Normal shock relations

shock77 · April 16, 2021, 11:00

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, 06:36

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

johnotter · March 19, 2025, 05:21

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.

EmanuelMeisel · December 3, 2025, 02:24

Good questions. There are older studies on shock waves in binary gas mixtures (e.g. “normal shock in a binary gas mixture”) which show shock structure and effects differ from single‑gas relations. However, most classical shock‑tube literature especially helium driver into air treat driver and driven gases separately, separated by a contact (slip) surface, with post‑shock mixing occurring due to diffusion or instabilities. Thus, assuming pure helium behind the shock may be acceptable for very short timescales and purely thermodynamic jump conditions but not if mixing, diffusion, or post‑shock species composition matters.

April 16, 2021, 11:00	Normal shock relations	#1
shock77 Senior Member Join Date: Dec 2019 Posts: 215 Rep Power: 9	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, 06:36		#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, 05:21		#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.

December 3, 2025, 02:24		#4
EmanuelMeisel New Member Emanuel B. Meisel Join Date: Oct 2025 Posts: 2 Rep Power: 0	Good questions. There are older studies on shock waves in binary gas mixtures (e.g. “normal shock in a binary gas mixture”) which show shock structure and effects differ from single‑gas relations. However, most classical shock‑tube literature especially helium driver into air treat driver and driven gases separately, separated by a contact (slip) surface, with post‑shock mixing occurring due to diffusion or instabilities. Thus, assuming pure helium behind the shock may be acceptable for very short timescales and purely thermodynamic jump conditions but not if mixing, diffusion, or post‑shock species composition matters.