological function and cost as the objective function, used the non-dominated sorting genetic algorithm II (NSGA-II) to optimize the shell and tube heat exchanger and obtained the Pareto solution set. Song and Cui [
29] carried out single/multi-objective optimization on the plate fin heat exchanger with the entropy production and operation cost as the objective functions, and optimized the comprehensive performance of the heat exchanger. The result of multi-objective optimization provides a flexible solution for practical production.
Specifically, some researchers also used genetic algorithm to optimize the design of a heat exchanger or energy system with SCO
2 or liquid metal as a working medium. Li et al. [
30] carried out the multi-objective optimization of LFR system with thermoelectric conversion efficiency and a power generation cost as objective functions, improved the overall economy of the system and obtained the optimal geometric parameters of the intermediate heat exchanger. Fan et al. [
31] proposed a CCHP system combined with a SCO
2 cycle, took a unit cost and efficiency as the objective functions and carried out multi-objective optimization using NSGA-II to obtain the best design performance of the system. The exergy efficiency is improved and the unit cost of the system is reduced after optimization. The temperature of the coal-fired power plant was optimized by Liu et al. [
32] in order to improve the efficiency and the best temperatures of the cold end and hot end were obtained. Saeed and Kim [
33] used the genetic algorithm to optimize the geometric structure of printed circuit heat exchanger with SCO
2 as a working medium and improve the hydraulic performance of the heat exchanger. To sum up, the genetic algorithm has been widely used in the design process of a heat exchanger, even with the working medium of SCO
2. However, for the design requirement of a primary heat exchanger in LFR where liquid lead and supercritical carbon dioxide (SCO
2) are employed as the working fluids on heat-side and cold-side of HE, respectively, only a few studies have been conducted.
In the present study, the genetic algorithm and NSGA-II are employed to carry out an optimization design for the primary heat exchanger (HE) in a lead-cooled fast reactor (LFR). A preliminary model of HE is first theoretically calculated by the subsection model based on equal heat transfer power, and then an optimization design of HE is conducted based on genetic algorithm with an entropy generation number and total pumping power as the objective functions. During the optimization process, the flow and heat transfer performance of the heat exchanger are evaluated. Then, numerical simulation based on Ansys-Fluent software is also conducted to study the flow and heat transfer performances of working fluids in the optimized heat exchanger.