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Edited by: Jun Wang, University of Wisconsin-Madison, United States

Reviewed by: Yacine Addad, Khalifa University, United Arab Emirates; Claudio Tenreiro, University of Talca, Chile; Hui Cheng, City University of Hong Kong, Hong Kong

This article was submitted to Nuclear Energy, a section of the journal Frontiers in Energy Research

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Supercritical-pressure light water-cooled reactors (SCWR) are the only water cooled reactor types in Generation IV nuclear energy systems. Startup systems, and their associated startup characteristic analyses, are important components of the SCWR design. To analyze the entire startup system, we propose a wall heat transfer model in a paper, based on the results from a supercritical transient analysis code named SCTRAN developed by Xi'an Jiao tong University. In this work, we propose a new heat transfer mode selection process. Additionally, the most appropriate heat transfer coefficient selection method is chosen from existing state-of-the-art methods. Within the model development section of the work, we solve the problem of discontinuous heat transfer coefficients in the logic transformation step. When the pressure is greater than 19 Mpa, a look-up table method is used to obtain the heat transfer coefficients with the best prediction accuracy across the critical region. Then, we describe a control strategy for the startup process that includes a description of the control objects for coolant flow rate, heat-exchange outlet temperature, system pressure, core thermal power, steam drum water-level and the once-through direct cycle loop inlet temperature. Different control schemes are set-up according to different control objectives of the startup phases. Based on CSR1000 reactor, an analytical model, which includes a circulation loop and once-through direct cycle loop is established, and four startup processes, with control systems, are proposed. The calculation results show that the thermal parameters of the circulation loop and the once-through direct cycle meets all expectations. The maximum cladding surface temperature remains below the limit temperature of 650°C. The feasibility of the startup scheme and the security of the startup process are verified.

Supercritical Water Reactor (SCWR) is the only water cooled reactor type in Generation IV nuclear energy systems. SCWR is an innovative system which is aimed for high thermal efficiency and economy. SCWR works at a high pressure, 25 MPa, with a core outlet temperature up to 500°C. Moreover, Canada's pressure vessel-type reactor outlet temperature even up to 625°C. So the cladding temperature can reach 650°C, far beyond the current pressurized water reactor. Supercritical water properties rapid changes at the trans-critical region, and neutron moderating ability would be weakened. The University of Tokyo was the first to study the startup procedure of SCWR. Since the startup procedure involves the process of cooling a reactor from a subcritical to supercritical state, analyzing SCWR-based startup thermo-hydraulic characteristics becomes an important consideration (Oka and Koshizuka,

The SCWR coolant loop is a once-through direct cycle that is very sensitive to disturbances. The startup procedure needs to be operated by the control system. Yuki et al. designed a control system of the SCLWR-H under steady state. The turbine inlet pressure is controlled by the turbine control valves. The main steam temperature is controlled by the feedwater flow rate. The core power is controlled by the control rods (Ishiwatari et al.,

The SCWR startup procedure must ensure that the Maximum fuel cladding surface temperature (MCST) does not exceed the limit 650°C. Accordingly, the heat transfer coefficient value is very important for the calculation of the cladding temperature. A complete set of heat transfer coefficients is needed to meet the wall heat transfer requirements for a smooth transition between the subcritical and supercritical heat transfer coefficients. Ishiwatari et al. (

SCTRAN was developed in Xi′an Jiao Tong University. It is a one-dimensional safety analysis code for SCWRs (Wu et al.,

Mass conservation equation

where:

Momentum conservation equation

Energy conservation equation

In numerical calculation, SCTRAN code adopts the staggered grid in fluid space discretization and adopts the control volume balance method to discrete fluid basic equations.

The SCTRAN module call diagram is shown in Figure

Module call diagram of SCTRAN.

Calculation flow chart of SCTRAN.

The wall heat transfer model mainly includes three parts: heat transfer modes, selection procedures of heat transfer modes (logic) and heat transfer correlations. To analyze the wall heat transfer characteristics of the SCTRAN code, a simulation of a pipe was made. The pipe fluid inlet temperature is 100°C, the outlet temperature is 500°C, the fixed flow rate per unit area is 500 kg·m^{−2}·s^{−1}, and the pipe is uniformly heated along the axial direction; the pressure varies from 1 to 28 MPa. The curves of the heat transfer coefficient are associated with pressure and enthalpy; they are shown in Figures

Relationship between the heat transfer coefficient, enthalpy and pressure from a low-pressure to high-pressure region.

Relationship between the heat transfer coefficient, enthalpy and pressure in a high-pressure region.

The heat transfer correlations used in SCTRAN.

Single-phase liquid | Collier correlation |
Sellars correlation |

Nucleate boiling | Thom correlation | Chen correlation |

Vaporization | Schrock-Grossman correlation | |

Transition boiling | Mcdonongh, Milich and King correlation | Chen-Sundaram-Ozkaynak correlation |

Film boiling | Groeneveld correlation |
Groeneveld-Leung PDO look-up table Bromely correlation |

Single phase vapor | Collier correlation |
Lahey correlation |

Condensation | Collier correlation | Nusselt correlation |

Supercritical water | Jackson-Hall correlation | Look-up table for trans-critical region |

Per the SCWR startup sequence (Table

Sliding pressure startup procedure.

Pressure/MPa | 0.1 | 0.1 → 6.5 | 6.5 → 25.0 | 25.0 | 25.0 |

Power/% | 0.1 | 0.1 → 0.1 | 0.1 → 9.0 | 9.0 → 25.1 | 25.1 → 100 |

Outlet temperature/°C | 80 | 80 → 280 | 280 → 374.5 | 375 → 500 | 500 |

inlet temperature/°C | 80 | 80 → 280 | 280 | 280 | 280 |

Flow rate/% | 25 | 25 | 25 | 25 | 25 → 100 |

SCWR control system.

Heat exchanger outlet temperature control | The temperature is kept constant by regulating the secondary side flow of the heat exchanger or the condenser. | |

Power control | The change of thermal power is sensitive to insertion reactivity. | |

Pressure control | The pressure is kept constant by regulating the opening of the control valves | |

Steam drum water level control | The water level is kept constant by regulating the flow rate discharge from the steam drum. | |

Once-through direct-cycle loop inlet-temperature control | The extraction steam flow rate is sensitive to new steam entering the heater. | |

Coolant flow rate control | The coolant flow rate is kept constant by regulating the opening of the control valves. |

Control system strategies for SCWR sliding pressure startups with circulation loop.

Bailey experiment and Subbotin experiment (Wu et al.,

Experimental conditions.

^{−2}·s^{−1} |
^{−2} |
^{−1} |
||
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Bailey-A 1257 | 18.1 | 4150.1 | 1,889,600 | 370.3 |

Bailey-A 1272 | 18.0 | 2766.7 | 1,072,561 | 227.7 |

Bailey-A 1305 | 18.1 | 2237.8 | 712,938 | 75.9 |

Bailey-A 1313 | 17.9 | 2224.3 | 971,614 | 269.4 |

Bailey-A 1332 | 18.0 | 4177.2 | 1,580,450 | 231.0 |

Bailey-A 1341 | 18.1 | 3621.1 | 1,403,793 | 145.1 |

Bailey-A 1342 | 17.9 | 3621.1 | 1,406,950 | 80.9 |

Subbotin 1.001 | 4.9 | 350 | 321,646 | −0.08 |

The CHF calculation correlation used in the new wall heat transfer model is the Groeneveld CHF look-up table developed in 2006 (Groeneveld et al.,

Variation of the Wall Temperature in Bailey Experiment.

Variation of the Wall Temperature in Subbotin Experiment.

Based on the various disturbances, this part demonstrates the steady ability of control system. The introduced linear perturbations include main steam temperature, system pressure, core power, coolant flow, and so on (Table

The disturbance conditions of control system.

Heat exchanger outlet temperature control | Regulating secondary side flowrate of heat exchanger | The core power increases linearly at 1% per second at 10 s | Heat exchanger outlet temperature |

System pressure control | Regulating the opening of the control valves. | Pressure increases linearly by 10% at 10 s | System pressure |

Thermal power control | Regulating withdrawn and insertion of control rods | Thermal power increases linearly by 10% at 10 s | Thermal power |

Steam drum water level control | Charging and letdown of steam drum | Coolant flow increased linearly by 10% at 10 s | steam drum water level |

Coolant flow rate control | Regulating the opening of the control valves. | Coolant flow increases linearly by 10% at 10 s | Coolant flow rate |

Once-through direct cycle loop inlet temperature control | Regulating the opening of the control valves. | Thermal power increases linearly by 10% at 10 s | Inlet temperature control |

When subjected to various disturbances, under the control of the control system, each control system can effectively controls the control target quickly and steadily (Figure

Control capability of control systems under disturbance conditions.

Typical startup schemes use a sliding startup system that includes a circulation loop for startup and a once-through direct loop (Figure

Transient performance of the startup procedure.

A new wall heat transfer model is developed for SCTRAN applications to analyze the SCWR startup characteristics. In the model, drastic changes to the heat transfer coefficient (calculated by the SCTRAN) near the critical region is resolved and the heat transfer coefficient from a subcritical to supercritical pressure is forecast precisely and smoothly.

Because the thermo-physical properties and transport properties of coolant change significantly from a subcritical to supercritical pressure, a control system is required to adjust the parameter changes during the startup procedure. Under the control strategy of the startup procedure, the system pressure, temperature, thermal power and flow rate can be regulated according to the startup objectives. The calculation results show that the thermal parameters of the circulation loop and the once-through direct cycle meet the requirement and the MCST remains below the limit temperature of 650°C.

YY wrote the manuscript. JS guided this research. LW, DW, and XZ critical revised the article.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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_{ρ}_{max}: the maximum insertion reactivity speed, cent/s

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