《流体力学 Fluid Mechanics》课程PPT教学课件（双语版）第八章 边界层理论

Mechanics of fluid

1 Mechanics of Fluid

体力学 第八论

2

Chapter 8 Boundary Layer Theory §8-1 Introduction 88-2 Basic Concept of boundary layer 88-3 The Motion Differential Equation of Boundary layer 2$8-4 Variable Thickness of Boundary layer 88-5 The Momentum Equation of boundary Layer and friction shear Stress 88-6 Laminar Boundary Layer of smooth Board Chapter 8 Exercises

3 Chapter 8 Boundary Layer Theory §8–1 Introduction §8–6 Laminar Boundary Layer of smooth Board Chapter 8 Exercises §8–5 The Momentum Equation of Boundary Layer and Friction shear Stress §8–4 Variable Thickness of Boundary Layer §8–3 The Motion Differential Equation of Boundary Layer §8–2 Basic Concept of Boundary Layer

第八章边界层理论 s8-1引言 §8-2边界层的基本概念 §8-3边界层的运动微分方程式 §8-4边界层中的各种厚度 §8-5边界层的动量方程式和摩擦切应力 §86光滑平板上的层流边界层 第八章习题

4 第八章 边界层理论 §8–1 引言 §8–6 光滑平板上的层流边界层 第八章 习题 §8–5 边界层的动量方程式和摩擦切应力 §8–4 边界层中的各种厚度 §8–3 边界层的运动微分方程式 §8–2 边界层的基本概念

Chapter 8 Boundary Layer Theory §8-1 Introduction The last chapter introduces Navier-Stokes equation and Reynolds equation, the differential continuity and these two equations form basic differential equation which find the solution of viscosity fluid dynamics As for they are nonlinear second-order partial differential equations Reynolds equation is not still be closed, usually we can not obtain the accuracy solution, people turn to seek approximate solution

5 Chapter 8 Boundary Layer Theory §8-1 Introduction The last chapter introduces Navier-Stokes equation and Reynolds equation, the differential continuity and these two equations form basic differential equation which find the solution of viscosity fluid dynamics. As for they are nonlinear second-order partial differential equations, Reynolds equation is not still be closed, usually we can not obtain the accuracy solution, people turn to seek approximate solution

论 第八章边界层理论 §8-1引言 上章介绍了纳维—斯托克斯方程与雷诺方程,它们与连续性微 分方程一起构成求解粘性流体动力学的基本微分方程。由于它们是 非线性的二阶偏微分方程,雷诺方程还无法封闭,所以在一般情况 下不易得到它们的精确解,所以人们转向寻求近似的解答

6 第八章 边界层理论 §8-1 引言 上章介绍了纳维—斯托克斯方程与雷诺方程，它们与连续性微 分方程一起构成求解粘性流体动力学的基本微分方程。由于它们是 非线性的二阶偏微分方程，雷诺方程还无法封闭，所以在一般情况 下不易得到它们的精确解，所以人们转向寻求近似的解答

We can obtain the analytic approximate solution when viscosity fluid moves by two methods as following, one is called"creeping flow theory which we neglect inertia force and make basic concept linearity when Re <<1. The other is to find boundary layer theory of resistance force of surrounding flow when Re <<1, it only considers flow viscosity inside the boundary layer, and the outside can be considered the potential flow of the ideal fluid This chapter introduces boundary layer of plane board for the approximate of linear surrounding flow and plane board surrounding flo

7 This chapter introduces boundary layer of plane board for the approximate of linear surrounding flow and plane board surrounding flow. We can obtain the analytic approximate solution when viscosity fluid moves by two methods as following, one is called “creeping flow theory” which we neglect inertia force and make basic concept linearity when . The other is to find boundary layer theory of resistance force of surrounding flow when , it only considers flow viscosity inside the boundary layer, and the outside can be considered the potential flow of the ideal fluid. Re 1 Re 1

论 粘性流体运动时的解析近似解至今在两种情况下才能获得, 种是Re<<1时,可忽略惯性力,使基本方程线性化,这就是所 谓蠕流理论;另一种是Re<<1时,求解物体绕流阻力的边界层理 论,它对流体的粘性仅局限于边界内考虑,而边界层之外的广大 主流区,可当作理想流体的势流。 本章主要研究平板上的边界层,因为流线体绕流与平板绕流 相接近

8 本章主要研究平板上的边界层，因为流线体绕流与平板绕流 相接近。 粘性流体运动时的解析近似解至今在两种情况下才能获得， 一种是 时，可忽略惯性力，使基本方程线性化，这就是所 谓蠕流理论；另一种是 时，求解物体绕流阻力的边界层理 论，它对流体的粘性仅局限于边界内考虑，而边界层之外的广大 主流区，可当作理想流体的势流。 Re 1 Re 1

88-2 The Basic Concept of Boundary Layer The Basic Difference Between Viscid Fluid and Ideal fluid viscid fluid has vIscOSIty When viscid fluid flows on stationary fixed boundary, its velocity is 0, with the increasing of the distance to the fixed boundary, the effect of fixed boundary or viscosity on flow will be decreased, flow velocity increases, finally approaches the arrival flow velocity U Definition:0 When Reynolds number of arrival flow is greater the extent which has variable velocity du/dy is limited to the thinnest layer near the fixed boundary, which is called boundary la ayer The flow thickness which the velocity increase from 0 to0.99U0 is called the thickness of boundary layer&

9 §8-2 The Basic Concept of Boundary Layer The Basic Difference Between Viscid Fluid and Ideal Fluid: viscid fluid has viscosity. When viscid fluid flows on stationary fixed boundary, its velocity is 0, with the increasing of the distance to the fixed boundary, the effect of fixed boundary or viscosity on flow will be decreased, flow velocity increases, finally approaches the arrival flow velocity . U0 The flow thickness which the velocity increase from 0 to 0.99 is called the thickness of boundary layer . U0  When Reynolds number of arrival flow is greater, the extent which has variable velocity is limited to the thinnest layer near the fixed boundary, which is called boundary layer. du dy Definition:

论 §8-2边界层的基本概念 粘性流体与理想流体的根本区别:粘性流体具有粘滞性。 当粘性流体在静止固定边界上流动时,流体在固定边界上的 速度为零,随与固体边界距离的增大,固体边界或粘性对流动的 影响逐渐减小,流速逐渐增大,最后接近来流流速U0° 定义: 当来流的雷诺数较高时,具有速度变化d小的范围只 限于靠近固体边界的极薄的一层内,此薄层称为边界层 流速由0增加到0.9处流体的厚度称为边界层的厚度d。 10

10 §8-2 边界层的基本概念 粘性流体与理想流体的根本区别：粘性流体具有粘滞性。 当粘性流体在静止固定边界上流动时，流体在固定边界上的 速度为零，随与固体边界距离的增大，固体边界或粘性对流动的 影响逐渐减小，流速逐渐增大，最后接近来流流速 U0 。 当来流的雷诺数较高时，具有速度变化 的范围只 限于靠近固体边界的极薄的一层内，此薄层称为边界层。 du dy 流速由 0 增加到0.99 U0 处流体的厚度称为边界层的厚度  。 定义：