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Edited by: Liangming Pan, Chongqing University, China

Reviewed by: Rita Mastrullo, Università degli Studi di Napoli Federico II, Italy; Zeyong Wang, Converge Science, United States

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.

The plate OTSG (once-through steam generator) with channel diameter of 1–3 mm has high volume-power ratio and powerful resistance to high temperature and high pressure. It can well satisfy the needs of high heat transfer performance and good security of integrated pressure vessel in nuclear power. Heat transfer characteristics of flow boiling in the channel have aroused increasing concerns from scholars in this field. In this paper, based on the experimental results achieved by the researcher in our team, the drift flux model is applied to simulate the flow boiling heat transfer coefficients in the rectangular channel with equivalent diameter of 1.7 mm to further explore the flow boiling mechanism in the channel. The drift velocities and the distribution parameters of drift flux model are obtained by the empirical correlations of the horizontal flow. The simulation boundary conditions comply to the experimental conditions, the simulation resolutions are obtained by using STAR-CCM+. The simulation results indicate that the heat transfer coefficients trends along the flow direction are consistent with the trends of the experimental data. The drift velocities and the distribution parameters have little effect on the heat transfer coefficients of the horizontal small channel. When the drift velocity is 0 and the distribution parameter is 1, compared with the experimental data, the heat transfer coefficients in the single-phase liquid convective heat transfer region of the flow at high pressure are well higher, while those in the region that from bobble flow to the slug flow of the flow increase, even though they are still lower in annular flow region. The error between the predicted and the experimental is from −50 to +50%. Similarly, the model predicted heat transfer coefficients during subcooled flow boiling at low pressure are generally lower than experimental data. And the error between the predicted and the experimental is from −60 to +10%.

After several severe accidents, the small modular reactor (SMR) design concepts are being developed for its good security and economic performance in recent years. The distinguishing feature of small modular reactor is that the pressurizer, the control rod drive mechanisms, all pumps and the steam generators are integrated into the reactor vessel. On the one hand, the small modular reactor can eliminate the coolant loss accident and enhance the safety in the process of accident. On the other hand, it can not only replace the traditional fossil fuel power plant, but also be used such as in underwater vehicle power system to increase the economy. Importantly, the small module reactor can realize the overall off-site manufacturing and transportation to the site for assembly, which greatly reduces the construction cycle and construction time of the power plant and reduces the cost (Rowinski et al., ^{2}/m^{3}, which can well meet the requirements of high volume power ratio, high heat transfer efficiency, high temperature resistance, and high pressure proof (Chen et al.,

A test loop for the studying of flow boiling characteristics in small channel of plate OTSG had been built in our laboratory. Schematic diagram of the experimental apparatus is shown in

Schematic diagram of the experimental apparatus.

The schematic diagram of the test section is represented in

The schematic diagram of the test section.

The mass flux G inside the channel are calculated by the measured mass flow rate:

Subcooled section length:

The vapor quality

The heat transfer coefficient at the measurement point is obtained as follows:

The subscript _{water, i} represents the temperature of the water. The temperature of the water rises linearly from the inlet temperature to the saturation temperature in the flow direction when the water is in subcooled state. In the boiling state, the temperature of the water represents the saturation temperature. Assuming that the pressure along the path decreases linearly from the inlet pressure to the outlet pressure and the corresponding saturation temperature evaluated by the software REFPROP 9.0.

The heat flux and channel wall temperature are evaluated by the one-dimensional Fourier heat conduction law in the direction perpendicular to the channel cross section, respectively:

Whereas, _{i} is the heat flux and _{w, i} is the channel wall temperature. Where _{i} and Δ_{i} represent the temperature difference and vertical distance between the thermocouples, respectively. _{Ti} refers to the thermocouple temperature.

Huang (

The flow patterns in the rectangular small channel at a low pressure and a high pressure.

Simulation cases based on experimental conditions.

_{in} |
^{2}·s)] |
^{2}) |
_{in} |
_{in} |
_{sat} |
_{out} |
||
---|---|---|---|---|---|---|---|---|

1 | 2.73 | 500 | 397.36 | 0.001444 | 450.12 | 501.77 | 2.727 | 1462.28 |

2 | 2.53 | 500 | 349.36 | 0.001462 | 447.09 | 497.55 | 2.521 | 1285.64 |

3 | 2.20 | 500 | 294.91 | 0.001476 | 445.86 | 490.32 | 2.193 | 1085.27 |

4 | 2.83 | 400 | 350.00 | 0.001207 | 474.56 | 503.7 | 2.826 | 1288.00 |

5 | 2.83 | 400 | 298.31 | 0.001207 | 474.56 | 503.7 | 2.826 | 1097.76 |

6 | 2.66 | 400 | 247.13 | 0.001212 | 460.12 | 500.21 | 2.650 | 909.44 |

7 | 2.63 | 300 | 292.94 | 0.000988 | 439.70 | 499.65 | 2.617 | 1078.02 |

8 | 0.21 | 500 | 299.40 | 0.00149 | 317.99 | 391.70 | 0.165 | 1101.78 |

9 | 0.34 | 400 | 297.94 | 0.001198 | 329.25 | 409.43 | 0.309 | 1096.44 |

10 | 0.38 | 300 | 295.57 | 0.000931 | 337.20 | 413.79 | 0.351 | 1087.71 |

Assumption:

The gas-liquid two-phase mixture is considered as a single fluid;

The gas-liquid two phases are in thermal equilibrium;

The gas-liquid two phases can move relative to each other.

Vapor quality:

Vapor volume fraction:

Mixture continuity:

Mixture momentum:

Mixture energy:

Solid equation:

Flow-solid interface equation:

The stress tensor:

Heat flux:

The effective thermal conductivity:

The mixture density:

The mixture velocity:

The mixture viscosity:

The mixture thermal conductivity:

The mixture-specific static enthalpy:

The mixture total energy:

The mixture total enthalpy:

The mean drift velocity of the vapor phase:

The volume-weighted mixture velocity:

The velocity of vapor phase:

The velocity of liquid phase:

The averaged drift velocity is formulated in a functional form as:

The distribution parameter:

The subscripts _{sat} is the saturation temperature. ρ_{vs} and ρ_{ls} are the densities of vapor and liquid at saturation temperature, respectively. _{vs} and _{ls} refer to the enthalpies of vapor and liquid at saturation temperature, respectively. _{v} is the force due to gravity.

The empirical correlations of the distribution parameter and the averaged drift velocity developed by Bhagwat and Ghajar (

The distribution parameter:

The averaged drift velocity:

The numerical model and boundary conditions is shown in

The numerical model and boundary conditions.

The thermo-physical properties of the solid materials.

ρ (kg/m^{3}) |
8,530 | 8,055 | 2,490 | 2,230 | 1,100 |

_{p} |
375 | 480 | 816 | 900 | 692 |

120 | 15 | 0.15 | 1.2 | 0.9 |

The mesh of numerical model is shown in

The mesh of numerical model.

The results of grid independent validation test.

The data reduction method of simulation is presented in

The data reduction method of simulation.

The relative error can be calculated as follow:

It should be noted that the proportions of different flow patterns mentioned in this results discussion are all taken from literatures of Huang (

^{2}·s), ^{2}]. The distribution parameters and drift velocities calculated by Bhagwat and Ghajar (_{0} = 1.02,_{vvj} = 0.05

The effects of the distribution parameters and the averaged drift velocities on the heat transfer coefficients.

The comparisons between experimental and numerical heat transfer coefficients at three heat fluxes of 294.91, 349.36, and 397.36 kW/m^{2}, a mass flux of 500 kg/(m^{2}·s) are shown in

The comparisons between experimental and numerical heat transfer coefficients for ^{2} and ^{2}·s).

The comparisons between experimental and numerical heat transfer coefficients for ^{2} and ^{2}·s).

The comparisons between experimental and numerical heat transfer coefficients for ^{2} and ^{2}·s).

The relative error at high pressure.

The influences of the pressures on the heat transfer coefficients for mass fluxes of 300 and 400 kg/(m^{2}·s), heat flux of 300 kW/m^{2} are illustrated in

The influences of the pressures on the heat transfer coefficients for ^{2} and ^{2}·s).

The influences of the pressures on the heat transfer coefficients for ^{2} and ^{2}·s).

The relative error at low pressure.

In this research, the drift flux model and homogeneous flow model are adopted to simulate the flow boiling heat transfer coefficients in small rectangular channel, The simulation software is STAR-CCM+. Conclusions are drawn as follows:

The drift velocities and the distribution parameters have little effects on the heat transfer coefficients of the plate OTSG and the effects can be neglected.

The homogeneous flow model under-predicts the heat transfer coefficients during subcooled flow boiling at low pressures. And the predictions of the homogeneous flow model at high pressures match better with the experimental results.

At high pressure, the relative error between prediction and experiment is from −50 to +50%. At low pressure, the relative error between prediction and experiment is from −60 to +10%.

According to the fluid-solid coupled 3-D simulations, the homogeneous flow model can predict the trends of heat transfer coefficients along the path at both high and low pressures. And at high pressure, the homogeneous flow model can well predict the heat transfer coefficients of plate OTSG in the region that from bobble flow to the slug flow. It is shown that the homogeneous flow model will be useful for evaluating the heat transfer characteristics of the plate OTSG.

All datasets generated for this study are included in the article/supplementary material.

XY carried out the establishment of boiling numerical model, geometric model, mesh models, the sampling of boundary conditions from experimental data, the results analysis as well as the writing of paper. LY provided the guideline of the research and modified the language of manuscript. ZT help finish the geometric modeling. SH and HL also provide guidance and assistance in the process. All authors worked together to define the methodology and procedures.

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.

Re | Reynolds number |

Height | |

Width | |

Length | |

_{sub} |
Subcooled section length |

_{h} |
Equivalent diameter |

Temperature | |

Δ_{i} |
Temperature difference between the thermocouples |

Δ_{i} |
Vertical distance between the thermocouples |

Vapor quality | |

Gravitational acceleration | |

Thermal conductivity | |

_{p} |
Constant pressure specific heat |

Total heating power | |

Mass flow | |

Mass flux | |

Heat flux | |

Total energy | |

Total enthalpy | |

Specific static enthalpy | |

_{0} |
Distribution parameter |

_{vj} |
Drift velocity |

The volume-weighted mixture velocity | |

α | Vapor volume fractions |

ρ | Densities |

μ | Dynamic viscosity |

Exp | Experimental parameter |

DFM | Drift flux model |

Relative error | |

HM | Homogeneous flow model |

Aluminum | |

Wall | |

Saturation condition | |

Liquid | |

Vapor | |

Solid | |

Mixture | |

Average | |

ith point or ith phase |