两平板间两组分稀薄气体振荡传热的数值模拟

doi:10.19596/j.cnki.1001-246x.8671

摘要/Abstract

摘要：

采用离散统一气体动理学方法(DUGKS)求解两组分气体McCormack模型, 模拟下板温度周期波动激发的两平板间两组分稀薄气体流动与传热问题, 分析系统稀薄参数、温度变化频率以及组分摩尔浓度对平板间流动与传热现象的影响。数值结果表明: 两平板间气体流动与传热呈现周期变化, 并且平板间存在最小局部温度的现象, 其位置与系统稀薄程度呈正比, 此外热渗透深度随着稀薄参数的减小而减小。热渗透深度随轻组分浓度的增大而先增大, 在轻组分浓度为0.6左右达到最高值, 最后减小并与单组分气体结果一致。

关键词: 混合气体, 流动传热, 热渗透深度, 离散统一气体动理学方法

Abstract:

In this paper, the discrete unified gas kinetic scheme (DUGKS) is used to solve the McCormack model of binary gas, simulate the flow and heat transfer of rarefied binary gas between two plates excited by the periodic fluctuation of lower plate temperature, and analyze the effects of system rarefied parameters, temperature change frequency and component molar concentration on the flow and heat transfer between plates. The numerical results show that the gas flow and heat transfer between the two plates change periodically, and we find that the minimum local temperature exists between the plates, and its position is inversely proportional to the degree of system thinning. In addition, it is found that the thermal penetration depth decreases with the increase of the rarefaction parameter. The heat penetration depth first increases with the increase of light component concentration, reaches the highest value when the light component concentration is about 0.6, and finally decreases and is consistent with the result of single component gas.

Key words: mixed gas, flow and heat transfer, heat penetration depth, discrete unified gas kinetic scheme

中图分类号:

O356

万启坤, 张月, 郭照立. 两平板间两组分稀薄气体振荡传热的数值模拟[J]. 计算物理, 2023, 40(6): 653-665.

Qikun WAN, Yue ZHANG, Zhaoli GUO. Numerical Simulation of Oscillating Heat Transfer of Rarefied Binary Gas Between Two Plates[J]. Chinese Journal of Computational Physics, 2023, 40(6): 653-665.

图/表 11

图1 问题结构示意图

Fig.1 Structure diagram of problem

表1 不同条件下的网格数和离散速度集((n，Nm/Gm)中物理空间离散网格数为n，采用梯形积分(N)/Gauss-Hermite积分或(G)离散的m个离散速度点。)

Table 1 Meshes and discrete velocity sets ((n, Nm/Gm) denotes the n grid points and m velocity points using the quadrature/Gauss-Hermite rules.)

	θ∈(0.1, 1)	θ∈(1, 10)	θ∈(10, ∞)	θ→∞
St≫1	(161, N96)	(161, N64)	(161, G28)	(161, G8)
St≈O(1)	(161, N96)	(81, N48)	(81, G28)	(81, G8)
St≪1	(161, N64)	(81, N48)	(81, G28)	(81, G8)

图2 (Kn，θ)=(0.01，59.88)，(0.1，5.305)，(10，0.040 1)时单组分气体温度幅值分布

Fig.2 Temperature amplitude distribution of single gas as (Kn, θ)=(0.01, 59.88), (0.1, 5.305), (10, 0.040 1)

图3 He-Xe混合气体以及单组分温度幅值分布(a) Kn=8.9，θ=10；(b) Kn=0.89，θ=10；(c) Kn=0.089，θ=10；(d) Kn=8.9，θ=1；(e) Kn=0.89，θ=1；(f) Kn=0.089，θ=1；(g) Kn=8.9，θ=0.1；(h) Kn=0.89，θ=0.1；(i) Kn=0.089，θ=0.1

Fig.3 Temperature amplitude distribution of the He-Xe mixtures and single gas (a) Kn=8.9, θ=10; (b) Kn=0.89, θ=10;(c) Kn=0.089, θ=10; (d) Kn=8.9, θ=1; (e) Kn=0.89, θ=1; (f) Kn=0.089, θ=1; (g) Kn=8.9, θ=0.1;(h) Kn=0.89, θ=0.1; (i) Kn=0.089, θ=0.1

图4 Kn=0.089且θ=0.1时，He和Xe及混合气体的温度幅值分布(a) C0=0.1; (b) C0=0.5; (c) C0=0.9

Fig.4 Temperature amplitude distribution of He and Xe components and the mixtures when Kn=0.089 and θ=0.1 (a) C0=0.1; (b) C0=0.5; (c) C0=0.9

图5 C0=0.5、θ=0.1时He-Xe混合气体的yL随Kn变化

Fig.5 yL of He-Xe mixture varying with Kn as C0=0.5 and θ=0.1

图6 He-Xe混合气体热流幅值分布(a) Kn=8.9，θ=10；(b) Kn=0.89，θ=1；(c) Kn=0.089，θ=0.1

Fig.6 Heat flux amplitude distribution of the He-Xe mixture (a) Kn=8.9, θ=10;(b) Kn=0.89, θ=1; (c) Kn=0.089, θ=0.1

图7 θ=0.1时(a)Ne-Ar及(b)He-Xe混合气体与单组分气体热渗透深度λT随Kn变化

Fig.7 The thermal penetration depth of (a) Ne-Ar and (b)He-Xe mixtures and single gas as θ=0.1

图8 θ=0.1时，Kn=0.089和Kn=0.177条件下He-Xe混合气体热渗透深度λT随C0的变化

Fig.8 The thermal penetration depth of He-Xe mixture for Kn=0.089 and Kn=0.177 as θ=0.1

图9 He-Xe混合气体速度uy的幅值分布(a) Kn=8.9，θ=10；(b) Kn=0.89，θ=1；(c) Kn=0.089，θ=0.1

Fig.9 The velocity amplitude of He-Xe mixture (a) Kn=8.9, θ=10; (b) Kn=0.89, θ=1; (c) Kn=0.089, θ=0.1

图10 C0=0.5时不同时刻He-Xe混合气体在平板间速度分布 (a) Kn=8.9，θ=10；(b) Kn=0.89，θ=1；(c) Kn=0.089，θ=0.1

Fig.10 Distribution of velocity of the He-Xe mixture between plates at four moments as C0=0.5 (a) Kn=8.9, θ=10; (b) Kn=0.89, θ=1; (c) Kn=0.089, θ=0.1

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