Critical Transition Reynolds Number for the Incompressible Flat-Plate Boundary Layer as Searched by Numerical Simulation
Year: 2023
Author: Yongming Zhang, Di Liu, Ning Li
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 4 : pp. 1056–1075
Abstract
The critical transition Reynolds number is the lowest value at which the turbulent flow can hold in real flows. The determination of the critical transition Reynolds number not only is a scientific problem, but also is important for some engineering problems. However, there is no available theoretical method to search the critical value. For the hypersonic boundary layer with significant importance for engineering problems, there is no available experimental method to search the critical value so far. Consequently, it is imperative to take numerical method to search it. In this paper, direct numerical simulations (DNS) method is employed to determine the critical transition Reynolds number for the incompressible flat-plate boundary layer. Firstly, under the assumption of parallel flow, the temporal mode DNS is performed to determine the critical value as $Re_{xpcr} =43767,$ which is quite close to the numerical results of other people. Secondly, under the condition of nonparallel flow, the spatial mode DNS is performed to determine the critical transition Reynolds number as $Re_{xcr}=3×10^5$, which is well consistent with the experimental results. In principle, the proposed method in this paper can be extended to the supersonic/hypersonic boundary layer, and that problem will be discussed in the subsequent papers.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0269
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 4 : pp. 1056–1075
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Critical transition Reynolds number flat-plate boundary layer DNS temporal mode spatial mode.