功能梯度材料环形热源三维瞬态温度场计算方法

doi:10.19596/j.cnki.1001-246x.8764

摘要/Abstract

摘要：

针对环形热源作用下功能梯度材料三维瞬态热传导分析复杂且耗时的问题, 通过傅里叶-拉普拉斯频响函数、拉普拉斯数值逆变换和二维离散傅里叶逆变换建立指数梯度材料环形热源热传导半解析方法, 并与三维傅里叶变换方法以及有限元方法(FEM)进行对比, 验证本文方法的可靠性。基于半解析方法对比环形热源和高斯热源作用下温度和温度梯度响, 算例表明: 温度和温度梯度分布对环形热源内、外径以及材料梯度指数响应不同; 相比高斯热源, 环形热源的温度场和温度梯度场相对均匀, 改变热源内外径可调节温度峰值和温度梯度峰值。

关键词: 环形热源, 功能梯度材料, 三维瞬态热传导, 半解析方法

Abstract:

In order to solve the complex and time-consuming problem of 3D transient heat conduction analysis of functionally gradient materials subjected to annular heat source, a semi-analytical method for the heat conduction of exponentially graded materials with an annular heat source is developed through Fourier-Laplace frequency response functions, numerical Laplace inversion and two-dimensional discrete Fourier inversion, which is compared with 3D Fourier transform method in literature and FEM to verify the reliability of the proposed method. Based on the semi-analytical method, the temperature and temperature gradient response, as well as the sensitivity of their peaks under annular and Gaussian heat sources are compared. Case studies show that the temperature and temperature gradient distribution have different responses to the inner and outer diameter of the annular heat source and the material gradient indices. Compared with Gaussian heat sources, annular heat sources have the relatively uniform temperature and temperature gradient fields. Changing the inner and outer diameter of the annular heat source can adjust the temperature peak and temperature gradient peak.

Key words: annular heat source, functionally graded material, 3D transient heat conduction, semi-analytical method

中图分类号:

TG151.1

索雪峰, 何登辉, 王华栋, 曹伟. 功能梯度材料环形热源三维瞬态温度场计算方法[J]. 计算物理, 2024, 41(3): 367-379.

Xuefeng SUO, Denghui HE, Huadong WANG, Wei CAO. Calculation Method of 3D Transient Temperature Fields in Functionally Graded Materials Subjected to Annular Heat Source[J]. Chinese Journal of Computational Physics, 2024, 41(3): 367-379.

图/表 19

图1 梯度材料的三维移动热源热传导模型

Fig.1 Three dimensional heat conduction model of graded material with moving heat source

图2 环形高斯热源功率密度分布

Fig.2 Power density distribution of annular Gaussian heat source

图3 三维温度场算法流程

Fig.3 Procedure of algorithm for 3D temperature field

图4 最大温度随时间变化

Fig.4 Variation of the maximum temperature with time

图5 沿X轴的温度分布(t=2 s)

Fig.5 Temperature distributions along X axis (t=2 s)

表1 本文方法与3D-FFT方法预测结果对比

Table 1 Predicted results from the present method and 3D-FFT method

Duration time t₀/s	T_max/℃ (Fig. 4, t=10 s)			T/℃ (Fig. 5, t=3 s, X=0)			CPU t/s
Duration time t₀/s	3D-FFT	Present study	Deviation	3D-FFT	Present study	Deviation	3D-FFT	Present study
t₀=1	-32.69	8.33	125.48%	459.90	462.63	0.59%	61.28	171.63
t₀=2	24.30	46.65	91.97%	319.11	315.35	1.49%	60.05	173.62
t₀=3	99.76	109.76	10.02%	194.97	197.33	1.21%	60.89	172.56

图6 环形热源加热有限元模型

Fig.6 Finite element model of annular heat source heating

图7 最大温度随时间变化

Fig.7 Variation of the maximum temperature with time

图8 沿X轴的温度分布(t=0.2 s)

Fig.8 Temperature distributions along X axis (t=0.2 s)

表2 本文方法与3D-FFT和FEM预测结果对比

Table 2 Comparisons of predicted results from the present method and FEM

Duration time t₀/s	T_max/℃ (Fig. 7, t=0.5 s)			T/℃ (Fig. 8, t=0.2 s, X=0)			CPU t/s
Duration time t₀/s	FEM	3D-FFT	Present study	FEM	3D-FFT	Present study	FEM	3D-FFT	Present study
t₀=0.1	63.64	59.87	62.50	173.52	170.98	184.39	1 623.42	49.63	120.36
t₀=0.2	110.60	101.57	106.83	108.35	104.21	118.96	1 931.85	51.26	122.44
t₀=0.3	108.04	98.69	105.84	68.36	63.03	72.85	1 736.64	51.31	123.56

图9 t=1 s时沿X轴的温度和温度梯度分布对比

Fig.9 Temperature distributions and gradients along X axis at t=1 s

图10 XZ平面的温度分布(a)高斯热源；(b)环形热源

Fig.10 Temperature distributions in XZ plane (a) Gaussian heat source; (b) annular heat source

图11 XY和XZ平面的温度梯度分布(a)高斯热源；(b)环形热源

Fig.11 Temperature gradient distributions in XY and XZ plane (a) Gaussian heat source; (b) annular heat source

图12 环形热源内外径对最大温度的影响(a)内径；(b)外径

Fig.12 Influence of inner and outer diameter of annular heat source on the maximum temperature (a)inner radius; (b) outer radius

图13 环形热源内外径对沿X轴温度分布的影响(a)内径；(b)外径

Fig.13 Influence of inner and outer diameter of annular heat source on temperature along X axis (a)inner radius; (b) outer radius

图14 环形热源内外径对沿X轴温度梯度分布的影响(a)内径；(b)外径

Fig.14 Influence of inner and outer diameter of annular heat source on temperature gradient distributions along X axis (a)inner radius; (b) outer radius

图15 材料梯度指数对最大温度的影响

Fig.15 Influence of material gradient index on the maximum temperature

图16 材料梯度指数对沿X和Z轴温度分布的影响(a)X轴；(b)Z轴

Fig.16 Influence of material gradient index on temperature distributions along X and Z axes (a) X axis; (b) Z axis

图17 材料梯度指数对沿X轴分布温度梯度的影响(a)z=0.0 mm；(b)z=0.10 mm

Fig.17 Influence of material gradient index on temperature gradient distributions along X axis at (a) z=0.0 mm and (b) z=0.10 mm

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