蒙特卡罗法求解二维各向异性导热-辐射耦合传热

doi:10.12068/j.issn.1005-3026.2025.20240040

摘要/Abstract

摘要：

为了探究二维各向异性材料中的导热-辐射耦合传热特性，基于随机游走的基本思想，在统一离散网格的基础上，开发了一种求解二维各向异性材料的导热-辐射耦合传热的计算方法，并验证了计算方法的准确性，分析了各向异性导热系数对传热特性的影响.结果表明，对于二维平板结构，当存在各向异性导热系数时，会导致平板温度场向相应的各向异性方向发生偏移；当 $k 12 *$ 与 $k 22 *$ 比值相同时，平板的各向异性基本保持不变；而当 $k 22 *$ 保持不变而 $k 12 *$ 增加时，会导致平板内温度传导的方向发生改变，导致平板内温度的均匀性降低.

关键词: 各向异性, 蒙特卡罗法, 统一网格, 耦合传热, 随机游走算法

Abstract:

In order to study the coupled thermal conductivity-radiation heat transfer characteristics of two-dimensional anisotropic materials， a computational method was developed for solving the coupled conduction-radiation heat transfer of two-dimensional anisotropic materials based on the basic idea of random walk for a uniform discrete mesh，and the accuracy of the computational method was verified. The effects of anisotropic thermal conductivity coefficient on the heat transfer characteristics were analyzed. The results show that for a two-dimensional plate， an anisotropic thermal conductivity coefficient results in a shift of the temperature field of the plate towards the corresponding anisotropy. The anisotropy of the plate is basically unchanged when the ratio of $k 12 *$ to $k 22 *$ is the same. The increase of $k 12 *$ leads to the change of the direction of the temperature conduction in the plate when the $k 22 *$ remains constant， which makes the temperature homogeneity decrease in the plate.

Key words: anisotropy, Monte Carlo method, uniform grid, coupled heat transfer, random walk algorithm

中图分类号:

TK 124

戈子健, 伊智, 李国军, 魏琳扬. 蒙特卡罗法求解二维各向异性导热-辐射耦合传热[J]. 东北大学学报（自然科学版）, 2025, 46(9): 58-64.

Zi-jian GE, Zhi YI, Guo-jun LI, Lin-yang WEI. Monte Carlo Method for Solving Two-Dimensional Coupled Anisotropic Conduction-Radiation Heat Transfer[J]. Journal of Northeastern University(Natural Science), 2025, 46(9): 58-64.

图/表 10

图1 二维离散节点模型

Fig.1 Two-dimensional discrete node model

表1 节点离散方程系数

Table 1 Coefficients of nodal discrete equation

P_W	P_S	P_E	P_N	P_NE	Q_ds
$1 P k 11 ∆ x 2$	$1 P k 22 ∆ y 2$	$1 P k 11 ∆ x 2 - k 12 + k 21 ∆ x ∆ y$	$1 P k 22 ∆ y 2 - k 12 + k 21 ∆ x ∆ y$	$1 P k 12 + k 21 ∆ x ∆ y$	$Q P$

表1 节点离散方程系数

Table 1 Coefficients of nodal discrete equation

P_W	P_S	P_E	P_N	P_NE	Q_ds
$1 P k 11 ∆ x 2$	$1 P k 22 ∆ y 2$	$1 P k 11 ∆ x 2 - k 12 + k 21 ∆ x ∆ y$	$1 P k 22 ∆ y 2 - k 12 + k 21 ∆ x ∆ y$	$1 P k 12 + k 21 ∆ x ∆ y$	$Q P$

图2 随机游走几何模型

Fig.2 Geometric model of random walk

图3 耦合质点随机移动流程图

Fig.3 Flowchart of random movement of coupled proton

图4 x/Lx =0.5位置y方向温度分布曲线

Fig.4 Temperature distribution curves along y-direction at x/Lx =0.5

表2 不同导热-辐射参数Ncr下，中轴线特定位置(x/Lx=0.5,y/Ly)的无量纲温度分布T/TR

Table 2 Dimensionless temperature T/TR at aspecific location on centerline(x/Lx=0.5,y/Ly) for different conduction-radiation parameter Ncr

N_cr	y/L_y	T/T_R
N_cr	y/L_y	DTM	LBM	本文方法
	0.3	0.737	0.738	0.736
1.0	0.5	0.630	0.631	0.630
	0.7	0.567	0.564	0.564
	0.3	0.760	0.759	0.758
0.1	0.5	0.663	0.662	0.662
	0.7	0.594	0.593	0.593
	0.3	0.790	0.788	0.785
0.01	0.5	0.725	0.722	0.726
	0.7	0.665	0.662	0.653

图5 x/Lx =0.5位置沿y方向的无量纲温度分布曲线

Fig.5 Dimensionless temperature distribution curves along y-direction at x/Lx =0.5

表3 计算条件

Table 3 Calculation conditions

计算条件	$k 12 *$	$k 22 *$
1	0.25	0.5
2	0.25	1.5
3	0.50	1.0
4	0.50	1.5

表3 计算条件

Table 3 Calculation conditions

计算条件	$k 12 *$	$k 22 *$
1	0.25	0.5
2	0.25	1.5
3	0.50	1.0
4	0.50	1.5

图6 平板无量纲温度云图（a）—条件1；（b）—条件2；（c）—条件3；（d）—条件4.

Fig.6 Dimensionless temperature cloud map of plate

图7 y/Ly =0.5位置沿x方向的无量纲温度分布曲线（a）—k12*与k22*比值相同；（b）—k22*保持恒定.

Fig.7 Dimensionless temperature distribution curves along x-direction at y/Ly =0.5

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