分子黏性对解析湍流壁面函数的影响

doi:10.12382/bgxb.2022.0370

摘要/Abstract

摘要：

基于可压缩解析壁面函数(MAWF),考虑高超声速湍流边界层内温度、密度和分子黏性系数变化规律,使用黏性底层边缘处的密度和黏性系数重新定义无量纲壁面距离,并在黏性底层内构造抛物型和双曲型分子黏性系数分布,建立了新的可压缩解析壁面函数,即抛物型(para-MAWF)和双曲型(hyper-MAWF)解析壁面函数。通过高超声速激波边界层干扰算例对其进行验证,并与密网格低雷诺数Lauder-Sharma(LS) k-ε模型和MAWF数值结果进行对比。研究结果表明:所构造的解析壁面函数有效提高了MAWF黏性底层内分子黏性系数和温度分布的预测精度,相较于MAWF其预测的壁面热流结果更接近实验结果;所构造的两种壁面函数中双曲型解析壁面函数预测的壁面热流更接近于实验值,考虑到两种壁面函数数值结果差异较小,在5%之内,且双曲型壁面函数公式更为简单,对于高超声速算例更推荐使用双曲型分布的解析壁面函数。

关键词: 高超声速湍流边界层, 双曲型分布, 抛物型分布, 无量纲壁面距离, 激波边界层干扰

Abstract:

Based on the characteristics of hypersonic turbulent boundary layers, such as temperature, density, and laminar viscosity, the modified analytical wall function is improved to include the alternative definition of the dimensionless wall distance using variables at the edge of the viscous sublayer and the parabolic and hyperbolic variations of viscosity coefficients in the sublayer, named as para-MAWF and hyper-MAWF, respectively. Hypersonic shock boundary layer interactions are used to verify these two wall functions, which are compared with the Lauder-Sharma k-ε using fine meshes and the modified analytical wall function (MAWF). The results show that the proposed wall functions will increase the accuracy of temperature and molecular viscosity variation in the viscous sublayer compared to results by the original MAWF. As a result, the predicted wall heat-flux aligns more closely with experimental measurements, especially in the separation region. The heat flux predicted by hyperbolic analytical wall function agrees better with the experimental value. Considering that the difference of the numerical results predicted by the two wall functions is less than 5%, the hyperbolic wall function is recommended for hypersonic flows due to its simpler formulation.

Key words: hypersonic turbulent boundary layer, hyperbolic variation, parabolic variation, nondimensional wall distance, shock wave turbulence boundary layer interaction

王新光, 陈琦, 万钊, 高晓成, 燕振国. 分子黏性对解析湍流壁面函数的影响[J]. 兵工学报, 2023, 44(7): 2041-2052.

WANG Xinguang, CHEN Qi, WAN Zhao, GAO Xiaocheng, YAN Zhenguo. Impact of Molecular Viscosity Variation on the Analytical Wall Function[J]. Acta Armamentarii, 2023, 44(7): 2041-2052.

图/表 13

图1 可压缩平板湍流边界层温度分布

Fig.1 Near-wall temperature distribution in the turbulence compressible boundary layer

图2 分子黏性系数分布示意图

Fig.2 Schematic diagram of molecular viscosity variation

图3 Ma=8.18算例粗网格解析温度(左)和分子黏性系数(右)分布与密网格低雷诺数模型结果对比

Fig.3 Comparison of the analytical temperature (left) and molecular viscosity (right) on the coarse mesh with the results of low-Re turbulence model when Ma=8.18

表1 Ma=8.18时2D斜激波边界层干扰来流条件

Table 1 Inflow conditions for the Ma=8.18 case impinging shock interactions

β/(°)	θ₀/mm	p_∞/(N·m^-2)	T_∞/K	T_w/K
5/10	0.94	430	81	300

图4 Ma=8.18算例网格无关性研究

Fig.4 Grid-independence study for the Ma=8.18 case

图5 Ma=8.18算例网格示意图

Fig.5 Sketch map of the mesh for Ma=8.18 case

图6 Ma=8.18算例边界层厚度0.94mm位置边界层内速度和温度分布

Fig.6 Boundary layer velocity and temperature distribution at the momentum thickness of 0.94mm for the Ma=8.18 case

图7 Ma=8.18,β=10°算例解析温度分布

Fig.7 Analytical temperature comparison when Ma=8.18, β=10°

图8 Ma=8.18,β=10°算例解析速度分布

Fig.8 Analytical velocity comparison when Ma=8.18, β=10°

图9 Ma=8.18算例激波产生器5°壁面压力(上)、摩阻(中)和热流(下)分布

Fig.9 Wall pressure (top), skin-friction (middle) and heat-flux (bottom) distribution for the Ma=8.18 case

表2 Ma=9.22压缩拐角来流条件

Table 2 Inflow conditions for the Ma=9.22 compression corner

Re/m^-1	p_∞/(N·m^-2)	T_∞/K	T_w/K	β/(°)
4.7×10⁷	2473.8	64.5	295	15,32,34,38

图10 Ma=9.22算例马赫数云图

Fig.10 Mach contours for the Ma=9.22 case

图11 Ma=9.22压缩拐角壁面热流

Fig.11 Wall heat-flux distribution for the Ma=9.22 compression corner

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