supersonic (Laval) nozzle, unphysical Mach number
 

Hello,

I am fairly new to ANSYS CFX and am struggling with the simulation of a Ma = 1,7 covergent-divergent nozzle.

My area ratio is 1.337 which leads to an isentropic exit Mach number of 1,7. From my understanding the exit Mach number is indepent of the pressure ratio (as long as sonic condition is reached at the nozzle throat). However, my simulation obviously depends on the exit pressure: If I decrease the exit pressure, the Mach number increses (over 1.7). It looks like the nozzle flow is even over-expanded (see the shock waves in the picture).

I tried many boundary conditions (subsonic, supersonic, opening) but only the subsonic BC converges:

IN subsonic
total pressure = 2 bar
turbulence: medium
static temperature = 380 K

OUT subsonic
average static pressure: 0.3 bar

WALL free slip

Does anybody have an idea, what my mistake could be?

Here is the Mach number plot of the nozzle: The red color indicates the areas where the Mach number exceeds 1.7. Hope that helps understanding my problem.

Thank you!

I do not understand your problem. Your results look believeable to me - you are close to your expected Mach 1.7 and superimposed on that you have some Mach wave reflections. This is all as expected.

That's true, but I don't understand where the Mach waves come from. The nozzle contour comes from the method of characteristics and the simulation is inviscid...

You have a sharp transition from the expansion section to the straight duct. This will create a Mach wave - and that is what you see. This is not a viscous effect, it is a compressibility effect. So no surprises there.

I assume you are comparing the simulation to a 1D model or an analytical solution of supersonic flow. These approaches ignore flow details and assume there are no sharp transition.

That was also my first thought, but my transition is smooth (see picture). I said I used the method of characteristics to calculate an ideal inviscid nozzle contour, as far as I know the flow should be parallel after the nozzle exit.

I discussed this topic with my colleague and he suggested that the disturbance comes from the grid. However, my grid is very fine (>500.000 nodes) and I cannot imagine that this would have just a big influence...

You are below nozzle design pressure on your outlet. You should expect to see what that series of mach waves.

If you dont want to see those, increase your back pressure.

If you think the Mach wave artefact is from your grid then simply changing the grid (significantly finer preferably, but coarser will probably work too) will show whether you are right. If the pattern changes then yes, it is a grid artefact.