CHAPTER 9 OBLIQUE SHOCK AND EXPANSION WAVES 斜激波和膨胀波 91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 90
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
0: Deflection angle(偏转角) M2<M1 M1>1 P2>p1 M1>1 p2>P1 Pr r2>7 M2>1 p2< 9T2<r1 (a) Concave sorne, (b)Convex corner FIGURE 9.1 Supersonic How 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 continuously 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
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 upstream at approximately the Disturbance due to body is propa mated upstream local speed of sound m via molecular collisions at approximately the Flo ow noving ed 物体存在的信息以近似等于 sewer than the peed 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 Fig9.2a, 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
• 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. Instea. they coalesce, forming a stand Disturbance due to body is propagated upstream viu molecular collisions Flow moving at approximately the fasier than the l speed af sound speed of sound FGURE 9.2 Propagation of disturbances. ( a)Subsonic Aow. (b)Supersonic Aow. 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92b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