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Unformatted text preview: Oblique Shock Waves In reality normal shock waves don’t often occur. Oblique shock waves are more common. We would like to know what causes them, and how we can calculate flow properties around them. 1 Shock Wave Angles When an aircraft is flying, it creates disturbances in the flow. These disturbance spread around with the speed of sound a . Figure 1 visualizes these disturbances for an airplane traveling from point A to point B . Figure 1: Visualization of the disturbances in a flow. When the airplane flies at a subsonic velocity ( V < a ), the disturbances can move upstream. If the airplane, however, flies at a supersonic speed ( V > a ), the disturbances can not. In fact, they all stay within a cone and stack up at the edge, forming a so-called Mach wave . This cone has an angle μ , where μ is called the Mach angle . From figure 1 it can be derived that sin μ = at V t = a V = 1 M . (1.1) The above relation is, however, only theoretical. In practice the shock wave doesn’t have an angle μ but an angle β , called the wave angle . For shock waves we always have β > μ . Finally there is the special case with β = 90 ◦ , at which we once more have a normal shock wave. So a normal shock wave is just a special case of the oblique shock wave. 2 Oblique Shock Wave Relations We will try to derive some relations for oblique shock waves. But before we can do that, we need to make some definitions. Figure 2: Properties of the oblique shock wave. 1 We know that the velocity V 1 before the shock wave is directed horizontally. We examine two components of this velocity: The component normal to the shock wave u 1 and the component tangential to the shock wave w 1 . Corresponding are the Mach number normal to the shock wave M n, 1 and the Mach number tangential to the shock wave M t, 1 . We can do the same for the velocities after the shock wave (but now with subscript 2). All the properties have been visualized in figure 2. Also note the deflection angle θ . Using the variables described above, we can derive some relations. It turns out that these relations are virtually the same as for a normal shock wave. There’s only one fundamental difference. Instead of using the total velocity, we only need to consider the component of the velocity normal to the shock wave (being u ). We then get ρ 1 u 1...
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- Fall '10
- Shock wave, deflection angle