Thermal-hydraulic analysis of the thermoelectric space reactor power system with a potassium heat pipe radiator

Annals of Nuclear Energy 136 (2020) 107018

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Thermal-hydraulic analysis of the thermoelectric space reactor power system with a potassium heat pipe radiator Wenwen Zhang a,b, Dalin Zhang a,b,⇑, Xiao Liu a,b, Wenxi Tian a,b, Suizheng Qiu a,b, G.H. Su a,b a b

School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, PR China Shaanxi Key Lab. of Advanced Nuclear Energy and Technology, School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, PR China

a r t i c l e

i n f o

Article history: Received 21 May 2019 Received in revised form 11 August 2019 Accepted 26 August 2019

Keywords: Space reactor Thermal-hydraulic Thermoelectric conversion Heat pipe radiator

a b s t r a c t The thermoelectric space reactor power system conceptual design incorporates fast reactor, liquidlithium primary coolant loops that transfer heat to potassium-filled high temperature heat pipes and thermoelectric generators. An integrated system analysis model was developed to study the operating characteristics of the space power system, which consisted of reactor thermal-hydraulic model, neutron kinetics model, thermoelectric energy conversion assembly (ECA) model, heat pipe radiator model etc. One-dimensional thermal-hydraulic model was applied to model the coolant circuit. Quasi twodimensional analysis models for heat transfer of fuel element, ECA and the heat pipe fin were established. Considering the thermoelectric conversion phenomena, an equivalent electric efficiency model was inserted in the ECA model. Both finite element method and thermal resistance network were applied to simulate the potassium heat pipe system. The normal operation condition and two demonstration accident scenarios (unprotected inadvertent movement of a sliding reflector and loss of heat pipes) were calculated to prove the capabilities of the new system model. Ó 2019 Published by Elsevier Ltd.

1. Introduction Military and civilian efforts in space will place demands on auxiliary systems that conventional designs cannot meet. For the operation in the outer space, the power system must have high system reliability and autonomy. Nuclear energy judiciously applied in the space missions has several distinctive advantages over the traditional energy. It has the long operating lifetime, compact size and low to moderate mass, and can operate in hostile space environments. For space power applications in the kilowatt and megawatt regime, there are a number of interesting advanced nuclear reactor technology and energy conversion options. These reactor designs include liquid metal cooled reactor (Bankston et al., 1985), heat pipe cooled reactor (Schriener and El-Genk, 2014), gas cooled reactor (Cassady et al., 2008) et al. The alkali metal (Zhang et al., 2016; Summerer et al., 2015), such as lithium, potassium, sodium or their binary mixture, is utilized as the reactor coolant. The energy conversion options covered in space nuclear program can be divided into two categories, static and dynamic conversions. The static conversion includes thermoelectric, thermionic, alkali metal thermal to electric et al (El-Genk, 2009). The ⇑ Corresponding author at: School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, PR China. E-mail address: [email protected] (D. Zhang). https://doi.org/10.1016/j.anucene.2019.107018 0306-4549/Ó 2019 Published by Elsevier Ltd.

dynamic energy conversion mainly consists of Brayton cycle, Rankine cycle and Stirling cycle (Mason, 2001). The USA and Russian (including the former Soviet Union) have developed or even launched series of space nuclear reactor power systems. The thermionic reactor power system TOPAZ-II, using the NaK-78 and single cell thermionic energy conversion in the reactor vessel, is a representative work of Russian space reactor design (Voss and Rodriguez, 1994). The US proposed a lithium-cooled reactor general design, SP-100 system, for a variety of mission types (Truscello, 1983), which can be coupled to various energy conversion systems. Synchronized with the space reactor power system design, the numerical simulations were also performed. The reactor, energy conversion and heat rejection radiator are the mainly three components of the space reactor system. Due to the unique structure and working principle of space reactor, it is impossible to model it with commonly used land-based light water reactor thermal-hydraulic system codes, such as RELAP5 and TRACE. Particularly, the alkali metal heat pipe components and thermoelectric assemblies are beyond the capabilities of these codes. Some special codes were developed to simulate the space power system. The El-Genk Group in New Mexico University operated a lot of intensive work, such as the Thermionic Transient Analysis Model (TITAM) (El-Genk et al., 1993; Paramonov, 1993) and the Space Nuclear Power Systems Analysis Model (SNPSAM) (El-Genk and Seo, 1986). The Matlab

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Simulink is also a practical analysis tool for the space reactor systems (El-Genk and Tournier, 2006). From the available literatures, some research institutes and national laboratories also developed corresponding analysis codes for their space reactor facilities, but the detailed information were not published (Voss, 1993). A system analysis code for the TOPAZ-II thermionic power system were developed in our previous work (Zhang et al., 2016). But this system has a special design configuration and is not representative in the space reactor power system family. It’s a single loop system with in-core electric generation and pumped loop radiator. In fact, the out-core energy conversion and heat pipe radiator are adopted by most of space reactor power systems. In order to develop new method to simulate these systems, a liquid-lithium cooled space reactor power system model with thermoelectric generators and potassium-filled heat pipe radiator was first established and introduced in this work. 2. System description and model development The external thermoelectric conversion nuclear power system has a quite different system design and arrangement from TOPAZ-II thermionic system. In this work, a technically mature space power concept, the 100kWe SP-100 system, is selected for the analysis. Fig. 1 shows the system configuration comparison. The reactor, energy conversion subsystem and heat rejection subsystem characteristics are summarized in Table 1. It is a lithiumcooled UN-fueled fast reactor coupled to external thermoelectric converters. The primary coolant transport loop mainly consists of the electromagnetic thermoelectric electromagnetic (TEM) pump, gas separator accumulator. The secondary coolant loop mainly consists of the pump and heat pipe radiator panels which reject waste heat into outer space. The thermoelectric energy conversion assembly connects the primary loop and secondary loop, which acts as both heat exchanger and electric generator. It is essential to develop new component and mechanism models for expanded capabilities. 2.1. Reactor neutronics and thermal-hydraulics model Fig. 2 shows the cross-section views of SP-100 reactor and TOPAZ-II reactor. The reactor configuration, arrangement, reactiv-

Table 1 Characteristics comparison between 100 kWe thermoelectric system and 5 kWe thermionic system. Parameter

Value

Reactor thermal power Electrical power Coolant Reactor neutron spectrum Reactor Fuel Fuel pin Reactivity control Power converter type Electromagnetic pump Effective radiator area Radiation element Radiator fin material

SP-100 system

TOPAZ-II system

2.4 MW

115 kW

106 kW Lithium Fast

4.5–5.5 kW 78w%K and 22w%Na Epithermal

UN Wire wrapped Be Slider & safety rods Thermoelectric Thermoelectric 98.5 m2 Potassium heat pipe C–C

UO2 TFE Control drums Thermionic DC conduction 7.2 m2 Radiating coolant pipe Copper with black enamel coating

ity control mechanism, the coolant and fuel are quite different. The main components of the reactor are: fuel and cladding, honeycomb structure, reflector supports, safety rods, grid for pin support, reactor vessel and core support structure. Uranium nitride and PWC-11 niobium are utilized as reactor fuel and structure material. There are 12 radial BeO reflector segments arranged out of the reactor vessel to control the reactor reactivity during normal operation. Three safety rods are arranged in the core for safety propose. For the purpose of the SP-100 reactor analysis, a revised thermal-hydraulic model coupled with neutron physical model was developed. The neutron model consists of point reactor kinetics model, reactivity feedback model and decay heat model. The neutron kinetics model of the SP-100 reactor takes three mechanisms of reactivity feedback into account: Doppler feedback reactivity qF (reactor fuel temperature), reactor core expansion feedback reactivity qE (structure material) and lithium expansion feedback reactivity qLi (coolant temperature).

qF ðtÞ ¼ aD ln

T F ðtÞ T F ð0Þ

Fig. 1. The configuration and schematic comparison between thermoelectric system and thermionic system.

ð1Þ

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Fig. 2. Cross-section views of TOPAZ-II reactor and SP-100 reactor.

qE ðtÞ ¼ aF ðT F ðtÞ  T F ð0ÞÞ þ aC ðT C ðtÞ  T C ð0ÞÞ þ aR ðT R ðtÞ  T R ð0ÞÞ

ð2Þ

qLi ðtÞ ¼ aLi ðT Li ðtÞ  T Li ð0ÞÞ

ð3Þ

The distribution of the core fission power was extracted from the reference (Akimov et al., 2012), in which the discrete ordinates neutral particle transport code TWODANT was selected to perform the physical simulation. The detailed structure of the fuel rod is presented in Fig. 3. The UN fuel active zone is surrounded by BeO neutron reflector materials for flattening the power and reducing the critical volume. A plenum is arranged at the end of the rod to accommodate the fission gasses released from the fuel pin. On the outer surface of the cladding, a wire wrap is attached helically to maintain the proper space between the fuel pins. The fuel rods are arranged in a triangular lattice inside the hexagonal fuel assembly. In the present model, the fuel pin was divided into small axial segments, as shown in Fig. 3(b). In each segment, the radial transient heat conduction equations were solved while heat conduction between the axial segments was neglected, for the high ratio of the length and radius of the fuel rod. The transient radial heat conduction equations of the fuel rod components can be written as follows: Fuel:

qF ðT F ÞcF ðT F Þ

  @T F ðr; tÞ 1 @ @T F ðr; tÞ ¼ kF ðT F Þr þ qðr; tÞ @t r @r @r

ð4Þ

where, qu is the density of the fuel; cu is the heat capacity of the fuel; ku is the fuel heat conductivity coefficient; q is the volume heat source of the fuel; TF is the temperature of the fuel. Nb-Zr cladding:

  @T ðr; tÞ 1 @ @T C ðr; tÞ ¼ kC ðT C Þr qC ðT C ÞcC ðT C Þ C @t r @r @r

ð5Þ

where, qc is the density of the cladding; cc is the heat capacity of the cladding; kc is the cladding heat conductivity coefficient; Tc is the temperature of the cladding. The equivalent secondary boundary condition is utilized for the outer surface of fuel and inner surface of cladding, which can be written as:

kF

  @T F rCI @T C ¼ hg T F jr¼rFO  T C jr¼r jr¼rFO ¼ kC j CI @r r FO @r r¼rCO The boundary condition on the cladding outer surface:

ð6Þ

kC

  @T C jr¼rCO ¼ hLi T C jr¼rCO  T Li @r

ð7Þ

where, hg is the equivalent fission gas gap heat transfer coefficient; hLi is the heat transfer coefficient between the lithium coolant and the cladding; TLi is the temperature of lithium. 2.2. Thermoelectric energy converter analysis model The thermoelectric conversion is a preferable technical option in static conversion candidates, for its technically maturity and compatibility. The 100 kWe SP-100 power system consists of 12 energy converter assemblies (ECAs), arranged between the primary coolant loop and radiator coolant loop. Fig. 4 shows the multistage structures of the ECA. In this design concept, each EAC consists of 6 substructures, which are named as thermoelectric converter assemblies (TCAs), as shown in Fig. 4(b). Fig. 4(c) presents the basic structure of TCA, in which 120 thermoelectric cells are aligned in parallel arrangement. The most basic power units are the thermoelectric couples of N and P Si-Ge alloy semiconductors. The TE unit is the basic element in the analysis model. Each TE unit consists of a P-N thermocouple module, a compatible liner, and a high voltage insulator material. In this work, a heat transfer model coupled with simplified thermoelectric conversion mechanism model was developed. Due to the symmetric configuration of the ECA, half of the primary lithium duct, one secondary lithium duct and the corresponding thermocouple were modeled in the TE unit, which is shown in Fig. 4(d). The basic governing equations of the heat transfer through the TE cell can be written as follows: The primary and secondary coolant ducts:

Aduct qduct cduct

@T duct @T duct ðt; yÞ ¼ W duct cduct @y @t  U duct hduct ðT duct ðt; yÞ  T W ðt; yÞÞ

ð8Þ

The hot side and cold side compliant pads:

qpad cpad

@T pad ðt; xÞ @T pad ðt; xÞ ¼ kpad @t @x

ð9Þ

The Si-Ge thermoelectric conversion:

qTE cTE

@T TE ðt; xÞ @ TE ðt; xÞ ¼ kTE ð1  gÞ @t @x

ð10Þ

where, Wduct is the coolant mass flow rate; Uduct is the duct perimeter; hc is the heat transfer coefficient; Tduct is the coolant tempera-

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Fig. 3. Schematics of the wire wrapped fuel element and calculating cell division.

ture; TW is the wall temperature; Tpad is the compliant pad temperature; TTE is the TE unit temperature. Several phenomena make a common contribution to the thermoelectric conversion, including Seebeck effect, Thomson effect, Peltier effect, Fourier effect and Joule heating (Schriener and ElGenk, 2014). The first three phenomena have reversible effect to the conversion while the last two have irreversible effect. In the present work, the SP-100 electric power was obtained by multiplying the heat transfer rates from the TE cell with the efficiency of the thermoelectric generators. The conversion efficiency is defined by the following equation:

g¼

RL I 2 Spn T 2 DT=IRi þ K g DT 2 =Ri I2  DT=2

ð11Þ

The RL =Ri is named as load factor M. The electric current I is equal to the total voltage divided by the resistance:

I¼

V t Spn DT Spn ðT 2  T 1 Þ ¼ ¼ Rt Ri ð1 þ MÞ Rt

ð12Þ

2.3. Alkali-metal heat pipe panel model Residual heat from the secondary lithium loop is radiated to outer space via potassium-filled heat pipes of the radiating panel. There are 12 radiating panels in this conception. Two arrays of heat pipes are inserted in the lithium coolant transport ducts. The finite

element method (FEM) and heat resistance network model were utilized to predict the performance of heat pipe radiator. Although FEM can provide the detailed information of the heat pipe operation, the numerical stability and calculating speed are not acceptable for the system analysis or real-time simulator. The heat resistance network analysis conjugated with a two-dimensional fin model was proposed, which is shown in Fig. 5. Compared with the former method, heat pipe network model is a simple and understandable practical model which has a faster calculating speed (Zuo and Faghri, 1998). As illustrated in Fig. 5, thermal resistances of the heat transfer processe from lithium coolant loop to radiating fin consist of the evaporator heat conduction resistances (R1, R2, R3), evaporation resistance (R4), steam flow resistance (R5), condensation resistance (R6), condenser section heat conduction resistances (R7, R8, R9), and axial resistances of adiabatic section (R10, R11, R12). Based on the heat transfer network system of the heat pipe, a transient temperature behavior predicting model was developed. The Ti(t) is the node temperature between two adjacent thermal resistances. The following conservation equation associated with the node temperature can be derived:

qi ci V i

dT i ðtÞ T i1 ðtÞ  T i ðtÞ T iþ1 ðtÞ  T i ðtÞ ¼ Pup þ Pdown i i dt Ri1 Riþ1

ð13Þ

where R is the thermal resistance of each segment of the pipe, and

P is the heat transfer area between adjacent thermal resistances.

W. Zhang et al. / Annals of Nuclear Energy 136 (2020) 107018

Fig. 4. Energy conversion assembly model.

Fig. 5. Heat pipe panel model.

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The heat pipe evaporator section outer surface boundary can be written as:

T 1 ðtÞ  T e ðtÞ k1 ¼ he ðT Li ðtÞ  T e ðtÞÞ d1 =2

ð14Þ

where d is the thickness and he is the heat transfer coefficient between coolant and outer surface of evaporator section. The outer surface boundary of condenser section can be estimated by the third thermal boundary condition as follows:

k9

T 9 ðtÞ  T c ðtÞ ¼ qCC ðtÞ d9 =2

ð15Þ

where qc-c is the radiating heat rejection from fin and heat pipe condenser outer surface. 2.4. Simulation method Fig. 6 shows the schematic flowchart of system model, which contains the main components. The reactor core is divided into two channels, which present the high enrichment fuel assembly and low enrichment fuel assembly, respectively. Due to partial loop operation was not considered in the present work, only one of the twelve loops was modeled. The representative loop contains core, reactor inlet plenum and outlet plenum, energy conversion component, electromagnetic pump, pipeline and heat radiating panel. The volume accumulator was treated as the pressure reference point during the calculation. A set of coupled nonlinear ordinary differential equations were finally derived from the mathematic models above to describe the system behavior and were solved by the GEAR method. The Gear method has a good performance on solving stiff differential equations (Gear, 1971).

3.1. Normal operation condition analysis As the initial condition of the demonstration accidents, the steady state analysis was firstly performed. Fig. 7 presents the axial temperature profiles of core components in both calculated channels and coolant temperature distributions in ECAs. The radial non-uniform power distribution leads to temperature difference between the two calculated channels. The maximum fuel temperature is 1681 K, much lower than that of TOPAZ-II system. It is understandable for the higher heat conduction coefficient of UN fuel and the simpler fuel rods configuration. The cladding temperature curve has the same tendency as the coolant temperature curve. The highest coolant temperature is 1393 K, which is much higher than the sodium-potassium coolant. Compared with the in-core thermionic conversion power system, the lower fuel temperature and higher coolant outlet temperature are the significant advantages of out-core thermoelectric conversion power system. In the ECAs, the coolant temperature of the primary duct falls from 1376 K to 1280 K while that of the secondary duct rises from 820 K to 873 K. It conduces to keep the temperature gradient across the TE unit to be uniform, leading to a higher conversion efficiency of the thermocouples. Fig. 8 shows the temperature and electrical efficiency profiles of TE unit. Due to the small heat conduction coefficient of semicon-

3. Results and discussion To demonstrate the prediction capability and performance of the thermoelectric power system model, the normal operation condition and two accident scenarios were calculated and analyzed. One is the unprotected reactivity insertion accident, which occurs due to the inadvertent movement of a reflector segment during the nominal operation condition. The other one is loss of heat sink accident, and herein, it is assumed 15% of heat pipes in the radiator panel are damaged by meteorites or space debris. Simplification of the accident process is sought appropriate for the situation where detailed parameter and test data are lacked. Thus, it was assumed that no subsequent action of safety system.

Fig. 7. Axial temperature distribution of the core components and TE unit coolant ducts.

Fig. 6. Flow chart of the models developed for the thermoelectric power system.

W. Zhang et al. / Annals of Nuclear Energy 136 (2020) 107018

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3.2. Unprotected inadvertent movement of a reflector segment

Fig. 8. Temperature contour and conversion efficiency of the TE unit.

ductor material and the thermoelectric conversion heat loss, the temperature gradient in the thermoelectric module is larger than other components. The efficiency decreases from 5.2% to 3.9%, and the average value is about 4.55%. This is consistent with the TE unit temperature profile. Besides the material properties, the electric efficiency also depends on the hot side temperature and temperature difference across the TE unit.

This transient calculation assumed that one of the slide reflectors had an inadvertent movement and a positive reactivity of 100 pcm was inserted. The initial operation of 50 s was at full power steady condition and the transient started from 50 s and continued until 500 s. As shown in Fig. 9(b), the reactor thermal power rose rapidly from the nominal power of 2.4 MW to 3.08 MW during the initial stage of transient. Due to negative reactivity feedback coefficient of reactor, it fell gradually to a new stable power level of 2.6 MW. As shown in Fig. 9(a), the Doppler feedback contributed to a minor change in the reactivity for the high U-235 enrichment. The most significant reactivity feedback part was caused by the expansion of reactor materials. And these materials have faster temperature response than the coolant. The maximum reactivity insertions of coolant and reactor materials were 19 pcm and 98 pcm, respectively, while that of Doppler effect was only 0.0013 pcm. The core coolant inlet temperature rose initially but more slowly than the outlet temperature in response to the increasing cooling across the energy conversion assembly. The highest core coolant outlet temperature and inlet temperature were 1427 K and 1337 K, respectively, lower than the lithium boiling point. The highest temperatures of fuel pellet and cladding were 1798 K and 1464 K, respectively, both below the safety limit values. Corresponding to coolant temperature, the TE converter efficiency response was shown in Fig. 9(d). The TE1 is the first calculated cell near the primary coolant inlet while the TE10 is the

Fig. 9. System responses in the inadvertent reflector movement accident.

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last calculated cell near the outlet. The conversion efficiency of TE1 went up from 5.17% to 5.65%, and that of TE10 increased from 3.93% to 4.29%. The electric power rose from 109.3 kW to 145.7 kW at the initial stage, in response to the rising power and energy conversion efficiency. The heat transfer enhancement in TE cell and rising of thermoelectric conversion efficiency made common effects on the electric power output.

ture. The heat transfer rate between the primary side and secondary side of the energy conversion assembly declined and the primary coolant average temperature rose, consequently. Meanwhile, it appeared that the fuel temperature responded faster than the cladding temperature during the initial stage of the transient. A power mismatch existed for the core power exceeding the total heat rejection rate of the damaged radiator panel. The temperature

3.3. Loss of heat pipes in the radiator panels This transient calculation assumed that part of the radiator panels was damaged due to meteorite impingement, and 15% of the heat pipes lost the normal heat transfer capability. In this condition, the pump would be expected to continue pumping at the same flow rate as normal condition, and no control action was activated. The system responses are shown in Fig. 10. The primary coolant average temperature and core material temperature began to rise at the initial stage. Consequently, the lithium and core material expansion caused an initial large negative reactivity insertion. As a result, the thermal power of the reactor started to drop and the material expansion reactivity feedback reversed to rise and became positive. The reactor power approached a new level of 2175 kW at about 350 s, 225 kW lower than the full power. The minimum reactivity insertions of the coolant and materials were 4.77 pcm and 2.76 pcm, while that of the Doppler effect was only 0.0001pcm. As shown in Fig. 10(c), reduction of radiator heat rejection capacity led to rising of the secondary coolant average tempera-

Fig. 11. Radiator coolant inlet and outlet temperature responses.

Fig. 10. System responses in loss of heat pipes accident.

W. Zhang et al. / Annals of Nuclear Energy 136 (2020) 107018

difference between the primary side and secondary side decreased, which caused the drop of thermoelectric conversion efficiency. Therefore, the electric efficiency of TE1 reduced from 5.17% to 4.67% and that of the TE10 fell from 3.93% to 3.54%. The electric power fell from the 109.2 kW to 89.3 kW during this transient. The average temperature of radiator would rose to compensate the heat pipe loss effect. Fig. 11 displays the transient responses of radiator inlet and outlet coolant temperature. Both the finite element model and the heat resistance network model of the heat pipe were used in this simulation. As we can see, the two models can provide almost the same calculation accuracy, but the network model cost much shorter time. 4. Summary and conclusions A new integrated model was developed for the thermoelectric reactor power system, which has the quite different working principle and more complicated system configuration than the thermionic power system. The following conclusions can be obtained: (1) It indicates the capability of the updated models to analyze the thermoelectric power system with a heat pipe radiator. The full power results had a good agreement with the designed values. And the heat resistance network of heat pipe and thermoelectric conversion model performed satisfactorily and reliably in the demonstration transients; (2) Different from the thermionic reactor, SP-100 reactor has a negative reactivity feedback coefficient which is beneficial to the control and safety of the system. Lithium coolant and structure material thermal expansions play the main role on the reactivity feedback while the Doppler feedback can almost be ignored for the high U-235 enrichment; (3) Addition of a mechanistic electromagnetic pump model and autonomous control model will likely be of interest in the following work to improve the current model to have the capabilities to analyze more severe or unique transients. And this model can also be a compatible and extensible tool for the design and analysis of other advanced space power systems.

Acknowledgement The present study is support by the National Natural Science Foundation of China (Grant Nos. 91326201)

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