Improvement and application of wall function boundary condition for high-speed compressible flows

• Published in: Science China. Technological sciences Vol. 56; no. 10; pp. 2501 - 2515
• Main Authors: Gao, ZhenXun, Jiang, ChongWen, Lee, ChunHian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2013
• Subjects: Boundary conditions; Computer simulation; Engineering; Heat flux; Heat transfer; Mathematical analysis; Mathematical models; Progress of Projects Supported by NSFC; Skin friction; Walls; 压缩速度; 可压缩流动; 壁面函数; 应用; 数值模拟; 湍流边界层; 边界条件; 高超音速; wall function boundary condition; heat flux; compressible flows; numerical simulation; skin friction
• ISSN: 1674-7321; 1869-1900
• DOI: 10.1007/s11431-013-5349-4

In order to develop a wall function boundary condition for high-speed flows so as to reduce the grid-dependence of the simula- tion for the skin friction and heat flux, a research was performed to improve the compressible wall function boundary condition proposed by Nichols. Values of parameters in the velocity law-of-the-wall were revised according to numerical experiments and the expression of temperature law-of-the-wall was modified based on theoretical analysis and numerical simulation. Be- sides, the formula of the heat conduction term in near-wall region was derived so that the coupling between the wall function boundary condition and CFD code was realized more accurately. Whereafter, the application study of the modified wall func- tion was carried out. The numerical case of supersonic turbulent boundary layer on a flat plate illustrated that the modified wall function produces reasonable results of skin friction and heat flux, and profiles of velocity, temperature and turbulent eddy viscosity for coarse grids with the initial wall spacing of y＋〈400, and that the modifications to the original wall function can obviously improve the simulation precision. As for the application of separation flows, it was found from the numerical cases of supersonic cavity flow and hypersonic axisymmetric compression comer that the compressible velocity law-of-the-wall originally established based on the fully-developed attached turbulent boundary layer approximately holds in the near-wall re- gion inside the separation flows, which ensures that reliable skin friction and heat flux can be given by the wall function inside the separation flows, while for the region near separation and reattachment points, the wall function gives results with a rela- tively large error, because the velocity law-of-the-wall used in the wall function takes on obvious deviation from the real ve- locity profiles near the separation and reattachment points.