Performance analysis of CBC-TEG power generation scheme with sintered lunar regolith heat storage for full-day continuous power supply to moonbase

Abstract

The continuous supply of electrical energy full-day has now become the biggest problem in establishing a moonbase. The closed Brayton cycle (CBC) coupled with thermoelectric generator (TEG) can effectively is proposed in this paper to solve this issue. The functions of the two power generation systems are different: CBC is for high power generation and TEG provides energy at nighttime or when solar energy is insufficient. After the study of full-day performance, it is concluded that CBC thermal efficiency gets 31.4% as the time advanced to lunar noon. Using TEG with CBC thermal efficiency below 0, the maximum energy conversion efficiency and power output of TEG are 0.67%, 1.8 kW, respectively. In the lunar nighttime, CBC working hours are directly affected by the flow rate. With limited mass TSUs, higher flow rate represents higher thermal energy consumption, and the power generation capacity of CBCs gradually diminishes. In addition, increasing the number of TEG stages has a directly effect on weight. The difference in weight between 1-stage and 4-stage is 4 times. CBC-TEG can solve the problem of continuous energy supply full-day, but parameters such as the operating flow rate and TEG stage number need to be selected according to practice needs.

Graphical abstract

Keywords

Closed Brayton cycle / thermoelectric generator / moonbase / thermal efficiency / power output

1 Introduction

Humans have been longing for planets such as the Moon and Mars for thousands of years. With the excessive consumption of resources on the Earth, the future of mankind will inevitably go to deep space. As the closest planet to the Earth, the Moon should be the 1st stop for human deep-space sciecntific exploration, and its importance cannot be overemphasized, both as a testing ground for human exploration of deep space and as a staging ground for deep space exploration (Zhang et al., 2022). In recent years, the world’s space powers have developed a series of plans for the exploration of deep space, the US Artemis plan states that 2025 will send two astronauts to the moon and stationed for two weeks, which will be a good basis for the feasibility of astronauts to land on Mars (Evans and Graham, 2020; Spedding et al., 2020). Russia also plans a manned mission to the moon in 2030, and bulid a complete habitable moonbase in 2035. Besides, Russia has launched the International Lunar Research Station (ILRS) project with China (Xu and Ou, 2023).

It is easy to see from the lunar exploration plans that the focus has shifted from manned lunar landings to the construction of permanently habitable bases on the Moon. However, there are many challenges in the construction of a moonbase, such as carbon, hydrogen, and oxygen cycles, construction materials, satellite navigation, and electronic information transmission, and so on. More importantly, energy supply is the basis of lunar construction. And with the input of electric energy, key technologies such as building materials production and information transmission can be realized.

At present, the energy generation technologies of the Moon mainly include photovoltaic (PV) power generation technology, thermoelectric power generation technology, and thermodynamic cycle system. PV power generation technology is a relatively mature and common power generation technology in space. PV panels convert light energy into electricity, and their conversion efficiency can reach 20%, especially gallium arsenide PV panels, and the conversion efficiency is increased to 30% (Hu et al., 2021a). However, on the backlight side, PV panels are difficult to generate electricity and are largely limited. In addition, photovoltaic panels are a kind of outdoor power generation equipment, the attachment of moon dust inevitably reduces the power generation effect (Pan et al., 2022). When left unmaintained, it is bound to cause difficulties in energy supply. Nowadays, the main task of the moonbase energy system is to work continuously throughout the day, and it is obvious that the PV system cannot be the core equipment for the generation of electricity on the Moon base (Li et al., 2023).

For thermoelectric generators (TEG), it is widely used in space. In the study of Liu et al. (2023a), they explored the use of heat pipe based TEG on the Moon, with solar energy and thermal storage material as the heat source and thermal storage material and deep space as the cold source for lunar daytime and nighttime, respectively. This system can achieve continuous daytime and nighttime power supply to the Moon, as well as a 6.5% efficiency. A number of radioisotope TEG models have been created, reaching the energy conversion efficiency of 6.7% (Bennett et al., 2008). USA engineers were getting ready to deploy cobalt-based TEGs as thermoelectric convert equipments for cutting-edge radioisotope power systems in order to boost TEG performance (Blessing et al., 2004). In many cases, other power generation systems can be combined with TEG to generate power, such as PV panels, organic Ranine cycle (ORC), etc. In Lou’s study (Lou et al., 2023), the ORC was combined with TEG to generate electricity. ORC thermal efficiency can reach 9% by using the groundwater supply and return water as the drive sources to operate ORC-TEG system. Mehdi et al. performed a 5E analysis of PV combined with TEG power generation system (Alian et al., 2022). With TEG, the efficiency of the system can reach 16.73%. And the combined system’s specific carbon mitigation is reduced to 1.42 ton/(yr∙m²). In general, the efficiency of TEGs is relatively low (SiGe based TEG reaches 12%) (Singh et al., 2018; Makki et al., 2016), TEGs can be combined with a variety of power generation systems to meet different needs.

As for the thermodynamic cycle, the main systems include closed Brayton system (CBC), ORC, Stirling power system, etc. CBC is a very widely used power generation system. In the study of Cheng et al. (2019), CBC is used in aircraft engines where the fuel is used as the cooling source and the combustion chamber wall coolant is the thermal fluid that drives the CBC to generate electrical energy. Similarly, Dang et al. (2023) taked low-temperature fuel and high-temperature fuel vapor as cold and heat source. This heat source is used to drive the CBC and fuel vapor turbine to generate electricity, which further enhances the electrical energy generation. Biondi and Toro (2019) proposed a CBC system for use in space and developed the corresponding numerical model. By enhancing the performance of the turbine blade material, the whole system is expected to reach a performance target of 30 kg/kW. Romano’s research focused on the heat removal from the space CBC system (Romano and Ribeiro, 2020). By optimizing this system, the optimal working temperature of the heat pipe on the cold source side was obtained between 450 and 500 K. Based on this operating range, a heat pipe made of titanium-water with a rectangular slot was selected as the wick structure. In summary, the CBC can achieve power generation at the megawatt level, with a simple structure, compact equipment, and potential for use in space (Ma et al., 2021). ORC is generally used in conjunction with other power generation systems, examples include CBC (Liu et al., 2022; Garcia, 2012; Yang et al., 2020; Sun et al., 2024), heat pump (Weitzer et al., 2022; Eppinger et al., 2020; Bellos and Tzivanidis, 2017), TEG (Lou et al., 2023; Ji et al., 2023; Lan et al., 2023), refrigeration system (Malwe et al., 2022; Ashwni and Sherwani, 2022; Mohtaram et al., 2022; Xia et al., 2023) and fuel cell (Baronci et al., 2015), etc. As for the Stirling power generation system, there are also many applications in space. In the the study of Hu et al. (2021a), they used the compacted lunar regolith heat storage to provide nighttime heat for the Stirling system, achieving a continuous day and night supply with an average power generation of 6.8 kW. And they also analyzed the compacted lunar regolith heat storage system to arrive at a reasonable stacking method (Hu et al., 2021b). However, Stirling generators are less airtight and and have low power generation per unit, Stirling power system is not a good choice when high power is required.

The use of CBC in space has received a lot of attention. However, the concern is that it is a high temperature power generation system. For variable temperature heat sources, it is difficult for CBC to generate electricity at all operating points, so a medium to low temperature power generation device needs to be coupled to complete continuous power generation. In the study of lunar energy system, solar radiation is exactly this variable operating heat source, then CBC is needed as the main power generation cycle and ORC as the bottom cycle (Liu et al., 2022). However, this approach results in excessive retrofitting costs for CBC. More critically, ORC also requires a certain temperature difference between the cold and hot sources, and it is not reasonable to apply ORC in the dawn phase of the Moon. Therefore, adding ORC cannot achieve a full cycle of one lunar day operation. It is extremely urgent to find a reasonable medium and low temperature power generation system to modify the CBC system at a minimum. With this need, this paper uses TEG as a medium and low temperature power generation system for the moonbase. Compared with ORC, lightness, economy, and reliability of TEG will be significantly improved. Closed brayton cycle- thermoelectric generator (CBC-TEG) connect the TEG to the gas cooler (GC). TEG has two functions in the CBC-TEG system: 1) when the heat source temperature is low, TEG can be used to extract heat directly to generate electricity; 2) when the heat source temperature is high, the waste heat from the CBC can be recovered. Addition of TEG is expected to obtain a continuous supply of energy with minimal modification.

Section 2, a mathematical model of moonbase power generation system (CBC-TEG) is described. Section 3, power output, operating intervals, and efficiency of the CBC-TEG all day are discussed in detail, as well as the influences of differen working parameters on the power generation performance.

2 Mathematical modeling

CBC-TEG is an energy system that generates electricity continuously (Fig. 1). The whole system consists of collector, heat storage unit (HSU), turbine, regenerator (REG), GC, compressor and TEG. The collector collects solar energy during the lunar day to raise the temperature of the CBC medium (7–1) before it flows into the turbine to produce energy (1–2). The exhaust gas passing through the turbine enters the REG (2–3) to decrease the temperature again, enabling the cascade utilization of energy. After this, the medium enters the GC (3–4), which radiates heat to deep space to cool down again. Combined with TEG on the GC, the temperature of hot temperature fluid and deep space can be used to generate electricity. Finally, compressor boosts the pressure of CBC medium (5–6) and then enters REG (6–7), where the temperature is raised. It should be noted that t solar radiation is extremely weak in the early morning, it is not appropriate to use CBC power generation system at this time. Using the GC that connects the TEG for power generation, the heated CBC medium goes directly to the GC. Different levels of thermal energy correspond to different modes of power generation.

CBC system is the same during the lunar nighttime, the only difference is the heat source. In the lunar nightime, the CBC is operated using the HSU as the drive energy source. Thermal energy is transferred to the moonbase cabin through the post-GC CBC medium. When the temperature of HSU is reduced to a certain level, the TEG on the GC is directly driven to generate electricity instead of CBC.

2.1 CBC system model description

2.1.1 HSU

HSU is the key to support the continuous operation of the power generation system during the lunar nighttime. In this paper, sintered lunar regolith is considered as a heat storage material (Table 1). The following equations represent the process of heat absorption and heat release (Liu et al., 2022; Liu et al., 2023b):

(1)\text{Night}Q=MC{p}_{\text{re}}(T_s-T_s^{\ast }),

(2)\text{Day}Q=MC{p}_{\text{re}}(T_s^{\ast }-T_s),

where T_s and T_s^{\ast } stand for the HSU starting temperature and the temperature of the following time step. M and Cp_re represent the sintered lunar regolith’s mass and specific heat capacity.

2.1.2 Turbine

In a turbine, CBC meidum expands in a roughly adiabatic manner. The medium pressure and enthalpy fall. The compression pressure ratio and cyclic pressure loss both set a limit on the turbine’s expansion rate. The following equation can be generated using the gas state equation (Naserian et al., 2017):

(3)\frac{T_1}{T_{\text{2s}}}={\left(\frac{p_1}{p_2}\right)}^{{\phi }_{1-2}},

(4){\phi }_{1-2}=\frac{k-1}{k},

where the average gas adiabatic coefficient in the 1–2 process is φ_1–2. The adiabatic coefficient of processes 1–2 is denoted by k. The ratio of the working medium actual expansion work to the turbine’s ideal expansion work is known as the turbine efficiency:

(5){\eta }_{\text{tur}}=\frac{H_1-H_2}{H_1-H_{2s}}=\frac{1}{c_{1-2}}\frac{T_1-T_2}{T_1-T_{2s}}.

The turbine exit temperature can be obtained by combining Eqs. (4) and (5). The work capacity of the turbine is calculated using Eq. (6):

(6)W_{\text{tur}}=\dot{m}{\overline{Cp}}_{1-2}\left(T_1-T_2\right).

Since the calculation methods of turbine and compressor are relatively similar, this paper doesn’t elaborate too much on the calculation process of the compressor.

2.1.3 Heat exchanger

The CBC-TEG system’s energy balance equation, whose principal application for heat exchangers is the REG, is presented below (Dai et al., 2019):

(7)\begin{array}{rl}{Q}_{\text{HEX}}=& \dot{m}{\overline{Cp}}_{\text{2}}\left(T_2-T_3\right)=\\ & \dot{m}{\overline{Cp}}_{\text{6function(){ return this.textTemplate; }7}}(T_7-T_6).\end{array}

2.1.4 Gas cooler

The GC discharges the heat from the exhaust gas while using deep space as a cooling source. The governing equations are defined by

(8)Q_{\text{rad}}=\sigma \epsilon A_{\text{rad}}(T_{\text{ra}}^4-T_{\text{amb}}^4)+P_{\text{TEG}}=h_{\mathrm{f}}{A}_{\text{rad}}(T_{\mathrm{f}}-T_{\mathrm{w}}),

where T_amb, T_w, and T_f are the deep space temperature, wall of GC, and CBC medium. h_f is the heat transfer coefficient of fluid in the GC channel. The detailed calculation process will be described in the following sections. CBC operating parameters are dispicted in Table 2.

2.1.5 Regenerator

In a thermodynamic cycle system, the REG plays a great role in recovering heat and increasing the fluid temperature. In the REG of CBC, its efficiency ε_REG is 0.9 (Glover et al., 2015). The governing equation of REG in CBC is

(9){\epsilon }_{\text{CBC,REG}}=\frac{h_7-h_6}{h_2-h_6}.

2.1.6 Working medium

Helium-xenon mixture (He-Xe) has good thermodynamic properties in power generation systems and are suitable for use in the space. Compared to supercritical carbon dioxide, He-Xe can provide higher power generation at a low pressure. The calculation method of the physical parameters of He-Xe can be found in (Dragunov et al., 2013; Xu et al., 2021; Malik et al., 2019).

2.2 TEG system model description

The energy transfer of GC is dispicted in Fig. 2. The temperature difference between high-temperature fluid in the GC channel and deep space is used as a driving energy source to make TEG power generation. CBC medium transfers heat to the channel wall. Then, the heat on the channel wall is transferred to each stage through heat conduction. Finally, the heat is radiated to the deep space through the radiating wall surface.

Using the idea of finite difference, the GC is divided into multiple control bodies along the medium flow direction. Energy equation of each control body is

(10)Q=h_{i,\text{f}}{A}_i\left(\overline{T_i}-T_{i,\text{wall}}\right),

(11)\overline{T_i}=\frac{T_{i,\text{in}}+T_{i,\text{out}}}{2}.

Among them, h_i,f, T_i,wall, \overline{T_i}, and A_i respresent convection heat transfer coefficient, GC channel wall temperature, temperature control, and heat exchange area, respectively.

The amount of heat transfer between the ceramic sheet and the hot end of the 1st TEG is equal to the thermal conductivity of the CBC high temperature fluid to the channel wall:

(12)Q=K_{\text{copper}}\left(T_{i,\text{wall}}-T_{\text{1,h}}\right),

where K_copper is the conductivity of the GC wall, as Eq. (13). T_i,wall and T_1,h are heat collector plate temperature and the first stage TEG high-temperature node temperature:

(13)K_{\text{copper}}=\frac{k_{\text{copper}}{A}_i}{{\theta }_{\text{copper}}}.

Among them, k_copper, A_i and θ_copper are conductivity, area, and thickness of GC wall, respectively.

The energy equation at the hot end of the 1st TEG can be expressed as (Singh et al., 2018)

(14)Q_i=S_{i,\text{h}}^{1}I{T}_{i,\text{h}}^1-0.5I^2{R}_{i,\text{in}}^1+K_{i,\text{pn}}^1\left(T_{i,\text{h}}^1-T_{i,\text{c}}^1\right),

(15)S_{i,\text{h}}^1={\alpha }_{i,\text{h}}^1-{\alpha }_{i,\text{c}}^1.

Among them, S_{i,\text{h}}^1, K_{i,\text{pn}}^1, R_{i,\text{in}}^1, and Q_i stand for the first stage TEG couple’s Seebeck coefficient, thermal conductivity, internal resistance, and the heat transferred to GC wall from CBC medium, respectively. The first stage TEG’s low-temperature node temperature is represented by T_{i,c}^1.

Seebeck coefficient of P, N elements are α_1,p and α_1,n, respectively. They can be defined by

(16)R_{\text{in}}=\frac{l_p}{{\sigma }_p{A}_p}+\frac{l_n}{{\sigma }_n{A}_n},

(17)K_{\text{pn}}=\frac{k_p{A}_p}{l_p}+\frac{k_n{A}_n}{l_n},

where A, k, σ, and l represent the area, thermal conductivity, resistivity, and length of the thermoelectric leg, respectively. P and N elements of TEG are indicated by the subscripts p and n, respectively.

The 1st stage low-temperature junction’s energy equilibrium equation is shown below:

(18)S_{i,\text{h}}^{1}I{T}_{i,\text{c}}^1+0.5I^2{R}_i^1+K_{i,\text{pn}}^1\left(T_{i,\text{h}}^1-T_{i,\text{c}}^1\right)=K_C^2\left(T_{i,\text{c}}^1-T_{i,\text{h}}^2\right).

The energy equation of the radiating wall of GC is

(19)K_{\text{ra}}\left(T_{i,\text{c}}^{\mathrm{J}}-T_{\text{ra}}\right)=\sigma \epsilon A_{\text{rad}}\left(T_{i,\text{ra}}^{\mathrm{J}}-T_{\text{amb}}^{\mathrm{J}}\right),

where K_ra indicates the thermal conductivity of the radiating surface of the GC, which can be obtained in the same way as the wall of the GC. The superscript J indicates the last stage of the TEG.

The output voltage is calculated as (Song et al., 2021)

(20)V=V_{\text{open}}-IR.

In Eq. (20), the calculation method of open-circuit voltage is

(21)V_{\text{open}}=\sum _{j=1}^J\sum _{i=1}^n{S}_{i,\text{h}}^j\left(T_{i,\text{h}}^j-T_{i,\text{h}}^j\right).

The current can be estimated by

(22)I=\frac{V_{\text{emf}}}{R_L+R_{\text{in}}}.

The power of TEG is shown as

(23)P_{\text{TEG}}=V\cdot I=\frac{V_{\text{open}}^2{R}_L}{{\left(R_L+R_{\text{in}}\right)}^2}.

TEG energy conversion efficiency η_TEG can be defined as

(24){\eta }_{\text{TEG}}=\frac{P_{\text{TEG}}}{Q_{\text{solar}}}\times 100\text{\%}.

The physical parameters of TEG (Table 3), ceramics plate, and copper can be found in Liu et al. (2023).

2.3 Solar radiation

Similar to the solar energy of the Earth, the solar radiation intensity of the Moon reaches its largest value at lunar noon, 1365 W/m². Besides, the radiation intensity S shows a trigonometric variation with time during 14 Earth days, as shown below. In Fig. 3, the trend of intensity can be found (Climent et al., 2014; Lu et al., 2016).

For

(25)S(t)=1300\times \sin \left(\frac{\pi \times t}{1274400}\right).

For

(26)S(t)=0.

Among them, S(t) is the intensity of the solar radiation. c is the number of Earth days, it begins at zero.

2.4 Solution approach and procedure of TEG

2.4.1 Solution approach

In this paper, a matrix formula is used to obtain the temperature at different nodes of the TEG, and the calculation formula is shown below [Liu et al., 2023a; Cheng et al., 2018]:

(27)B\cdot T=C.

The expressions of B and C are

(28)B=\left[\begin{array}{ccccc}\dot{m}\overline{C{p}_{i,\text{f}}}+0.5A_i{h}_{i,\text{f}}& -A_i{h}_{i,\text{f}}& 0& 0& 0\\ 0.5A_i{h}_{i,\text{f}}& -A_i{h}_{i,\text{f}}-K_{i,\text{C}}^{\mathrm{j}}& -K_C^{\mathrm{j}}& 0& 0\\ 0& -K_{i,\text{C}}^{\mathrm{j}}& S_i^{\mathrm{j}}I-K_{i,\text{pn}}^{\mathrm{j}}-K_{i,\text{C}}^{\mathrm{j}}& K_{i,\text{C}}^{\mathrm{j}}& 0\\ 0& 0& K_{i,\text{pn}}^{\mathrm{j}}& S_i^{\mathrm{j}}I-K_{i,\text{pn}}^{\mathrm{j}}-K_{i,\text{C}}^{\mathrm{j}}& K_{i,\text{C}}^{\mathrm{j}}\\ 0& 0& 0& K_{i,\text{C}}^{\mathrm{j}}& -K_{i,\text{C}}^{\mathrm{j}}\end{array}\right](i=1,2\cdots n;j=1,2,3,4),

where i and j represent node divided along the GC length and TEG stage, repectively.

(29)T=\left[\begin{array}{c}{T}_{i,\text{out}}\\ T_w\\ T_{i,h}\\ T_{i,\text{c}}\\ T_{\text{ra}}\end{array}\right](i=1,2\cdots n),

(30)C=\left[\begin{array}{c}\dot{m}\overline{C{p}_{i,\text{f}}}{T}_{i,\text{in}}-0.5A_i{h}_{i,\text{f}}{T}_{i,\text{in}}\\ -0.5A_i{h}_{i,\text{f}}{T}_{i,\text{in}}\\ 0.5I^2{R}_{i,\text{in}}^{\mathrm{j}}\\ -0.5I^2{R}_{i,\text{in}}^{\mathrm{j}}\\ \sigma \epsilon A_i\left(T_{\text{re}}^4-4^4\right)\end{array}\right](i=1,2\cdots n;j=1,2,3,4).

Repeated iterations are used to obtain the T matrix’s solution.

2.4.2 Calculation procedure

In the calculation process, the initial values of CBC medium temperature, CBC medium mass flow rate, the temperatures at each location are first entered (T_kth). First assume the temperature of the radiant surface of the GC and the length of the GC (denoted by n), establish the calculation matrix as shown in Eq. (27), obtain the temperatures T_kth at different locations. After repeated iterations to obtain the results that satisfy the residuals and then enter the iteration of T_ra. If the computational residuals of T_ra are not satisfied, the temperature of T_ra is increased by 0.1 K, and iterative calculations are performed until the computational residuals are satisfied. After that, the calculation result of the next GC space step is calculated, and the calculation procedure are the same. When the calculation space step is larger than the set total GC length, determine whether the exit temperature of the fluid is lower than 343.15 K. If it is lower, output the result, otherwise increase the GC length until the GC outlet temperature reaches 343.15 K. The GC length will be increased until the GC outlet temperature reaches 343.15 K. The specific calculation procedure is illustrated in Fig. 4.

3 Results and discussions

3.1 Mathmatical model validation

To verify the correctness of the proposed mathematical model, the results were compared with those studied by other scholars. The CBC-TEG model does not have a well-formed mathematical model. Therefore, the CBC and TEG are validated separately (Tables 4 and 5). Figure 5 represents the comparison of the results of Xu et al. (2021) and Cheng et al. (2018) with the CBC model and TEG model presented. The operational parameters of the model are shown in Tables 4 and 5. There are little differences in the relative errors between the proposed model and the program’s simulated data (the maximum relative error of the CBC thermal efficiency is 4.09%, and the maximum relative error of the TEG power output is 1.28%), which confirms the accuracy of the simulation findings.

3.2 Daytime performance analysis

3.2.1 CBC performance analysis

In the CBC-TEG energy system, CBC is mainly used for high power generation, and TEG is used to meet the power generation in case of insufficient heat source, and finally to achieve the purpose of continuous power generation daytime and nighttime. To evaluate the power generation capacity of the CBC-TEG, the CBC operating interval is first obtained. Figure 6 illustrate the variation of η_th,CBC throughout the daytime in the case of the maximum CBC pressure, 600 kPa. η_th,CBC gradually increases with time. The turning point is at moon noon, when the thermal efficiency reaches 31.4%, which is caused by solar radiation. It is worth noting that the CBC thermal efficiency becomes negative before 3.6 days and after 12.2 days, respectively, when it can be called the CBC infeasible area. The rest of the time period is called the CBC feasible area. Working with TEG in areas where CBC is not feasible can generate electricity for any period.

Figure 7 illustrates that the length of CBC operating time at different CBC operating pressures. It can be found that as the CBC pressure increases, the CBC working time decreases. 400 kPa operating pressure is 5.9 days shorter than the CBC runnable time length at 1300 kPa operating pressure, which is more than double. This is mainly because the power consume in the compressor increases as the maximum pressure increases. When the solar radiation intensity is low, the CBC medium has a limited temperature rise in the collector, resulting in even lower power generation in the turbine. Therefore, in the morning and evening of the Moon, the compressor of CBC will consume much more work than the power generation in the turbine. To obtain the longest operating time, it is more appropriate to choose a maximum pressure in the range of 400 kPa−800 kPa.

In this paper, it is considered that when the thermal efficiency is less than 0, the CBC stops working and its thermal efficiency and energy output are set to 0. Figs. 8(a) and 8(b) represent η_th,CBC and power output at different CBC maximum pressures during the lunar daytime. From the figure below, it is easy to see that in the case of the maximum pressure of CBC reaches 500 kPa, η_th,CBC can reach 32.8% (P_CBC is 91.24 kW). When the maximum pressure of CBC is 700 kPa, the power output reaches a maximum of 101.8 kW (thermal efficiency is 28.12%). The reason why the maximum η_th,CBC and power output are not at one point is mainly due to two reasons. 1) The higher the maximum pressure of CBC, the higher the outlet temperature of the CBC compressor. The CBC medium is heated in the REG and then enters the solar collector. CBC medium is heated by solar energy, the heat transfer area of the collector can be smaller with a fixed outlet temperature. A small collector area means lower heat absorption. Therefore, in general, as the pressure increases, the thermal efficiency gradually increases. 2) When CBC pressure increases, the compressor power consumption increases, which will lead to a simultaneous decrease in thermal efficiency and power output. Turbine power generation is also on the rise, but not the same amount as compressor power consumption. The power output reaches a maximum value when it increases to 700 kPa, and then shows a decreasing trend. Under the influence of these two factors, the thermal efficiency and power output do not increase simultaneously, but both illustrate the trend of first increase and then decrease. Considering the working time of CBC, η_th,CBC, and P_CBC, it is more appropriate to set the maxinmum pressure of CBC to 600 kPa.

3.2.2 TEG performance analysis

TEG operates throughout the entire lunar daytime. TEG has two functions: as a coupled power generation system for the CBC for high temperature heat source. TEG acts as the only power generation equipment for low temperature heat source. As an example, the power generation effect of TEG is investigated at the maximum CBC pressure of 600 kPa. Figure 9 shows that the temperature change of the CBC meidum over the entire GC. CBC medium temperature in the TEG system for different number of stages shows a gradual decrease. Among them, the temperature increases gradually with the increase of stage. The reason is that high TEG level means high thermal resistance, resulting in difficulties in heat dissipation. The length also shows a trend of gradual increase in order to reach the condition of the outlet temperature of 343.15 K. However, the change trend is not significant, and the difference between 1-stage and 4-stage is only less than 2 m, indicating that increase in thermal resistance, while causing more difficulty in dissipating heat, does not have a significant effect (it is the radiation thermal resistance that is critical in affecting the heat transfer).

In this paper, two parameters, η_TEG and power output, are the key parameters for TEG performance study. Figures 10 (a) and 10 (b) represent the power output and η_TEG at different number of stages, respectively. With the increase of TEG stage, it leads to an increasing in η_TEG and power output. This is due to the positive correlation between the number of TEG stage and the thermal resistance. According to the Seebeck effect, high temperature difference means high voltage, thus boosts the power output up to 1.8 kW. Intersetingly, η_TEG in this paper is low, up to 0.67%, which is not consistent with many in the literature (Montero et al., 2022; Chen et al., 2021). This is because in most of the scholars’ research is to use high temperature and low temperature fluids as cold and hot sources for heat transfer. If we consider this problem using the idea of thermal resistance network, the thermal resistance (thermal conductivity) between TEG stages does not differ much from the thermal resistance (convection heat transfer) between hot and cold fluids. The different point is that, the research in this paper is to use the high temperature fluid as the heat source (convection heat transfer) and the deep space as the cold source (radiation). In this case, the thermal resistance of deep space radiation is much larger than the thermal conductivity thermal resistance of TEG, and most of the temperature difference will be reflected between the radiation surface of the GC and the deep space, rather than the high temperature end and TEG’s low temperature end. Therefore, the resulting η_TEG will be lower. It is true that η_TEG is relatively low, but the role of TEG is still important as a replacement energy source or as a waste heat recovery device when there is no electrical energy output.

The reason for the low value of η_TEG can also be seen in Fig. 11. Figures 11(a) and 11(b) show the temperature distribution of the radiation surface of TEG (T_ra) and the temperature of each node inside the TEG. It is easy to see that the effect of different stages on the temperature of each node is small. The temperature difference of the radiating surface does not differ by 10 K at different stages, indicating that increasing the thermal resistance by means of the TEG does not lead to heat dissipation misery. The change in node temperature is much smaller, and although increasing the number of TEG stages can increase the power generation level, the increase is limited. The temperature difference between the radiation surface temperature and the high temperature end of the first stage is up to 22.91 K (in the 4-stage case), while the lowest is 6.89 K (in the 1-stage case). According to the Seebeck effect, a small temperature difference must represent a small potential difference. In summary, the TEG generation effect is limited in the case of cooling by radiation for the cold source.

Figure 12 shows the TEG output power per unit length at different number of stages. This parameter characterizes the level of TEG power generation per unit length. Among them, the 4-stage TEG has the largest value, which can reach 51.36 W/m, and the 1-stage has the smallest, which is 11.05 W/m. The difference between the two is 80%, which means that the number of stages has a great impact on the power output per unit length of TEG. From Fig. 9, it can be seen that although the increase in the number of TEG stages leads to a larger thermal resistance to heat transfer, this has little effect on the length of the GC, this is because the major thermal resistance is still the radiation thermal resistance.

It is also important to consider the GC area and the additional weight due to the increase of TEG for space energy system. Figure 13 represents GC area and the weight of the TEG for different number of stages. It is not difficult to see from this figure that the heat transfer area shows a gradual increase with the increase of the number of stages, but the increase trend is not significant. This is mainly because the increase in thermal resistance of multi-stage TEGs is not significant, hence the heat transfer area does not change significantly. However, the same cannot be said for weight, as an increase in the number of stages results in a doubling of the weight of the TEG, from 56.24 kg for a 1-stage TEG to 237.14 kg for a 4-stage TEG, which is an increase of about four times. For a large power generation system, a hundred kilograms of equipment is acceptable. Take CBC as an example, its power-to-weight ratio generally does not exceed 10 W/kg, and the power-to-weight ratio of TEG in this paper can reach 7.59 W/kg. Therefore, it is reasonable to choose a 4-stage TEG as a power generation system.

In this paper, it is considered that the TEG generates electrical energy for continuous energy supply during the period of η_th,CBC < 0. With the maximum operating pressure of the CBC at 600 kPa, the TEG generates electricity as shown below. 4-stage TEG is used to evaluate the power generation performance. Figures 14(a) and 14(b) show the energy output versus the inlet and outlet temperature variation of the GC under the infeasible region of the lunar day CBC, respectively. As the intensity of solar radiation increases, the P_CBC of the system tends to increase up to 0.73 kW. Although the power output is limited, this at least achieves the effect of continuous power supply for the entire lunar daytime. It is possible to complete the maintenance start-up of the moonbase power generation equipment, which is essential for the operation process of large energy systems. In addition, as the increase of solar radiation intensity, the inlet and outlet temperatures show a gradual increase for the same length of GC. The inlet temperature of CBC medium can reach up to 447.63 K and the outlet temperature is 288.38 K.

3.3 Nighttime performance analysis

3.3.1 CBC performance analysis

Compared with the lunar daytime power generation, the lunar night performance is more worth exploring. The heat is stored in HSU during the lunar daytime, and the heat is transferred to the CBC-TEG or single TEG during the lunar nighttime to generate electricity for continuous energy supply. The mass flow rate should be reduced to the range of 0.01-0.05 kg/s for the energy system to work continuously in the night. Figure 15 shows the variation of η_th,CBC during the lunar nighttime. In this paper, the effect of the variation of the medium mass flow rate on the η_th,CBC during the lunar nighttime is also investigated, and η_th,CBC can reach 37.52%. In addition, when the mass flow rate of CBC medium is below 0.2 kg/s, the CBC can operate under the whole lunar nighttime. With the increase of mass flow rate, the point at which the η_th,CBC < 0 is continuously advanced to the 11th, 9th and 7th day, respectively. This is due to the lower the mass flow rate of CBC medium, the less heat will be extracted from HSU, HSU can support the CBC operation for a longer period.

Figure 16 represents the change of the power output at different mass flow rates of CBC medium. As the mass flow rate increases, the upper limit of P_TEG increases dramatically and can reach up to 4.61 kW. However, it decreases to 0 in a short period of time. P_CBC basically remains around 1 kW for the case of mass flow rate of 0.01 kg/s. This is because the heat from HSU of the system is always sufficient and the heat consumption of the CBC is small. This can be seen in Fig. 17. After 14 Earth days, the temperature of HSU has only decreased by 228 K. The maximum temperature drop can reach 368 K. In fact, the choice of mass flow rate is a control scheme, and it is based on whether the high-power generation or the long CBC operating time is the criterion. Therefore, the appropriate mass flow rate should be selected according to the reasonable lunar nighttime energy demand.

3.3.2 TEG Performance analysis

In the period of η_th,CBC < 0, 4-stage TEG is used as a power generator in this paper. Fig. 18 represents the change of the power output of the TEG when η_th,CBC < 0 during the lunar nighttime. From this figure, it can be found that the power output of TEG shows a decreasing trend as time advances. This is because the temperature of HSU gradually decreases as the heat is used, it leads to a decrease in the power output of TEG. When the heat source temperature is high enough, P_TEG can reach 118 W. When the mass flow rate is 0.03 kg/s, the TEG can generate power during the lunar nighttime, realizing the full-day energy supply for moonbase. In a word, the introduction of TEG solves the problem of mismatched CBC heat source and has reached the purpose of continuous energy supply daytime and nighttime.

4 Conclusions

To achieve the purpose of continuous energy supply to the moonbase all day. This work proposes the CBC-TEG power generation system. Through numerical modeling, the effect of CBC power generation under different maximum pressures and the performance of TEG power generation under the infeasible area of CBC are obtained. In addition, the performance under the lunar night is analyzed. The detailed conclusions are shown below.

1) The optimal operating maximum pressure of CBC during the lunar daytime is 400−800 kPa. Considering the η_th,CBC, P_CBC, and operating time of CBC, the best CBC maximum operating pressure is 600 kPa.

2) Due to the large thermal resistance of radiation to deep space, most of the temperature difference is generated in the TEG radiation surface and deep space, and a small part of the temperature difference is distributed in the TEG, so η_TEG is too low. Its maximum η_TEG is only 0.67%, and the P_TEG,max is 1.8 kW.

3) The arrangement of TEG above the GC increases the thermal resistance of the whole equipment and reduces the heat transfer effect of radiation to deep space, but the reduction is limited. Besides, the heat transfer area of the 4-stage compared to the 1-stage TEG is increased by only 8 m². But for the weight of TEG, the weight is increased by 4 times, and the 4-stage TEG reaches 237.14 kg.

4) During the lunar nighttime, the operating time of CBC is affected by the CBC medium mass flow rate, which gradually decreases as the medium flow rate increases. The η_th,CBC can reach up to 37.52%. P_TEG,max is 118 W during the time period when η_th,CBC is below 0.

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