Self-consistent parabolized stability equation (PSE) method for compressible boundary layer

Self-consistent parabolized stability equation (PSE) method for compressible boundary layer
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可压缩边界层自洽抛物化稳定性方程(PSE)方法

DOI:
10.1007/s10483-015-1951-9
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发表时间:
2015-06
期刊:
Applied Mathematics and Mechanics (English Edition )
影响因子:
--
通讯作者:
Su Caihong
Su Caihong
中科院分区:
其他
文献类型:
--
作者:
Zhang Yongming;Su Caihong

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抛物稳定性方程(PSE)方法已被证明是研究边界层稳定性和过渡问题的一种有效而方便的工具。然而,在其原始公式中,对于非线性问题,每个傅立叶模式的复波数是由所谓的锁相规则确定的,这导致波数不自洽。本文提出了一种改进方法,使其自洽。其主要思想是,不允许波数是复数,而是保持所有波数为实数,并且每个模态的增长或衰减简单地表现为其形状函数的模量的增长或衰减。通过与直接数值模拟(DNS)对马赫数为6的可压缩边界层问题的结果进行比较,说明了新公式的有效性。
The parabolized stability equation (PSE) method has been proven to be a useful and convenient tool for the investigation of the stability and transition problems of boundary layers. However, in its original formulation, for nonlinear problems, the complex wave number of each Fourier mode is determined by the so-called phase-locked rule, which results in non-self-consistency in the wave numbers. In this paper, a modification is proposed to make it self-consistent. The main idea is that, instead of allowing wave numbers to be complex, all wave numbers are kept real, and the growth or decay of each mode is simply manifested in the growth or decay of the modulus of its shape function. The validity of the new formulation is illustrated by comparing the results with those from the corresponding direct numerical simulation (DNS) as applied to a problem of compressible boundary layer with Mach number 6.
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