Thermal-hydraulic analysis of space nuclear reactor TOPAZ-II with modified RELAP5

Thermal-hydraulic analysis of space nuclear reactor TOPAZ-II with modified RELAP5 1 first-author 2 1 1 1 corresp Corresponding author: szqiu@mail.xjtu.edu.cn Corresponding author: szqiu@mail.xjtu.edu.cn szqiu@mail.xjtu.edu.cn 1 Department of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China Department of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China China Institute of Atomic Energy, Beijing 102413, China China Institute of Atomic Energy, Beijing 102413, China With the advantages of high reliability, power density, and long life, nuclear power reactors have become a promising option for space power. In this study, the Reactor Excursion and Leak Analysis Program 5 (RELAP5), with the implementation of sodium-potassium eutectic alloy (NaK-78) properties and heat transfer correlations, is adopted to analyze the thermal-hydraulic characteristics of the space nuclear reactor TOPAZ-II. A RELAP5 model including thermionic fuel elements (TFEs), reactor core, radiator, coolant loop, and volume accumulator is established. The temperature reactivity feedback effects of the fuel, TFE emitter, TFE collector, moderator, and reactivity insertion effects of the control drums and safety drums are considered. To benchmark the integrated TOPAZ-II system model, an electrical ground test of the fully integrated TOPAZ-II system, the V-71 unit, is simulated and analyzed. The calculated coolant temperature and system pressure are in acceptable agreement with the experimental data for the maximum relative errors of 8% and 10%, respectively. The detailed thermal-hydraulic characteristics of TOPAZ-II are then simulated and analyzed at the steady state. The calculation results agree well with the design values. The current work provides a solid foundation for space reactor design and transient analysis in the future. Space nuclear reactor TOPAZ-II Thermal-hydraulic analysis RELAP5 modification 1 Introduction 1 With the strong demand for space exploration, the requirement for nuclear power technology featuring high reliability, high power density, long service life, small volume, and light weight in civil and military space missions is increasing. The former Soviet Union and USA have designed several types of space nuclear reactor systems including a thermoelectric conversion reactor system, thermionic conversion reactor system, Brayton cycle reactor system, and Stirling cycle reactor system [ 1 1 - 4 4 1-4 ] . The TOPAZ-II reactor system is the most advanced and experienced space nuclear power reactor based on thermionic conversion [ 5 5 ] . In the 1960s, extensive experimental research based on direct energy conversion technology was conducted by the former Soviet Union. The test program, including mechanical, thermal management, ground nuclear, and electrical heated thermal vacuum tests, was conducted to confirm the TOPAZ-II system’s operational performance [ 6 6 ] . In the 1990s, a joint Thermionic (TI) program between the Air Force and Department of Energy in the USA was established and tests of the TOPAZ-II system with electrical heated thermionic fuel elements (TFEs) were conducted at the Thermionic System Evaluation Test (TSET) facility [ 7 7 ] . The TOPAZ-II TFEs have undergone extensive testing with electrical heating to optimize the operational parameters [ 8 8 ] . In addition to experimental tests, numerical simulations have also been performed. The Thermionic Integrated Transient Analysis Model (TITAM) code was developed to investigate the steady and transient performance of a single cell TFE with either fission or electrical heating [ 9 9 ] . The start-up process of TOPAZ-II and a non-credible start-up accident with TOPAZ-II prior to launch were simulated with the TITAM [ 10 10 , 11 11 ] . The TOPAZ-II system responses under accident conditions were modeled by the Russian dynamics analytical simulator called ENSY. The accident conditions included switch failure during start-up, neutron regulator switch failure during start-up, and a loss of coolant accident (LOCA) [ 12 12 ] . The Code for Extended Non-linear Transient Analysis of Extraterrestrial Reactors (CENTAR) was developed to quantify the operator’s response time of the TSET following an interruption in vacuum chamber cooling [ 13 13 ] . The Transient Analysis code of Space Thermionic Nuclear reactor (TASTIN) was developed by Xi’an Jiaotong University to analyze the transient thermal-hydraulic characteristics of TOPAZ-II [ 14 14 , 15 15 ] . RELAP5, as the best estimate transient simulation tool for reactors cooled by light water or heavy water, does not include the capability to perform the thermal-hydraulic analysis of the sodium-potassium eutectic alloy-cooled (NaK-78) space nuclear reactor owing to the lack of the related physical properties and heat transfer correlations of NaK-78. In this study, the thermodynamic and transport properties of NaK-78 and heat transfer correlations for liquid metals were implemented in the RELAP5 code. The RELAP5 model for TOPAZ-II including TFEs, reactor core, coolant loop, radiator, and volume accumulator was established. The TOPAZ-II ground test V-71 unit was simulated with the modified RELAP5 to verify and validate the developed model. Based on verification and validation, the steady state with nominal power and start-up procedures of TOPAZ-II were simulated and analyzed. This work aims to provide a valid method to conduct thermal-hydraulic analysis of space nuclear reactors. 2 TOPAZ-II description 1 The TOPAZ-II is a thermionic space reactor system that can generate 4.5–5.5 kW of electricity utilizing the in-core thermionic conversion units. The major subsystems of the TOPAZ-II are the (1) NaK-78-cooled reactor with epithermal neutron energy spectrum, (2) lithium-hydride radiation shield, (3) electromagnetic (EM) pump for circulating the coolant, (4) radiator for waste heat rejection into space, (5) cesium reservoir assembly for supplying cesium vapor for the operation of the TFEs, and (6) instrumentation and control (I & C) system for regulating the reactor power. Figure 1 Figure 1 displays the TOPAZ-II schematic diagram. The nuclear reactor incorporates 37 single-cell TFEs. Thirty-four of the TFEs are connected in series to provide electricity. The other three are connected in parallel to provide power for the electromagnetic (EM) pump. The reactor power can be controlled by rotating the three safety drums and nine control drums. A radial cross section of the TOPAZ-II reactor core is depicted in Figure 2 Figure 2 . The main design parameters of TOPAZ-II are summarized in Table 1 Table 1 . Additional TOPAZ-II system information can be found in reference [ 16 16 ] . 1 1 Parameter 1 1 Value 1 1 Lifetime (Year) 1 1 3 1 1 Thermal power at BOL/MAX (kWth) 1 1 115/135 1 1 TFEs electrical power (kWe) 1 1 4.5–5.5 1 1 Conversion efficiency at BOL 1 1 5.2% 1 1 Voltage (V) 1 1 27±0.8 1 1 Reactor neutron spectrum 1 1 Epithermal 1 1 Reactor fuel 1 1 UO 2 1 1 Fuel enrichment 1 1 96% U-235 1 1 Fuel loading (kg) 1 1 27 1 1 Reactor core diameter (mm) 1 1 260 1 1 Reactor core height (mm) 1 1 375 1 1 Coolant type 1 1 NaK-78 (78% K, 22% Na) 1 1 Coolant temperature at core inlet (K) 1 1 743 1 1 Coolant temperature at core outlet (K) 1 1 843 1 1 Coolant mass flow rate (kg/s) 1 1 1.3 1 1 System pressure (MPa) 1 1 0.1 1 1 Radiator mass (kg) 1 1 46 1 1 Number of radiator elements 1 1 78 1 1 Radiator fin material 1 1 Copper with black enamel coating 1 1 Radiator surface (m 2 ) 1 1 7.2 1 1 Radiator emissivity 1 1 0.86 1 1 Reactor control 1 1 9 control drums and 3 safety drums 1 1 Moderator 1 1 ZrH 1.85 1 1 Primary system material 1 1 Stainless steel 1 1 TFE emitter material 1 1 Monocrystal Mo with 3% Nb 1 1 TFE collector material 1 1 Polycrystal Mo 1 1 Shield material 1 1 LiH for neutron and stainless steel for gamma 1 1 Number of TFE elements in core 1 1 37 3 RELAP5 Modification and Modeling 1 3.1. Thermo-physical properties of NaK-78 2 RELAP5 is coded in a modularized program using top-down structuring. The code top-level structure consists of the data input (INPUT), transient calculation (TRNCTL), and result stripping (STRIP) blocks. To simulate the NaK-78 alloy-cooled space reactors, subroutines in the INPUT and TRNCTL blocks must be modified. The thermo-physical properties of the NaK-78 alloy (78% K and 22% Na) are implemented into the RELAP5 code. The required properties are the isothermal compressibility, specific volume, thermal expansion coefficient, specific enthalpy, specific heat capacity and transport properties of thermal conductivity, surface tension, and dynamic viscosity. Based on Raoult’s law, the vaporization curve of NaK-78 can be expressed as [ 17 17 ] : <math display="block" id="M1"><mrow><mi>lg</mi><mo stretchy="false">(</mo><mi>P</mi><mo>/</mo><mn>1.3</mn><mo stretchy="false">)</mo><mo>=</mo><mn>9</mn><mo>−</mo><mn>4367</mn><mo>/</mo><mi>T</mi><mo>,</mo></mrow></math> where <math id="M2"><mi>P</mi></math> is the pressure (Pa) and <math id="M3"><mi>T</mi></math> is the temperature (K). 3.1.1 Liquid thermo-physical properties 3 The density of the liquid NaK-78 alloy changes with temperature. It was reported by Qian [ 18 18 ] and the linear fitted formulation can be expressed as the following form with 1% maximum error: <math display="block" id="M4"><mrow><msub><mi>ρ</mi><mtext>l</mtext></msub><mo>=</mo><mn>946.65</mn><mo>−</mo><mn>0.245</mn><mo>×</mo><mi>T</mi><mo>,</mo></mrow></math> where <math id="M5"><mrow><msub><mi>ρ</mi><mtext>l</mtext></msub></mrow></math> is the liquid density (kg/m 3 ). The specific volume <math id="M6"><mrow><msub><mi>υ</mi><mtext>l</mtext></msub></mrow></math> is <math display="block" id="M7"><mrow><msub><mi>υ</mi><mtext>l</mtext></msub><mo>=</mo><mn>1</mn><mo>/</mo><msub><mi>ρ</mi><mtext>l</mtext></msub><mo>.</mo></mrow></math> The adiabatic compressibility of liquid NaK-78 is related to sound speed and can be expressed as in Eq. (4). The isothermal compressibility of NaK-78 is related to the adiabatic compressibility and can be defined as in Eq. (5). <math display="block" id="M8"><mrow><msub><mi>k</mi><mtext>s</mtext></msub><mo>=</mo><mn>1</mn><mo>/</mo><mo stretchy="false">(</mo><mi>ρ</mi><msup><mi>c</mi><mn>2</mn></msup><mo stretchy="false">)</mo><mo>,</mo></mrow></math> <math display="block" id="M9"><mrow><msub><mi>k</mi><mtext>t</mtext></msub><mo>=</mo><msub><mi>k</mi><mtext>s</mtext></msub><mo>+</mo><mo stretchy="false">(</mo><mi>T</mi><msup><mi>α</mi><mn>2</mn></msup><mo stretchy="false">)</mo><mo>/</mo><mo stretchy="false">(</mo><mi>ρ</mi><msub><mi>c</mi><mtext>p</mtext></msub><mo stretchy="false">)</mo><mo>,</mo></mrow></math> where <math id="M10"><mrow><msub><mi>k</mi><mtext>s</mtext></msub></mrow></math> is the adiabatic compressibility (Pa -1 ), <math id="M11"><mrow><msub><mi>k</mi><mtext>t</mtext></msub></mrow></math> is the isothermal compressibility (Pa -1 ), <math id="M12"><mi>c</mi></math> is the sound speed (m/s), <math id="M13"><mrow><msub><mi>c</mi><mtext>p</mtext></msub></mrow></math> is the specific heat capacity ( <math id="M14"><mrow><mtext>J</mtext><mo>/</mo><mo stretchy="false">(</mo><mtext>kg</mtext><mo>·</mo><mtext>K</mtext><mo stretchy="false">)</mo></mrow></math> ), <math id="M15"><mi>α</mi></math> is the thermal expansion coefficient (K -1 ), and <math id="M16"><mi>ρ</mi></math> is the density (kg/m 3 ). The sound speed of liquid NaK-78 can be expressed as <math display="block" id="M17"><mrow><mi>c</mi><mo>=</mo><mn>1906.2</mn><mo>−</mo><mn>0.53</mn><mi>T</mi><mo>.</mo></mrow></math> The coefficient of thermal expansion can be obtained from Eq. (7). <math display="block" id="M18"><mrow><mi>V</mi><mo>=</mo><msub><mi>V</mi><mn>0</mn></msub><mrow><mo>[</mo><mrow><mn>1</mn><mo>+</mo><mi>α</mi><mo stretchy="false">(</mo><mi>T</mi><mo>−</mo><mn>273</mn><mo stretchy="false">)</mo></mrow><mo>]</mo></mrow><mo>,</mo></mrow></math> where <math id="M19"><mi>V</mi></math> is the volume of liquid NaK-78 and <math id="M20"><mrow><msub><mi>V</mi><mn>0</mn></msub></mrow></math> is the volume of liquid NaK-78 at 273 K. The thermal expansion coefficient <math id="M21"><mi>α</mi></math> is assumed to be a constant of <math id="M22"><mrow><mn>2.77</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math> <math id="M23"><mrow><msup><mtext>K</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> . The specific heat capacity of NaK-78 can be obtained from the following equation [ 19 19 ] : <math display="block" id="M24"><mrow><msub><mi>c</mi><mtext>p</mtext></msub><mo>=</mo><mn>1097.04</mn><mo>−</mo><mn>0.556</mn><mi>T</mi><mo>+</mo><mn>3.431</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup><msup><mi>T</mi><mn>2</mn></msup><mo>.</mo></mrow></math> The specific enthalpy of liquid NaK-78 can be expressed as the following form: <math display="block" id="M25"><mrow><msub><mi>h</mi><mtext>l</mtext></msub><mo>=</mo><mn>938.6</mn><mo>×</mo><mo stretchy="false">(</mo><mi>T</mi><mo>−</mo><mn>273</mn><mo stretchy="false">)</mo><mo>−</mo><mn>1.0962</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup><msup><mrow><mo stretchy="false">(</mo><mi>T</mi><mo>−</mo><mn>273</mn><mo stretchy="false">)</mo></mrow><mn>2</mn></msup><mo>+</mo><mn>7.0555</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup><msup><mrow><mo stretchy="false">(</mo><mi>T</mi><mo>−</mo><mn>273</mn><mo stretchy="false">)</mo></mrow><mn>3</mn></msup><mo>+</mo><mn>0.05636</mn><mo>×</mo><mo stretchy="false">(</mo><mi>T</mi><mo>−</mo><mn>273</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mi>e</mi><mrow><mo>−</mo><mn>0.004055</mn><mo>×</mo><mo stretchy="false">(</mo><mi>T</mi><mo>−</mo><mn>273</mn><mo stretchy="false">)</mo></mrow></msup><mo>,</mo></mrow></math> where <math id="M26"><mrow><msub><mi>h</mi><mtext>l</mtext></msub></mrow></math> is the specific enthalpy (J/kg). Equation (9) is fitted with the experimental data with 0.3% maximum error. The specific internal energy <math id="M27"><mrow><msub><mi>u</mi><mtext>l</mtext></msub></mrow></math> can be obtained by <math display="block" id="M28"><mrow><msub><mi>u</mi><mtext>l</mtext></msub><mo>=</mo><msub><mi>h</mi><mtext>l</mtext></msub><mo>−</mo><mi>P</mi><mo>·</mo><msub><mi>υ</mi><mtext>l</mtext></msub><mo>.</mo></mrow></math> The differential equation of specific entropy can be expressed as [ 20 20 ] <math display="block" id="M29"><mrow><mtext>d</mtext><mi>s</mi><mo>=</mo><mfrac><mrow><msub><mi>c</mi><mtext>p</mtext></msub></mrow><mi>T</mi></mfrac><mtext>d</mtext><mi>T</mi><mo>−</mo><msub><mrow><mo stretchy="false">(</mo><mfrac><mrow><mo>∂</mo><mi>υ</mi></mrow><mrow><mo>∂</mo><mi>T</mi></mrow></mfrac><mo stretchy="false">)</mo></mrow><mtext>P</mtext></msub><mtext>d</mtext><mi>P</mi><mo>.</mo></mrow></math> Substituting specific volume and specific heat capacity into Eq. (11) and integrating the equation, the liquid specific entropy can be expressed as <math display="block" id="M30"><mrow><msub><mi>s</mi><mtext>l</mtext></msub><mo>=</mo><msub><mi>c</mi><mtext>p</mtext></msub><mtext>ln</mtext><mo stretchy="false">(</mo><mi>T</mi><mo>/</mo><msub><mi>T</mi><mtext>0</mtext></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>s</mi><mrow><mtext>l0</mtext></mrow></msub><mo>−</mo><mn>0.245</mn><mo stretchy="false">(</mo><mi>P</mi><mo>-</mo><msub><mi>P</mi><mtext>0</mtext></msub><mo stretchy="false">)</mo><mo>·</mo><msup><mrow><mo stretchy="false">(</mo><mn>946.65</mn><mo>-</mo><mn>0.245</mn><mi>T</mi><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>,</mo></mrow></math> where <math id="M31"><mrow><msub><mi>s</mi><mrow><mtext>l</mtext><mn>0</mn></mrow></msub></mrow></math> is the reference liquid specific entropy at <math id="M32"><mrow><msub><mi>T</mi><mtext>0</mtext></msub></mrow></math> and <math id="M33"><mrow><msub><mi>P</mi><mtext>0</mtext></msub></mrow></math> , <math id="M34"><mrow><msub><mi>c</mi><mtext>p</mtext></msub></mrow></math> is the specific heat capacity ( <math id="M35"><mrow><mtext>J</mtext><mo>/</mo><mo stretchy="false">(</mo><mtext>kg</mtext><mo>·</mo><mtext>K</mtext><mo stretchy="false">)</mo></mrow></math> ), and <math id="M36"><mrow><msub><mi>s</mi><mtext>l</mtext></msub></mrow></math> is the specific entropy ( <math id="M37"><mrow><mtext>J</mtext><mo>/</mo><mo stretchy="false">(</mo><mtext>kg</mtext><mo>·</mo><mtext>K</mtext><mo stretchy="false">)</mo></mrow></math> ). 3.1.2 Vapor thermo-physical properties 3 In TOPAZ-II, the coolant temperature ranges from 300 K to 850 K during the start-up and normal operation; the phenomena of coolant boiling is expected to be avoided during the accident scenarios. Therefore, the vapor NaK-78 alloy is not important and is simplified as the ideal gas. The vapor density of NaK-78 can be calculated as follows: <math display="block" id="M38"><mrow><msub><mi>ρ</mi><mtext>g</mtext></msub><mo>=</mo><mfrac><mi>P</mi><mrow><mi>R</mi><mo>·</mo><mi>T</mi></mrow></mfrac><mo>,</mo></mrow></math> where <math id="M39"><mi>R</mi></math> represents the gas constant and is <math id="M40"><mrow><mn>229.26</mn><mtext> J</mtext><mo>/</mo><mtext>(kg</mtext><mo>·</mo><mtext>K)</mtext></mrow></math> . Similarly, the specific enthalpy for vapor NaK-78 can be represented as <math display="block" id="M41"><mrow><msub><mi>h</mi><mtext>g</mtext></msub><mo>=</mo><msub><mi>c</mi><mrow><mtext>pg</mtext></mrow></msub><mo stretchy="false">(</mo><mi>T</mi><mo>-</mo><msub><mi>T</mi><mtext>0</mtext></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>h</mi><mrow><mtext>g0</mtext></mrow></msub><mo>,</mo></mrow></math> where <math id="M42"><mrow><msub><mi>h</mi><mrow><mi>g</mi><mn>0</mn></mrow></msub></mrow></math> is the reference vapor specific enthalpy at <math id="M43"><mrow><msub><mi>T</mi><mtext>0</mtext></msub></mrow></math> and <math id="M44"><mrow><msub><mi>P</mi><mn>0</mn></msub></mrow></math> . The vapor specific internal energy can be expressed as <math display="block" id="M45"><mrow><msub><mi>u</mi><mtext>g</mtext></msub><mo>=</mo><msub><mi>h</mi><mtext>g</mtext></msub><mo>−</mo><mi>P</mi><mo>·</mo><msub><mi>υ</mi><mtext>g</mtext></msub><mo>.</mo></mrow></math> The specific entropy of vapor NaK-78 can be calculated as <math display="block" id="M46"><mrow><msub><mi>s</mi><mtext>g</mtext></msub><mo>=</mo><msub><mi>c</mi><mrow><mtext>pg</mtext></mrow></msub><mi>l</mi><mi>n</mi><mo stretchy="false">(</mo><mfrac><mi>T</mi><mrow><msub><mi>T</mi><mtext>0</mtext></msub></mrow></mfrac><mo stretchy="false">)</mo><mo>−</mo><mi>R</mi><mi>l</mi><mi>n</mi><mo stretchy="false">(</mo><mfrac><mi>P</mi><mrow><msub><mi>P</mi><mtext>0</mtext></msub></mrow></mfrac><mo stretchy="false">)</mo><mo>+</mo><msub><mi>s</mi><mrow><mtext>g0</mtext></mrow></msub><mo>,</mo></mrow></math> where <math id="M47"><mrow><msub><mi>s</mi><mrow><mtext>g0</mtext></mrow></msub></mrow></math> represents the vapor specific entropy at the triple point and <math id="M48"><mrow><msub><mi>s</mi><mtext>g</mtext></msub></mrow></math> is the specific entropy ( <math id="M49"><mrow><mtext>J/(kg</mtext><mo>·</mo><mtext>K</mtext><mo stretchy="false">)</mo></mrow></math> ). 3.2 Transport properties 2 Transport properties including the thermal conductivity <math id="M50"><mi>λ</mi></math> ( <math id="M51"><mrow><mtext>W/(m</mtext><mo>·</mo><mtext>K)</mtext></mrow></math> ), surface tension <math id="M52"><mi>σ</mi></math> ( <math id="M53"><mrow><mtext>N/m</mtext></mrow></math> ), and dynamic viscosity, <math id="M54"><mi>μ</mi></math> ( <math id="M55"><mrow><mtext>Pa</mtext><mo>·</mo><mtext>s</mtext></mrow></math> ) are required in the RELAP5 code modification. The thermal conductivity of liquid NaK-78 is implemented as [ 19 19 ] <math display="block" id="M56"><mrow><mi>λ</mi><mo>=</mo><mn>14.11</mn><mo>+</mo><mn>0.0327</mn><mi>T</mi><mo>−</mo><mn>2.2</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup><msup><mi>T</mi><mn>2</mn></msup><mo>.</mo></mrow></math> Equation (17) is mainly in terms of the experimental data, with 0.8% maximum error. The surface tension of the liquid NaK-78 changed with temperature can be obtained in terms of the surface tension of sodium and potassium. The linear fitted formulation can be expressed as <math display="block" id="M57"><mrow><mi>σ</mi><mo>=</mo><mn>1.357</mn><mo>−</mo><mn>7.192</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup><mo stretchy="false">(</mo><mi>T</mi><mo>−</mo><mn>273</mn><mo stretchy="false">)</mo><mo>.</mo></mrow></math> The dynamic viscosity of NaK-78 can be expressed as <math display="block" id="M58"><mrow><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><mi>μ</mi><mo>=</mo><mn>0.116</mn><msup><mi>ρ</mi><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup><mi>exp</mi><mo stretchy="false">(</mo><mn>668</mn><mi>ρ</mi><mo>/</mo><mi>T</mi><mo stretchy="false">)</mo><mo>,</mo><mtext> </mtext><mi>T</mi><mo>≤</mo><mn>773</mn><mtext> K</mtext></mrow></mtd></mtr><mtr><mtd><mrow><mi>μ</mi><mo>=</mo><mn>8.2</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><msup><mi>ρ</mi><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup><mi>exp</mi><mo stretchy="false">(</mo><mn>979</mn><mi>ρ</mi><mo>/</mo><mi>T</mi><mo stretchy="false">)</mo><mo>,</mo><mtext> </mtext><mi>T</mi><mo>></mo><mn>773</mn><mtext> K</mtext><mo>.</mo></mrow></mtd></mtr></mtable></mrow></mrow></mrow></math> 3.3 Heat transfer correlations for liquid metal 2 In the modified RELAP5, the heat transfer correlation [ 21 21 ] for the liquid metal convection heat transfer in tube is <math display="block" id="M59"><mrow><mi>N</mi><mi>u</mi><mo>=</mo><mn>6.0</mn><mo>+</mo><mn>0.025</mn><msup><mrow><mrow><mo>[</mo><mrow><mn>0.014</mn><mi>R</mi><msup><mi>e</mi><mrow><mn>0.45</mn></mrow></msup><mi>P</mi><msup><mi>r</mi><mrow><mn>0.2</mn></mrow></msup><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msup><mi>e</mi><mrow><mo>−</mo><mfrac><mrow><mn>71.8</mn></mrow><mrow><mi>R</mi><msup><mi>e</mi><mrow><mn>0.45</mn></mrow></msup><mi>P</mi><msup><mi>r</mi><mrow><mn>0.2</mn></mrow></msup></mrow></mfrac></mrow></msup><mo stretchy="false">)</mo><mi>P</mi><mi>e</mi></mrow><mo>]</mo></mrow></mrow><mrow><mn>0.8</mn></mrow></msup><mo>,</mo></mrow></math> where <math id="M60"><mrow><mi>N</mi><mi>u</mi></mrow></math> represents the Nusselt number, <math id="M61"><mrow><mi>R</mi><mi>e</mi></mrow></math> is the Reynolds number, <math id="M62"><mrow><mi>P</mi><mi>r</mi></mrow></math> represents the Prandtl number, and <math id="M63"><mrow><mi>P</mi><mi>e</mi></mrow></math> represents the Peclet number. Equation (20) is appropriate to fully develop the flow, and the Nusselt number for the laminar flow regime in tube is <math display="block" id="M64"><mrow><mi>N</mi><mi>u</mi><mo>=</mo><mn>4.36</mn><mtext> for </mtext><mi>R</mi><mi>e</mi><mo><</mo><mn>3000</mn></mrow></math> The convection heat transfer correlation [ 22 22 ] for annular pipes with liquid metals is <math display="block" id="M65"><mrow><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><mi>N</mi><mi>u</mi><mo>=</mo><mn>5.25</mn><mo>+</mo><mn>0.0188</mn><mi>P</mi><msup><mi>e</mi><mrow><mn>0.8</mn></mrow></msup><msup><mrow><mo stretchy="false">(</mo><msub><mi>D</mi><mn>2</mn></msub><mo>/</mo><msub><mi>D</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mrow><mrow><mn>0.3</mn></mrow></msup><mo>,</mo><msub><mi>D</mi><mn>2</mn></msub><mo>/</mo><msub><mi>D</mi><mn>1</mn></msub><mo>></mo><mn>1.4</mn></mrow></mtd></mtr><mtr><mtd><mrow><mi>N</mi><mi>u</mi><mo>=</mo><mn>5.8</mn><mo>+</mo><mn>0.02</mn><mi>P</mi><msup><mi>e</mi><mrow><mn>0.8</mn></mrow></msup><mo>,</mo><msub><mi>D</mi><mn>2</mn></msub><mo>/</mo><msub><mi>D</mi><mn>1</mn></msub><mo>→</mo><mn>1</mn></mrow></mtd></mtr></mtable></mrow></mrow><mo>,</mo></mrow></math> where <math id="M66"><mrow><msub><mi>D</mi><mn>1</mn></msub></mrow></math> is the inner diameter and <math id="M67"><mrow><msub><mi>D</mi><mn>2</mn></msub></mrow></math> is the external diameter. The convection heat transfer correlation [ 23 23 ] for rod bundles with liquid metals is <math display="block" id="M68"><mrow><mi>N</mi><mi>u</mi><mo>=</mo><mn>4.0</mn><mo>+</mo><mn>0.16</mn><msup><mrow><mo stretchy="false">(</mo><mi>P</mi><mo>/</mo><mi>D</mi><mo stretchy="false">)</mo></mrow><mrow><mn>5.0</mn></mrow></msup><mo>+</mo><mn>0.33</mn><msup><mrow><mo stretchy="false">(</mo><mi>P</mi><mo>/</mo><mi>D</mi><mo stretchy="false">)</mo></mrow><mrow><mn>3.8</mn></mrow></msup><msup><mrow><mo stretchy="false">(</mo><mi>P</mi><mi>e</mi><mo>/</mo><mn>100</mn><mo stretchy="false">)</mo></mrow><mrow><mn>0.86</mn></mrow></msup><mtext> for </mtext><mn>1.1</mn><mo><</mo><mi>P</mi><mo>/</mo><mi>D</mi><mo><</mo><mn>1.4</mn><mtext>  </mtext><mn>10</mn><mo><</mo><mi>P</mi><mi>e</mi><mo><</mo><mn>5000</mn><mo>,</mo></mrow></math> where <math id="M69"><mrow><mi>P</mi><mo>/</mo><mi>D</mi></mrow></math> is the rod or tube pitch-to-diameter ratio. 3.4 RELAP5 modeling 2 The RELAP5 model for the TOPAZ-II system was developed and the nodalization of the TOPAZ-II system is presented in Figure 3 Figure 3 . The established model contains virtually all the main structures including in-core TFEs, reactor core, pump, radiator, primary loop, and volume accumulator. Owing to the TFE layout symmetry, the TFEs in the same circumference were simplified as one coolant channel in the RELAP5 model. Thirty-seven TFEs were divided into four coolant channels including 1, 6, 12, and 18 TFEs, respectively, as indicated in Figure 4 Figure 4 . They were modeled as component 210, 220, 230, and 240. Components 210, 220, 230, and 240 are annulus-type hydraulic components with 24.5 mm inner diameter, 25.9 mm outer diameter, and 375 mm height. In the RELAP5 model, coolant Channel 1 was defined as a hot channel; the other three coolant channels were simplified as average channels. Both sides of a coolant channel were coupled with heat structures. The complex TFE ring structures of fuel, fission gas gap, emitter, cesium gap, collector, stainless steel inner wall, stainless steel outer wall, helium gap, and ZrH moderator were modeled in the heat structures with an outer diameter of 17 mm, 17.3 mm, 19.6 mm, 20.6 mm, 23.4 mm, 23.8 mm, 24.5 mm, 26.6 mm, 27.5 mm, and 37.1 mm, respectively. A schematic of the TFE cross section is presented in Fig. 5 Fig. 5 . The radiator is an uncommon component compared to a convection nuclear system. The radiator consists of an upper header, lower header, and 78 radiator coolant channels (as indicated in Fig. 1 Fig. 1 ). The radiator fin material is copper with black enamel coating and the effective radiator surface is 7.2 m 2 . The upper header (Component 400) and lower header (Component 800) of the radiator are circular ring structures. The radiator is a circular cone truncated structure. Owing to the symmetry of the headers and radiator, the 78 coolant channels in the radiator were simplified into 20 channels divided into four groups based on the coolant flow direction in the upper header. Each group corresponds to a coolant flow direction and contains five coolant channels in parallel with equivalent flow area. The coolant channel is 22.1 mm in diameter and 1830 mm in height. The radiator model displayed in Fig. 3 Fig. 3 is only one group of radiator parallel channels. The other three groups of radiator parallel channels exist in the RELAP5 model, however, are not displayed in Fig. 3 Fig. 3 . The outsides of the radiator coolant channels have rectangular-type heat structures to model the copper fins. The surface radiation emissivity of the copper fins is 0.86. The top view of radiator and the radiator simplification process are displayed in Fig. 6 Fig. 6 . The detailed hydraulic components illustrated are listed in Table 2 Table 2 . 1 1 Component 1 1 Component Type and Geometrical Information 1 1 100 1 1 Time dependent junction: EM pump 1 1 110, 120 1 1 Pipe: coolant pipe from EM pump to inlet plenum (1.73×10 -3 m 3 in flow area, 2.93 m in  height ) 1 1 200 1 1 Branch: core inlet plenum (6.9×10 -3 m 3 in flow area, 0.014 m in height) 1 1 210 1 1 Pipe: hot channel (5.54×10 -5 m 3 in flow area, 0.375 m in height) 1 1 220, 230, 240 1 1 Pipe: average channel (5.54×10 -5 m 3 in flow area, 0.375 m in height) 1 1 300 1 1 Branch: core outlet plenum (6.9×10 -3 m 3 in flow area, 0.014 m in height) 1 1 310, 320 1 1 Pipe: coolant pipe from core outlet plenum to radiator upper header (8.67×10 -4 m 3 in flow area, 2.93 m in height) 1 1 400 1 1 Branch: radiator upper header (3.62×10 -3 m 3 in flow area, 0.73 m in length) 1 1 601–605 1 1 Pipe: radiator coolant channel (3.85×10 -4 m 3 in flow area, 1.83 m in height) 1 1 800 1 1 Branch: radiator lower header (8.67×10 -4 m 3 in flow area, 3.93 m in length) 1 1 820 1 1 Time dependent volume: volume accumulator 1 1 901, 902 1 1 Pipe: coolant pipe from radiator lower header to EM pump (1.73×10 -3 m 3 in flow area, 3.85 m in height) 4 Results and discussions 1 4.1 Verification and validation 2 To benchmark the fully integrated TOPAZ-II system model, the model predictions were compared with the steady-state measurements for an electrically heated, fully integrated TOPAZ-II system, the V-71 unit. The V-71 unit is the first electrically heated ground test of a complete thermionic space nuclear power system [ 24 24 ] . For the V-71 unit, the fuel pellets were replaced by electrically heated tungsten; the thermal heat flux to the emitter was assumed uniform along the active emitter. The comparisons of the calculated and measured coolant temperatures at the core inlet and core outlet are displayed in Fig. 7 Fig. 7 . The calculated values are in acceptable agreement with the experimental data. The maximum relative error is 8% as indicated in Fig. 8 Fig. 8 . The error between the calculated results and the experimental data can be caused by the error of the coolant mass flow rate. The comparison of the calculated and measured system pressure are displayed in Fig. 9 Fig. 9 . The maximum relative error is 10% as indicated in Fig. 10 Fig. 10 . The system pressure mainly influences the subcooling degree of the coolant, which is approximately 300 K in normal operation; hence, the maximum relative error of 10% in the local region is acceptable. 4.2 Steady-state analysis 2 The steady-state analysis of TOPAZ-II was performed with the modified RELAP5. The comparisons between the steady-state results and design values are presented in Table 3 Table 3 ; the calculated results agree well with the design values. 1 1  Parameter 1 1 Design value 1 1 Calculated value 1 1 Reactor thermal power (kW)  (fixed parameter) 1 1 115 1 1 115 1 1 Coolant temperature at core inlet (K) 1 1 743 1 1 744 1 1 Coolant temperature at core outlet (K) 1 1 843 1 1 844 1 1 Coolant mass flow rate (kg/s) (fixed parameter) 1 1 1.32 1 1 1.32 The radial temperature distribution of the TFE at different positions in the average coolant channel is displayed in Fig. 11 Fig. 11 . Five typical positions are indicated in Fig. 11 Fig. 11 . The fuel maximum temperature of 1941 K appears in the fuel center of Position 2. Because the thermal conductivity of the cesium vapor is low and electric power is generated between emitters and collectors, a clear temperature reduction appears in the cesium vapor gap. Owing to the high thermal conductivity coefficient and large heat capacity, the radial temperature distribution in the moderator is uniform. The radial temperature distribution in the reflector is smooth, and the temperature distribution is virtually the same as the coolant temperature. Figures 12 Figures 12 and 13 13 display the axial temperature distribution of each TFE component in the hot channel. The axial temperature distribution of the fuel pellets depends on the axial power curve and radial heat conduction. A maximum fuel pellet temperature of 2039 K appears in the middle of the fuel, which is considerably less than the melting temperature of approximately 3100 K. The axial temperature distribution of the fission gas and emitter is mainly determined by the radial heat conduction from the fuel pellets. The temperature variation trend is consistent with the fuel temperature distribution. Owing to the low thermal conductivity of cesium vapor, the temperature distribution of the components outside the cesium vapor is less influenced by the fuel temperature distribution and more influenced by the coolant axial temperature distribution. Figure 14 Figure 14 illustrates the coolant temperature distributions along the flow direction in four coolant channels and two radiator channels. The core coolant Channel 1 is the hot channel; the other three channels are average channels. The outlet coolant temperature in the hot channel is 10 K higher than that in the average channel outlet. The maximum coolant temperature is 854 K, which is considerably less than its saturation temperature of approximately 1100 K. The coolant temperature increase in the core is approximately 101 K and the coolant temperature decrease in the radiator is approximately 96 K. This is because approximately 5% of the heat is radiated into space from the primary hot leg and cold leg. The coolant temperature has no change in core inlet reflector and core outlet reflector. Figure 15 Figure 15 presents the local coolant temperature, coolant saturation temperature, and coolant subcooling degree of the primary system. The coolant is heated in the core, the core average channel outlet temperature attains a maximum of 844 K, and the coolant subcooling degree reaches a minimum of 260 K. There is a small amount of heat loss by radiation from the coolant pipes; the coolant temperature decreases marginally along the coolant flow direction. As the coolant flows through the radiator, the coolant temperature decreases to 746 K. When the coolant flows through the pump, the increase of the system pressure increases the coolant saturation temperature. The coolant temperature reaches a minimum value of 744 K after flowing through the pump. Therefore, the maximum value of coolant subcooling, in degrees, 370 K, occurs at the outlet of the EM pump. It can be concluded that the steady-state operation of TOPAZ-II is safe and reliable because of the higher design margin. 5 Conclusion 1 In this study, the thermos-physical properties and transport properties of NaK-78 and the relevant heat transfer correlations were implemented into the RELAP5 code. After modification, the modified RELAP5 was adopted to simulate and analyze the TOPAZ-II reactor system. A RELAP5 model including the core, TFEs, radiator, coolant loop, and volume accumulator, was established. The ground test of the TOPAZ-II system, the V-71 unit, was adopted to benchmark the modified RELAP5 model. The steady-state condition of TOPAZ-II was simulated and analyzed. Based on the above analysis, the following conclusions can be obtained: (1) The V-71 unit was simulated using the modified RELAP5 with a comparison of the experimental data. The maximum relative error of the coolant temperatures was 8% and the maximum relative error of the system pressure was 10%. Further, the maximum error only occurred in special positions around 40 kW. The acceptable agreement between the calculated results and experimental data preliminarily verifies and validates the modified RELAP5 model. This proves the capability of the modified RELAP5 to analyze the TOPAZ-II system. (2) The steady-state calculated results agree well with the reactor-designed values. The maximum coolant outlet temperature was 854 K, which has a large margin of approximately 250 K to the boiling point. The fuel maximum temperature was 2039 K, which is considerably less than the melting temperature of approximately 3100 K. This proves the good safety performance of the designed TOPAZ-II at the steady state. The transient safety characteristics should be assessed as a next step. This work provides a solid foundation for a space nuclear reactor design and transient analysis in the future. References L.S. Mason , A comparison of Brayton and Stirling space nuclear power systems for power levels from 1 kilowatt to 10 megawatts . AIP Conference Proceedings: Space Technology and Applications International Forum (STAIF-2000) on Space Exploration and Transportation - Journey into the Future . 552 ( 1 ). 1017 - 1022 ( 2001 ). DOI: 10.1063/1.1358045 http://doi.org/10.1063/1.1358045 A comparison of Brayton and Stirling space nuclear power systems for power levels from 1 kilowatt to 10 megawatts G.L. Bennett , R.J. Hemler , A. Schock , Space nuclear power: An overview . J. Propul. Power . 12 ( 5 ), 901 - 910 ( 1996 ). DOI: 10.2514/3.24121 http://doi.org/10.2514/3.24121 Space nuclear power: An overview D. Buden , Summary of space nuclear reactor power systems (1983-1992). Idaho National Engineering Laboratory Report (1993), Report ID: INEL/MISC-93085 . https://inis.iaea.org/collection/NCLCollectionStore/_Public/25/070/25070118.pdf https://inis.iaea.org/collection/NCLCollectionStore/_Public/25/070/25070118.pdf Summary of space nuclear reactor power systems (1983-1992). Idaho National Engineering Laboratory Report (1993), Report ID: INEL/MISC-93085 A.J. Glassman , Summary of Brayton cycle analytical studies for space-power system applications . Sol. Energy . 7 ( 1964 ). https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19640020187.pdf https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19640020187.pdf Summary of Brayton cycle analytical studies for space-power system applications R.S Dabrowski , US-Russian Cooperation in Science and Technology: A Case Study of the TOPAZ Space-Based Nuclear Reactor International Program . Connections the Quarterly Journal . 13 ( 1 ), 71 - 87 ( 2013 ). http://procon.bg/bg/system/files/13.1.05_dabrowski.pdf http://procon.bg/bg/system/files/13.1.05_dabrowski.pdf US-Russian Cooperation in Science and Technology: A Case Study of the TOPAZ Space-Based Nuclear Reactor International Program S.S. Voss , E.A. Rodriguez , Russian TOPAZ II System Test Program (1970–1989) . AIP Conference Proceedings: 11th Symposium on Space Nuclear Power and Propulsion . 301 ( 1 ), 803 - 812 ( 1994 ). DOI: 10.1063/1.2950273 http://doi.org/10.1063/1.2950273 Russian TOPAZ II System Test Program (1970–1989) J.F. Fairchild , J.P. Koonmen , F.V. Thome , Thermionic system evaluated test (TSET) facility description . AIP Conference Proceedings: Ninth Symposium on Space Nuclear Power Systems . 246 ( 1 ), 836 - 842 ( 1992 ). DOI: 10.1063/1.41884 http://doi.org/10.1063/1.41884 Thermionic system evaluated test (TSET) facility description V.P. Nicitin , B.G. Ogloblin , A.N. Luppov et al ., Special features and results of the "TOPAZ II" nuclear power system tests with electric heating . AIP Conference Proceedings: Ninth Symposium on Space Nuclear Power Systems . 246 ( 1 ), 41 - 46 ( 1992 ). DOI: 10.1063/1.41803 http://doi.org/10.1063/1.41803 Special features and results of the "TOPAZ II" nuclear power system tests with electric heating M.S. El‐Genk , H. Xue , C. Murray et al ., TITAM thermionic integrated transient analysis model: Load‐following of a single‐cell TFE . AIP Conference Proceedings: Ninth Symposium on Space Nuclear Power Systems . 246 ( 1 ), 1013 - 1022 ( 1992 ). DOI: 10.1063/1.41776 http://doi.org/10.1063/1.41776 TITAM thermionic integrated transient analysis model: Load‐following of a single‐cell TFE M.S. El‐Genk , D.V. Paramonov , A.C. Marshall , Startup Simulation of the TOPAZ‐II Reactor System for Accident Conditions . AIP Conference Proceedings: 11th Symposium on Space Nuclear Power and Propulsion . 301 ( 1 ), 1059 - 1068 ( 1994 ). DOI: 10.1063/1.2950104 http://doi.org/10.1063/1.2950104 Startup Simulation of the TOPAZ‐II Reactor System for Accident Conditions M.S. El‐Genk , H. Xue , D.V. Paramonov . Start‐up simulation of a thermionic space nuclear reactor system . AIP Conference Proceedings: 10th Symposium on Space Nuclear Power and Propulsion . 271 ( 2 ), 935 - 950 ( 1993 ). DOI: 10.1063/1.43119 http://doi.org/10.1063/1.43119 Start‐up simulation of a thermionic space nuclear reactor system S.S. Voss , The TOPAZ II space reactor response under accident conditions . Presented at the International Topical Meeting on the Safety of Advanced Reactors , Pittsburgh, PA , 18-20 Apr. 1994 . https://www.osti.gov/biblio/10115301 https://www.osti.gov/biblio/10115301 The TOPAZ II space reactor response under accident conditions V.H. Standley , D.B. Morris , M.J. Schuller , CENTAR modeling of the TOPAZ‐II: Loss of vacuum chamber cooling during full power ground test . AIP Conference Proceedings: Ninth Symposium on Space Nuclear Power Systems . 246 ( 1 ), 1129 - 1134 ( 1992 ). DOI: 10.1063/1.41770 http://doi.org/10.1063/1.41770 CENTAR modeling of the TOPAZ‐II: Loss of vacuum chamber cooling during full power ground test W.W. Zhang , Z.Y. Ma , D.L. Zhang , et al ., Transient thermal–hydraulic analysis of a space thermionic reactor . Ann. Nucl. Energy . 89 , 38 - 49 ( 2016 ). DOI: 10.1016/j.anucene.2015.10.035 http://doi.org/10.1016/j.anucene.2015.10.035 Transient thermal–hydraulic analysis of a space thermionic reactor W.W. Zhang , D.L. Zhang , W.X. Tian , et al . Thermal-hydraulic analysis of the improved TOPAZ-II power system using a heat pipe radiator . Nucl. Eng. Des . 307 , 218 - 233 ( 2016 ). DOI: 10.1016/j.nucengdes.2016.07.020 http://doi.org/10.1016/j.nucengdes.2016.07.020 Thermal-hydraulic analysis of the improved TOPAZ-II power system using a heat pipe radiator S.S. Voss , TOPAZ-II System Description . Proceedings of the Fourth International Conference on Engineering, Construction, and Operations in Space , Albuquerque, NM . 717 - 728 ( 1994 ). https://inis.iaea.org/collection/NCLCollectionStore/_Public/25/040/25040534.pdf https://inis.iaea.org/collection/NCLCollectionStore/_Public/25/040/25040534.pdf TOPAZ-II System Description C.B. Jackson , Liquid Metals Handbook. Sodium-NaK Supplement . Atomic Energy Commission , Washington, DC ; Liquid Metals Handbook. Sodium-NaK Supplement Bureau of Ships, Report ID: TID-5277 (1955) . https://www.osti.gov/biblio/4376530 https://www.osti.gov/biblio/4376530 Bureau of Ships, Report ID: TID-5277 (1955) Z.Y. Qian , Thermal Properties of Low Melting Point Metals . ( Science Press , China , 1985 ), In Chinese Thermal Properties of Low Melting Point Metals O.J. Foust , Sodium-NaK engineering handbook . ( Gordon & Breach Science Pub ., 1972 ), p. 102 . Sodium-NaK engineering handbook M. Zemansky , R. Dittman , Heat and Thermodynamics . ( McGraww-Hill Inc. Pub ., 1997 ). p. 53 Heat and Thermodynamics S. Aoki , O.E. Dwyer , Current liquid-metal heat transfer research in Japan . Tokyo Inst. of Tech. , Report ID: NSA-29-000316 . 1973 . https://www.osti.gov/biblio/4423836 https://www.osti.gov/biblio/4423836 Current liquid-metal heat transfer research in Japan O.E. Dwyer , P.S. Tu , Bilateral heat transfer to liquid metals flowing turbulently through annuli . Nucl. Sci. Eng ., 21 ( 1 ), 90 - 105 ( 1965 ). DOI: 10.13182/NSE65-A21018 http://doi.org/10.13182/NSE65-A21018 Bilateral heat transfer to liquid metals flowing turbulently through annuli N.E. Todreas , M.S. Kazimi , Nuclear systems: thermal hydraulic fundamentals . ( CRC press , 2012 ), p. 306 . Nuclear systems: thermal hydraulic fundamentals D.V. Paramonov , M.S. El‐Genk , Comparison of a TOPAZ‐II Model with Experimental Data from the V‐71 Unit Tests . AIP Conference Proceedings: 11th Symposium on Space Nuclear Power and Propulsion . 301 ( 1 ), 829 - 843 ( 1994 ). DOI: 10.1063/1.2950277 http://doi.org/10.1063/1.2950277 Comparison of a TOPAZ‐II Model with Experimental Data from the V‐71 Unit Tests 10.1007/s41365-018-0537-3 This work was supported by the China National Postdoctoral Program for Innovative Talents (No. BX201600124), China Postdoctoral Science Foundation (No. 2016M600796), and the National Natural Science Foundation of China (No. 11605131). 2018-08-07 2018-10-19 2018-10-22 2019-01-02 2019-01-01 2021-04-10 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2019 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-018-0537-3 http://dx.doi.org/10.1007/s41365-018-0537-3 . 2019 Nuclear Science and Techniques 01 30