# Can a transonic airfoil have two shock waves?

I am currently running CFD cases on a transonic airfoil at Mach 0.75 and performing an angle-of-attack sweep to evaluate its performance. When I reached the angle of attack of 4.5 degrees (which I appreciate is very high for transonic flight, but tested nonetheless), a dual shock was formed on the suction side. Is this physically possible?

I understand how the suction-side flow may reaccelerate after a shock with favourable pressure gradient and possibly exceed sonic again, leading to a second shock, but wouldn't it just produce a single, stronger shock downstream?

I attached the two flowfields, colored by Mach number, with the first image representing the angle of attack of 4.5 and the second at 3.5 degrees.

Following jayS answer, I plotted the Cp for the two airfoils seen above, for comparison to the chart found.

• I wouldn't say that 4.5° is "very high" in such absolute terms. It depends on the phase of flight and the manoeuvre being performed. – Federico Sep 7 '17 at 10:34
• Yes, true, but we are talking about transonic flight conditions. The 4.5deg gave me a Cl of 0.79, Cd of 0.043 and a wing loading of 1170kg/m^2, which is quite high in my opinion. If my calculations are correct, it's the equivalent of doing a 1.5G banking turn on an A380 at cruise – GSammons Sep 7 '17 at 11:00
• Sure, I acknowledge that, what I would propose is that you somehow mention in in your question, for example by saying "I appreciate is very high for the given flight speed, but tested nonetheless". The current phrasing could be interpreted as you saying that 4.5 is always high. – Federico Sep 7 '17 at 11:20

## 1 Answer

Very Interesting results. I must say I have never before seen such a peculiar case. Yes, theoretically it seems possible to have this situation, but it's difficult to say if this is possible in reality or not. I found another similar behavior mentioned here:

One of the three aerofoils has dual shock.

It's difficult to say whether it's a physically correct situation or a mere artifact of CFD, especially without data on type of solver, type of simulation, numerical methods employed, mesh details etc. It would be advisable to simulate the same case in another code and see what results are seen.

• Yes, I am currently busy finishing my dissertation, but intend on playing with more cases on different meshes. I have all the information on the solver, but I didn't want to overwhelm with CFD information, when the answer was possibly one of aeronautics alone. Yes, I will try this in another solver and report back within a week – GSammons Sep 7 '17 at 10:19