CHAPTER 9 OBLIQUE SHOCK AND EXPANSION WAVES 斜激波和膨胀波 9.1引言 第八章我们讨论了正激波,本章我们讨论斜激波,及超音速流场 中的另一个重要特征——膨胀波。 Nave angle:激波角,激波与激波上游来流的夹角 of oblique shocks, namely, the case where the wave angle is 900 y A normal shock wave is simply a special case of the general family
CHAPTER 9 OBLIQUE SHOCK AND EXPANSION WAVES 斜激波和膨胀波 9.1 引言 第八章我们讨论了正激波, 本章我们讨论斜激波, 及超音速流场 中的另一个重要特征——膨胀波。 Wave angle: 激波角, 激波与激波上游来流的夹角。 A normal shock wave is simply a special case of the general family of oblique shocks, namely, the case where the wave angle is 900 . β
e: Deflection angle(偏转角) ① M2 P2>P1 M1>1 P1>p P1 P ① T. >7 M2> P P2<p1 T2<I (a)Concare sorne (5)Convex corner FIGURE 9.1 Supersonic Row over a comer. Across the oblique shock wave, Across the expansion wave. the the mach number Mach number continuously discontinuously decreases, and increases, and the pressure the pressure density and density, and temperature temperature discontinuously continuousl y decrease Increase
Across the oblique shock wave, the Mach number discontinuously decreases, and the pressure, density, and temperature discontinuously increase. θ: Deflection angle (偏转角） Across the expansion wave, the Mach number continuously increases, and the pressure, density, and temperature continuously decrease
Hence an expansion wave is the direct antithesis of a shock wave 因此,膨胀波是激波的一个正相反的对应物 Oblique shock and expansion waves are prevalent in two-and three-dimensional supersonic flow. These waves are inherently two dimensional in nature. in contrast to the one-dimensional normal shock waves discussed in Chap. 8. That is, in Fig.9.la and b, the flow-field properties are a function x and y. The purpose of the present chapter is to determine and study the properties of these oblique waves 斜激波和膨胀波在二维、三维超音速流动中是很普遍的。这些 波在本质上是二维的,与第八章讨论的一维正激波相反。即, 在图91a和b中,流场特性是x、y的函数。本章的目的就是确 定和研究这些斜波(斜激波和膨胀波)的性质
Hence, an expansion wave is the direct antithesis of a shock wave. 因此，膨胀波是激波的一个正相反的对应物。 Oblique shock and expansion waves are prevalent in two- and three-dimensional supersonic flow. These waves are inherently twodimensional in nature, in contrast to the one-dimensional normal shock waves discussed in Chap.8. That is, in Fig. 9.1a and b, the flow-field properties are a function x and y. The purpose of the present chapter is to determine and study the properties of these oblique waves. 斜激波和膨胀波在二维、三维超音速流动中是很普遍的。这些 波在本质上是二维的，与第八章讨论的一维正激波相反。即， 在图9.1a和b中，流场特性是x 、 y的函数。本章的目的就是确 定和研究这些斜波（斜激波和膨胀波）的性质
What is the physical mechanism that creates waves in a supersonic fow?超音速流中产生波的物理机理是什么? The information is propagated Za upstream at approximately the Disturbance dus to body is propagated upstream local speed of sound m viu molecular collisions at approximately the Flow moving speed of sound 物体存在的信息以近似等于 wer than the apeed of sound 当地音速的速度传播到上游 去 a) If the upstream flow is subsonic as shown in Fig 9.2a, the disturbances have no problem working their way upstream, thus giving the incoming flow plenty of time to move out of the way of the body 如图92a所示,如果上游是亚音速的,扰动可以毫不困难地传播 到远前方上游,因此,给了来流足够的时间以绕过物体
• What is the physical mechanism that creates waves in a supersonic flow? 超音速流中产生波的物理机理是什么？ If the upstream flow is subsonic , as shown in Fig.9.2a, the disturbances have no problem working their way upstream, thus giving the incoming flow plenty of time to move out of the way of the body. 如图9.2a所示，如果上游是亚音速的， 扰动可以毫不困难地传播 到远前方上游，因此，给了来流足够的时间以绕过物体。 The information is propagated upstream at approximately the local speed of sound. 物体存在的信息以近似等于 当地音速的速度传播到上游 去
Disturbances cannot work thelr way upstream. Instead. they coalesce, forming a stand wave Mos> Disturbance due to body is propagated upstream viu molecular collisions Flow movin at approximately the fasier than the speed af sound speed of sound FIGURE Popa gaton of disturbances. (a)Subsonic Aow.(b)Supersonic fow On the other hand, if the upstream flow is supersonic, as shown in Fig 9.2b, the disturbances cannot work their way upstream; rather, at some finite distances from the body, the disturbance waves pile up and coalesce, forming a standing wave in front of the body 在另一方面如图9.2b所示,如果上游是超音速的,扰动不能一直向上 游传播,而是在离开物体某一距离处聚集并接合,形成一静止波
On the other hand, if the upstream flow is supersonic, as shown in Fig.9.2b, the disturbances cannot work their way upstream; rather, at some finite distances from the body, the disturbance waves pile up and coalesce, forming a standing wave in front of the body. 在另一方面,如图9.2b所示，如果上游是超音速的,扰动不能一直向上 游传播，而是在离开物体某一距离处聚集并接合，形成一静止波
Hence, the physical generation of waves in a supersonic flow--both shock and expansion waves--is due to the propagation of information via molecular collisions and due to the fact that such propagation cannot work its way into certain regions of the supersonic flow 因此超音速流中激波和膨胀波产生的物理原因是:通 过分子碰撞引起的信息传播和这种传播不能到达超音 速流中某些区域
Hence, the physical generation of waves in a supersonic flow—both shock and expansion waves—is due to the propagation of information via molecular collisions and due to the fact that such propagation cannot work its way into certain regions of the supersonic flow. 因此,超音速流中激波和膨胀波产生的物理原因是: 通 过分子碰撞引起的信息传播和这种传播不能到达超音 速流中某些区域
Why are most waves oblique rather than normal to the upstream fow?为什么大部分激波与来流成斜角而不是垂直的呢? 马赫波 Supersonic Subset v>a v<a 马赫角 A SIn (b) FIGURE 93 Another way of visualizing the propagation of disturbances in(a)subsonic and(b)supersonic dow. u=sin (9.1)
• Why are most waves oblique rather than normal to the upstream flow? 为什么大部分激波与来流成斜角而不是垂直的呢? V M a Vt at 1 sin = = = M 1 sin −1 = (9.1) 马赫波 马赫角
M>1 FIGURE 9 Relation between the oblique shock-wave angle and the Mach angle. If the disturbances are stronger than a simple sound wave, then the wave front becomes stronger than a mach wave creating an oblique shock wave at an angle to the freestream, where p>u. This comparison is shown in Fig. 9.4. However, the physical mechanism creating an oblique shock isis essentially the same as that described above for the mach wave 如果扰动比一个简单声波强,其引起的波前就会比马赫波强,产生 个与来流夹角为β的斜激波,且β>μ。这一比较在图94中给出。然而, 斜激波产生的物理机理与上面描述的马赫波的产生完全相同
If the disturbances are stronger than a simple sound wave, then the wave front becomes stronger than a Mach wave, creating an oblique shock wave at an angle to the freestream, where β>μ. This comparison is shown in Fig. 9.4 . However, the physical mechanism creating an oblique shock is is essentially the same as that described above for the Mach wave. 如果扰动比一个简单声波强,其引起的波前就会比马赫波强,产生一 个与来流夹角为 β的斜激波,且β>μ。这一比较在图9.4中给出。然而， 斜激波产生的物理机理与上面描述的马赫波的产生完全相同
补充:激波与膨胀波的形成机理的进一步理解 dHE=I 激波的形成: 以右图活塞在一维长管中压缩为 例.设有一根很长的直管,管内 气体原是静止的.热力学参数是 p1,p1,T1.从=0起到t为止活塞 向右作急剧地加速运动,tt1以 后匀速前进 特征 (b) 居后的波比前边的波快,每道波 都在追赶它前面的波.过渡区 AA-BB的长度随时间增长而越来 越短,最后压缩到一起形成激 波
补充：激波与膨胀波的形成机理的进一步理解 激波的形成： 以右图活塞在一维长管中压缩为 例．设有一根很长的直管，管内 气体原是静止的．热力学参数是 p1 ,ρ1 ,T1 ．从t=0起到t=t1为止活塞 向右作急剧地加速运动， t=t1 以 后匀速前进． 特征： 居后的波比前边的波快，每道波 都在追赶它前面的波．过渡区 AA-BB的长度随时间增长而越来 越短，最后压缩到一起形成激 波．
膨胀波的形成: 上例中一旦活塞停止运动, ∷ 活塞与前进气体之间在瞬时 内会出现真空.这时气体在 压差作用之下,必发生向后 的膨胀运动,以填真空.这 时气体微团是向左运动的, 但膨胀变化这个界线(膨胀 波)却会自动地在p2气体中 向右推进. 特征:居后的波比前面的波 D 慢,越走,段落拉得越长, 不会集中起来 (b)
膨胀波的形成： 上例中一旦活塞停止运动， 活塞与前进气体之间在瞬时 内会出现真空．这时气体在 压差作用之下，必发生向后 的膨胀运动，以填真空．这 时气体微团是向左运动的， 但膨胀变化这个界线（膨胀 波）却会自动地在p2气体中 向右推进． 特征：居后的波比前面的波 慢，越走，段落拉得越长， 不会集中起来．