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Reliability and loading-following studies of a heat pipe cooled, AMTEC conversion space reactor power system
Annals of Nuclear Energy 130 (2019) 82–92
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Reliability and loading-following studies of a heat pipe cooled, AMTEC conversion space reactor power system Ge Li a,⇑, Li Huaqi a,b, Shan Jianqiang a a b
Xi’an Jiaotong University, Xi’an 710049, China Northwest Institute of Nuclear Technology, Xi’an 710024, China
a r t i c l e
i n f o
Article history: Received 31 August 2018 Received in revised form 12 February 2019 Accepted 16 February 2019
Keywords: SRPS AMTEC Load following Radiator Safety and reliability
a b s t r a c t During the progress and development of the space technology, the space reactor power system (SRPS) is one of the best options for providing high power density, long-term life, light weight, and high reliability space power for civil or military space missions. The heat pipe cooled SRPS (HPS) equipped with the static conversion technology Alkali Metal Thermal-to-Electric Conversion units (AMTEC) has good inherent dynamic characteristic for frequent change load following of the space mission power, with high safety and reliability. This paper analyzed the system safety and reliability of an AMTEC conversion HPS, the load following characteristics of the AMTEC conversion and the HPS’s performance in response to partial surface area loss of potassium heat pipe radiator. The results show the following. (1) As the external load resistance increases, the AMTEC thermoelectric conversion efficiency and electric power output both increase to the maximum, and then decrease. The maximum thermoelectric conversion efficiency and electric power output correspond to different critical external load values. The load following capacity of the AMTEC HPS exists only when the external load demands exceed a critical value. (2) When the potassium heat pipe radiator’s surface area is partially lost because of the impact of a meteorite, the reactor thermal power, the AMTEC conversion efficiency and the electric power output also decrease, except the radiator temperature due to the radiator area loss. The waste heat rejection, the conversion efficiency and electric power output of the system decrease proportionally to the radiator’s surface area loss. To ensure the safety and reliability of the SRPS, the reactor thermal power will run down after the loss of the radiator’s surface area. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction With the progress and development of the space technology, the future demands for civil or military space missions focus on high power density (>100 kWe), long term life (7–10 years), light weight, high safety and high reliability of space power (Su et al., 2016). Compared to solar power, chemical power and other traditional space power, the space reactor power system (SRPS) is independent from the space environment and has an edge on the above characteristics. Thus, SRPS can better meet the power demands of the space missions. SRPS reactor cores can be usually classified into thermal spectrum reactors, such as SNAP10-A (Hawley, 1967) and TOPAZ (Gunther, 1990), and fast spectrum reactors. The thermal spectrum reactors are mainly suitable for low-power levels or shorter missions, while the fast spectrum reactors are compact and suitable ⇑ Corresponding author. E-mail address: [email protected] (L. Ge). https://doi.org/10.1016/j.anucene.2019.02.029 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
for high-power levels. SRPS could mainly be cooled using alkali liquid-metal heat pipe, directly circulating liquid metal or binary noble gas mixture of He–Xe. The alkali liquid-metal heat pipe can provide good heat transfer and don’t require an external pump. The radiative radiator with C–C fin structure is the main choice for the radiators of the SRPS. The energy conversion devices of SRPS are mainly divided into static energy conversions, such as thermoelectric (TE) (Metzger and El-Genk, 1991), thermionic (TI) (Lamp and Donnovan, 1991), or AMTEC (El-Genk and Tournier, 2004), and dynamic energy conversions, such as free-piston stirling engines (FPSPs) (Gary and Neill, 2004) or closed Brayton cycle (CBC) (Gallo and El-Genk, 2009). Among them, AMTEC conversion not only has the characteristics of a static thermoelectric conversion device such as a large radiator heat rejection temperature and an inherent load following capability, but also has a high conversion efficiency (>20–25%). At present, there are many researches on the inherent load following capability of the SRPS with TI (ElGenk et al., 1992) and TE (El-Genk et al., 1988; Parlos and Fetiye, 2000) static thermoelectric conversion devices. However, there is
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less research on the system load following capability under reactive feedback conditions for the heat pipe cooling SRPS with AMTEC conversion, it is necessary to study the safety features of AMTEC conversion. The SPRS carries properties of long-term operation in the space environment (7–10 years), changing missions (frequent changes in load demands) and unmanned operation. It is the great task for us how to ensure the safety and reliability of SRPS orbiting in space. The radiation radiator is an essential equipment for the waste heat discharge of the SRPS, and its performance greatly influences the performance of the SRPS. The heat dissipation capacity of the radiation radiator is a function of the heat dissipation plate area and the radiator temperature. The radiator panels exposed in space are prone to be impacted by meteorites and lost part of the heat dissipation area. The radiator panel in the space environment is prone to be exposed. Part of the heat dissipation area is lost due to the impact of debris impact, which has affected the reliable operation of the space reactor power supply. Among all types of space reactors, the SRPS applies the heat pipe cooled, static AMTEC conversion and potassium heat pipe radiator in its design. It becomes one of the best options space power because of good heat transfer performance, easy to startup from a frozen state, inherent load following characteristics and so on. The University of New Mexico’s Institute for Space and Nuclear Power Studies (UNM-ISNPS) has developed the concept design of the SRPS, named SAIRS. SAIRS employs fast-spectrum reactors cooled by sodium heat pipes, C–C armored, potassium heat pipes radiators, W/LiH material c/n shields, and AMTEC units (El-Genk and Tournier, 2004). Compared with other types of SRPS, SAIRS has the characteristics of avoiding single point failure and low specific mass (<26.9 kg/kWe). Its rated electric power is 110 kWe and its output voltage is 400 V. SAIRS uses 18 6.11 kWe NAAMTEC units and integrates them into six thermoelectric conversion modules, each of which contains three Na-AMTEC units. The cold end of each module is connected with the potassium heat pipe radiator plate for heat dissipation, and the hot end is coupled with 10 sodium heat pipes in the core for heat transfer. The design ensures the safety of operation redundancy. This paper takes the typical heat pipe cooled and AMTEC converted SRPS called SAIRS as the research object, and uses the heat pipe cooling fast reactor system transient analysis code TAPIRS (Yuan and Shan, 2016) to analyze its load following characteristics and on-orbit operation safety and reliability. Firstly, the effect of external load resistance and endpoint temperature on the performance of modular AMTEC was studied. Secondly, the transient response of the SAIRS system under the change of load demand was studied, and the load following characteristics and safety reliability of the SAIRS system under the condition of negative feedback were further analyzed. Finally, the effect of loss of some surface area of the radiant radiator on the performance of SAIRS was studied.
2. Description of TAPIRS code The TAPIRS code is developed by Xi’an Jiaotong University for the SRPS with heat pipe cooled, AMTEC energy conversion and heat pipe radiator. It can calculate various transient conditions, including steady state conditions, startup process, heat pipe failure, AMTEC failure, loss of heat sink area and control drum failure. The models of TAPIRS mainly include the reactor core power transient model, UN fuel rod heat transfer model, heat pipe model, AMTEC model, heat pipe radiation radiator model, etc., as shown in Fig. 1. The reactor core power transient model uses the standard point reactor kinetics equations with six delayed neutron groups (Wright
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and Houts, 2001). The solution of the equations is based on highorder endpoint floating method that is applicable to both rigid and inconspicuous cases (Yuan and Hu, 1995). The reactive feedback of the reactor core considers the Doppler effect of the UN fuel element, the fuel expansion of the core, and the temperature reactive feedback of the coolant. The heat transfer model of the core UN fuel rod neglects the axial heat conduction, and assumes that the heat conduction is axisymmetric. The ordinary differential equation of the UN fuel temperature calculation using the lumped parameter method is derived by the volume averaging method. Where, the heat transfer control equation is derived from the Fourier Law and energy conservation law (Wulff, 1980). The heat pipe model mainly includes the high-temperature heat pipe startup model and the normal transient model, namely the free molecular flow model, the ‘‘planar forward” startup model of the transition zone, and the continuous flow thermal resistance network and cyclic process model (Zuo and Faghri, 1998). The free molecular flow model uses the energy balance as a premise to deduce the transient heat transfer equations for the evaporation section and the adiabatic section of the heat pipe, considering the changes in the solid working medium in the wick, as well as the evaporation of the working medium at the interface. The ‘‘plane forward” startup model adopts a closed theoretical analysis model, and it is suitable for the intermediate transition stage. The thermal resistance network and cycle model is a simple heat pipe transient analysis model, including the thermal resistance network model and the working fluid thermodynamic cycle model. The above three models constitute a complete reactor core hightemperature heat pipe transient analysis model. The AMTEC analysis model (Tournier, 1997) mainly includes: (1) The thermal model, which calculates the AMTEC temperature and parasitic heat loss. (2) The pressure loss model, which calculates the alkali metal working fluid pressure loss in AMTEC. (3) The electrical model, which calculates the BASE ionic losses, electrical losses in current collectors and connecting leads, total electrical current and the developed potential in the BASE, as functions of temperatures of BASE and condenser, and sodium pressures across the BASE. (4) The resistance model, which calculates the structural resistance of each part of AMTEC. (5) Circulation flow model, which calculates the mass flow rate at the liquid-return porous artery, as a function of pressure and temperatures. The heat pipe radiator model uses the lumped parameter ‘‘twopoint analysis model” of the heat pipe analysis (Gaeta, 1988).
3. AMTEC steady-state performance A steady-state AMTEC unit performance analysis code, SNPS_AMTEC (Zhu et al., 2016), consists of three models: The pressure loss model, the electric model and the heat loss model. The steady-state load following characteristics of AMTEC are determined by analyzing the influence of the cold and hot end temperature, external load resistance and input power on the performance of the AMTEC unit. Fig. 2 shows the steady state responses of AMTEC units when the BASE temperature is 1123 K and the cold end temperature is 670 K. Fig. 2a shows the change of AMTEC thermoelectric conversion efficiency and output power with external load RL. With the increase of external load resistance, the AMTEC conversion efficiency and output power increase to 26.9% and 8.2 kWe respectively, and then decrease gradually. The two critical external load resistance values are about 1.14 X and 0.18 X respectively, and they are almost independent of the AMTEC end temperatures, as shown in Fig. 3. Fig. 2b shows the curves of AMTEC output current and voltage varying with external load resistance. The AMTEC
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Fig. 1. Schematic diagram of the TAPIRS code.
Fig. 2. Steady state response of AMTEC as a function of external load resistance and input thermal power.
component of the SAIRS is designed to connected in series in 3 parallel strings (each with 6 AMTEC units connected in series) for redundancy, while providing a terminal voltage of 400 V DC. Thus,
the output voltage of a single AMTEC unit must be 400/6 = 66.7 V DC. It means the AMTEC external load resistance should be greater than 0.9 X.
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Fig. 3. Efficiency and electric power versus AMTEC temperature and external load.
Fig. 2c shows the input and discharge power as a function of external load for the given hot and cold end temperature. As the external load increases, the input power decreases. As analyzed by Fig. 2a and c, when the external load is greater than the critical value of 0.18 X, the output electric power can be increased by reducing the external load resistance and increasing the input power. It means that the AMTEC has load following capability. When it is less than the critical value of 0.18 X, increasing the input power does not increase the output electric power, and the AMTEC does not have the load following capability. Fig. 2d shows the AMTEC conversion efficiency and output power as a function of input power. With the increase of input power, the AMTEC conversion efficiency and output electric power increase firstly to the maximum values 26.9% and 8.2 kWe respectively and then gradually reduce, but their extreme point positions are not the same. Therefore, AMTEC has inherent load following capability within a certain range, and it does not have inherent load following capability beyond the critical value of external load.
Fig. 3a shows a 2D graph of the AMTEC conversion efficiency as a function of the external load resistance and the cold end temperature (AMTEC BASE hot end temperature is 1123 K). As Figs. 3a and 4a show that the AMTEC conversion efficiency slowly increases to the maximum value about 28% with the increase of the cold end temperature, and then decreases rapidly. This is because the temperature difference between the hot and cold ends decreases and the parasitic heat loss Qrej decreases when the cold end temperature increases from 400 K to 800 K, so the thermoelectric conversion efficiency increases slowly until the maximum efficiency is reached at first. When the cold end temperature is higher than 650–700 K, the saturated vapor pressure at the low-pressure end increases rapidly, which makes the electrochemical potential of BASE decrease rapidly, leading to a rapid decrease of output electric power and conversion efficiency. The conversion efficiency corresponding to the maximum output electric power also has the same change rule. Fig. 3b shows a 2D graph of the AMTEC output electric power as a function of the external load resistance and the cold end temper-
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Fig. 4. AMTEC maximum efficiency and maximum electric power versus AMTEC temperature.
ature (AMTEC BASE hot end temperature is 1123 K). It can be seen from Figs. 3b and 4a that as the increase of the cold end temperature, the output power is basically unchanged at first, but when the temperature is greater than 650–700 K, the output power decreases rapidly. Fig. 3c and d show the 2D graph of AMTEC conversion efficiency and output electric power as a function of BASE temperature respectively (cold end temperature is 670 K). Figs. 2, 3d and 4b show that the AMTEC conversion efficiency and the output electric power increase with the BASE temperature increasing. But, the exit temperature of the nuclear reactor should be kept as low as possible (<1300 K). 4. Space reactor power system reliability 4.1. Radiator potassium heat pipe’s performance TAPIRS code does not include a detailed transient heat pipe model for the radiator, but the effect of the potassium heat pipe heat transfer limit on SRPS’s performance at lower power levels should be considered. The heat transfer characteristics of the radiator potassium heat pipe were analyzed by using the heat pipe heat transfer analysis code SNPS-HP (Li et al., 2015). At higher radiator temperature (>900 K), the capillary limit of the potassium heat pipe is less than the radiator radiation operation curve. Therefore, the system waste heat is assumed to be a function of the capillary limit. When the system is operating at a lower radiator temperature (<600 K), the sonic limit and viscous limit of potassium heat pipe are less than the radiator radiation operation curve, and the system waste heat is a function of the sonic limit and the viscous limit. When the radiator temperature is in the range of 600 K and 900 K, the waste heat is limited by the increase in the temperature of the radiator and its quadratic relationship and is significantly lower than the heat transfer limit of the potassium heat pipes. Under these operating conditions, decreasing the reactor thermal power reduces the radiator temperature and, consequently, reduces the amount of waste heat rejected. The results can be seen in Fig. 5. Fig. 5 also compares the waste heat rejection from each radiator heat pipe as a function of the radiator temperature for an ambient temperature of 250 K. The results in Fig. 5 neglected the temperature difference between the evaporator and the condenser regions of the heat pipe. In fact, this temperature difference could be about
Fig. 5. Preformation of radiator potassium heat pipe.
10 K during the sonic operation of the heat pipes, considering the influence of the surface view factor and the C–C fin efficiency. As Fig. 5 indicates, the system waste heat rejection is limited by the radiator for system thermal power between 240 kW and 1220 kW. For thermal power less than 240 kW, the system waste heat rejection is constrained by the sonic limit and viscous limit of the radiator potassium heat pipes. For thermal power greater than 1220 kW, the system waste heat rejection is constrained by the capillary limit of the radiator potassium heat pipes. 4.2. System safety characteristics of rear radiator surface’s partial area loss It is assumed that the outer surface of the rear radiator plate C– C fins loses 80% of the heat transfer area due to possible external causes after 500 s of normal operation. Fig. 6 shows the results of system safety characteristics of rear radiator surface’s partial area loss. It shows that, since the radiator area is suddenly reduced, the waste rejection power is instantaneously reduced. Then the
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Fig. 6. The SRPS performance of a partial loss of the rear radiator’s surface area.
waste rejection power increases as the surface temperature of the radiator increases to ensure the normal discharge of the waste heat (seen in Fig. 6a and b). Moreover, the cold end temperature of the AMTEC unit increases, while the hot end temperature of AMTEC unit rises less (seen in Fig. 6c), resulting in a decrease in the temperature difference between the two ends of the AMTEC. Such a temperature difference decrease causes the decrease in AMTEC conversion efficiency (seen in Fig. 6d). The pressure difference between the high and low pressure chambers in the AMTEC is reduced, so that the output voltage of the AMTEC is reduced, and the output current is also reduced. The effective heat power and output electric power of the core are reduced. This is because the radiator temperature is increased to offset the effect of the reduction of the radiator area. And the temperature change of the AMTEC hot end is alleviated by the change of AMTEC efficiency, so the temperature of the core fuel remains essentially the same. This indirectly proves the load following characteristics of AMTEC. 4.3 SRPS’s performance of partial radiator surface area loss In this section the SRPS’s performance characteristics under the rear radiator surface’s partial area loss (potassium heat pipe condenser section) are studied, and the results are shown in Fig. 7. The output electric power, the waste rejection power and the reac-
tor thermal power decrease with the increase of the failure area ratio (seen in Fig. 7a). Although the partial loss of the rear radiator’s surface area causes both hot and cold end temperatures of the AMTEC unit to increase, but the temperature difference between two ends of the AMTEC decreases (seen in Fig. 7b). Such a temperature difference decrease causes the decrease in AMTEC conversion efficiency (seen in Fig. 7c), resulting in a lower output electric power. As the proportion of the failure area increases, the temperature of the AMTEC increases, but the temperature difference between the two ends decreases (Fig. 7b), and the load current and voltage decrease as the fractional loss of the rear radiator’s surface area increases. It is also illustrated from Fig. 7 that the radiator surface area loss has little effect on the SAIRS system’s output electric power. For example, a 60% loss of the rear radiator’s surface area causes the SAIRS system’s output electric power to decrease only by 19%. Such a small decrease is due to the increase in the radiator temperature because of the partial loss of its surface area. It enhances the heat rejection capability of the remaining surface, which is proportional to the fourth power of the radiator’s temperature. The increase in the radiator’s heat rejection capability greatly compensates for the decrease caused by the rear radiator’s surface area loss, resulting in a small decrease in the system’s output electric power.
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Fig. 7. Effects on The SRPS performance of a partial loss of the radiator’s surface area.
5. Load following of space reactor power system 5.1. Transient response to the change of load demand The response characteristics of the SAIRS to a 35% change in the load demand by simply adjusting the external load resistance have been studied, and the results are shown in Fig. 8. Assuming the system runs in steady state at the load demand rated power of 110 kW for 200 s, and then the load demand power is reduced to 72 kW in 300 s. The load demand power is kept in 72 kW for 2000 s, and then recovers to 110 kW within 300 s (seen in Fig. 8a). As shown in Fig. 8a, the desired target load demand change operation is achieved by adjusting the external load resistance. However, because of the thermal inertia of the system, there is a certain delay on the output electric power change. Changes in load demand can be met by adjusting the external load resistance in the load following range. The AMTEC conversion efficiency increases from 27.28% initially to 29.08% (a 6.6% rise), following a 35% decrease in the load electrical power demand (Fig. 8c). Deducing the load demand by 35% causes the load voltage to increase from its nominal value of 408 to 589 V DC and the load current
to decrease from its nominal value of 88 to 41 A (Fig. 8b), and the reactor thermal power to decrease from its nominal value of 400 kW to 245 kW (a 38.7% drop) (Fig. 8a). Such a drop in the reactor thermal power occurs without active interference but is caused by the inherent load following characteristic of the AMTEC unit and the negative reactivity feedback of the nuclear reactor. Due to the improvement of the AMTEC conversion efficiency in this process (Fig. 8c), the reactor thermal power decreases (38.7%) more than the output electric power decreases (35%). The increase in the conversion efficiency of the AMTEC is due to the increase in the temperature difference between the ends of the AMTEC as the output electric power decreases (Fig. 8d). 5.2. Dynamic characteristics of external load resistance changes Fig. 9a–f present the dynamic characteristics of SAIRS when the external load resistance changes from 0.77 X to 0.4 X. The results show that the reactor thermal power and the output electric power increase as the external load resistance increases. At the beginning, the reactor UN fuel pellet temperature and cladding temperature are decreased (seen in Fig. 9b), and the positive reactivity is intro-
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Fig. 8. Transient response of SRPS system to a change in load demand.
duced into the core, resulting in an increase in reactor thermal power (seen in Fig. 9a) form 403 kW to 488 kW. As the reactor thermal power increases, the temperature of the fuel increases (seen in Fig. 9b and c). The AMTEC cold end temperature and the radiator temperature are increased, resulting the AMTEC temperature difference between the two ends to decrease and the AMTEC conversion efficiency to decrease from 27.28% to 23.25% (seen in Fig. 9d). So as the Fig. 9f shows, the AMTEC voltage decreases from 408 V DC to 301 V DC. However, because of the decrease in external load resistance, the load current is increased from 88 A initially to 125.6 A (seen in Fig. 9e), resulting in an increase in the final output electric power. 5.3. Load following capability In this section, the system operation characteristic of SAIRS are discussed, and the results are shown in Fig. 10a–f. The results are obtained by varying the load demand or external load resistance from an open-circuit condition (zero load demand) to the shortcircuit current (or maximum operation current), considering the reactor reactivity feedback. The advantage of the heat pipe cooled, AMTEC Conversion SAIRS SRPS is that it can operate stably in the load following area because of the AMTEC load following characteristic and the negative temperature reactivity feedback in the SAIRS reactor.
As Fig. 10b shows, the load following characteristic of the system is effective within the peak electric power. When the load demand increases and the corresponding electric power exceeds the peak value, the AMTEC and the power system will become non-load following. During the non-load following area, the load electric power will decrease as the load demand (or load current) increases. The load following parts of the SAIRS system are expressed in solid lines, and the non-load following parts are expressed in dashed lines which should be avoided. As the load current increases, it is necessary to adjust the external load resistance (Fig. 10a). The result shown in Fig. 10a indicates that if the external load resistance is greater than the critical resistance value of 0.4 X, reducing the external load resistance can improve the electrical power output. It means the SAIRS system has inherent load following characteristics. The reactor UN fuel pellet temperature increases as the load current increases (seen in Fig. 10c), because the reactor thermal power increases as the load current increases (seen in Fig. 10b). But the UN fuel cladding temperature and reactor heat pipe temperature decrease as the load current increases (seen in Fig. 10c) due to the decrease in the AMTEC hot end temperature (seen in Fig. 10d). The AMTEC cold end temperature and the radiator temperature increase with the load current increases (seen in Fig. 10d). The SAIRS temperature variations cause the temperature difference between the two ends of the AMTEC unit
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Fig. 9. The SRPS performance of external load resistance.
to decrease, resulting in the conversion efficiency of AMTEC increases with the increase of load current to the maximum and then decreases (seen in Fig. 10e). And the external load voltage decreases as the load current increases due to the load resistance decreases. 6. Summary and conclusions This paper has discussed the load following characteristics of a heat pipe cooled, AMTEC conversion SRPS, as well as the system’s safety and reliability with a partial loss of the rear radiator’s
surface area. This research was conducted using the Transient Analysis of Heat Pipe Space Reactor Power System (TAPIRS) developed by Xi’an Jiaotong University. The results show that, at steady-state, the AMTEC efficiency and output electric power both firstly increase to maximum value, and then decrease as the external load resistance increases. There are two different critical external load values which make the efficiency or electric power up to peak values. The AMTEC SRPS is inherent load following only above a critical value of the external load demands (or larger than critical external load resistance); below this point, the system is non-load following.
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Fig. 10. Loading following characteristics of SRPS.
The results also show that when the potassium heat pipe radiator’s surface area is partial losing, the reactor thermal power, AMTEC conversion efficiency and output electric power are decreased, but the radiator temperature is increased. In addition, the waste heat rejection, the conversion efficiency and electric power output of the system decrease proportionally to the percentage of loss in the radiator’s surface area. The loss of the radiator’s surface area causes the reactor thermal power to run down to ensure the safety and reliability of the SRPS. Although this low conversion efficiency reduces the electric power output of the system,
the simultaneous increase in the radiator’s surface temperature enhances the heat rejection capability of the remaining radiator surface, causing the system’s electric power to decreases lowly with the radiator’s surface area loss increasing. Acknowledgments This work is supported by the National Natural Science Foundation of China with the grant No. 11375143, which is gratefully acknowledged.
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Reliability and loading-following studies of a heat pipe cooled, AMTEC conversion space reactor power system Ge Li a,⇑, Li Huaqi a,b, Shan Jianqiang a a b
Xi’an Jiaotong University, Xi’an 710049, China Northwest Institute of Nuclear Technology, Xi’an 710024, China
a r t i c l e
i n f o
Article history: Received 31 August 2018 Received in revised form 12 February 2019 Accepted 16 February 2019
Keywords: SRPS AMTEC Load following Radiator Safety and reliability
a b s t r a c t During the progress and development of the space technology, the space reactor power system (SRPS) is one of the best options for providing high power density, long-term life, light weight, and high reliability space power for civil or military space missions. The heat pipe cooled SRPS (HPS) equipped with the static conversion technology Alkali Metal Thermal-to-Electric Conversion units (AMTEC) has good inherent dynamic characteristic for frequent change load following of the space mission power, with high safety and reliability. This paper analyzed the system safety and reliability of an AMTEC conversion HPS, the load following characteristics of the AMTEC conversion and the HPS’s performance in response to partial surface area loss of potassium heat pipe radiator. The results show the following. (1) As the external load resistance increases, the AMTEC thermoelectric conversion efficiency and electric power output both increase to the maximum, and then decrease. The maximum thermoelectric conversion efficiency and electric power output correspond to different critical external load values. The load following capacity of the AMTEC HPS exists only when the external load demands exceed a critical value. (2) When the potassium heat pipe radiator’s surface area is partially lost because of the impact of a meteorite, the reactor thermal power, the AMTEC conversion efficiency and the electric power output also decrease, except the radiator temperature due to the radiator area loss. The waste heat rejection, the conversion efficiency and electric power output of the system decrease proportionally to the radiator’s surface area loss. To ensure the safety and reliability of the SRPS, the reactor thermal power will run down after the loss of the radiator’s surface area. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction With the progress and development of the space technology, the future demands for civil or military space missions focus on high power density (>100 kWe), long term life (7–10 years), light weight, high safety and high reliability of space power (Su et al., 2016). Compared to solar power, chemical power and other traditional space power, the space reactor power system (SRPS) is independent from the space environment and has an edge on the above characteristics. Thus, SRPS can better meet the power demands of the space missions. SRPS reactor cores can be usually classified into thermal spectrum reactors, such as SNAP10-A (Hawley, 1967) and TOPAZ (Gunther, 1990), and fast spectrum reactors. The thermal spectrum reactors are mainly suitable for low-power levels or shorter missions, while the fast spectrum reactors are compact and suitable ⇑ Corresponding author. E-mail address: [email protected] (L. Ge). https://doi.org/10.1016/j.anucene.2019.02.029 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
for high-power levels. SRPS could mainly be cooled using alkali liquid-metal heat pipe, directly circulating liquid metal or binary noble gas mixture of He–Xe. The alkali liquid-metal heat pipe can provide good heat transfer and don’t require an external pump. The radiative radiator with C–C fin structure is the main choice for the radiators of the SRPS. The energy conversion devices of SRPS are mainly divided into static energy conversions, such as thermoelectric (TE) (Metzger and El-Genk, 1991), thermionic (TI) (Lamp and Donnovan, 1991), or AMTEC (El-Genk and Tournier, 2004), and dynamic energy conversions, such as free-piston stirling engines (FPSPs) (Gary and Neill, 2004) or closed Brayton cycle (CBC) (Gallo and El-Genk, 2009). Among them, AMTEC conversion not only has the characteristics of a static thermoelectric conversion device such as a large radiator heat rejection temperature and an inherent load following capability, but also has a high conversion efficiency (>20–25%). At present, there are many researches on the inherent load following capability of the SRPS with TI (ElGenk et al., 1992) and TE (El-Genk et al., 1988; Parlos and Fetiye, 2000) static thermoelectric conversion devices. However, there is
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less research on the system load following capability under reactive feedback conditions for the heat pipe cooling SRPS with AMTEC conversion, it is necessary to study the safety features of AMTEC conversion. The SPRS carries properties of long-term operation in the space environment (7–10 years), changing missions (frequent changes in load demands) and unmanned operation. It is the great task for us how to ensure the safety and reliability of SRPS orbiting in space. The radiation radiator is an essential equipment for the waste heat discharge of the SRPS, and its performance greatly influences the performance of the SRPS. The heat dissipation capacity of the radiation radiator is a function of the heat dissipation plate area and the radiator temperature. The radiator panels exposed in space are prone to be impacted by meteorites and lost part of the heat dissipation area. The radiator panel in the space environment is prone to be exposed. Part of the heat dissipation area is lost due to the impact of debris impact, which has affected the reliable operation of the space reactor power supply. Among all types of space reactors, the SRPS applies the heat pipe cooled, static AMTEC conversion and potassium heat pipe radiator in its design. It becomes one of the best options space power because of good heat transfer performance, easy to startup from a frozen state, inherent load following characteristics and so on. The University of New Mexico’s Institute for Space and Nuclear Power Studies (UNM-ISNPS) has developed the concept design of the SRPS, named SAIRS. SAIRS employs fast-spectrum reactors cooled by sodium heat pipes, C–C armored, potassium heat pipes radiators, W/LiH material c/n shields, and AMTEC units (El-Genk and Tournier, 2004). Compared with other types of SRPS, SAIRS has the characteristics of avoiding single point failure and low specific mass (<26.9 kg/kWe). Its rated electric power is 110 kWe and its output voltage is 400 V. SAIRS uses 18 6.11 kWe NAAMTEC units and integrates them into six thermoelectric conversion modules, each of which contains three Na-AMTEC units. The cold end of each module is connected with the potassium heat pipe radiator plate for heat dissipation, and the hot end is coupled with 10 sodium heat pipes in the core for heat transfer. The design ensures the safety of operation redundancy. This paper takes the typical heat pipe cooled and AMTEC converted SRPS called SAIRS as the research object, and uses the heat pipe cooling fast reactor system transient analysis code TAPIRS (Yuan and Shan, 2016) to analyze its load following characteristics and on-orbit operation safety and reliability. Firstly, the effect of external load resistance and endpoint temperature on the performance of modular AMTEC was studied. Secondly, the transient response of the SAIRS system under the change of load demand was studied, and the load following characteristics and safety reliability of the SAIRS system under the condition of negative feedback were further analyzed. Finally, the effect of loss of some surface area of the radiant radiator on the performance of SAIRS was studied.
2. Description of TAPIRS code The TAPIRS code is developed by Xi’an Jiaotong University for the SRPS with heat pipe cooled, AMTEC energy conversion and heat pipe radiator. It can calculate various transient conditions, including steady state conditions, startup process, heat pipe failure, AMTEC failure, loss of heat sink area and control drum failure. The models of TAPIRS mainly include the reactor core power transient model, UN fuel rod heat transfer model, heat pipe model, AMTEC model, heat pipe radiation radiator model, etc., as shown in Fig. 1. The reactor core power transient model uses the standard point reactor kinetics equations with six delayed neutron groups (Wright
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and Houts, 2001). The solution of the equations is based on highorder endpoint floating method that is applicable to both rigid and inconspicuous cases (Yuan and Hu, 1995). The reactive feedback of the reactor core considers the Doppler effect of the UN fuel element, the fuel expansion of the core, and the temperature reactive feedback of the coolant. The heat transfer model of the core UN fuel rod neglects the axial heat conduction, and assumes that the heat conduction is axisymmetric. The ordinary differential equation of the UN fuel temperature calculation using the lumped parameter method is derived by the volume averaging method. Where, the heat transfer control equation is derived from the Fourier Law and energy conservation law (Wulff, 1980). The heat pipe model mainly includes the high-temperature heat pipe startup model and the normal transient model, namely the free molecular flow model, the ‘‘planar forward” startup model of the transition zone, and the continuous flow thermal resistance network and cyclic process model (Zuo and Faghri, 1998). The free molecular flow model uses the energy balance as a premise to deduce the transient heat transfer equations for the evaporation section and the adiabatic section of the heat pipe, considering the changes in the solid working medium in the wick, as well as the evaporation of the working medium at the interface. The ‘‘plane forward” startup model adopts a closed theoretical analysis model, and it is suitable for the intermediate transition stage. The thermal resistance network and cycle model is a simple heat pipe transient analysis model, including the thermal resistance network model and the working fluid thermodynamic cycle model. The above three models constitute a complete reactor core hightemperature heat pipe transient analysis model. The AMTEC analysis model (Tournier, 1997) mainly includes: (1) The thermal model, which calculates the AMTEC temperature and parasitic heat loss. (2) The pressure loss model, which calculates the alkali metal working fluid pressure loss in AMTEC. (3) The electrical model, which calculates the BASE ionic losses, electrical losses in current collectors and connecting leads, total electrical current and the developed potential in the BASE, as functions of temperatures of BASE and condenser, and sodium pressures across the BASE. (4) The resistance model, which calculates the structural resistance of each part of AMTEC. (5) Circulation flow model, which calculates the mass flow rate at the liquid-return porous artery, as a function of pressure and temperatures. The heat pipe radiator model uses the lumped parameter ‘‘twopoint analysis model” of the heat pipe analysis (Gaeta, 1988).
3. AMTEC steady-state performance A steady-state AMTEC unit performance analysis code, SNPS_AMTEC (Zhu et al., 2016), consists of three models: The pressure loss model, the electric model and the heat loss model. The steady-state load following characteristics of AMTEC are determined by analyzing the influence of the cold and hot end temperature, external load resistance and input power on the performance of the AMTEC unit. Fig. 2 shows the steady state responses of AMTEC units when the BASE temperature is 1123 K and the cold end temperature is 670 K. Fig. 2a shows the change of AMTEC thermoelectric conversion efficiency and output power with external load RL. With the increase of external load resistance, the AMTEC conversion efficiency and output power increase to 26.9% and 8.2 kWe respectively, and then decrease gradually. The two critical external load resistance values are about 1.14 X and 0.18 X respectively, and they are almost independent of the AMTEC end temperatures, as shown in Fig. 3. Fig. 2b shows the curves of AMTEC output current and voltage varying with external load resistance. The AMTEC
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Fig. 1. Schematic diagram of the TAPIRS code.
Fig. 2. Steady state response of AMTEC as a function of external load resistance and input thermal power.
component of the SAIRS is designed to connected in series in 3 parallel strings (each with 6 AMTEC units connected in series) for redundancy, while providing a terminal voltage of 400 V DC. Thus,
the output voltage of a single AMTEC unit must be 400/6 = 66.7 V DC. It means the AMTEC external load resistance should be greater than 0.9 X.
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Fig. 3. Efficiency and electric power versus AMTEC temperature and external load.
Fig. 2c shows the input and discharge power as a function of external load for the given hot and cold end temperature. As the external load increases, the input power decreases. As analyzed by Fig. 2a and c, when the external load is greater than the critical value of 0.18 X, the output electric power can be increased by reducing the external load resistance and increasing the input power. It means that the AMTEC has load following capability. When it is less than the critical value of 0.18 X, increasing the input power does not increase the output electric power, and the AMTEC does not have the load following capability. Fig. 2d shows the AMTEC conversion efficiency and output power as a function of input power. With the increase of input power, the AMTEC conversion efficiency and output electric power increase firstly to the maximum values 26.9% and 8.2 kWe respectively and then gradually reduce, but their extreme point positions are not the same. Therefore, AMTEC has inherent load following capability within a certain range, and it does not have inherent load following capability beyond the critical value of external load.
Fig. 3a shows a 2D graph of the AMTEC conversion efficiency as a function of the external load resistance and the cold end temperature (AMTEC BASE hot end temperature is 1123 K). As Figs. 3a and 4a show that the AMTEC conversion efficiency slowly increases to the maximum value about 28% with the increase of the cold end temperature, and then decreases rapidly. This is because the temperature difference between the hot and cold ends decreases and the parasitic heat loss Qrej decreases when the cold end temperature increases from 400 K to 800 K, so the thermoelectric conversion efficiency increases slowly until the maximum efficiency is reached at first. When the cold end temperature is higher than 650–700 K, the saturated vapor pressure at the low-pressure end increases rapidly, which makes the electrochemical potential of BASE decrease rapidly, leading to a rapid decrease of output electric power and conversion efficiency. The conversion efficiency corresponding to the maximum output electric power also has the same change rule. Fig. 3b shows a 2D graph of the AMTEC output electric power as a function of the external load resistance and the cold end temper-
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Fig. 4. AMTEC maximum efficiency and maximum electric power versus AMTEC temperature.
ature (AMTEC BASE hot end temperature is 1123 K). It can be seen from Figs. 3b and 4a that as the increase of the cold end temperature, the output power is basically unchanged at first, but when the temperature is greater than 650–700 K, the output power decreases rapidly. Fig. 3c and d show the 2D graph of AMTEC conversion efficiency and output electric power as a function of BASE temperature respectively (cold end temperature is 670 K). Figs. 2, 3d and 4b show that the AMTEC conversion efficiency and the output electric power increase with the BASE temperature increasing. But, the exit temperature of the nuclear reactor should be kept as low as possible (<1300 K). 4. Space reactor power system reliability 4.1. Radiator potassium heat pipe’s performance TAPIRS code does not include a detailed transient heat pipe model for the radiator, but the effect of the potassium heat pipe heat transfer limit on SRPS’s performance at lower power levels should be considered. The heat transfer characteristics of the radiator potassium heat pipe were analyzed by using the heat pipe heat transfer analysis code SNPS-HP (Li et al., 2015). At higher radiator temperature (>900 K), the capillary limit of the potassium heat pipe is less than the radiator radiation operation curve. Therefore, the system waste heat is assumed to be a function of the capillary limit. When the system is operating at a lower radiator temperature (<600 K), the sonic limit and viscous limit of potassium heat pipe are less than the radiator radiation operation curve, and the system waste heat is a function of the sonic limit and the viscous limit. When the radiator temperature is in the range of 600 K and 900 K, the waste heat is limited by the increase in the temperature of the radiator and its quadratic relationship and is significantly lower than the heat transfer limit of the potassium heat pipes. Under these operating conditions, decreasing the reactor thermal power reduces the radiator temperature and, consequently, reduces the amount of waste heat rejected. The results can be seen in Fig. 5. Fig. 5 also compares the waste heat rejection from each radiator heat pipe as a function of the radiator temperature for an ambient temperature of 250 K. The results in Fig. 5 neglected the temperature difference between the evaporator and the condenser regions of the heat pipe. In fact, this temperature difference could be about
Fig. 5. Preformation of radiator potassium heat pipe.
10 K during the sonic operation of the heat pipes, considering the influence of the surface view factor and the C–C fin efficiency. As Fig. 5 indicates, the system waste heat rejection is limited by the radiator for system thermal power between 240 kW and 1220 kW. For thermal power less than 240 kW, the system waste heat rejection is constrained by the sonic limit and viscous limit of the radiator potassium heat pipes. For thermal power greater than 1220 kW, the system waste heat rejection is constrained by the capillary limit of the radiator potassium heat pipes. 4.2. System safety characteristics of rear radiator surface’s partial area loss It is assumed that the outer surface of the rear radiator plate C– C fins loses 80% of the heat transfer area due to possible external causes after 500 s of normal operation. Fig. 6 shows the results of system safety characteristics of rear radiator surface’s partial area loss. It shows that, since the radiator area is suddenly reduced, the waste rejection power is instantaneously reduced. Then the
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Fig. 6. The SRPS performance of a partial loss of the rear radiator’s surface area.
waste rejection power increases as the surface temperature of the radiator increases to ensure the normal discharge of the waste heat (seen in Fig. 6a and b). Moreover, the cold end temperature of the AMTEC unit increases, while the hot end temperature of AMTEC unit rises less (seen in Fig. 6c), resulting in a decrease in the temperature difference between the two ends of the AMTEC. Such a temperature difference decrease causes the decrease in AMTEC conversion efficiency (seen in Fig. 6d). The pressure difference between the high and low pressure chambers in the AMTEC is reduced, so that the output voltage of the AMTEC is reduced, and the output current is also reduced. The effective heat power and output electric power of the core are reduced. This is because the radiator temperature is increased to offset the effect of the reduction of the radiator area. And the temperature change of the AMTEC hot end is alleviated by the change of AMTEC efficiency, so the temperature of the core fuel remains essentially the same. This indirectly proves the load following characteristics of AMTEC. 4.3 SRPS’s performance of partial radiator surface area loss In this section the SRPS’s performance characteristics under the rear radiator surface’s partial area loss (potassium heat pipe condenser section) are studied, and the results are shown in Fig. 7. The output electric power, the waste rejection power and the reac-
tor thermal power decrease with the increase of the failure area ratio (seen in Fig. 7a). Although the partial loss of the rear radiator’s surface area causes both hot and cold end temperatures of the AMTEC unit to increase, but the temperature difference between two ends of the AMTEC decreases (seen in Fig. 7b). Such a temperature difference decrease causes the decrease in AMTEC conversion efficiency (seen in Fig. 7c), resulting in a lower output electric power. As the proportion of the failure area increases, the temperature of the AMTEC increases, but the temperature difference between the two ends decreases (Fig. 7b), and the load current and voltage decrease as the fractional loss of the rear radiator’s surface area increases. It is also illustrated from Fig. 7 that the radiator surface area loss has little effect on the SAIRS system’s output electric power. For example, a 60% loss of the rear radiator’s surface area causes the SAIRS system’s output electric power to decrease only by 19%. Such a small decrease is due to the increase in the radiator temperature because of the partial loss of its surface area. It enhances the heat rejection capability of the remaining surface, which is proportional to the fourth power of the radiator’s temperature. The increase in the radiator’s heat rejection capability greatly compensates for the decrease caused by the rear radiator’s surface area loss, resulting in a small decrease in the system’s output electric power.
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Fig. 7. Effects on The SRPS performance of a partial loss of the radiator’s surface area.
5. Load following of space reactor power system 5.1. Transient response to the change of load demand The response characteristics of the SAIRS to a 35% change in the load demand by simply adjusting the external load resistance have been studied, and the results are shown in Fig. 8. Assuming the system runs in steady state at the load demand rated power of 110 kW for 200 s, and then the load demand power is reduced to 72 kW in 300 s. The load demand power is kept in 72 kW for 2000 s, and then recovers to 110 kW within 300 s (seen in Fig. 8a). As shown in Fig. 8a, the desired target load demand change operation is achieved by adjusting the external load resistance. However, because of the thermal inertia of the system, there is a certain delay on the output electric power change. Changes in load demand can be met by adjusting the external load resistance in the load following range. The AMTEC conversion efficiency increases from 27.28% initially to 29.08% (a 6.6% rise), following a 35% decrease in the load electrical power demand (Fig. 8c). Deducing the load demand by 35% causes the load voltage to increase from its nominal value of 408 to 589 V DC and the load current
to decrease from its nominal value of 88 to 41 A (Fig. 8b), and the reactor thermal power to decrease from its nominal value of 400 kW to 245 kW (a 38.7% drop) (Fig. 8a). Such a drop in the reactor thermal power occurs without active interference but is caused by the inherent load following characteristic of the AMTEC unit and the negative reactivity feedback of the nuclear reactor. Due to the improvement of the AMTEC conversion efficiency in this process (Fig. 8c), the reactor thermal power decreases (38.7%) more than the output electric power decreases (35%). The increase in the conversion efficiency of the AMTEC is due to the increase in the temperature difference between the ends of the AMTEC as the output electric power decreases (Fig. 8d). 5.2. Dynamic characteristics of external load resistance changes Fig. 9a–f present the dynamic characteristics of SAIRS when the external load resistance changes from 0.77 X to 0.4 X. The results show that the reactor thermal power and the output electric power increase as the external load resistance increases. At the beginning, the reactor UN fuel pellet temperature and cladding temperature are decreased (seen in Fig. 9b), and the positive reactivity is intro-
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Fig. 8. Transient response of SRPS system to a change in load demand.
duced into the core, resulting in an increase in reactor thermal power (seen in Fig. 9a) form 403 kW to 488 kW. As the reactor thermal power increases, the temperature of the fuel increases (seen in Fig. 9b and c). The AMTEC cold end temperature and the radiator temperature are increased, resulting the AMTEC temperature difference between the two ends to decrease and the AMTEC conversion efficiency to decrease from 27.28% to 23.25% (seen in Fig. 9d). So as the Fig. 9f shows, the AMTEC voltage decreases from 408 V DC to 301 V DC. However, because of the decrease in external load resistance, the load current is increased from 88 A initially to 125.6 A (seen in Fig. 9e), resulting in an increase in the final output electric power. 5.3. Load following capability In this section, the system operation characteristic of SAIRS are discussed, and the results are shown in Fig. 10a–f. The results are obtained by varying the load demand or external load resistance from an open-circuit condition (zero load demand) to the shortcircuit current (or maximum operation current), considering the reactor reactivity feedback. The advantage of the heat pipe cooled, AMTEC Conversion SAIRS SRPS is that it can operate stably in the load following area because of the AMTEC load following characteristic and the negative temperature reactivity feedback in the SAIRS reactor.
As Fig. 10b shows, the load following characteristic of the system is effective within the peak electric power. When the load demand increases and the corresponding electric power exceeds the peak value, the AMTEC and the power system will become non-load following. During the non-load following area, the load electric power will decrease as the load demand (or load current) increases. The load following parts of the SAIRS system are expressed in solid lines, and the non-load following parts are expressed in dashed lines which should be avoided. As the load current increases, it is necessary to adjust the external load resistance (Fig. 10a). The result shown in Fig. 10a indicates that if the external load resistance is greater than the critical resistance value of 0.4 X, reducing the external load resistance can improve the electrical power output. It means the SAIRS system has inherent load following characteristics. The reactor UN fuel pellet temperature increases as the load current increases (seen in Fig. 10c), because the reactor thermal power increases as the load current increases (seen in Fig. 10b). But the UN fuel cladding temperature and reactor heat pipe temperature decrease as the load current increases (seen in Fig. 10c) due to the decrease in the AMTEC hot end temperature (seen in Fig. 10d). The AMTEC cold end temperature and the radiator temperature increase with the load current increases (seen in Fig. 10d). The SAIRS temperature variations cause the temperature difference between the two ends of the AMTEC unit
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Fig. 9. The SRPS performance of external load resistance.
to decrease, resulting in the conversion efficiency of AMTEC increases with the increase of load current to the maximum and then decreases (seen in Fig. 10e). And the external load voltage decreases as the load current increases due to the load resistance decreases. 6. Summary and conclusions This paper has discussed the load following characteristics of a heat pipe cooled, AMTEC conversion SRPS, as well as the system’s safety and reliability with a partial loss of the rear radiator’s
surface area. This research was conducted using the Transient Analysis of Heat Pipe Space Reactor Power System (TAPIRS) developed by Xi’an Jiaotong University. The results show that, at steady-state, the AMTEC efficiency and output electric power both firstly increase to maximum value, and then decrease as the external load resistance increases. There are two different critical external load values which make the efficiency or electric power up to peak values. The AMTEC SRPS is inherent load following only above a critical value of the external load demands (or larger than critical external load resistance); below this point, the system is non-load following.
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Fig. 10. Loading following characteristics of SRPS.
The results also show that when the potassium heat pipe radiator’s surface area is partial losing, the reactor thermal power, AMTEC conversion efficiency and output electric power are decreased, but the radiator temperature is increased. In addition, the waste heat rejection, the conversion efficiency and electric power output of the system decrease proportionally to the percentage of loss in the radiator’s surface area. The loss of the radiator’s surface area causes the reactor thermal power to run down to ensure the safety and reliability of the SRPS. Although this low conversion efficiency reduces the electric power output of the system,
the simultaneous increase in the radiator’s surface temperature enhances the heat rejection capability of the remaining radiator surface, causing the system’s electric power to decreases lowly with the radiator’s surface area loss increasing. Acknowledgments This work is supported by the National Natural Science Foundation of China with the grant No. 11375143, which is gratefully acknowledged.
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