Transient blast wave simulation set-up
 

Hi,
I am trying to set-up a 2D (z-axis 1 cell thick) simulation of the compressible airflow through a constant area duct which has a travelling blast wave pass along the duct. I am assuming the blast wave travels normal to the duct wall and I am not interested in the source point of the blast and the radial expansion outwards. The blast wave is the Friedlander waveform (https://en.wikipedia.org/wiki/Blast_wave) and for this testcase I will use the data in the wikipedia picture (Ps=10kPa and t*=100ms). Assuming ISA sea-level conditions for the reference ambient air properties then this peak overpressure value gives a shock velocity of U=429.9m/s and a peak wind velosity behind in the shock front of u=133.1m/s (https://www.fourmilab.ch/etexts/www/effects/eonw_3.pdf).

The image shows the very basic set-up where the transient pressure travels from the inlet and out through the outlet, but it does not reflect back. I have defined the Friedlander waveform as an expression (excluding the rapid pressure rise because I cannot include that in the same expression) and applied it at the inlet but no other suitable combination of boundary conditions works or seems obvious. Any suggestions on the boundary conditions? This is not the shock tube problem, is just a travelling wave. Once this works I can change the shape of the duct.

Thanks

You could make the duct long enough that the wave cannot travel to the end and reflect back in the time you simulate. But this distance might be longer than practical as blast waves go pretty quick.

Have a look at the beta feature of non-reflecting boundary conditions. I do not know much about it but it might be useful.

An alternative approach is to grossly coarsen the mesh just before the pipe exit boundary and use the dissipation of a coarse mesh to reduce the reflection. Use a GGI to connect a grossly coarse mesh to the rest of your mesh. This has worked well for some people.

Thanks Glenn.

What would you suggest for the inlet? I am thinking of the mixed velocity inlet with the blast wave expression for the pressure but I am not sure on the velocity value; zero perhaps, and the pressure changes the velocity.

As the flow goes in both directions it sounds like you need an opening with a specified pressure. Make sure you think about whether specifying the dynamic pressure or static pressure is the most appropriate.

Glenn, why would the flow go in both directions? This is not like the shock tube where the removal of the diaphragm in the middle of the shock tube causes effects in both directions. This is just a shock wave passing through still air from inlet to outlet and then its gone.

Your wikipedia link shows there is a negative pressure region after the initial positive pressure.

If you are only modelling the positive pressure bit with forwards flow then use an inlet with a defined pressure.

As I cannot get the blast wave in a duct to work correctly I have changed my approach. To test the set-up I am trying to repeat the simulation in https://www.researchgate.net/profile...cd2f000000.pdf, which simulated the blast wave from a point source using an expression inside a cube with 2 cylinders off it: all the faces of the model are walls (no inlets/outlets). The paper explains most of the set-up, but my simulation still failed after so many iterations; the pressure monitor points do not look correct. Are there any tricks/small details required in the set-up to get it to work?

Thanks

As you have not shown any information about what you are getting I can't help you much.

But this simulation should be manageable. Likewise your previous simulation should also be manageable, I would not give up on it.

As you seem to be having systematic problems on this type of simulation I would recommend you go back to some basic benchmark simulations and get them working well first. If you do the simple shock tube problem with an initial condition of a pressure difference from one side of the tube to the other in a long rectangular duct will walls on both ends - then you should be able to model the shocks and rarefactions in this, including the reflections. There are analytical solutions to the inviscid case so I would compare against that.

For instance I used the analytical shock tube as a benchmark in my PhD thesis: https://opus.lib.uts.edu.au/handle/2100/248 in section 5.2. The optimisation of the solver parameters on that model was used in the engine model which was the object of the work.