Onset of three-dimensionality, equilibria, and early transition in flow over a backward-facing step
Onset of three-dimensionality, equilibria, and early transition in flow over a backward-facing step
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DOI：
10.1017/s0022112091003488
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发表时间：
1991-10
影响因子：
3.7
通讯作者：
L. Kaiktsis;G. Karniadakis;S. Orszag
中科院分区：
文献类型：
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作者：
L. Kaiktsis;G. Karniadakis;S. Orszag
利用不可压缩Navier-Stokes方程的直接数值解，对后台阶流动的三维平衡和向湍流过渡进行了数值研究。数值方法是一种高精度混合谱/谱元方法，具有有效的粘性流出边界条件。三维的外观在名义上二维几何研究了代表性的雷诺数范围从开始的三维分岔到后来的过渡阶段。通过标准相关系数和新的三维指数，以及瞬时和时间平均流线模式和涡量等值线来识别强三维区域。研究结果表明，三维特征发生在一次和二次再循环带的边界处，主河道是最稳定的流动成分。有。因此，剪切层中有较强的二次失稳，主要是由于台阶角产生的二次失稳。在上游剪切层的作用下，下游的流动被激发，在空间和时间上形成与托尔米恩-施里希廷波非常相似的波形，特征频率为f1；在上游，在剪切层存在另一个不相称的频率f2。如果在频率接近f1或f2的流入处施加外部激励，则双频流锁定到单频；然而，较小振幅的激励可能引起强烈的准周期响应。在锁定或准周期状态下，这种激励可以显著增加或减少（超过20%）主分离带XR的长度。超临界雷诺数下的二次不稳定性导致的平衡状态产生沿展向调制的流动，相应的再附着位置XR发生变化。虽然三维可以部分解释高雷诺数Re下XR的数值预测与实验结果之间的差异，但差异的主要来源是入流条件，特别是叠加在平均流量上的外部干扰，后者也是实验室实验中发现的稍早转变的主要原因。
A numerical study of three-dimensional equilibria and transition to turbulence in flow over a backward-facing step is performed using direct numerical solution of the incompressible Navier-Stokes equations. The numerical method is a high-order-accurate mixed spectral/spectral-element method with efficient viscous outflow boundary conditions. The appearance of three-dimensionality in nominally two-dimensional geometries is investigated at representative Reynolds numbers ranging from the onset of three-dimensional bifurcation to later transitional stages. Strongly three-dimensional regions are identified through standard correlation coefficients and new three-dimensionality indices, as well as through instantaneous and time-average streamline patterns and vorticity contours. Our results indicate that onset of three-dimensionality occurs at the boundaries between the primary and secondary recirculating zones with the main channel flow, the latter being the most stable flow component. There is. therefore, strong secondary instability in the shear layers, mainly due to the one emanating from the step corner. The flow further downstream is excited through the action of the upstream shear layers acquiring a wavy form closely resembling Tollmien–Schlichting waves both spatially and temporally with a characteristic frequency f1; upstream, at the shear layer another incommensurate frequency, f2, is present. The two-frequency flow locks-in to a single frequency if external excitations are imposed at the inflow at a frequency close to f1 or f2; the smaller amplitude excitations, however, may cause a strong quasi-periodic response. Such excitations may significantly increase or decrease (by more than 20%) the length of the primary separation zone XR at lock-in or quasi-periodic states. The equilibrium states resulting from the secondary instability at supercritical Reynolds numbers produce a flow modulated in the spanwise direction, with corresponding variations in the reattachment location XR. While three-dimensionality explains partially the discrepancy between numerical predictions and experimental results on XR at higher Reynolds number Re, the main source of discrepancy is attributed to the inflow conditions, and in particular to external disturbances superimposed on the mean flow, the latter being the main reason also for the somewhat earlier transition found in laboratory experiments.