[mfrl]

Dear all,
I am trying to solve unsteady flows with supersonic jets flowing in an external ambient (e.g. quiescent air or an external flow).
At the outlet, the flow can have both supersonic and subsonic regions. Moreover, at the same point of the outlet boundary, the flow can switch from subsonic to supersonic because of the imping jet unsteady motions.
It is well-known that, according to the hyperbolic nature of the flow equations, the flow conditions at the outlet boundary must be exptrapolated from the interior (i.e. zeroGradient option) if the flow is supersonic, whereas a boundary condition (e.g. the static pressure) must be imposed if the flow is subsonic locally.

This Bc is very common and useful in solving transonic flows. It is robust and has a strong physical meaning.

Unluckily, I was not able to find it in the OF devoted literature and references.

I am wondering if some OF user/developer has already implemented this kind of boundary condition.

Many mixed BC's in OF are based on the sign of the velocity normal (Un) to the boundary, but I found none checking for the sign of (Un-a) , being "a" the local speed of sound.

The typical workaround used by the OF users is the waveTransmissive BC, which is more tricky and can easily lead to ill-posed problems when combined with other BCs. Often, it does not even preserve the imposed ambient pressure.


Thank you
Mrfl

[AlphaSierra]

Hi MF,

I have run a few cases where the flow at the outlet has been both subsonic and supersonic as well. I usually use inletOutlet BC for the outlet. This gives me satisfactory results. Hope this helps.

Anjay

[mfrl]

Dear Anjay,


at the best of my knowledge, the inletOutlet BC is zeroGradient if (U_n >0) and fixedValue otherwise.
In compressible flow the correct BC is zeroGradient if (U_n > U_sound) and fixedValue otherwise.
This means that the pressure must be imposed at the subsonic outlet, even if U_n>0.
I am unable to fix this issue in rhoCentralFoam because I do not have any knowledge of C++.


Thank you for your help,





Mrfl

Originally Posted by AlphaSierra

Hi MF,

I have run a few cases where the flow at the outlet has been both subsonic and supersonic as well. I usually use inletOutlet BC for the outlet. This gives me satisfactory results. Hope this helps.

Anjay

[schuyler]

You are right about the hyperbolic nature of the supersonic flow. But uniform convection can be parabolic (for instance a boundary layer), which has some similar attributes in terms of direction of information propagation.

Depending on the case, I have had success in using the zeroGradiant boundary condition for subsonic outlets. The key is whether or not you can successfully apply a fully defined inlet. In many cases, you cannot. Do you know what the pressure at the outlet should be? If not, and it is intended to be an output of the simulation, I would leave it as zeroGradient in both super and subsonic cases. If you know the pressure, it should probably be that for both cases no?

Have you tried the subsonic case while keeping the zeroGradient or inletOutlet?

[mfrl]

Dear Schuyler, many thanks for you answer.


From my numerical tests I can say that rhocentralFoam works fine, if the internal flow only is simulated, that is when the boundary conditions are identified clearly and some how fixed in time. Nozzle flows for subsonic/supersonic cases w/o embedded shocks are obtained correctly.


The problems arise when the outflow ambient is also simulated. The worst case is the outflow in quiescent air.

For the nozzle inlet, I used totalPressure/temperature conditions. As far as the nozzle get choked, the inlet is ok.

The problem is how to deal with the boundaries of the external flow domain.

I tried many combinations.

Tipically, the correct flow generated initially but it is deteriorated either by the interactions with the outlet boundary (e.g. by using inletOulet BCS), or by a series of pressure waves traveling through the flowfield and leading finally to the flow instability. Often thaes instability are generated a the outlet and bounced back by other boundaries of the external flowfield



The most successful cases were obtained by using
nozzle_inlet = Total conditions P & T, u=zeroGradient

external_flow_inlet and Outlet = WaweTransmissive

farfield = fixedValue or inletOutlet
I was not able to maintain the correct pressure level in the external ambient with the waveTransmisse boundary for all the external domain, so that I introduced the farfield boundary.



I tested also the invicid solution for the same problem. I observed that if the grid is coarse enough, the numerical viscosity is able to lead the system to a steady state. Just by increasing the number of cells, the same test fails.

By analizing the documentation, I have not found a way to enforce the classical BCs of compressible flow solver, based of the characteristic signals (e.g. a Riemann-based logic).



In my case I cannot overcome the issue just by a trick, because the outlet is partly subsonic, partly supersonic and the boundary conditions for the same cell can vary during the transient.

I believe that the BC for compressible outlet should fix the problem.

I was just tring to replicate it without going to change the OF code.



Thank you again,


Mrfl

Originally Posted by schuyler

You are right about the hyperbolic nature of the supersonic flow. But uniform convection can be parabolic (for instance a boundary layer), which has some similar attributes in terms of direction of information propagation.
epending on the case, I have had success in using the zeroGradiant boundary condition for subsonic outlets. The key is whether or not you can successfully apply a fully defined inlet. In many cases, you cannot. Do you know what the pressure at the outlet should be? If not, and it is intended to be an output of the simulation, I would leave it as zeroGradient in both super and subsonic cases. If you know the pressure, it should probably be that for both cases no?

Have you tried the subsonic case while keeping the zeroGradient or inletOutlet?