# 超临界二氧化碳矩形回路自然循环稳态数值研究Steady State Numerical Study on the Natural Cyclic of Supercritical Carbon Dioxide in a Rectangle Loop

Abstract: Due to the admirable thermal characteristics in the supercritical region, carbon dioxide is considered for use as working fluid of Brayton cycle, which could achieve higher efficiency compared with steam Rankine cycle. Natural circulation is the technical basis for improving passive safety of systems, and the steady-state characteristics are essential for the design of supercritical carbon dioxide power conversion system. In order to study the steady-state characteristics of the natural circulation of supercritical carbon dioxide, a three-dimensional steady-state simulation of the heat transfer characteristics of the natural circulation of supercritical carbon dioxide in a small rectangular loop was carried out by using the CFD method. The simulation parameters are as follows: the height difference of cold and hot section is 1.0 m, the pressure range is 7 - 11 MPa, and the heating wall temperature range is 320 - 370 K. The simulation results show that the local temperature in the horizontal tube increases gradually from the bottom to the top due to the drastic thermal properties changes near the quasi-critical point and the influence of buoyancy and gravity. When the fluid temperature reaches near the quasi-critical temperature, the mass flow rate, heat transfer power and surface heat transfer coefficient increase significantly. Based on the simulation results, the relationship between steady-state Reynolds number Re and modified Grashof number Grm is fitted. The simulation results can provide reference for the design and analysis of passive safety system of supercritical carbon dioxide.

ABSTRACT

Due to the admirable thermal characteristics in the supercritical region, carbon dioxide is considered for use as working fluid of Brayton cycle, which could achieve higher efficiency compared with steam Rankine cycle. Natural circulation is the technical basis for improving passive safety of systems, and the steady-state characteristics are essential for the design of supercritical carbon dioxide power conversion system. In order to study the steady-state characteristics of the natural circulation of supercritical carbon dioxide, a three-dimensional steady-state simulation of the heat transfer characteristics of the natural circulation of supercritical carbon dioxide in a small rectangular loop was carried out by using the CFD method. The simulation parameters are as follows: the height difference of cold and hot section is 1.0 m, the pressure range is 7 - 11 MPa, and the heating wall temperature range is 320 - 370 K. The simulation results show that the local temperature in the horizontal tube increases gradually from the bottom to the top due to the drastic thermal properties changes near the quasi-critical point and the influence of buoyancy and gravity. When the fluid temperature reaches near the quasi-critical temperature, the mass flow rate, heat transfer power and surface heat transfer coefficient increase significantly. Based on the simulation results, the relationship between steady-state Reynolds number Re and modified Grashof number Grm is fitted. The simulation results can provide reference for the design and analysis of passive safety system of supercritical carbon dioxide.

Keywords:Supercritical Carbon Dioxide, Steady-State, Natural Circulation, CFD, Heat Transfer

1. 引言

2. 计算模型建立

2.1. 几何模型建立

Figure 1. Schematic diagram of the geometry of the simulation loop

a) CO2在矩形回路中以单相状态流动；b) 系统运行在稳态条件下；c) 除CHX和HHX以外，剩余管段为绝热壁面；d) 加热段和冷却段初始壁面为恒温。

2.2. 数值计算方法

(a) 截面网格 (b) 弯管处网格

Figure 2. Mesh generation of the loop

$m={\int }_{0}^{A}\rho udA$

$\mathrm{Re}=\frac{4m}{\pi du}$

$G{r}_{m}=\frac{g\beta {d}^{3}{\rho }^{2}Q{H}_{0}}{A{u}^{3}{C}_{p}}$

$Q=m{C}_{p}\Delta T$

${T}_{avg}=\frac{{T}_{CHX}+{T}_{HHX}}{2}$

2.3. 2拟临界物性分析

CO2拟临界点附近的物性变化剧烈，图3显示的是在给定压力条件下比热容随温度的变化。从图中可以看出在达到拟临界温度时，比热容瞬间达到最大值，同时随着压力的升高，拟临界温度也逐渐升高。在拟临界点附近物性的剧烈变化对CO2作为换热工质的影响程度如何值得关注，更重要的是在模拟过程中对CO2物性的处理上，利用理想气体方程不能准确反映物性剧烈变化的，应采用真实物性。

Figure 3. The changes of Cp in different pressure

2.4. 物性处理

3. 结果分析

Figure 4. Real properties of CO2 (Cp as example, the data comes from REFPROP)

Table 1. Text matrix used for the current investigation

3.1. 回路温度分布

Figure 5. Distribution of bulk fluid temperature along the loop

3.2. 回路横截面温度分布

(a) 加热段温度 (b) 冷却段温度 (c) 加热段流体速度 (d) 冷却段流体速度

Figure 6. Distribution of temperature and velocity in cross section

3.3. 速度和温度分布

Figure 7. Temperature contour in cross section

Figure 8. Velocity distribution of the whole loop

3.4. 质量流量及换热功率

Figure 9. Effect of heating wall temperature on mass flow rate

Figure 10. Effect of heating wall temperature on heat transfer power (HHX)

3.5. 表面换热系数

Figure 11. Effect of system pressure on surface heat transfer coefficient

3.6. Re和Grm关系式的拟合

Vijayan关系式 [10]：

$\mathrm{Re}=1.96{\left(G{r}_{m}d/{L}_{t}\right)}^{\frac{1}{2.75}}$

$\mathrm{Re}=1.786{\left(G{r}_{m}d/{L}_{t}\right)}^{\frac{1}{2.74}}\left(30000\le \mathrm{Re}\le 90000\right)$

Figure 12. Fitting formula compare with Vijiayan

4. 结论

1) 在加热段和冷却段为理想的几何对称和热对称时，自然循环的流动方向是具有随机性的，因此，需要自然循环沿着既定的方向流动，需要按照需求布置不对称性，更利于系统的稳定运行；

2) 在拟临界附近，由于物性的剧烈变化及浮升力的作用，温度和速度在三维空间中的分布不是对称均匀的，呈现管内上部温度高于下部温度，水平管段尤为明显，竖直管段温度分布均匀；

3) 在7~11 MPa范围内，质量流量和换热功率随着加热壁面温度的升高而升高，且在拟临界点处达到最大，随后开始降低；

4) 基于模拟结果，拟合了新的关于超临界二氧化碳流动换热的Re和修正Grm关系式，对超临界二氧化碳自然循环设计和分析具有一定的参考价值。

[1] Bai, Z.W., Zhang, G.Q., Li, Y.Y., Xu, G. and Yang, Y.P. (2018) A Supercritical CO2 Brayton Cycle with a Bleeding Anabranch Used in Coal-Fired Power Plants. Energy, 142, 731-738.
https://doi.org/10.1016/j.energy.2017.09.121

[2] Kumar, P., Dutta, P., Murthy, S.S. and Srinivasan, K. (2016) Solar Driven Carbon Dioxide Brayton Cycle Power Generation with Thermal Compression. Applied Thermal Engineering, 109, 854-860.
https://doi.org/10.1016/j.applthermaleng.2016.06.112

[3] Manjunath, K., Sharma, O.P. and Kaushik, S.C. (2018) Thermodynamic Analysis of a Supercritical/Transcritical CO2 Based Waste Heat Recovery Cycle for Shipboard Power and Cooling Applications. Energy Conversion and Management, 155, 262-275.
https://doi.org/10.1016/j.enconman.2017.10.097

[4] Li, M.J., Zhu, H.H., Guo, J.Q., Wang, K. and Tao, W.Q. (2017) The Development Technology and Applications of Supercritical CO2 Power Cycle in Nuclear Energy, Solar Energy and Other Energy Industries. Applied Thermal Engineering, 26, 255-275.
https://doi.org/10.1016/j.applthermaleng.2017.07.173

[5] 黄彦平, 王俊峰. 超临界二氧化碳在核反应堆系统中的应用[J]. 核动力工程, 2012, 33(3): 21-27.

[6] Zhang, X., Chen, L. and Yamaguchi, H. (2010) Natural Convective Flow and Heat Transfer of Supercritical CO2 in a Rectangular Circulation Loop. Heat and Mass Transfer, 53, 4112-4122.
https://doi.org/10.1016/j.ijheatmasstransfer.2010.05.031

[7] Chen, L., Zhang, X.R. and Jiang, B. (2014) Effects of Heater Orientations on the Natural Circulation and Heat Transfer in a Supercritical CO2 Rectangular Loop. Journal of Heat Transfer, 136, paper052501.
https://doi.org/10.1115/1.4025543

[8] Du, Z., Lin, W. and Gu, A. (2010) Numerical Investigation of Cooling Heat Transfer to Supercritical CO2 in a Horizontal Circular Tube. The Journal of Supercritical Fluids, 55, 116-121.
https://doi.org/10.1016/j.supflu.2010.05.023

[9] Yadav, A.K., Gopal, M.R. and Bhattacharyya, S. (2012) CFD Analysis of a CO2 Based Natural Circulation Loop with End Heat Exchangers. Applied Thermal Engineering, 36, 288-295.
https://doi.org/10.1016/j.applthermaleng.2011.10.031

[10] Vijayan, P.K. (2002) Experimental Observations on the General Trends of the Steady State and Stability Behaviour of Single-Phase Natural Circulation Loops. Nuclear Engineering and Design, 215, 139-152.
https://doi.org/10.1016/S0029-5493(02)00047-X

[11] Yadav, A.K., Gopal, M.R. and Bhattacharyya, S. (2012) CO2 Based Natural Circulation Loops: New Correlations for Friction and Heat Transfer. International Journal of Heat and Mass Transfer, 55, 4621-4630.

[12] Lisboa, P.F., Fernandes, J., Simoes, P.C., Mota, J.P.B. and Saatdjian, E. (2010) Computational Fluid-Dynamics Study of a Kenics Static Mixer as a Heat Exchanger for Supercritical Carbon Dioxide. The Journal of Supercritical Fluids, 55, 107-115.
https://doi.org/10.1016/j.supflu.2010.08.005

[13] Bau, H.H. and Torrance, K.E. (1981) Transient and Steady Behavior of an Open, Symmetrically Heated, Free Convection Loop. Heat and Mass Transfer, 24, 597-609.
https://doi.org/10.1016/0017-9310(81)90004-1

[14] Chen, L., Zhang, X.R., Deng, B.L. and Jing, B. (2013) Effects of Inclination Angle and Operation Parameters on Supercritical CO2 Natural Circulation Loop. Nuclear Engineering and Design, 265, 895-908.
https://doi.org/10.1016/j.nucengdes.2013.06.037

[15] Liu, G., Huang, Y., Wang, J., et al. (2015) Effect of Buoyancy and Flow Acceleration on Heat Transfer of Supercritical CO2 in Natural Circulation Loop. International Journal of Heat & Mass Transfer, 91, 640-646.
https://doi.org/10.1016/j.ijheatmasstransfer.2015.08.009

Top