# How to identify shock waves and expansion waves on a representation of the mach number?

This image is a representation of the Mach number for $$M_{\infty}=2.0$$ I am very new to CFD and high speed aerodynamics. I'm trying to analyse this image, specifically to understand why the velocity decreases behind the trailing edge.

On the following image, I've tried to identify shock waves (1 and 3) and expansion waves (2) when the direction of the flow changes. However, after an expansion wave, the velocity should increase and it is not the case here so my interpretation must be false. How?

Thank you

## 1 Answer

Your airfoil is traveling supersonic at around Mach 2.

1. First the flow encounters a bow shock. Away from the leading edge, the bow shock morphs into an oblique shock. You can clearly see Mach number rapidly decreasing after the shock.

2. After passing through the thickest point of the airfoil, the expansion wave begins due to gradually increasing expansion angle. You can see Mach increasing, all the way up to around Mach 2.2.

3. At the trailing edge, the flow encounters a compression angle if you consider the wake as a boundary. Here, an oblique shock is encountered. Since oblique shock is less powerful than a normal shock, you can clearly see that Mach isn't decreasing as much as after the bow.

• why is there a shock wave at the trailing edge at all? from the view of air molecules, they are 0 mach. Suddenly the object bumps into them with mach2, air molecules can't get out of the way, so there is shockwave. There are air pinned in the bow area, so the shockwave doesn't happen at the surface of the object. If there is a trailing edge shock wave, it must mean: the parasitic boundary layer air on the object is traveling faster than mach1 with respect to air in region (2) in the above diagram.
– eliu
Commented May 1, 2020 at 17:58
• @eliu "from the view of air molecules, they are 0 mach"? You're thinking from an external observer pov, which isn't really relevant here. With respect to the airfoil, the free-stream is traveling at Mach 2. Likewise, immediately adjacent to the airfoil boundary, the flow is standing-still with respect to the airfoil, even though sitting on the ground you'll see it moving at Mach 2.
– JZYL
Commented May 1, 2020 at 18:13
• I am trying to understand this from observer's pov. It at least enhances my understanding. As it emphasize the fact that is the air that was dragged alone by a plane crashing into stationary air. That's fundamental cause of the shockwave. And the stationary air was accelerated in such sudden way caused the immense drag and sound barrier. But I think your answer confirmed my "crashing" idea.
– eliu
Commented May 1, 2020 at 19:47
• Expansion begins right after the bow shock due to the concave contour of the airfoil. At the thickest point ambient speed is regained already and the flow accelerates further. All of the surface is the source of one big expansion fan. Also, it would be nice to mention the boundary layer as it is clearly visible. Commented May 1, 2020 at 20:36
• Would anyone wish to consider doing the analysis with a supersonic airfoil design. This data seems to show a lot of drag at Mach 2. Where would the CP be with that particular airfoil? Commented May 2, 2020 at 0:53