A universal velocity transformation for boundary layers with pressure gradients
A universal velocity transformation for boundary layers with pressure gradients
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DOI：
10.1017/jfm.2023.570
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发表时间：
2023-08
影响因子：
3.7
通讯作者：
Peng E. S. Chen;Wen Wu;K. Griffin;Yipeng Shi;Xiang I. A. Yang
中科院分区：
文献类型：
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作者：
Peng E. S. Chen;Wen Wu;K. Griffin;Yipeng Shi;Xiang I. A. Yang
当边界层受到强压力梯度作用时，壁面对数律不能反映平均流。在这样的边界层中，平均流受到施加的压力梯度的时空历史的影响;并且解释历史效应仍然是一个挑战。这项工作的目的是发展一个通用的平均流量标度的边界层受到任意不利或/和有利的压力梯度。我们从Navier-Stokes方程中推导出一个速度变换，它考虑了历史效应，并将平均流映射到壁面的正则律。转换测试对通道流动突然施加不利或有利的压力梯度，边界层流动受到不利的压力梯度，和Couette-Poiffille流与流向压力梯度。结果表明，转换后的速度分布符合壁面平衡规律。
Abstract The logarithmic law of the wall does not capture the mean flow when a boundary layer is subjected to a strong pressure gradient. In such a boundary layer, the mean flow is affected by the spatio-temporal history of the imposed pressure gradient; and accounting for history effects remains a challenge. This work aims to develop a universal mean flow scaling for boundary layers subjected to arbitrary adverse or/and favourable pressure gradients. We derive from the Navier–Stokes equation a velocity transformation that accounts for the history effects and maps the mean flow to the canonical law of the wall. The transformation is tested against channel flows with a suddenly imposed adverse or favourable pressure gradient, boundary layer flows subjected to an adverse pressure gradient, and Couette–Poiseuille flows with a streamwise pressure gradient. It is found that the transformed velocity profiles follow closely the equilibrium law of the wall.