Nonlinear streak computation using boundary region equations
Nonlinear streak computation using boundary region equations
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使用边界区域方程进行非线性条纹计算
DOI：
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发表时间：
2012
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通讯作者：
C. Martel
中科院分区：
文献类型：
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作者：
J A Martín;C. Martel
本文应用边界区方程模拟平板边界层中展向周期条纹阵的非线性演化。著名的BRE公式是从高雷诺数极限下的完整Navier-Stokes方程得到的，并提供了三维边界层条纹的正确渐近描述。本文提出了一种快速、稳健的流向推进格式来实现它们的数值积分。文献中的典型条纹计算对应于线性条纹或使用直接数值模拟（DNS）或非线性抛物化稳定性方程（PSE）计算的小振幅非线性条纹。我们使用的BREs数值计算高振幅条纹，一种方法，需要更低的计算工作量比DNS，并没有一致性和收敛性问题的PSE。结果表明，随着条纹振幅的增大，非线性效应的影响，流场结构发生了很大的变化。横向运动（在壁面法向流向平面）变得更加重要，并强烈扭曲流向速度分布，最终与线性情况完全不同。我们详细分析了非线性饱和条纹产生的流型，并与现有的实验结果进行了比较。
The boundary region equations (BREs) are applied for the simulation of the nonlinear evolution of a spanwise periodic array of streaks in a flat plate boundary layer. The well-known BRE formulation is obtained from the complete Navier–Stokes equations in the high Reynolds number limit, and provides the correct asymptotic description of three-dimensional boundary layer streaks. In this paper, a fast and robust streamwise marching scheme is introduced to perform their numerical integration. Typical streak computations present in the literature correspond to linear streaks or to small-amplitude nonlinear streaks computed using direct numerical simulation (DNS) or the nonlinear parabolized stability equations (PSEs). We use the BREs to numerically compute high-amplitude streaks, a method which requires much lower computational effort than DNS and does not have the consistency and convergence problems of the PSE. It is found that the flow configuration changes substantially as the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-streamwise plane) becomes more important and strongly distorts the streamwise velocity profiles, which end up being quite different from those of the linear case. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks and compare them with available experimental results.