Hi all,

I'm just getting started in hypersonic modelling and I'm trying find out why some codes can handle flows up to say mach 7 but fails after this. What is the difference between supersonic and hypersonic codes? Is there a code that can handle mach 50 and above?

Thanks

Mark

One of the biggest differences is the inclusion of chemistry, real gas effects, and other issues that arise as the kinetic energy of the flow becomes high enough to cause the gas to no longer behave as an ideal or thermally perfect gas. Without such accounting, you will have issues trying to run a typical compressible code above ~ Mach 6. One issue I have personally seen in this regard is in areas of sudden expansion that create pockets of high Mach number. In real life the rise in kinetic energy will produce dissociation and possibly even ionization that takes energy out of the flow and serves to limit the max. velocity and min. pressure/density. Without these effects it is very easy for a compressible code to compute quite happily down to a zero density/pressure state. There are codes that can handle very high Mach number flows. I recommend that you familiarize yourself with the nature of hypersonic flows and the essential differences with supersonic flow, before you settle on one code. Hypersonic simulations are much more complex than supersonic. John Anderson's book on hypersonic flows is a good starting point.

That's very interesting. So say you disregard the dissociation and insanely apply your Euler equations to Mach 20 flows, you will get numerical problems due to unrealistic energy balance...? How will this surface: as a stability problem, convergence problem, ... all of the above? Can you recommend any paper on this subject?

I don't have any papers right off the top of my head, only experience from a job I did a couple of years ago (was my first foray into hypersonic modeling). I would recommend looking at Anderson's book and check his references. I also know that Graham Candler at UMinn has done quite a bit of work modeling hypersonic flows. I'm also not saying that you will always run into problems - depending on the geometry you may not see any issues. What I am saying is that there is a lot of physics that needs to be considered as the Mach number increases if you want to get realistic answers.

"What I am saying is that there is a lot of physics that needs to be considered as the Mach number increases if you want to get realistic answers."

I suspect the numerical errors (along with any turbulence modelling) in the solution far exceed these correction terms in practice. Most of the missing physics you mention are routinely ignored in hypersonic flow papers that appear in Journals such as JFM - the M(ach No.)-> infinity limit is often exploited to simplify analytic results. The problem is usually caused by the advection of a positive quantity such as density which, when close to zero, can become negative due to numerical discretization errors. The main effect of the extra physics terms I suspect is through a "if test" stopping the density going negative.

Peter Jacob at Hypersonic center in the Universtiy of Queensland created a very good code, that could handle mach 50 and above

Thanks for all your advice guys

Mark