﻿ 聚变堆液态金属包层MHD流动和传热数值模拟程序开发与验证 Development and Validation of Numerical Simulation Program for MHD Flow and Heat Transfer in Liquid Metal Blanket of Fusion Reactor

Nuclear Science and Technology
Vol. 07  No. 03 ( 2019 ), Article ID: 31203 , 8 pages
10.12677/NST.2019.73012

Development and Validation of Numerical Simulation Program for MHD Flow and Heat Transfer in Liquid Metal Blanket of Fusion Reactor

Jiajia Han1,2,3, Weihua Wang1,2*

1Institute of Plasma Physics, Chinese Academy of Sciences, Hefei Anhui

2University of Science and Technology of China, Hefei Anhui

3PLA Army Academy of Artillery and Air Defense, Hefei Anhui

Received: June 17th, 2019; accepted: July 2nd, 2019; published: July 9th, 2019

ABSTRACT

The effect of magnetohydrodynamic effect on the flow and heat transfer of liquid metal in liquid blanket of fusion reactor is studied. A numerical simulation program of MHD flow and heat transfer distribution is developed. The flow and heat transfer phenomena in liquid blanket of fusion reactor are simulated by numerical method. The numerical simulation program is based on the four-step projection method to calculate the flow field distribution in the blanket under strong magnetic field. The temperature distribution is obtained by using the finite volume method. The results of numerical simulation are verified by standard examples and energy conservation methods. It provides a reference for the study of the flow and heat transfer characteristics of liquid metals in the blanket of fusion reactor.

Keywords:MHD, Heat Transfer, Temperature Distribution, Numerical Method

1中国科学院合肥物质科学研究院等离子体物理研究所，安徽 合肥

2中国科学技术大学，安徽 合肥

3陆军炮兵防空兵学院基础部物理教研室，安徽 合肥

1. 引言

2. 控制方程与数值方法

2.1. 控制方程

$\nabla \cdot u=0$ (1)

$\frac{\partial u}{\partial t}+u\cdot \nabla u=-\nabla p+\frac{1}{Re}\nabla \cdot \left(\nabla u\right)+N\left(J×B\right)$ (2)

${\nabla }^{2}\varphi =\nabla \cdot \left(u×B\right)$ (3)

$\frac{\partial T}{\partial t}+\nabla \cdot \left(uT\right)=\frac{1}{Pe}{\nabla }^{2}T+EcN{J}^{2}+\Phi$ (4)

p——压力；

B——磁感应强度；

J——电流密度；

T——温度。

2.2. 数值方法

Figure 1. Structural sketch of discrete grid

$\int \frac{\partial T}{\partial t}\text{d}v+\int \nabla \cdot \left(uT\right)\text{d}v=\left[\frac{1}{Pe}\int {\nabla }^{2}T\text{d}v+\int \left(EcN{J}^{2}+\Phi \right)\text{d}v\right]$ (5)

$\int \frac{\partial T}{\partial t}\text{d}v=\frac{T-{T}^{0}}{\Delta t}$ (6)

$\begin{array}{l}\int {\nabla }^{2}T\text{d}v=\left(\frac{{T}_{i+1,j,k}-{T}_{i,j,k}}{{x}_{i+1,j,k}-{x}_{i,j,k}}-\frac{{T}_{i,j,k}-{T}_{i-1,j,k}}{{x}_{i,j,k}-{x}_{i-1,j,k}}\right)\Delta y\Delta z+\left(\frac{{T}_{i,j+1,k}-{T}_{i,j,k}}{{y}_{i,j+1,k}-{y}_{i,j,k}}-\frac{{T}_{i,j,k}-{T}_{i,j-1,k}}{{y}_{i,j,k}-{y}_{i,j-1,k}}\right)\Delta x\Delta z\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\left(\frac{{T}_{i,j,k+1}-{T}_{i,j,k}}{{z}_{i,j,k+1}-{z}_{i,j,k}}-\frac{{T}_{i,j,k}-{T}_{i,j,k-1}}{{z}_{i,j,k}-{z}_{i,j,k-1}}\right)\Delta x\Delta y\end{array}$ (7)

$\int \nabla \cdot \left(uT\right)\text{d}v=\left(u{f}_{i+1,j,k}{T}_{i,j,k}-u{f}_{i-1,j,k}{T}_{i-1,j,k}\right)\Delta y\Delta z$ (8)

$\int \left(EcN{J}^{2}+\Phi \right)\text{d}v=\left(EcN{J}^{2}+\Phi \right)\Delta x\Delta y\Delta z$ (9)

2.3. 边界条件

Figure 2. Internal structure of ITER vacuum vessel

$\begin{array}{l}\frac{\text{d}T}{\text{d}x}=0\\ \frac{\text{d}T}{\text{d}y}=0\\ \frac{\text{d}T}{\text{d}z}=0\end{array}$ (10)

3. 结果与讨论

Figure 3. Grid independence verification result

3.1. 速度分布

(a) (b)

Figure 4. Shercliff’s case results (Ha = 500, Re = 10); (a) Three dimensional velocity distribution of a cross section at x = 3.0; (b) Compare between numerical results and analytical results

(a) (b)

Figure 5. Hunt’s case results (Ha = 1000, Re = 500); (a) Three dimensional velocity distribution of a cross section at x = 3.0; (b) Compare between numerical results and analytical results

Table 1. Pressure gradient and flow rate for Shercliff’s case and Hunt’s case

3.2. 温度分布

$\Phi \cdot V=\sum \rho {c}_{p}u\left({T}_{out}-{T}_{in}\right)\Delta y\Delta z$ (11)

$V$ ——流道体积；

$\rho$ ——密度；

cp——比热容；

Tin——入口温度；

Tout——出口温度。

$\Delta \epsilon =\frac{|\Phi \cdot V-\sum \rho {c}_{p}u\left({T}_{out}-{T}_{in}\right)\Delta y\Delta z|}{\Phi \cdot V}$ (12)

Figure 6. Temperature distribution of Hunt case: Ha = 1000, Re = 500

4. 结论

Development and Validation of Numerical Simulation Program for MHD Flow and Heat Transfer in Liquid Metal Blanket of Fusion Reactor[J]. 核科学与技术, 2019, 07(03): 83-90. https://doi.org/10.12677/NST.2019.73012

1. 1. Abdou, M.A., Morley, N.B. and Ying, A.Y. (2005) Overview of Fusion Blanket R&D in the US over the Last Decade. Nuclear Engineering and Technology, 37, 401-422.

2. 2. Wong, C.P.C., Salavy, J.F., Kim, Y., Kirillov, I., Rajendra Kumar, E., Morley, N.B., et al. (2008) Overview of Liquid Metal TBM Concepts and Programs. Fusion Engineering and Design, 83, 850-857. https://doi.org/10.1016/j.fusengdes.2008.06.040

3. 3. Shercliff, J.A. (1953) Steady Motion of Conducting Fluids in Pipes under Transverse Magnetic Fields. Proceedings of the Cambridge Philosophical Society, 49, 136-144. https://doi.org/10.1017/S0305004100028139

4. 4. Hunt, J.C.R. (1965) Magnetohydrodynamic Flow in Rectangular Ducts. Journal of Fluid Mechanics, 21, 577-590. https://doi.org/10.1017/S0022112065000344

5. 5. Ni, M.-J., Munipalli, R., Morley, N.B., Huang, P. and Abdou, M.A. (2007) A Current Density Conservative Scheme for Incompressible MHD Flows at a Low Magnetic Reynolds Number. Part I: On a Rectangular Collocated Grid System. Journal of Computational Physics, 227, 174-204. https://doi.org/10.1016/j.jcp.2007.07.025

6. 6. Smolentsev, S., Morley, N.B., et al. (2008) MHD and Heat Transfer Considerations for the US DCLL Blanket for DEMO and ITER TBM. Fusion Engineering and Design, 83, 1788-1791. https://doi.org/10.1016/j.fusengdes.2008.04.002

7. 7. 袁保山, 姜韶风, 陆志鸿. 托卡马克装置工程基础[M]. 北京: 原子能出版社, 2011: 381-387.

8. NOTES

*通讯作者。