A space power system of free piston Stirling generator based on potassium heat pipe

Abstract

The power system of a free piston Stirling generator (FPSG) based on potassium heat pipes has been developed in this paper. Thanks to the advantages of long life, high reliability, and high overall thermal efficiency, the FPSG is a promising candidate for nuclear energy, especially in space exploration. In this paper, the recent progress of FPSG based on nuclear reactor for space use was briefly reviewed. A novel FPSG weighted only 4.2 kg was designed, and one dimensional thermodynamic modeling of the FPSG using Sage software was performed to estimate its performance. The experiment results indicated that this FPSG could provide 142.4 W at a thermal-to-electric efficiency of nearly 17.4%. Besides, the power system integrated with four FPSGs and potassium heat pipes was performed and the single machine failure test was conducted. The results show that this system could provide an electrical power of 300 W at an overall thermal efficiency of 7.3%. Thus, it is concluded that this power system is feasible and will have a great prospect for future applications.

Keywords

free piston Stirling generator (FPSG) / potassium heat pipe / power system / energy conversion

Introduction

With rising space exploration activities, it is urgent to possess a longer life and more reliable space energy system to support exploration task [¹]. The traditional power sources, like chemical and fuel cell batteries, are only suitable for short-term tasks due to their short longevity and low efficiency. Although the efficiency of solar cells have increased substantially recently, they have reached the limit of their development and can be used only in near-Earth orbits and for satellite-borne equipment [²]. Relative to the above energy, the space nuclear power reactor is an excellent option, which can operate continuously and provide sustainable and reliable electricity for up to15 years and have lighter weight, higher power density, and simpler structure [³,⁴]. The vital importance is that not only can it used as sources of electrical power, but also as sources of heat to support life and productive activities at bases beyond Earth. Over the past 60 years, the energy conversion technologies for space nuclear reactor power systems comprise three static (SiGe, Segmented and Cascaded Thermoelectric, Alkali Metal Thermal to Electric Conversion) and two dynamic methods (FPSG and Closed Brayton engine), of which FPSG is more prominent with its high efficiency and long life [⁵,⁶].

The FPSG is a heat engine operated by cyclic compression and expansion (Stirling cycle) of some gases, which outputs its power via a linear generator. Owing to its advantages of extremely long life, high reliability, simple configuration, and excellent efficiency at low hot-to-cold temperature ratios, many studies focusing on the modeling and experimental investigation of FPSG based on nuclear reactor systems have been conducted [⁷,⁸].

Based on the US space reactor programs of the last five decades, a small fission power system named kilopower was proposed, which helped fill in the existing technology gap of compact power systems in the 1–10 kW range, enabling new higher power NASA science and human exploration missions [⁹]. The kilopower system used alkali metal heat pipes to supply heat to Stirling convertors to produce electricity and titanium water heat pipes to remove the waste heat and transport it to the radiators where it is rejected to space [¹⁰]. The Kilowatt Reactor Using Stirling Technology (KRUSTY) was designed to be representative of a 5-kW kilopower space reactor. The thermal power of its test ranged from 1.5 to 5.0 kWt, with a fuel temperature of up to 880°C. Each 80-We-rated Stirling engine produced 90 We at a component efficiency of 35% and an overall system efficiency of 25%, which was the first nuclear-powered operation of a truly new reactor technology in the US for over 40 years [¹¹,¹²].

However, this power systems till has major disadvantages. The overall system efficiency is relatively low, mainly due to the issues of acceptable heat transfer among the fuel, core heat pipes, FPSG and reflectors. Other disadvantages include the ability to demonstrate stable operation, dynamic response, load following characteristics, gravity effects on the performance of the heat pipes, the high heat resistance and high strength materials, startup-rod system, and etc [¹³–¹⁵].

In this paper, a novel FPSG was developed to offer a thermal-to-electric efficiency of 17.8% with an electrical power output of 142.4W and a comparison was made between the simulation results and experiment dates. Besides, a pilot setup that used the electrical heaters instead of nuclear reactor to transfer heat to the heat heads of four Stirling engines through the potassium heat pipe stack was constructed to investigate the performance of the new power system in detail and lay the foundation for future applications.

Single prototype engine

Fundamental structure

Figure 1 shows the FPSG configuration, which operates with six main components including a heater, a regenerator, a cooler, a displacer, a piston, and a linear alternator. The linear alternator mainly consists of a coil, a bearing to suspend it, and an electromagnetic circuit. The FPSG generally operates according to a closed thermodynamic cycle called the Stirling cycle. The ideal Stirling cycle includes four thermodynamic processes such as constant temperature expansion, constant volume heat addition, constant temperature compression, and constant volume heat rejection (see Fig. 2). According to Fig. 1, the volume of the expansion space is augmented as the gas is heated in the expansion space, which results in the movement of the piston to bottom dead center (processes 1–2). Next, in the constant volume process, the displacer moves upwards and accordingly, the working gas enters the compression space (processes 2–3). Then, as the heat is released to the cold source, the gas is contracted, and thus, the piston moves to its top dead center (processes 3–4). Eventually, in another constant volume process, the displacer moves downwards, and the gas enters the expansion space, resulting in an increase in the gas pressure (processes 4–1) [¹⁶]. The coil connected to the piston is moved to convert the mechanical energy to electrical power.

To improve the calculation accuracy, the commercially available software Sage developed by Gedeon Associates was utilized. Sage is a 1-dimensional thermodynamic analysis tool for Stirling cycle modeling, design, and optimization [¹⁷]. As shown in Fig. 3, various components of the FPSG were connected in a certain order. In this model, key design parameters such as the fin spacing, temperature, pressures, and etc. of the system and components can be determined as well as the estimated system efficiency. The corresponding author has used Sage for Stirling engine design and analysis in the past 20 years. The sage model results are typically validated by Stirling engine performance testing and mapping. The tested cycle efficiency of a well-designed Stirling engine is within 5% of predicted values. The physical picture and parameters of the engine are presented in Fig. 4 and Table 1, respectively. The final prototype was designed which was only about 4.2 kg.

Experimental study

Figures 5 and 6 describe the layout for the experimental apparatus including an electrical heating system, a water-circulating cooling system, a load test system, an excitation system, a vacuum system, and a data collection system.

The main measuring instruments comprise of temperature sensors, pressure sensors, and acceleration sensors. A calibrated K-type sheathed thermocouple (with accuracy class 1) was placed in the center of the electric heater to monitor the heating temperature and another two thermocouples of the same type were evenly mounted at the expansion and compression space to measure the temperature of the actual gas. The dynamic pressure in the bounce space and work space was monitored using high-precision dynamic pressure sensors (model CYG1409F, with a measuring range of 0–10 MPa and an accuracy of 0.01MPa), which were respectively placed in the back cover and compression space. Two unidirectional vertical patch accelerometers (model GWT-1B, with an accuracy of 1%) placed in displacer spring and piston spring were used to measure the acceleration of displacer and piston vibration. The displacement curves of displacer and piston vibration were indirectly obtained according to a certain mathematical conversion relationship. Before the actual measurement, acceleration sensors were calibrated with a standard displacement sensor. The electrical power extracted from the linear alternator was consumed using a rheostat. Simultaneously, a 150 F electric capacitor was connected in series in the circuit to suppress the electrical inductance induced by the coil, making the circuit reach a resonance state.

Currently, the generator was started up relying on external excitation. Therefore, the excitation system was connected in parallel to the load circuit. After the engine being started, the excitation power was disconnected and the load was completely powered by the generator. Before the experiment, the entire system was vacuumed and then was charged with a certain pressure of helium to ensure the purity of the gas. In the experiment, multiple heating rods were inserted into the heating head to provide an adjustable heating power. To reduce heat loss, the heating head was wrapped and was thermally insulated using the aluminum silicate insulation cotton.

It is necessary to analyze the experimental error. For direct measurement parameters including mean pressure, pressure wave, current, voltage, electrical power, and temperature, the experimental errors are calculated according to the maximum permissible error of the sensors. For indirect measurement parameters including thermal-to-electric efficiency, the experimental errors are calculated by using the error transfer formula [¹⁸]

(1)\mathrm{\Delta }y={\displaystyle \frac{\partial f}{\partial a}}\mathrm{E}a+{\displaystyle \frac{\partial f}{\partial b}}\mathrm{\Delta }b+{\displaystyle \frac{\partial f}{\partial c}}\mathrm{\Delta c,}

wherey = f(a,b,c) denotes the indirect measurement parameter; a, b, and c denote the direct measurement parameters; Δa, Δb and Δc denote the errors of a, b, and c, respectively; and ∆y denotes the error of y resulting from Δa, Δb and Δc.

Figure 7 depicts the resulting of electrical power and thermal-to-electric efficiency at different heat temperatures. As expected, the electrical power increases with the increasing heat temperature, while the thermal-to-electric efficiency slightly changes and has a maximum value. It is obviously noted that the simulation results are much better than the experiment results. The difference between experiments and simulations in electrical output is within 15%. One reason for this is that the maximum measurement error is approximately 3%. The other reason is probably that the shuttle heat loss, pumping loss, regenerator heat loss, and leakage loss have been considered in the model, while some heat losses such as thermal conduction loss at the heat hand and the radiation with the environment are not considered. Finally, the prototype FPSG offered 142.4 W electrical power, with a thermal-to-electric efficiency of 17.4%, at a charge pressure of 5 MPa, an input heating power of 818W, and a load resistance of 50 W.

Experiment of new power system

Based on the existing technology, the above mentioned 4 FPSGs were utilized as the heat-to-electricity converters in the power system. As a principle verification experimental device, this paper primarily focuses on the design and experiment of the power system.

Fundamental structure

The layout of the power system is illustrated in Fig. 8, which mainly consists of an electrically heated reactor core to simulate the performance of the uranium fuel, four high temperature potassium heat pipes, a heat collector block, four FPSGs and a water-circulating cooling system. As shown in Fig. 9, the heat pipe consists of a container, working fluid, wick structure with three sections (an evaporation section, an adiabatic section, and a condensation section). The heat generated by the four heating rods enters the heat pipes and the potassium liquid in the evaporator at the end of the heat pipe is evaporated. Then, the potassium vapor travels up the heat pipe where the thermal can be received by the four Stirling converters at the condenser interface. When the potassium vapor releases its latent heat and condenses back into the liquid phase, the capillary force pumps it back to the evaporator and the cycle continues. This passive thermal transport operates solely on thermal energy, which requires no electrical power for pumping [¹⁹]. This is an important design feature, which reduces the parasitic losses of the power system and simplifies system startup and control.

The heat collector block was made of ODS copper, including 8 through-thickness holes to accommodate eight potassium heat pipes numbered as A–H (as exhibited in Fig. 10) from the reactor and four radial holes for FPSG heater heads. The four FPSGs were arranged in the horizontal dual-opposed configuration, which could reduce system vibration at a certain degree.

Figure 11(a) shows the simulation temperature distribution on the heat collector block resulting from the reactor heat pipes. The resulting temperature gradient at the Stirling heater heads is shown in Fig. 11(b). Due to the high thermal conductivity, the copper block was provided with excellent heat spreading and fairly uniform block temperatures. The temperatures of Stirling heat heads varied from about 769 K to 764 K and temperature difference with the block was only less than 10 K.

Potassium heat pipes were arranged evenly in the collector block vertically. Alloy 600 was the baseline encapsulating material for heat pipes because of its known compatibility and prior experience with sodium as well as its high temperature strength and creep resistance. In the experiment, thermocouples (with an accuracy of 0.1 K) were placed at different positions of each part to measure the temperature. The insulation sections of each heat pipe were uniformly arranged in the longitudinal direction. There were eight measuring points in the evaporation section and the condensation section. Besides, three measuring points were deployed at the center of the heater head of each engine and at the two sides. To calculate the heat rejected, two calibrated PT100 platinum resistance thermometers (with an accuracy of 0.1 K) and a flow meter (with an accuracy of 0.1%) were used to ensure the precision of the measurements in each water cycle. All of the signals were simultaneously collected and recorded using the dynamic signal acquisition system. The final physical installation of the experimental device is shown in Fig. 8.

Start-up experiment

First, the instrument control and water-cooling system were started before starting the electric heater power system. The total heating power and temperature of electric heating rods versus time during the system startup are presented in Fig. 12. The initial heating power of a single electric heating rod was 500 W and was gradually increased until finally stabilized at a single 1040 W. When the temperature of the heater head reached the starting standard, the excitation signal was triggered to excite the FPSG, sequentially.

Figure 13 displays the evolution of the temperature of each temperature measuring point on the axial surface at the H heat pipe in the experiment. The typical temperature front phenomenon of the high temperature heat pipe startup process could be clearly observed in Fig. 13. At the beginning (at 15 min), the temperatures of the evaporation section were much higher than others, as the heat pipe did not start work and there was less heat flowing through it. As the heat pipe started working (e.g., at 45 min and 60 min), the temperatures of the evaporation section and adiabatic section were nearly the same, but there still existed larger temperature drops between the adiabatic section and condensation section because of the heat capacity of the heat collector block. Then, the temperatures of the heat collector block rose. At 90 min and 100 min, the temperatures of the three sections kept nearly consistent, which meant that the whole heat pipe was fully started. At 180 min, as the Stirling engines started operating, the heat flow in the heat pipe increased, the temperature dropped between the adiabatic section, and the condensation section reappeared. But the total temperature drop in the longitudinal direction of the entire heat pipe was only 50°C when stabilized.

Figures 14 and 15 show the variations of some parameters of the FPSGs during operation. As expected, the output electrical power and its frequency gradually increased with the heat head temperature rising. Due to the difference in thermal resistance between the heat head surface of the engines and the heat collector block, the starting temperatures of engines were different. It can be clearly observed that No. 1 and No. 3 FPSGs were started first at 376°C and 374°C respectively. Then No. 2 and No. 4 FPSGs were started later because of the actual uneven heat distribution, whose starting temperature were at 391.5°C and 391.9°C respectively. Therefore, it can be concluded that FPSG can only be activated when the heat head temperature is high enough, which is up to the heat transfer ability of the heat pipe. In other words, the starting time of the engine system is mainly determined by the heat pipe: the faster the heat pipe starts, the faster the heating head of the generator heats up, and the earlier the FPSG starts. In Fig. 15, it could be noted that the frequency of No. 1 and No. 4, or of No. 2 and No. 3 FPSGs which were arranged in horizontal dual-opposed configuration remained almost the same. Therefore, the vibration could be well reduced to each other and the FPSGs operated quietly during the experiment.

The system ran stably at least 10 h. The working parameters are shown in Table 2. The efficiency of the FPSG can be described as

(2){ç}_{\mathrm{FPSG}}={\displaystyle \frac{w_{\mathrm{e}}}{w_{\mathrm{e}}+Q_{\mathrm{w}}}},

where w_e and Q_w respectively denote the electrical power and the heat rejected by the cooling water.

The overall thermal efficiency is defined as

(3){ç}_{\mathrm{overall}}={\displaystyle \frac{w_{\mathrm{e}}}{Q_{\mathrm{input}}}},

(4)Q_{\mathrm{input}}=w_{\mathrm{e}}+Q_{\mathrm{w}}+Q_{\mathrm{loss}},

where Q_input and Q_loss denote the input heating powerand heat lost through the thermal radiation between the external thermal insulation and theenvironment, respectively.

From Table 2, it can be observed that the mean efficiency of FPSGs is nearly 8% and the overall thermal efficiency is about 7.36% with an electrical power of over 300 W.

However, the overall efficiency of the power system was relatively lower compared with the efficiency of a single FPSG perhaps because of the following reasons. First, a part of the heating rod at the bottom of the system was exposed to the environment with no insulation material to avoid the overheating of the heating rods in the core. This thermal power loss was calculated to be over 600 W. Next, the temperature of the outer surface of the insulation material reached 60°C, and as a result, the amount of heat dissipated also accounted for a large proportion. Finally, due to the heat radiation, the temperature of the upper floor fixed to the engine was very high. Therefore, the temperature in the casing of the FPSG reached at about 60°C, which further affected the performance of the engine.

Single FPSG failure test

The fault tolerance of the power system plays an important role in achieving the high-performance system. The single machine failure test can potentially verify whether the system can continue to operate stably when the FPSG breaks down and can evaluate the safety of the system to a certain extent. Thus, in this paper, No. 2 FPSG was closed deliberately to study the transient response of the system.

As shown in Figs. 16–18, No. 2 engine was stopped at 30 min and started again at about 320 min. During this period, the system heating power remained almost constant at 2800 W and the total output electrical power (of the remaining 3 FPSGs) was instantly reduced at 150 W, and then gradually increased at about 180 W 2 h later, with an overall thermal efficiency of 6.4%. When No. 2 engine was restarted, the system output electrical power (of 4 the units) was rapidly increased at 250 W. Especially, the output power of No. 2 FPSG had a peak value, which was caused by the large amount of heat accumulated at the hot end. After 1.5 h, the output electrical power gradually increased at 200 W, with an overall thermal efficiency of about 7.3%. This feature is significant as it indicates that the power system can still work and maintain a certain thermal-to-electric efficiency when a machine failed.

A comparison of Figs. 17 and 18 suggests that the heat head temperature in the FPSG is consistent with the heat of the heat pipe. As expected, when No. 2 FPSG closed, the temperature of the heat head of FPSGs and the three sections in heat pipe H gradually raised; when started again, the temperature gradually decreases. At the same time, it can be found that the heat head temperature of No. 2 FPSG increased by about 47°C (the highest), while the other FPSGs only increased by about 30°C, because the heat cannot be taken away by No.2 FPSG and accumulated at the place close to the heat head of No.2 engine, which caused the uneven temperature distribution in the heat collect block.

Conclusions

In this paper, a comprehensive power system based on four FPSGs and the potassium heat pipe was developed. Besides, a novel FPSG which was only 4.2 kg was designed and tested. Moreover, a sage model was utilized to predict and optimize the performance of the FPSG. The FPSG could provide a thermoelectric efficiency of 17.4% and an output power of 142.4 W when the temperature at the hot end and cold end was 574°Cand 10°C respectively, and the input power was 818 W.

Furthermore, four FPSGs were successfully coupled with the potassium heat pipe in the power system, which verified the feasibility of the technical scheme. Currently, the power system could offer an electrical power of approximately 300 W with a system efficiency of 7.3%. The experiment of fault simulation demonstrated that even if a single generator failed, the system could still operate normally, indicating that the FPSG could work independently at different temperatures, which verified the reliability of the entire system which was beneficial for practical applications.

However, the overall efficiency of the power system is still relatively low compared with the theoretical efficiency and the test efficiency of a single Stirling engine. A lot of work should still be done to optimize the whole system. For example, the insulation layer should be redesigned to reduce the heat loss, the contact thermal resistance among components at high temperature should be reduced, and the performance of FPSG needs to be further improved.

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