_{2}Brayton Cycle as Power Conversion System

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Supercritical CO_{2} Brayton cycle is a good choice of thermal-to-electric energy conversion system, which owns a high cycle efficiency and a compact cycle configuration. It can be used in many power-generation applications, such as nuclear power, concentrated solar thermal, fossil fuel boilers, and shipboard propulsion system. Transient analysis code for Supercritical CO_{2} Brayton cycle is a necessity in the areas of transient analyses, control strategy study, and accident analyses. In this paper, a transient analysis code SCTRAN/CO2 is developed for Supercritical CO_{2} Brayton Loop based on a homogenous model. Heat conduction model, point neutron power model (which is developed for nuclear power application), turbomachinery model for gas turbine, compressor and shaft model, and PCHE type recuperator model are all included in this transient analysis code. The initial verifications were performed for components and constitutive models like heat transfer model, friction model, and compressor model. The verification of integrated system transient was also conducted through making comparison with experiment data of SCO2EP of KAIST. The comparison results show that SCTRAN/CO2 owns the ability to simulate transient process for S-CO2 Brayton cycle. SCTRAN/CO2 will become an important tool for further study of Supercritical CO_{2} Bryton cycle-based nuclear reactor concepts.

Supercritical CO2(s-CO_{2}) Brayton cycle is a promising power conversion technology, which has advantages like compact system configuration compared to steam generation system, higher efficiency, and less need of water consumption. It has aroused great interests among industry and academia of different energy types, especially in nuclear and solar energy [

Many researchers studied the feasibility of using s-CO_{2} Brayton cycle as power conversion system for nuclear applications. One option is to use s-CO_{2} Brayton cycle to cool the reactor core directly. Figure _{2} Brayton cycle. The s-CO_{2} entering the reactor core is heated to high temperature by the thermal energy released in the core. Then high-temperature s-CO_{2} flows into the gas turbine and drives the shaft to rotate. The generator connected with the shaft can produce electricity. After the expansion process through the turbine, s-CO_{2} depressurized to a lower pressure, which is usually slightly over the critical pressure. The high-temperature low pressure s-CO_{2} enters the recuperator to heat the s-CO_{2} to required inlet temperature for the reactor at the high pressure side. After transferring energy to the high pressure side, the low pressure side s-CO_{2} is then cooled to be close to the critical temperature of s-CO_{2} by secondary water flow in the precooler. The s-CO_{2} flow rejects heat in the precooler and makes sure that the high density s-CO_{2} is compressed by the compressor. High pressure leaving the compressor is heated by the low pressure side coolant and enters the reactor core, as described before. In the development of this type of reactor concepts, the concept of reactor core cooled by s-CO_{2} should be developed as well as the configuration of s-CO_{2} Brayton cycle. As the only successfully operated CO_{2} cooled reactor, Advanced Gas Reactor (AGR) uses CO_{2} coolant at 4.33MPa and bundled fuel pins formed by oxide fuel and stainless-steel cladding [_{2} cooled fast reactor, the operational characteristics, safety issues, and behavior of the fuel, cladding, and coolant could provide great reference for S-CO_{2} cooled fast reactor core design. Pope [_{2} cooled fast reactor concept coupled with recompression S-CO_{2} Brayton cycle. This concept owns a core design with Tube in Duct (TID) assemblies and advanced shielding material, advanced cladding materials for high burn-up fuel, and high temperature. Oxide fuel was selected as the fuel form for its chemical compatibility with CO_{2}. Accident analysis and safety design have been carried out for this concept [_{2} at pressure of 20MPa is proposed by Parma et al. from Sandia National Laboratories [_{2}-cooled Micro Modular Reactor (MMR) with 36.2 MWth power is developed by [

Schematic map of nuclear reactor system cooled by s-CO2 Brayton cycle.

Another option to apply S-CO_{2} Brayton cycle working as the power conversion system of existing Gen IV reactor concept, which tries to take advantages of large amount of R&D work of these new concepts and improve the cycle efficiency at the same time. Feasibility of S-CO_{2} Brayton coupled to sodium fast reactor concept KALIMER-600 [_{2} Brayton cycle configuration, as well as the transient performance and control strategy of these concepts, has been carried out, which shows great potential for applying S-CO_{2} Brayton cycle on these new reactor concepts. A summary of the core design and Brayton cycle design of the above nuclear applications is listed in Table

Overview of current study on S-CO_{2} Brayton cycle study working as power conversion system on nuclear applications.

Concept Name | - | MMR | SC-GFR | - | KALIMER-600 | STAR-LM | SSTAR |
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Developing | - | KAIST | SNL | MIT | KAERI | Argonne National Laboratory | Argonne National Laboratory |

Institution | |||||||

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Brayton cycle | - | direct | direct | direct | indirect | indirect | indirect |

coupled method | |||||||

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Core Part | thermal power (MW) | 36.2 | 200 | 2400 | 1528.9 | 400 | 45 |

Pressure (MPa) | 20 | 20 | 20 | 0.1 | 0.1 | 0.1 | |

Fuel type | UC fuel | UO2 | UO2BeO | U-TRU-10%Zr | TRU-N Enriched to N15 | Nitride fuel | |

Cladding type | Stainless steel | High Ni | ODS MA956 | Mod.HT9 | Co-extruded | - | |

Stainless steel | Si-enhanced | ||||||

F/M stainless | |||||||

steel with F/M | |||||||

substrate | |||||||

Core outlet temperature | 550 | 650 | 650 | 545.3 | 578 | 565.8 | |

Mass flow rate (kg/s) | 180 | 920 | 11708 | 7731.3 | 19708 | 2125 | |

Coolant | CO2 | CO2 | CO2 | Sodium | Pb | Pb | |

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Power Conversion System | Brayton cycle type | simple cycle | no specific design | recompression cycle | recompression cycle | recompression cycle | recompression cycle |

Cycle mass flow rate | 180 | - | 2927 | 8076.6 | 2276 | 239.3 | |

T/P of compressor | 60.8/8.0 | - | 32/7.69 | 31.25/7.4 | 31.25/7.4 | 31.25/7.4 | |

T/P of compressor outlet (°C/MPa) | 142.2/20.0 | - | 60.9/20 | 84.8/20.0 | 85/20.0 | 84.9/20.0 | |

T/P of recompression compressor inlet | - | - | 70.9/7.71 | 91.2/7.46 | 86.3/7.405 | 90.9/7.401 | |

T/P of recompression compressor outlet | - | - | 159.1/20.0 | 189.4/19.98 | 183.8/19.98 | 189.8/20 | |

T/P of turbine inlet | 550/19.93 | - | 650/19.45 | 508.0/19.74 | 540.0/19.88 | 541.4/19.99 | |

T/P of turbine outlet (°C/MPa) | 440.75/8.16 | - | 529.9/7.93 | 394.2/7.6 | 426.9/7.713 | 420.1/7.435 | |

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Reference | - | [ | [ | [ | [ | [ | [ |

Transient analysis code is a necessity for study of control strategy, dynamic characteristic, and safety analysis for S-CO_{2} Brayton cycle direct or indirect cooled reactors. According to the features of Brayton cycle coupled reactor applications, the transient analysis code should possess the ability to simulate reactor core, precooler, recuperator, and turbomachinery including compressor, gas turbine and rotating shaft model.

Different transient analysis codes have been developed to satisfy the demand for control strategy and accident study for s-CO_{2} Brayton cycle direct or indirect cooled reactors. A transient analysis code MMS-LMR was developed to simulate the system transient and evaluate control logics for sodium-cooled fast reactor KALIMER-600 [_{2}, and modules like reactor, pipe, Na-CO_{2} heat exchanger, recuperator, and compressor. Code MARS has been applied to carry out up-power and down-power transient simulation for the Supercritical CO_{2} Integral Experimental Loop (SCIEL) [_{2} properties near critical point and turbomachinery performance map were incorporated into the original GAMMA+ which was previously a transient analysis code for Very High-Temperature Reactor (VHTR) system developed by KAERI. The performance map for GAMMA+ is produced by KAIST-TMD, which is an in-house code to design the turbomachinery. GAMMA+ code simulation ability near critical point has been validated with comparing with the experiment data from SCO2PE [_{2} properties and compressor and turbine models, which could help to simulate the s-CO_{2} Brayton cycle. It has been used to analyze the safety performance for s-CO_{2} cooled fast reactors with passive safety system under loss of coolant accident and loss of generator load accident [_{2} fluid plus the turbomachinery shaft dynamics equation. This code has been applied to various applications, such as transient and control strategies analysis of s-CO_{2} Brayton cycle coupled to lead-cooled fast reactor [_{2} Integrated System Test [_{2} Brayton cycle coupled to sodium-cooled fast reactor [_{2}) as well as Brayton turbomachinery components to enhance its ability to simulate s-CO_{2} Brayton cycle [_{2} Brayton cycle [

Through the overview of the current transient analysis code development for nuclear application related Brayton cycle, we can find most of the codes are developed based on existing transient analysis codes with incorporating CO_{2} property, turbomachinery models, and PCHE models. The validation work is based on experimental data produced by s-CO_{2} Brayton cycle experimental platforms, such as 100 kWe s-CO_{2} power cycle system facility constructed by the cooperation of Knolls Atomic Power Laboratory (KAPL) and Bettis Atomic Energy Laboratory (BAEL) in 2012 [_{2} integral experiment loop (SCIEL) constructed by Korea Atomic Energy Research Institute (KAERI) [

As China is also launching projects into s-CO_{2} Brayton cycle development for concentrated solar thermal, fossil fuel boilers, and nuclear power, transient analysis code for S-CO2 Brayton cycle is urgently needed to help in predesigning of experimental facility, as well as the new Brayton cycle-based reactor concept development. The development of a transient analysis code is presented in this paper. SCTRAN [_{2} Brayton cycle by adding accurate thermal property and constitutive model for CO_{2}, turbomachinery models (including compressor, gas turbine, and shaft). Due to the lack of experiment data, the current validation strategy is to make simple validation with limited experiment data and code-to-code comparison with other codes like GAMMA+. The initial verification for SCTRAN/CO2’s ability to do component model simulation and cycle simulation is carried out.

SCTRAN is a one-dimensional safety analysis code for SCWRs, which applies homogeneous model to simulate the fluid flow. The homogeneous model assumes the two phases of coolant are in thermal equilibrium state and the velocity difference of the two phases is zero. Compared to drift model and two-phase model, this model needs less constitutive correlations and is easy to be solved numerically. For most of the transient or accident case in s-CO_{2} Brayton cycle, the coolant will stay in gas state. That is the reason why homogeneous model is adopted to develop the transient analysis code for s-CO_{2} Brayton cycle. The conservative equations of mass, momentum, and energy are as follows.

Mass conservative equation is

Momentum conservative equation is

Energy conservative equation is

Based on staggered grid method, control volume balance method, and one-order upwind difference scheme applying to the time derivative related items, a numerical procedure is developed with which the mass and energy of the control volumes and the mass flow of the junctions can be obtained conveniently.

In order to calculate the core power and its reactivity feedback effects, SCTRAN applies the fission decay heat equation and point neutron kinetics equation with six groups of delayed neutron to calculate the core power.

SCTRAN’s ability to simulate the transients and accidents of SCWR has been verified by comparing with APROS code and RELAP5-3D code [

In order to make SCTRAN suitable for s-CO_{2} Brayton cycle-based reactor system, accurate CO_{2} property package and heat transfer and friction models for carbon dioxide and turbomachinery models including gas turbine, compressor, and rotating shaft should be developed.

The goal of compressor model is to calculate the flow condition inside the compressor and at the compressor outlet. A quasistatic status is assumed for flow inside compressor under which situation the performance map could be used to evaluate the efficiency and pressure ratio of compressor. The solution of compressor model should include pressure rise which could be used for fluid momentum conservation equation, enthalpy increase which was needed in fluid energy conservation equation, and torque which is needed for shaft model to simulate rotating speed.

Figure

Ideal and realistic compression process inside compressor.

The pressure rise and adiabatic efficiency through the compressor are obtained from the performance map which is specially produced for the targeted compressor by other specific codes. As the compressor pressure ratio is regarded to be obtained from compressor performance map according to the rotating speed and coolant flow rate, the pressure increase through compressor can be obtained:_{p} denotes the compressor pressure ratio and

Assuming that no heat dissipated in the compression process, the compressor power acting on the fluid is

In the ideal compression process, the ideal work produced by compressor equals the energy increase of s-CO_{2} flowing through the compressor:

The compressor component will be regarded as a normal junction and volume when incorporating into SCTRAN. The pressure rise calculated by compressor model will be added to the momentum conservation equation of the represented junction and the enthalpy change calculated by compressor model will be added to the energy conservation equation of the represented volume.

Figure

Ideal and realistic expansion process inside gas turbine.

For fluid enthalpy increase,

For pressure drop,

For total torque of gas turbine,

In the Brayton cycle, there are many turbomachineries connected to the shaft, which include gas turbine, compressor, generator, and control system. The shaft model for evaluation shaft rotating speed is as follows:

An independent and accurate thermal property model for carbon dioxide over a large parameter range is needed to be incorporated into code SCTRAN. Generally, there are three methods to calculate the fluid thermal property in thermal hydraulic analysis codes, which include property lookup tables or figures, solution of fluid state equations, and direct calculation of fitting correlation. In method of property tables or figures, the fluid thermal property is plotted in figures or tabulated in tables, which is easy for users to find property for certain state. However, the calculation efficiency of this method is low, which makes it hard to be applied in large thermal analysis codes which needs to calculate the fluid property repeatedly. The solution of fluid state equation is based on strict theoretical and experimental study. Thus, this method can produce fluid property with high accuracy. However, these basic fluid state equations are complex and time-consuming because iterations are needed to get the final results. The method of fitting correlation is to get a mathematical correlation with certain prediction accuracy for fluid property based on the existing thermal property data. The mathematical correlation can be polynomial expression or some other type. This method with the merits of small computational effort and high prediction accuracy can be conveniently programmed into thermal analysis codes. It has been widely used in thermal analysis codes. Thus the method of fitting polynomial correlation was applied in this paper to develop the CO2 property package.

The based thermal property data which is used for fitting correlations comes from NIST REFPROP. The thermal property package covers pressure range of 0.1~20MPa and temperature range of 0~991°C. Parameters including saturated liquid and vapor enthalpy, temperature, specific volume, and dynamic viscosity have been obtained through the pressure and enthalpy. The property calculation is divided into three regions based on pressure and enthalpy, which are subcooled area, superheated region 1 (enthalpy over 360 kJ/kg but below 600 kJ/kg), and superheated region 2 (enthalpy over 600 kJ/kg). Table _{2} property and NIST REFPROP 9.0. It seems that the developed package can predict CO_{2} property very well in most property range with a relative error lower than 0.5%. However, for property near critical point, very large prediction error exists. The prediction performance of the developed CO_{2} property package at near critical point area should be improved in the future work.

Relative prediction error of the developed CO_{2} property package compared to NIST REFPROP 9.0.

_{ 2 } | | | |
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Saturated liquid enthalpy | | - | ±0.015% |

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Saturated vapor enthalpy | | - | ±0.009% |

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Temperature | T | subcooled area | -0.05% to 0.1%, 99% of which is within relative errors of ±0.05% |

superheated region 1 | ±0.2%, 99% of which is within relative errors of ±0.1% | ||

superheated region 2 | -0.1% to 0.25%, 99% of which is within relative errors of ±0.05% | ||

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Specific volume | v | subcooled area | -0.5% to 1%, 99% of which is within relative errors of ±0. 5% |

superheated region 1 | -1% to 4%, 99% of which is within relative errors of ±1%. | ||

superheated region 2 | -0.5% to 0.1%, 95% of which is within relative errors of ±0.1% | ||

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Dynamic viscosity | - | -1.5% to 0.5%, 99% of which is within ±0.5% |

For the straight semicircular flow channels in PCHE, correlation Gnielinski is applied ([^{6} and Pr between 0.5 and 2000.

The friction is evaluated by correlation Zigrang-Sylvester, which is an approximate explicit correlation of Colebrook-White correlation [

Wang et al. [^{6}, and surface relative roughness (ratio of roughness over tube diameter) is 0.005, 0.015, and 0.025. The system pressure and coolant flow Reynolds number cover the operation and transient conditions in s-CO_{2} Brayton cycle. The temperature range is a little bit narrow compared to that of s-CO_{2} Brayton cycle. So the experiment data in [^{6}. From the figure we can find that the prediction results in laminar flow area and turbulent flow area fit well with the experiment data.

Comparison for friction coefficient of various roughness between experimental data and SCTRAN/CO2 prediction.

A heat transfer experiment about PCHE which use s-CO_{2} and water as the heat transfer media in conditions relevant to the precooler in the s-CO_{2} Brayton cycle is conducted by [_{2} loop. The heat exchange happens in the PCHE, which has overall dimensions of 120×200×1200mm. The s-CO_{2} inlet temperature of the PCHE could be controlled by adjusting the power supply. Some large temperature difference tests are carried out to simulate the working conditions of the precooler in the Brayton cycle.

Schematic diagram of the experiment loop [

Several large temperature difference tests are simulated by SCTRAN/CO2 to verify that if correlation Gnielinski is capable of simulating the working conditions of precooler. The nodalization of SCTRAN/CO2 is shown in Figure _{2} and water side for case 6 predicted by SCTRAN/CO2 becomes closer to the experiment data. Considering the balance between prediction accuracy and calculation time, 20 nodes are selected to simulate the PCHE.

SCTRAN/CO2 nodalization for PCHE.

Mesh size sensitivity on outlet temperature prediction for PCHE in case 6.

Table _{2} side, the operation pressure is about 8 MPa, and the s-CO_{2} inlet temperature is held constant at 88°C with mass flow rate of 100, 200, 300, 400, and 500 kg/hr. For the water side, the mass flow rate is set to 700 kg/hr, and the water inlet temperatures varied to achieve the desired S-CO_{2} outlet temperature. For test B6~B10, the target S-CO_{2} outlet temperature is 36°C and, for test B11~B15, the target S-CO_{2} outlet temperature is 38°C.

Details of the experimental conditions.

TEST NO. | | | | | | |
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MPa | Kg/hr | °C | °C | kg/hr | °C | |

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B6 | 8.003 | 100.53 | 88.63 | 36.07 | 701.59 | 35.63 |

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B7 | 8.001 | 200.77 | 88.10 | 35.98 | 699.78 | 35.11 |

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B8 | 7.972 | 297.14 | 89.36 | 36.20 | 701.8 | 35.05 |

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B9 | 8.003 | 401.01 | 87.92 | 36.05 | 701.77 | 33.28 |

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B10 | 7.995 | 500.61 | 87.93 | 35.90 | 700.09 | 31.28 |

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B11 | 8.003 | 100.03 | 87.68 | 37.94 | 697.80 | 37.68 |

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B12 | 8.005 | 199.73 | 88.85 | 37.97 | 697.80 | 37.53 |

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B13 | 7.998 | 301.31 | 88.17 | 38.03 | 699.86 | 37.48 |

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B14 | 8.020 | 404.29 | 88.97 | 38.29 | 701.62 | 37.58 |

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B15 | 7.998 | 501.79 | 88.09 | 38.01 | 702.25 | 36.83 |

Figure _{2} outlet temperature. The square dots represent the simulation result using 2D-FLUENT by [

Temperature distribution of water and s-CO2 side predicted by SCTRAN/CO2 for test B6.

The comparison for S-CO2 outlet temperature between experimental data and simulation result.

Due to lack of design and experiment data on compressor performance, the verification of compressor model is carried out through code-to-code compressor with RELAP5-3D code on compressor consuming power and GAMMA+ on the outlet temperature prediction in the open literature.

Fisher and Davis [

Figure _{2} flow rate between 0.4 and 1.0. The performance map of the compressor in [

Nodalization of the recompressing compressor.

Figure

Predicted compressor consuming power by SCTRAN/CO2 and RELAP5-3D.

Bae et al. [_{2} test loop (SCO2PE) near critical point operation. Two different compressor operation conditions near the critical point are designed to verify the GAMMA+ predicted result for the compressor outlet temperature. Figure

Experiment data from SCO2PE and predicted result from SCTRAN/CO2 and GAMMA+ on the compressor outlet temperature.

Experiment(SCO2PE data) | GAMMA | SCTRAN/CO2 | ||
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Compressor outlet temperature/°C | case 1 | 38.3 | 42.2(+3.9) | 40.55(+2.25) |

case 2 | 45.8 | 46.5(+0.7) | 46.67(+0.87) | |

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Compressor outlet pressure/MPa | case 1 | 8.65 | 8.65 | 8.65 |

case 2 | 9.12 | 9.12 | 9.15 | |

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compressor efficiency | case 1 | 58.6 | 58.6 | 58.6 |

case 2 | 36.1 | 36.1 | 36.1 |

Nodalization of GAMMA code [

According to the two verifications for compressor model, the compressor model in code SCTRAN/CO2 can predict reasonable compressor consuming power and outlet temperature. The prediction accuracy of code SCTRAN/CO2 is close to those of RELAP5-3D and GAMMA+, as well as the experiment data produced by SCO2PE facility. However, if the quasisteady compressor model is suitable for transient performance, prediction is still uncertain. The reason for not carrying out transients on analysis of compressor, turbine, or shaft is that no corresponding experimental or numerical data is found in the open literature. More transient experiments on compressor and turbine performance should be established to validate turbomachinery model in SCTRAN/CO2 in the future.

SCO2PE (Supercritical CO_{2} Pressurizing Experiment) is a s-CO_{2} compressor test facility which aims to collect CO_{2} compressor operation and performance data [_{2} and a secondary water system. The CO_{2} loop includes a canned motor type compressor, a heat exchanger, an expansion valve, and pipes. The s-CO_{2} flow through the compressor is pressurized and heated. Then it is depressurized through the expansion valve with an isentropic process. The s-CO_{2} flow leaving the expansion valve will enter the heat exchanger and be cooled by the secondary water flow. The schematic diagram of the SCO2PE loop is shown in Figure _{2} Brayton cycle used for nuclear application. However, the steady and transient experiment data obtained from this facility could be used to validate steady performance of the compressor and the transient behavior of closed compressor loop.

Nodalization of SCTRAN/CO2 model and steady-state result at each node.

The nodalization of SCTRAN/CO2 is shown in Figure

A reduction in water cooling transient is initialized by reducing the water flow rate from 0.25 kg/s to 0.17 kg/s in 50 seconds. The water cooling reduction transient is one of the accidents anticipated in Brayton cycle cooled nuclear application. The transient simulation by SCTRAN is illustrated in Figure _{2} in the loop increases, which further results in the loop pressure rise. Figure _{2} closed loop.

Pressure and temperature variation during the cooling reduction transient.

SCTRAN is originally a transient analysis code for supercritical water reactor (SCWR). It has been applied to carry out accident analysis and safety system design for different types of SCWR [_{2} cooled nuclear application. A lot of works on numerical algorithms, computational time step control, and convergent criteria have been studied when SCTRAN is used for supercritical water reactor. The numerical algorithms between SCTRAN/CO2 and SCTRAN are all the same. That is the reason why this part is not included in the paper. However, the time step and the mesh size should be carefully selected after sensitivity analysis. For the s-CO_{2} Brayton cycle part, the transient turbomachinery model is developed and verification of transient analysis of closed s-CO_{2} loop in Section _{2} Brayton cycle in any type due to the fact that the compressor, turbine, and shaft component are modeled separately. The performance of the closed Brayton cycle could be evaluated qualitatively, not quantitatively. For further validation of SCTRAN/CO2, a large amount of experiment data on transient turbomachinery performance and transient cycle operation is still in urgent need. For further application in accident analysis for s-CO_{2} cooled reactor, SCTRAN/CO2 needs to incorporate an overall heat transfer package for a wide operation parameter, ranging from supercritical to subcritical pressure and high to low mass flow rate, for the fuel buddle inside the core as well as the micro flow channels of the PCHE. Only with the overall validation on these aspects, SCTRAN/CO2 could be further used for accident analysis, safety system, and control system design for s-CO_{2} Brayton cycle.

A transient analysis code SCTRAN/CO2 was developed through incorporating accurate thermal property, heat transfer model and friction model for CO2, and turbomachinery model including compressor, gas turbine and rotating shaft. The initial verification work on friction model with tube experimental data and compressor model with results of RELAP5-3D was carried out to testify the code programing. The verification work on heat transfer correlation and compressor model with experimental data is to validate their applicability on s-CO_{2} applications. The results of cycle simulation indicate that SCTRAN/CO2 owns the ability to simulate transient conditions for closed s-CO_{2} Brayton cycle. The following conclusions can be made:

The friction model in SCTRAN/CO2 was able to predict the right friction coefficient in a wide Reynolds number of 200-10^{6}.

The Gnielinski correlation in code SCTRAN/CO2 could predict a reasonable outlet temperature of the heat exchanger which works under the operation conditions of the precooler.

The compressor model of SCTRAN/CO2 could predict accurate compressor consuming power and outlet temperature, which indicate that it can be used for Brayton cycle simulation.

Transient simulation of SCO2PE indicates that SCTRAN/CO2 owns the ability to conduct transient simulations for s-CO_{2} Brayton cycle. However, accurate turbomachinery performance map should be developed and incorporated into the code in the future for simple and recompression Brayton cycle analysis.

Area/m^{2}

Specific heat capacity/J·(kg·K)^{−1}

Hydrodynamic diameter/m

Friction coefficient

Gravitational acceleration/m^{2}·s^{−1}

Reynolds number

Time/s

Fluid velocity/m·s^{−1}

Mass flow rate/kg·s^{−1}

Gravity acceleration /m·s^{−2}

Enthalpy/J·kg^{−1}

Specific saturated liquid enthalpy/J·kg^{−1}

Specific saturated gas enthalpy/J·kg^{−1}

Pressure ratio

Pressure/MPa

Heat flux/W·m^{−2}

Specific entropy/J·(kg·K)^{−1}

Length/m

Internal energy/J·kg^{−1}

Heat source/ J·kg^{−1}.

Neutron flux

Efficiency

Torque/ N·m

Dynamic viscosity/ N·s·m^{−2}

Density/kg·m^{−3}.

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

The authors would like to express their special thanks for the financial support from National Natural Science Foundation of China (Grant no. 11605132) and Nuclear Power Institute of China.

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_{2}Brayton cycle for a sodium-cooled fast reactor using the plant dynamics code