chapter8(1)---正激波及有关问题-空气动力学英文课件.ppt

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1、CHAPTER 8 NORMAL SHOCK WAVES AND RELATED TOPICSCHAPTER 8 NORMAL SHOCK WAVES AND RELATED TOPICS第八章第八章 正激波及有关问题正激波及有关问题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,如由爆炸产生的波及物体在介质中超音速运动而引起的波.8.1 INTRODUCT

2、IONThe 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 focus of this chapter is on normal shock waves,as sketched in Fig.8.1.The supersonic flow over a

3、 blunt body and the supersonic flow established inside a nozzle are shown in Fig.8.1.第八章的路线图:正激波基本控制方程的推导音速能量方程的特殊形式什么情况下流动是可压缩的?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用皮托管测量可压缩流的流动速度图8.2 第八章路线图Consider the rectangular control volume abcd given by the dashed line in Fig.8.3.The shock wave is inside the

4、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。In the process,we observe four important physical facts about the flow given in Fig.8.3:在进行过程中，注意图8.3给出的四个重要物理事实：1.The flow is steady,i.e./t=0.流动是定常的。2.The flow

5、is adiabatic:no heat is added or taken away from the control volume.流动是绝热的，没有加入和带出控制体的热量。3.There are no viscous effects on the sides of the control volume.控制体的边界上没有粘性的作用。4.There are no body forces;f=0。没有体积力。连续方程：(8.1)(8.2)动量方程：(8.3)x方向分量：(8.4)(8.6)能量方程：(8.7)(8.10)Discussion:Finally,we note that Eqs.

6、(8.2),(8.6),(8.10)are not limited to normal shock waves;they describe the changes 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

7、,p=p(x),u=u(x),etc.,is 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、,(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）What is the physical mechanism of the propagation of sound waves?声波传播的物理机理是什么？How can we calculate the speed of sound?我们怎样计算声音的速度？What properties of the gas does it depend on?声音由气体的什么特性决定？The purpose of this section is to address these questions.本节

9、的目的就是要回答、讨论这些问题。the regions of energized molecules are also regions of slight variations in the local temperature,pressure,and density.Hence,as this energy wave from the firecracker passes over our eardrum,we“hear”the slight pressure changes in the wave.This is sound,and the propagation of the energ

10、y wave is simply the propagation of a sound wave through the gas.当爆竹爆炸时,化学能(基本上是热释放的形式)被传递到紧邻爆竹的空气分子上.这些接收到能量的分子无规则地向四周运动.他们会与其相邻分子相碰撞,并将高能量传给其相邻分子.通过这种“多米诺”效应，爆竹释放出的能量通过分子间的碰撞传播出去。更进一步，因为T,p和作为气体的温度、压强和密度是分子微观运动的宏观平均值，接收到能量的分子所占区域也是温度、压强和密度发生微小变化的区域。因此，当能量波传递到我们的耳膜时，我们“听”到声波中微小的压强变化。这就是声音，能量波的传播实际上

11、就是声波在气体中传播。macroscopic:宏观的 microscopic:微观的Consider a sound wave propagating through a stagnant gas with velocity a,as sketched in Fig.8.4a.Here,the sound wave is moving from right to left into a stagnant gas(region1),where the local pressure,temperature,and density are p,T,and ,respectively.Behind t

12、he sound wave(region 2),the gas properties are slightly different and given by p+dp,T+dT,and +d,respectively.假设声波在气体中以速度a在静止气体中传播，如图8.4a所示。这里，声波从右向左进入当地压强、温度和密度分别为p,T,and 的静止气体区（区域1）。在声波之后（区域2），其气体的性质与区域1的气体性质有微小的不同，分别用p+dp,T+dT,和 +d来表示。采用图8.4b进行分析的优点是：原来的非定常问题转化成了定常问题，可以采用与图8.3分析静止正激波类似的方法分析声波。Plea

13、se note that the sound wave in Fig.8.4b is nothing more than an infinitely weak normal shock wave.请注意，图8.4b所示的声波就是无限弱的正激波。声波与激波的不同之处在于：通过激波流动特性发生突变，是一个间断（discontinuities)，是一个绝热但不等熵过程；通过声波流动特性发生无限小的微弱变化，流动特性变化是连续的，是一个等熵过程。Finally,the gradients within the wave are very small-the changes dp,dT,d and da

14、 are infinitesimal。Therefore,the influence of dissipative phenomena(viscosity and thermal conduction)is negligible.最后，我们还知道通过声波发生的气体特性变化非常小变化量可用无限小的微分dp,dT,d and da 来表示。因此，耗散现象（粘性与热传导）的影响可以忽略不计。对图8.4b应用连续方程：（8.11)忽略微分的乘积dad：（8.12)或对图8.4b应用动量方程：（8.13)略去微分的乘积：（8.14)（8.12b)（8.14)将(8.12b)式 代入(8.14)式（）得：

15、即：（8.17)（8.18)Equation(8.18)is a fundamental expression for the speed of sound in a gas.方程(8.18)是气体音速的一个基本表达式。假设气体是量热完全的。对于这种情况，等熵关系式（7.32)成立。（8.19)（8.20)(8.23)应用状态方程：(8.25)which is our final expression for the speed of sound;it clearly states that the speed of sound in a calorically perfect gas is

16、a function of temperature only.是我们得到的音速计算公式的表达式；它清楚地表明，对于量热完全气体，音速是温度的唯一函数。What properties of the gas does it depend on?声音由气体的什么特性决定？马赫数的物理意义：考虑一沿流线运动的流体微元。其单位质量的动能和内能分别为 和e。动能和内能的比为：Hence,we see that the square of the Mach number is proportional to the ratio of kinetic energy of a gas flow.In other words,the Mach number is a measure of the directed motion of the gas compared with the random thermal motion of the molecules.因此，我们看到马赫数的平方正比于气体动能内能之比。用另一句话说：马赫数是气体的有序运动和分子无规则热运动的程度对比的度量。