Exact theory of material spike formation in flow separation
Exact theory of material spike formation in flow separation
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流动分离中材料尖峰形成的精确理论
DOI：
10.1017/jfm.2018.206
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发表时间：
2017
影响因子：
3.7
通讯作者：
S. Hamer
中科院分区：
文献类型：
--
作者：
Christopher M Roundy;Chase M. Nunez;Logan F. Thomas;L. Auckland;Wendy Tang;Jack J. Richison;Breanna R. Green;C. Hilton;M. J. Cherry;A. Pauvolid;G. Hamer;W. Cook;S. Hamer
我们发展了一个框架不变的理论，在流动分离过程中的材料尖峰形成在一个无滑移边界的二维流与任意时间的依赖性。基于近壁物质线的精确曲率演化，我们的理论确定了固定和移动流分离，在短时间间隔内也是有效的，并承认严格的瞬时限制。作为一个副产品，我们推导出显式公式的物质线曲率的演变和曲率率一般可压缩流。我们确定的物质主干首先作为前体，后来作为非定常拉格朗日流分离的中心。我们还发现了一个以前未被发现的尖峰点，分离的骨干连接到边界，并推导出基于墙的分析公式，其位置。最后，我们的理论解释了非定常流中离壁分离的感觉，并提供了这种感觉是合理的条件。我们说明了我们的结果在几个分析和实验流。
We develop a frame-invariant theory of material spike formation during flow separation over a no-slip boundary in two-dimensional flows with arbitrary time dependence. Based on the exact curvature evolution of near-wall material lines, our theory identifies both fixed and moving flow separation, is effective also over short time intervals, and admits a rigorous instantaneous limit. As a byproduct, we derive explicit formulae for the evolution of material line curvature and the curvature rate for general compressible flows. The material backbone that we identify acts first as the precursor and later as the centrepiece of unsteady Lagrangian flow separation. We also discover a previously undetected spiking point where the backbone of separation connects to the boundary, and derive wall-based analytical formulae for its location. Finally, our theory explains the perception of off-wall separation in unsteady flows and provides conditions under which such a perception is justified. We illustrate our results on several analytical and experimental flows.