## 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 \({}^{\circ}\)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 \({}^{\circ}\)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.