Keywords

1 Introduction

In the traditional nuclear reactor, the Rankine steam cycle is used in the energy conversion system. Because the reactor can only provide saturated steam at about 320 ℃, it can not provide superheated steam at a higher temperature to meet the need of Rankine cycle to improve efficiency, so the efficiency is relatively low. The lead-cooled fast reactor gas turbine cycle combines the gas turbine with the modular lead-cooled fast reactor, and uses the high-temperature gas generated by the lead- cooled fast reactor to directly drive the gas turbine to do work for high-efficiency power generation. It can break through the temperature limit of the steam cycle, and use intermediate cooling and regenerative technologies to improve efficiency, thus becoming an important direction for the study of high-efficiency power generation of the lead-cooled fast reactor.

The earliest gas-cooled reactor power cycle device combined with helium turbine began to develop in the late 1960’s. From 1968 to 1981, Germany cooperated with the United States and Switzerland to complete the HHT (HTR with helium turbine) experimental program for the helium turbine power conversion system [1]. The purpose of the plan was to study the technology of high temperature gas-cooled reactor power generation with helium turbine, including turbine, compressor, hot gas duct, materials, heat exchanger and other component technologies.

In the early 1990’s, with the support of the U.S. Department of energy, MIT carried out the research on modular high temperature gas-cooled reactor (MGR) helium turbine cycle power plant [2], and proposed two technical schemes, namely direct helium turbine cycle scheme (MGR-GT) and indirect helium turbine cycle scheme (MGR-GTI). Necsa of South Africa has carried out research on PBWR of pebble bed modular high temperature gas-cooled reactor [3]. PBWR adopts standard Brayton cycle with closed water-cooled precooler and intercooler. The United States and Russia cooperated in the research of GT-MHR [4] and adopted the design of closed Brayton cycle power conversion system.

In recent years, foreign scholars have carried out a lot of theoretical research on the scheme and system characteristics of helium turbine cycle system [5,6,7,8,9,10,12]. Professor Wang Jie from the Institute of nuclear energy technology design and research, Tsinghua University, China [13,14,15] respectively carried out thermodynamic analysis and optimization calculation for the direct helium cycle, open air cycle and indirect nitrogen cycle of the high temperature gas-cooled reactor, and carried out aerodynamic design for the turbine compressor. The results show that helium direct circulation is an ideal choice, but it is difficult based on the existing technical level. The closed indirect circulation of helium or nitrogen is a relatively realistic scheme at present, which can realize the idea of gas turbine circulation and accumulate technology for the direct circulation in the future. State power corporation research institute are carrying out the research on 100 MW lead-cooled fast reactor (BLESS-D) to meet the public's demand for a safer, more economical and more environmentally friendly nuclear power system [16,17,18,19]. It is a pool-style reactor with LBE (lead and bismuth eutectic alloy) as the coolant. It is mainly used to study the key problems and technologies of lead cooled fast reactor, verify and demonstrate relevant solutions. Among, The thermal power cycle system adopts different working fluid scheme, such as water, supercritical carbon dioxide, Helium.

In this paper, the thermodynamic calculation of helium re-compression Brayton cycle is carried out for 100 MWt lead-cooled fast reactor. The effects of core outlet temperature, turbine outlet pressure, high-pressure compressor outlet pressure, low pressure compressor outlet pressure and recuperator outlet temperature on thermal efficiency of the system are analyzed. The design parameters of helium re-compression Brayton cycle for 100 MWt lead-cooled fast reactor are optimized, which can provide an important theoretical reference for the design of power cycle system of lead-cooled fast reactor.

2 Helium Brayton Cycle Introduction

2.1 Thermophysical Properties of Helium

Table  1 shows the comparison of thermophysical properties between helium and other working fluids under standard conditions. It can be seen from Table 1 that, compared with other working fluids, helium has the following physical properties: strong thermal conductivity, large specific heat, small gas density and large is entricity index.

The effects of these special thermophysical properties of helium on the helium Brayton cycle are as follows:

  1. (1)

    The gas density is small, so a high circulating pressure is required to increase its density;

  2. (2)

    The isentropic index is large, so under the same temperature difference, the pressure ratio is small, so it is difficult to compress;

  3. (3)

    The specific heat is large, so under the same temperature difference, the cycle specific work is large, and the expansion work of the turbine and the compression work of the compressor are larger than those of other gases.

Helium is very close to ideal gas in the range of 0–1000 ℃, 0.1–10 MPa, and its specific heat and adiabatic index are almost constant. Compared with air, helium has a higher specific heat (about 5 times that of air), so the compression ratio of helium is small under the same temperature difference, and the mass flow of helium is small under the same output power. Helium also has good heat transfer characteristics and small friction characteristics, which is conducive to improve the efficiency of the heat exchanger and reduce the volume of the heat exchanger.

Table 1. THE COMPARISON OF THERMO PHYSICAL PROPERTIES BETWEEN HELIUM AND OTHER WORKING FLUIDS (1ATM, 0 ℃)
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2.2 Helium Closed Re-compression Brayton Cycle Process

There are many specific circulation modes in the helium turbine circulation scheme. From the point of view of improving power generation efficiency, helium turbine direct circulation is an ideal choice. In other words, the high-temperature and high-pressure gas produced by the reactor core is used to directly drive the turbine to generate electricity.

Figure 1 shows the flow chart of helium closed re-compression Brayton cycle [14] which is the scheme to realize the direct cycle of helium turbine. This cycle scheme adopts recuperator and intermediate cooling of gas flow in the process of compression to improve thermal efficiency of the system. The system is composed of turbine, recuperator, high-pressure compressor, low-pressure compressor, intercooler, precooler, generator and corresponding pipelines.

The working process is as follows: 1-2a refers to the isentropic compression process of low-temperature and low-pressure helium in the low-pressure compressor; 2a-2b refers to the constant pressure heat release process of helium in the intercooler (ICL); 2b-2 refers to the isentropic compression process of cooled helium in the high-pressure compressor; 2–3 shows the heat absorption process of high pressure helium at the high pressure side of the recuperator (RPT); 3–4 refers to the constant pressure heat absorption process of high temperature and high pressure helium in the reactor; 4–5 refers to the isentropic expansion process of high-temperature helium in the turbine. The expansion work is used to drive the high-pressure compressor, low-pressure compressor and generator. 5–6 shows the constant pressure heat release process of helium at the low pressure side of the recuperator (RPT). 6–1 shows the constant pressure heat release process of cooled helium in the precooler (PCL). Finally, the low-temperature and low-pressure helium enters the low-pressure compressor for isentropic compression to complete the whole cycle.

Fig. 1.
figure 1

HELIUM BRAYTON CYCLE WITH RE-COMPRESSION

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3 Influence of Key Parameters on Thermal Efficiency of the System

The mathematical model of helium closed recompression Brayton cycle of 100 Wt lead cooled fast reactor is established by using MATLAB software. Thermal efficiency of the system is expressed by the following formula:

$$ \eta = f(\tau ,\gamma ,\overline{\theta ,} \, \overline{\eta }_{{\text{c}}} $$

where, \(\tau\) refers to the circulating temperature ratio which is the ratio of the absolute temperature of the high-temperature heat source to the low-temperature heat source of the system; \(\gamma\) refers to the circulating pressure ratio which is ratio of the inlet pressure to the outlet pressure of high-pressure compressor and low-pressure compressor; The physical property vector \(\overline{\theta }\) is composed of the ratio of the specific heat at constant pressure for the compression process and the endothermic process, the ratio of the specific heat at constant pressure for the expansion process and the endothermic process, and the isentropic index. For helium, the specific heat at constant pressure and specific heat at constant volume are constant, the ratio of specific heat at constant pressure is 1, and the isentropic index is 1.67. Component efficiency vector is composed of recuperator efficiency, turbine efficiency, compressor efficiency and pressure loss. Limited by today's manufacturing level, after taking a group of reasonable values according to literature [13], as shown in Table 2, the component efficiency vector becomes a constant vector. The whole cycle is steady-state calculation. Therefore, thermal efficiency of the system is mainly determined by the circulating temperature ratio and circulating pressure ratio.

Table 2. COMPONENT EFFICIENCY AND RESSURE LOSS
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3.1 Influence of the Core Outlet Temperature

Figure 2 shows the influence of different core outlet temperature on the thermal efficiency of the system under the conditions of high-pressure compressor outlet pressure of 5.6 MPa, low-pressure compressor outlet pressure of 4.9 MPa and recuperator outlet temperature of 80 ℃. With the increase of core outlet temperature, thermal efficiency of the system increases. When the core outlet temperature increases from 400 ℃ to 500 ℃, thermal efficiency of the system increases by 86%. Therefore, under the conditions of reactor thermal conditions and core materials, increasing the core outlet temperature can increase the output power of the system.

Fig. 2.
figure 2

VARIATION OF THERMAL EFFICIENCY OF THE SYSTEM WITH CORE OUTLET TEMPERATURE

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3.2 Influence of the Turbine Outlet Pressure

Figure 3 shows the influence of turbine outlet pressure on thermal efficiency of the system under the conditions of high-pressure compressor outlet pressure of 5 MPa, reactor core outlet temperature of 400 ℃ and low-pressure compressor outlet pressure of 3.5 MPa. With the increase of the turbine outlet pressure, thermal efficiency of the system first increases and then decreases. The reason is that with the increases of turbine pressure, the power consumption of the low-pressure compressor decreasing and the net power of the system increasing. However, with the further increase of the pressure, the output power of the turbine decreases rapidly, resulting in the decrease of the net output power and the decrease of thermal efficiency of the system. That is, there is an optimal turbine outlet pressure, which well matches the turbine output power and compressor power consumption, so as to maximize thermal efficiency of the system.

Fig. 3.
figure 3

VARIATION OF THERMAL EFFICIENCY OF THE SYSTEM WITH TURBINE OUTLET PRESSURE

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3.3 Influence of the High-Pressure Compressor Outlet Pressure

Figure 4 shows the influence of high-pressure compressor outlet pressure on thermal efficiency of the system under the conditions of low-pressure compressor outlet pressure of 4.18 MPa, reactor core outlet temperature of 500 ℃ and recuperator outlet temperature of 142.5 ℃. With the increase of the high-pressure compressor outlet pressure, thermal efficiency of the system increases. Therefore, increasing the high-pressure compressor outlet pressure can improve thermal efficiency of the system, but subject to the current technical conditions, the high-pressure compressor outlet pressure is usually lower than 7 MPa.

Fig. 4.
figure 4

VARIATION OF THERMAL EFFICIENCY OF THE SYSTEM WITH HIGH-PRESSURE COMPRESSOR OUTLET PRESSURE

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3.4 Influence of the Low-Pressure Compressor Outlet Pressure

Figure 5 shows the influence of low-pressure compressor outlet pressure on thermal efficiency of the system under the conditions of high-pressure compressor outlet pressure of 5 MPa, reactor core outlet temperature of 400 ℃ and recuperator outlet temperature of 167.5 ℃. With the increase of low-pressure compressor outlet pressure, thermal efficiency of the system decreases. The reason is that the specific capacity at the inlet of the low-pressure compressor is large. Under the same pressure ratio, the compression work is much greater than that of the high-pressure compressor. At the beginning, with the increase of the low-pressure compressor outlet pressure, the power consumption of the low-pressure compressor increases relatively slowly, which is less than the power consumption reduced by the high-pressure compressor, resulting in the increase of thermal efficiency of the system. When the low-pressure compressor outlet pressure is continuously increased, although the power consumption of the high-pressure compressor decreases, the power consumption of the low-pressure compressor increases faster, resulting in the decline of thermal efficiency of the system.

Fig. 5.
figure 5

VARIATION OF THERMAL EFFICIENCY OF THE SYSTEM WITH LOW-PRESSURE COMPRESSOR OUTLET PRESSURE.

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3.5 Influence of the Recuperator Low-Pressure Side Outlet Temperature

Figure 6 shows the influence of the recuperator outlet temperature at low-pressure side on thermal efficiency of the system under the conditions of high-pressure compressor outlet pressure of 5.6 MPa, reactor core outlet temperature of 400 ℃ and low-pressure compressor outlet pressure of 4.9 MPa. With the increase of the recuperator outlet temperature at low-pressure side, thermal efficiency of the system decreases. The reason is that after the outlet temperature at low-pressure side increases, the regenerative degree of the recuperator decreases, the cooling capacity of the precooler increases, and the high-temperature heat generated by the compressor is not fully utilized, resulting in the increase of heat absorption of the system and the decrease of thermal efficiency of the system.

Fig. 6.
figure 6

VARIATION OF THERMAL EFFICIENCY OF THE SYSTEM WITH RECUPERATOR OUTLET TEMPERATURE AT LOW-PRESSURE SIDE

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To sum up, in order to improve the thermal efficiency of the helium Brayton cycle, the reactor core outlet temperature should be increased as much as possible, the design scheme of the recuperator should be reasonably optimized, the system regenerative efficiency should be increased, the compression ratio should be reasonably distributed in combination with the characteristics of the high and low pressure compressor, and the of the high pressure compressor outlet pressure should be increased as much as possible.

4 Optimization Results of He Closed Re-compression Brayton Cycle

Through the analysis of the influence of different key parameters on helium closed re-compression Brayton cycle, it can be concluded that the turbine inlet temperature can be taken as 400–600 ℃, the low-pressure compressor inlet temperature is taken as 35 ℃ for lead-cooled fast reactor. Considering that the maximum pressure limit of the system is 7.0 MPa, the high-pressure compressor outlet pressure is set as 5.0 MPa. Table 3 shows the optimization results of he closed re-compression Brayton cycle of lead-cooled fast reactor with thermal power of 100 MW under three different working conditions. Thermal efficiency of the system. When the core outlet temperature reaches 600 ℃,Thermal efficiency of the system reaches 34.8%.

Table 3. OPTIMIZATION RESULTS OF HE CLOSED RE-COMPRESSION BRAYTON CYCLE
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5 Conclusions

  1. (1)

    Thermal efficiency of helium re-compression Brayton cycle system increases with the increase of high-pressure compressor outlet pressure, increases with the increase of core outlet temperature, decreases with the increase of recuperator outlet temperature and increases first and then decreases with the increase of turbine outlet pressure.

  2. (2)

    The optimized parameters of helium re-compression Brayton cycle system of lead-cooled fast reactor with thermal power of 100 MW under three different core outlet temperatures are obtained, which provides an important theoretical reference for the design of power cycle system of lead-cooled fast reactor. When the core outlet temperature reaches 600 ℃, thermal efficiency of the system reaches 34.8%.

  3. (3)

    At present, the technical level of helium re-compression Brayton cycle still has some limitations. The research on the materials of helium turbine device, the deposition of radioactive products on turbine blades and the integrated layout are still need to be carried out in the future.