论文标题
在Kármán势头融合方法和Pohlhausen Paradox上
On the Kármán momentum-integral approach and the Pohlhausen paradox
论文作者
论文摘要
这项工作探讨了从没有压力梯度的动量综合方程之后的简单关系。结果表达式使我们能够将速度曲线（y）$的边界层特性与假定的流函数及其壁衍生物相对于壁正态坐标，$ y $。因此，通常在经典专着中评估和制表的干扰，位移和动量厚度以及皮肤摩擦和阻力系数可以很容易地确定给定的配置文件，$ f（ξ）= u/u $。这里$ξ= y/δ$表示边界层坐标。然后，使用这些表达方式为1921年Pohlhausen多项式悖论提供合理的解释，即，与使用立方或二次多种物质相比，速度四分之一的四分之一代表导致速度的四分之一代表的准确预测。我们不仅确定了这种行为的基本因素，而且还概述了以任何顺序克服其表现的程序。这使我们能够得出最佳的分段近似值，这些近似不会受到影响Pohlhausen $ f（ξ）=2ξ-2ξ^3 +ξ^4 $的特定限制。例如，我们的替代配置文件，$ f（ξ）=（5ξ-3ξ^3+ξ^4）/3 $，当在粘性和热分析中纳入kármán-pohlhausen方法中时，将导致精度提高精度。 Then noting the significance of the Blasius constant, $\bar{s} \approx 1.630398$, this approach is extended to construct a set of uniformly valid solutions, including $F(ξ)=1-\exp[-\bar{s}ξ(1+\bar{s}ξ/2+ξ^2)]$, which continues to hold beyond the boundary-layer edge as $ y \ rightarrow \ infty $。鉴于其大大减少了误差，通过与其他模型进行比较，显示了后者实际上等效于Blasius解决方案。
This work explores simple relations that follow from the momentum-integral equation absent a pressure gradient. The resulting expressions enable us to relate the boundary-layer characteristics of a velocity profile, $u(y)$, to an assumed flow function and its wall derivative relative to the wall-normal coordinate, $y$. Consequently, disturbance, displacement, and momentum thicknesses, as well as skin friction and drag coefficients, which are typically evaluated and tabulated in classical monographs, can be readily determined for a given profile, $F(ξ)=u/U$. Here $ξ=y/δ$ denotes the boundary-layer coordinate. These expressions are then employed to provide a rational explanation for the 1921 Pohlhausen polynomial paradox, namely, the reason why a quartic representation of the velocity leads to less accurate predictions of the disturbance, displacement, and momentum thicknesses than using cubic or quadratic polynomials. Not only do we identify the factors underlying this behaviour, we proceed to outline a procedure to overcome its manifestation at any order. This enables us to derive optimal piecewise approximations that do not suffer from the particular limitations affecting Pohlhausen's $F(ξ)=2ξ-2ξ^3 +ξ^4$. For example, our alternative profile, $F(ξ)=(5ξ-3ξ^3+ξ^4)/3$, leads to an order-of-magnitude improvement in precision when incorporated into the Kármán-Pohlhausen approach in both viscous and thermal analyses. Then noting the significance of the Blasius constant, $\bar{s} \approx 1.630398$, this approach is extended to construct a set of uniformly valid solutions, including $F(ξ)=1-\exp[-\bar{s}ξ(1+\bar{s}ξ/2+ξ^2)]$, which continues to hold beyond the boundary-layer edge as $y\rightarrow\infty$. Given its substantially reduced error, the latter is shown, through comparisons to other models, to be practically equivalent to the Blasius solution.
