chapter 8 NORMAL SHOCK WAVES AND RELATED TOPICS

6. Isentropic flow properties calculation.
7. The relation between compressibility and mach number. 8. How to calculate the normal shock waves properties. 9. The principle of pitot tube in subsonic and supersonic flow.
You will know in this chapter
1. The control equations cross the normal shock waves.
2. How to calculate the speed of sound and what does it depend on?
defined as one-dimensional flow. Thus, Eqs. (8.2),(8.6),(8.10)
are governing equations for one-dimensional, steady,
adiabatic, inviscid flow.
讨论： 最后，我们应注意,方程(8.2),(8.6),(8.10) 并不
that take place in any steady, adiabatic, inviscid flow where only one direction is involved. That is, in Fig. 8.3 the flow is in the x direction only . This type of flow, where the flow-field variables are functions of x only, [p= p(x), u=u(x),etc.], is
Normal shock waves occur frequently in nature. The study of normal shacks waves is important.
Road map for chap. 8:
8.2正激波基本控制方程的推导 8.3声速
8.4能量方程的特殊形式 8.5什么情况下流动是可压缩的? 8.6用于计算通过正激波气体特性变化的方 程的详细推导; 物理特性变化趋势的讨论 8.7用皮托管测量可压缩流的流动速度 图8.2 第八章路线图
激波是瞬态压缩，因此不可能是可逆过程。压缩 流体所需的能量来自上游流体的动能，动能转化 为内能，波后熵增加，做有用功的能力下降。 激波非常薄，只有几个分子自由程的厚度。认为 流动参数在激波处发生间断。本课程只研究激波 前后的参数变化，不研究激波内的变化过程。
我有1个大气压
跨过薄薄的激波，我变 成了20个大气压！
CHAPTER 8 NORMAL SHOCK WAVES AND RELATED TOPICS 第八章 正激波及有关问题
Shock wave: A large-amplitude compression wave, such as that produced by an explosion, caused by supersonic motion of a body in a medium. 激波是一个大振幅波,如由爆炸产生的波或物体在介质中超音速 运动而引起的波.
状态方程：
e2 cv T2
焓：
h2 cp T2
h2 e2 p2u2
Discussion: Finally, we note that Eqs. (8.2),(8.6),(8.10) are not
limited to normal shock waves; they describe the changes
3. The relation between the speed of sound and the compressibility. 4. The physical meaning of speed of sound and mach number. 5. The energy equations empressed by speed of sound and temperature.
声波的传播机理
The physical mechanism of sound propagation in a gas is based on molecular motion. 声音在气体中的传播机理基于分子的运动。
For example: firecracker goes off. 例如：点燃爆竹
(8.7)
u1 u2 h1 h2 2 2
2
2
(8.10)
定常，绝热，无粘，量热完全气体
连续： 动量：
1u1 2u2
p1 u p2 2u2
2 1 1 2
(8.2)
(8.6)
能量：
u1 u2 h1 h2 2 2
p2 2 R T2
2
2
(8.10)
只适用于正激波,他们描述了只包含一个方向的定常、绝热、
无粘流动。在图8.3中，流动只沿x方向进行。 这种类型的 流动被定义为一维流动，其流场变量只是x的函数[p= p(x),
u=u(x),等等]。因此，方程(8.2),(8.6),(8.10) 是一维、
定常、绝热、无粘流动的控制方程。
8.3 SPEED OF SOUND 音速(声速)
PART 3
Inviscid, Compressible Flow
主讲：邓 磊 E-mail: leideng@ 2012.10 Department of Fluid Mechanics, School of Aeronautics, Northwestern Polytechnicl University, Xi’an, China
分子间能量传播的多米诺效应。
注： 1、注意区分介质本身微观的运动速度和宏观的声波传播速度。 2、空气中分子无规则运动的平均速度为 8RT / 。 3、声速约为分子无规则运动速度的3/4.
4、可以设想：声速只与温度有关？
Calculation of the speed of sound
Although the propagation of sound is due to molecular collisions, we do not use such a microscopic picture for our derivation. Rather, we take advantage of the fact that the macroscopic properties p, T, ρ,etc., change across the wave, and we use our macroscopic equations of continuity, momentum, and energy to analyze these changes. 尽管声音的传播是由于分子碰撞引起的,我们在推导气体音速 的方程时并不采用这一微观物理画面.相反,我们利用气体的宏 观性 p, T, ρ等 通过声波将发生变化这一事实, 应用连续、动 量、能量宏观方程来分析这些变化。
Shock！！
激波分类： 正激波（Normal Shock Wave）：波面垂直于流动方向 斜激波（Oblique Shock Wave）：波面与流动方向的夹角小于90°
8.1 INTRODUCTION The purpose of this chapter and Chap.9 is to develop shock-wave theory, thus giving us the means to calculate the changes in the flow properties across a wave. 本章和第九章的目的是推导激波理论,因而得出计算通过激波的 流动特性变化量的公式。
The purpose of this section is to address these questions： 本节的目的就是要回答、讨论这些问题：
• What is the physical mechanism of the propagation of
sound waves? 声波传播的物理机理是什么？
s
V dS V p dS
s

(8.3)
压强合力 流出的动量- 流入的动量
p1 A p2 A
mu2
mu1
p1 A p2 A mu2 mu1
p1 u p2 2u2
2 1 1
2
(8.6)
能量方程：
V2 e 2 V ds pV dS s S
通过激波的流动，无外功无粘绝热流。
Consider the rectangular control volume abcd given by the dashed line in Fig.8.3. The shock wave is inside the control volume. 考虑矩形控制体abcd如图8.3 虚线所示，激波在控制体 内。 We apply the integral form of conservation equations to this control volume. 我们对这个控制体应用积分形 式动量方程。
8.2 THE BASIC NORMAL SHOCK EQUATIONS 正激波的基本方程
P2 ρ2 T2
V2R
Vs
V1R=0 P1 ρ1 T1
P2 ρ2 T2
V2
V1 P1 ρ1 T1
+（-Vs）
x
x
(a)运动的正激波
P
V