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Boundary layer development in the flow field between a rotating and a stationary disk

机译:旋转盘与固定盘之间流场中的边界层发展

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This paper discusses the development of boundary layers in the flow of a Newtonian fluid between two parallel, infinite disks. One of the disks is rotating at a constant angular velocity while the other remains stationary. An analytical series approximation and a numerical solution method are used to describe the velocity profiles of the flow. Both methods rely on the commonly used similarity transformation first proposed by Von Kármán [T. von Kármán, ZAMM1, 233 (1921)]10.1002/zamm.19210010401. For Re _h < 18, the power series analytically describe the complete velocity profile. With the numerical model a Batchelor type of flow was observed for Re _h > 300, with two boundary layers near the disks and a non-viscous core in the middle. A remarkable conclusion of the current work is the coincidence of the power series' radius of convergence, a somewhat abstract mathematical notion, with the physically tangible concept of the boundary layer thickness. The coincidence shows a small deviation of only 2% to 4%.
机译:本文讨论了牛顿流体在两个平行的无限圆盘之间流动的边界层的发展。其中一个磁盘以恒定的角速度旋转,而另一个磁盘保持静止。使用解析级数逼近和数值解法来描述流的速度分布。两种方法都依赖于VonKármán[T. vonKármán,ZAMM1,233(1921)] 10.1002 / zamm.19210010401。对于Re _h <18,幂级数以解析方式描述完整的速度曲线。使用数值模型,观察到Re _h> 300的Batchelor类型的流,在圆盘附近有两个边界层,中间有一个非粘性岩心。当前工作的一个显着结论是幂级数的收敛半径(某种程度上是抽象的数学概念)与边界层厚度的物理有形概念的重合。巧合显示出仅2%到4%的小偏差。

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