Engineering Application of Boundary Layer Theory Define friction resistance force of aircraft and naval vessel Define coefficient value of theoretical flow velocity on overflow dam Define the incorporation point of high velocity flow in steep groove Define the flow resistance force and water head loss Characteristics of boundary layer I The thickness of boundary layer is smaller than characteristic length I of object, 8<<1, 07>0,that is extreme thickness of boundary layer 2 The thickness of boundary layer is increased in the flow direction on plane board Because with the length increase of plane board, friction loss is also increased, fluid internal energy is decreased, so flow velocity is, in order to meet the continuity requirement, the thickness of boundary layer is increased
11 Define friction resistance force of aircraft and naval vessel; Define coefficient value of theoretical flow velocity on overflow dam; Define the incorporation point of high velocity flow in steep groove; Define the flow resistance force and water head loss. Because with the length increase of plane board, friction loss is also increased, fluid internal energy is decreased, so flow velocity is, in order to meet the continuity requirement, the thickness of boundary layer is increased. Engineering Application of Boundary Layer Theory: 1、The thickness of boundary layer is smaller than characteristic length of object, ,that is extreme thickness of boundary layer. l , → 0 l l Characteristics of Boundary Layer: 2、 The thickness of boundary layer is increased in the flow direction on plane board
论 边界层理论在实际工程中的应用: 飞机和舰船的摩擦阻力确定; 溢流坝面理论流速系数值的确定; 陡槽中高速水流掺气点的确定; 水流阻力与水头损失的确定。 边界层的特点: 边界层的厚度δ与物体的特征长度l相比是非常小的, <1%7→0,即边界层极薄 2、边界层的厚度在平板上沿流动方向增加。 因为随着平板长度的增加,摩擦损失亦增加,流体内部的能 量减少,流速亦减少,为了满足连续条件,边界层的厚度增大
12 飞机和舰船的摩擦阻力确定； 溢流坝面理论流速系数值的确定； 陡槽中高速水流掺气点的确定； 水流阻力与水头损失的确定。 1、边界层的厚度 与物体的特征长度 相比是非常小的， ，即边界层极薄。 l , → 0 l l 因为随着平板长度的增加，摩擦损失亦增加，流体内部的能 量减少，流速亦减少，为了满足连续条件，边界层的厚度增大。 边界层理论在实际工程中的应用： 边界层的特点： 2、边界层的厚度 在平板上沿流动方向增加
3 laminar flow section transition section and turbulent flow section also exists in the boundary layer, under the transition section and turbulent flow section, there also exists a bottom layer do of laminar flow. As shown in Fig. 8-1 Laminar Flow Transition Turbulent Flow Boundary layer U Boundary Laver Section DO 0 B ottom Layer o linar Floy X Fig 8-1 Boundary Layer Structure 13
13 3、laminar flow section, transition section and turbulent flow section also exists in the boundary layer, under the transition section and turbulent flow section, there also exists a bottom layer of laminar flow. As shown in Fig.8-1. 0 U0 U0 U0 x y x cr x 0 Laminar Flow Boundary Layer Transition Section Turbulent Flow Boundary Layer Bottom Layer of Laminar Flow Fig.8-1 Boundary Layer Structure
论 3、边界层中也存在着层流区、过渡区和紊流区,过渡区 和紊流区下面也存在一个层流底层δ0。如图8-所示。 U 层流边界层过渡区紊流边界层 DO 6层流底层 图81边界层结构 14
14 3、边界层中也存在着层流区、过渡区和紊流区，过渡区 和紊流区下面也存在一个层流底层 0 。如图8—1所示。 U0 U0 U0 x y x cr x 0 层流边界层 过渡区 紊流边界层 层流底层 图 8—1 边 界 层 结 构
With the thickness increase of boundary layer restriction effect of viscosity on flow in the boundary layer is decreased, and inertia function is increased. Laminar flow will turn into turbulent flow when viscosity can not control water particle motion, just like the flow in the cylindrical pipe, this phenomenon is called transition of transition section and turbulent flow sections r of flow under the boundary layer, and there exists a bottom layer Assuming flow velocity in main flow is Uo, the distance to the front of plane is x, the Renault number is Uox Re (8—1) Usually we take Reynolds number at transition point is Re≈5×103 (8-2) 15
15 With the thickness increase of boundary layer, restriction effect of viscosity on flow in the boundary layer is decreased, and inertia function is increased. Laminar flow will turn into turbulent flow when viscosity can not control water particle motion, just like the flow in the cylindrical pipe, this phenomenon is called transition of boundary layer, and there exists a bottom layer of flow under the transition section and turbulent flow section . 0 Assuming flow velocity in main flow is , the distance to the front of plane is x , the Renault number is U0 v U x x 0 Re = （8—1） Usually we take Reynolds number at transition point is 5 Rec 510 （8—2）