具有非零压力梯度的湍流边界层模型
A Model of a Turbulent Boundary Layer With a Non-Zero Pressure Gradient
AI总结：
提出一个湍流边界层模型，将中间区域分为两个自相似结构，分别由不同标度律描述，并研究了压力梯度对指数β的影响，实验数据与模型吻合。
摘要：
根据作者提出的湍流边界层模型，在没有外部湍流的情况下，粘性底层与外流之间的中间区域由两个明显分离的自相似结构组成。这些结构中的速度分布由两种不同的标度律描述。靠近粘性底层的区域的平均速度u由先前获得的依赖于雷诺数的标度律描述：$ϕ= u/u_*=Aη^α$, $A= rac{1}{\sqrt{3}} \ln Re_Λ+ rac 52$, $α= rac{3}{2\ln Re_Λ}$, $η= u_* y/ν$。（这里$u_*$是动力速度或摩擦速度，y是离壁面的距离，$ν$是流体的运动粘度，雷诺数$Re_Λ$由数据良好定义）在靠近外流的区域，标度律不同：$ϕ= Bη^β$。对于零压力梯度边界层，通过处理各种实验数据发现幂次$β$接近0.2（存在一些分散）。我们在此表明，对于非零压力梯度边界层，在逆压梯度情况下幂次$β$大于0.2，在顺压梯度情况下小于0.2。相似性分析表明，系数B和幂次$β$都依赖于$Re_Λ$和一个与压力梯度成正比的新无量纲参数P。分析了Perry、Marušić和Jones (1)-(4)最近的实验数据，结果与我们提出的模型一致。
英文摘要：
According to a model of the turbulent boundary layer proposed by the authors, in the absence of external turbulence the intermediate region between the viscous sublayer and the external flow consists of two sharply separated self-similar structures. The velocity distribution in these structures is described by two different scaling laws. The mean velocity u in the region adjacent to the viscous sublayer is described by the previously obtained Reynolds-number-dependent scaling law $ϕ= u/u_*=Aη^α$, $A=\frac{1}{\sqrt{3}} \ln Re_Λ+ \frac 52$, $α=\frac{3}{2\ln Re_Λ}$, $η= u_* y/ν$. (Here $u_*$ is the dynamic or friction velocity, y is the distance from the wall, $ν$ the kinematic viscosity of the fluid, and the Reynolds number $Re_Λ$ is well defined by the data) In the region adjacent to the external flow the scaling law is different: $ϕ= Bη^β$. The power $β$ for zero-pressure-gradient boundary layers was found by processing various experimental data and is close (with some scatter) to 0.2. We show here that for non-zero-pressure-gradient boundary layers, the power $β$ is larger than 0.2 in the case of adverse pressure gradient and less than 0.2 for favourable pressure gradient. Similarity analysis suggests that both the coefficient B and the power $β$ depend on $Re_Λ$ and on a new dimensionless parameter P proportional to the pressure gradient. Recent experimental data of Perry, Marušić and Jones (1)-(4) were analyzed and the results are in agreement with the model we propose.
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