Impact of Molecular Viscosity Variation on the Analytical Wall Function

doi:10.12382/bgxb.2022.0370

Abstract

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

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.

Figures/Tables 13

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

Fig.2 Schematic diagram of molecular viscosity variation

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

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

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

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

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

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

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

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

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

Fig.10 Mach contours for the Ma=9.22 case

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

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