论文标题
规范流的皮肤摩擦系数的整体关系
Integral relations for the skin-friction coefficient of canonical flows
论文作者
论文摘要
我们证明了福卡塔（Fukagata）等人。 （2002年）的自由流边界层的身份简化为von Karman动量积分方程，与皮肤摩擦系数和动量厚度相关时，当用于获得身份的积分中的上限被认为是渐近的大。如果使用有限的上限，则身份的术语伪装取决于界限本身。与通道和管道流不同，在自由流边界层的情况下，无法量化雷诺应力对壁切应力的影响，因为雷诺应力从身份中消失了。通过在流动动量方程式上执行其他积分获得的无限数量的替代身份也简化为von Karman方程。发现通道流的类似身份，其中物理术语对壁剪应力的相对影响取决于连续整合的数量，这表明仅在Fukagagata等人发现的原始身份中区分了对皮肤摩擦系数的层状和湍流贡献。 （2002）。在大量整合的极限中，这些身份归类为皮肤摩擦系数的定义，并在通道和管道流中发现了新颖的两倍整合身份。此外，在研究Renard＆Deck（2016）之后，我们将皮肤摩擦系数分解为与流向方向的整体厚度变化的总和。我们利用能量厚度和惯性厚度，该厚度由与平均流壁正常正常相关的厚度组成，以及与平均流向速度的流向不均匀性相关的厚度。因此，流向动量方程对摩擦阻力的不同项的贡献是通过这些积分厚度量化的。
We show that the Fukagata et al. (2002)'s identity for free-stream boundary layers simplifies to the von Karman momentum integral equation relating the skin-friction coefficient and the momentum thickness when the upper bound in the integrals used to obtain the identity is taken to be asymptotically large. If a finite upper bound is used, the terms of the identity depend spuriously on the bound itself. Differently from channel and pipe flows, the impact of the Reynolds stresses on the wall-shear stress cannot be quantified in the case of free-stream boundary layers because the Reynolds stresses disappear from the identity. The infinite number of alternative identities obtained by performing additional integrations on the streamwise momentum equation also all simplify to the von Karman equation. Analogous identities are found for channel flows, where the relative influence of the physical terms on the wall-shear stress depends on the number of successive integrations, demonstrating that the laminar and turbulent contributions to the skin-friction coefficient is only distinguished in the original identity discovered by Fukagata et al. (2002). In the limit of large number of integrations, these identities degenerate to the definition of skin-friction coefficient and a novel two-fold integration identity is found for channel and pipe flows. In addition, we decompose the skin-friction coefficient as the sum of the change of integral thicknesses with the streamwise direction, following the study of Renard & Deck (2016). We utilize an energy thickness and an inertia thickness, which is composed of a thickness related to the mean-flow wall-normal convection and a thickness linked to the streamwise inhomogeneity of the mean streamwise velocity. The contributions of the different terms of the streamwise momentum equation on the friction drag is thus quantified by these integral thicknesses.
