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Similarity analysis for turbulent boundary layers subject to pressure gradient and heat transfer.

机译：受压力梯度和热传递影响的湍流边界层的相似性分析。

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The asymptotic invariance principle (AIP) and the Near-Asymptotic method have been successfully explored for the non-equilibrium turbulent boundary layer, the turbulent boundary layer with separation, and the forced convection turbulent boundary layer subject to the external pressure gradient.; Using the AIP, it is found that even the non-equilibrium flows, defined as the pressure parameter Λ ≠ constant, are in equilibrium but only locally. Each local region of these flows is characterized by a constant pressure parameter. The adverse pressure gradient (APG) region of a non-equilibrium flow is characterized by a single value of Λ ≅ 0.22, which is the same as the case of equilibrium flows. In addition, it has been found that the outer part of separating boundary layers also remains in equilibrium and is characterized by a constant pressure parameter. The pressure parameter, Λ&thetas;, is nearly the same for all the APG flows with eventual separation; in particular, Λ&thetas; = 0.21 ± 0.01. Subsequently, a single velocity profile should exist for all APG flows, which has been confirmed by the Zagarola/Smits scaling, U∞δ∗/δ.; Using the pressure parameter Λ&thetas; along with the integral momentum equation, a shape factor of Hsep = 2.76 ± 0.23 is predicted for the turbulent boundary layer at separation. This value is in close agreement with the intermittent transitional detach (ITD) position for the experimental data studied here. With the correlation from Sandborn & Kline (1961), a “separation zone” has been proposed, which proves to be very meaningful in predicting separation in boundary layer flows. Moreover, this separation zone emphasizes the fact that separation in the turbulent boundary layer is a process instead of a single event as indicated by Simpson et al. (1981) and others.; Furthermore, the similarity analysis is developed for a 2-D steady incompressible forced convection turbulent boundary layer subject to the external pressure gradient. Two new scalings have been obtained for the inner and outer region, respectively. When normalized by the new scalings, all the temperature profiles collapse into a single curve regardless of the effects from the pressure gradient, upstream conditions and the Péclet number dependence. Using the new temperature scalings, a power law function has been derived for the temperature profile in the overlap region by means of the Near-Asymptotic method. Meanwhile, the inner composite temperature profile and the wake function have been proposed empirically. Thus, the entire composite temperature profile is constructed and presented, which can describe the experimental data with ZPG and APG very well over the entire boundary layer even at the finite Péclet number. The prediction error has been calculated with an uncertainty less than 3% for the ZPG flow and 5% for the APG flow. Furthermore, a power form of the heat transfer law has been predicted, and a theoretical prediction of the thermal displacement thickness is also proposed.; The results are compared with the classical studies, and some other recent investigations. These new scalings and new composite temperature profiles perform much better than others, especially in removing the effects from upstream conditions and different strengths of the pressure gradient.
机译：对于非平衡湍流边界层，分离的湍流边界层以及受外部压力梯度影响的强迫对流湍流边界层，已经成功地探索了渐近不变性原理（AIP）和近渐近方法。使用AIP，发现甚至被定义为压力参数Λ≠ constant 的非平衡流也处于平衡状态，但仅局部存在。这些流动的每个局部区域的特征在于恒定的压力参数。非平衡流的逆压梯度（APG）区域的特征在于单个值≅≅0.22，这与平衡流的情况相同。此外，已经发现，分离边界层的外部也保持平衡并且以恒定的压力参数为特征。对于所有最终分离的APG流量，压力参数Λθs几乎相同；特别是Λ＆thess; = 0.21±0.01。随后，所有APG流量都应存在一个速度分布，这已通过Zagarola / Smits缩放比例， U ∞δ ∗ /确认。 δ.;使用压力参数Λθs和积分动量方程，可预测湍流的形状因子 H sep = 2.76±0.23分离时的边界层。该值与此处研究的实验数据的间歇过渡分离（ITD）位置非常吻合。利用桑德伯恩和克莱恩（Sandborn＆Kline，1961）的相关性，提出了一个“分离带”，这对预测边界层流的分离非常有意义。而且，这个分离区强调了这样一个事实，即湍流边界层的分离是一个过程，而不是辛普森等人（1981）等人指出的单个事件。此外，针对受外部压力梯度影响的二维稳定不可压缩强迫对流湍流边界层进行了相似性分析。分别为内部和外部区域获得了两个新的缩放比例。通过新的缩放比例进行归一化后，所有温度曲线都将折叠为一条曲线，而不受压力梯度，上游条件和佩克利数依赖性的影响。使用新的温度标度，已经通过近渐近法为重叠区域中的温度分布导出了幂律函数。同时，根据经验提出了内部复合材料温度分布和尾流函数。因此，构建并给出了整个复合温度曲线，即使在有限的佩克利数下，也可以很好地描述ZPG和APG在整个边界层上的实验数据。计算出的预测误差的不确定性对于ZPG流量小于3％，对于APG流量小于5％。此外，已经预测了热传递定律的幂形式，并且还提出了热位移厚度的理论预测。将结果与经典研究和其他一些近期研究进行了比较。这些新的缩放比例和新的复合温度曲线的性能要比其他更好，尤其是在消除上游条件和压力梯度不同强度的影响方面。

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