Normal shock relations

shock77 · April 16, 2021, 10:00

Hello,

I am currently trying to solve the normal shock relations for two species. I have basically a shock tunnel, where a moving shock propagetes from a high pressurized helium chamber into a air chamber with ambient pressure and temperature.

Therefore before the moving shock there is air with y=1,4 and R = 287 and behind the shock there is helium with y=1.67 and R = 2077.

My questions are:

1. Is there any literature where this problem has already been solved? Unfortunately I couldn't find any.

2. Is the assumption correct, that behind the shock there is pure helium or is there some sort of mixing? I would say it is pure helium, since the pressure behind the shock is higher than ambient pressure, so backflow is not possible. Just want to make sure I am not missing an important aspect.

Thanks in advance!

hunt_mat · June 22, 2023, 05:36

Are you after the simple solution if the shock relations? Aren't these found in every look on gas dynamics?

johnotter · March 19, 2025, 04:21

Hello,

Yes, for perfect gases I believe there is an analytical relationship for what you describe (shock tube relations). Have a look at Chapter 7 (specifically 7.8) in Anderson's "Modern Compressible Flow". If this doesn't have what you're looking for then this is a good reference book for approaching the problem from first principles!

Otherwise, you could simulate a shock tube with an unsteady 1D or 2D CFD simulation. Anderson's "Computational Fluid Dynamics" has an example CFD code for a 1D shock tube.

April 16, 2021, 10:00	Normal shock relations	#1
shock77 Senior Member Join Date: Dec 2019 Posts: 215 Rep Power: 8	Hello, I am currently trying to solve the normal shock relations for two species. I have basically a shock tunnel, where a moving shock propagetes from a high pressurized helium chamber into a air chamber with ambient pressure and temperature. Therefore before the moving shock there is air with y=1,4 and R = 287 and behind the shock there is helium with y=1.67 and R = 2077. My questions are: 1. Is there any literature where this problem has already been solved? Unfortunately I couldn't find any. 2. Is the assumption correct, that behind the shock there is pure helium or is there some sort of mixing? I would say it is pure helium, since the pressure behind the shock is higher than ambient pressure, so backflow is not possible. Just want to make sure I am not missing an important aspect. Thanks in advance!

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June 22, 2023, 05:36		#2
hunt_mat Senior Member Matthew Join Date: Mar 2022 Location: United Kingdom Posts: 184 Rep Power: 5	Are you after the simple solution if the shock relations? Aren't these found in every look on gas dynamics?

March 19, 2025, 04:21		#3
johnotter New Member John Otter Join Date: Mar 2025 Posts: 5 Rep Power: 2	Hello, Yes, for perfect gases I believe there is an analytical relationship for what you describe (shock tube relations). Have a look at Chapter 7 (specifically 7.8) in Anderson's "Modern Compressible Flow". If this doesn't have what you're looking for then this is a good reference book for approaching the problem from first principles! Otherwise, you could simulate a shock tube with an unsteady 1D or 2D CFD simulation. Anderson's "Computational Fluid Dynamics" has an example CFD code for a 1D shock tube.