[rabea matouk]

Hello,

I have some hydrodynamic waves reflections on the outlet of computational domain using outlet pressure boundary condition so I decided to implement the non reflecting boundary conditions in our in-house code which is incompressible navier-stockes finite elements/spectral code because we will use the aerodynamic sources to compute the radiated noise in the aeroacoustics study so it is so sensitive to have accurate aerodynamics results near the outlet.

I'd like your help to start and to provide me with references please.

Thanks in advance

[leflix]

For incompressible flows you can use Orlanski boundary condition.

[rabea matouk]

Thank you leflix for your advice and help.

You mean the convective BC:

dU/dt + Un*dU/dn = 0

could you please give me more details and advice
, this is my first try to implement BC?

U is the longitudinal and vertical velocities or I have to apply it for the three velocity components?

[leflix]

yes indeed it is this boundary condition.
You need to use this boundary condition for the three velocity components indeed.
dU/dt + Un*dU/dn = 0
dV/dt + Un*dV/dn = 0
dW/dt + Un*dW/dn = 0
the choice of the convective velocity Un is tricky check the paper of Orlansky, many choices are possible.

[rabea matouk]

Thank you very much leflix. I'll try to implement and test it. the convective velocity Un is really tricky but I'll try several suggestions and see the results.

[Parth04]

thnx lefflix

[Parth04]

for almost constant velocity flow at outlet can i use C = U , u = 1.0; , remains almost constant at outlet section , , , thnx in advance

[rabea matouk]

I think we can use Un = U (free stream) for the u equation but what about v and w since the phase velocity is different.

[calf.Z]

Originally Posted by leflix

yes indeed it is this boundary condition.
You need to use this boundary condition for the three velocity components indeed.
dU/dt + Un*dU/dn = 0
dV/dt + Un*dV/dn = 0
dW/dt + Un*dW/dn = 0
the choice of the convective velocity Un is tricky check the paper of Orlansky, many choices are possible.

Thank you for the information you gave.

Do you have some experience in the implement of the convective boundary condition in openfoam? I am quite new in this area. Thank you.

[LuckyTran]

Originally Posted by calf.Z

Thank you for the information you gave.

Do you have some experience in the implement of the convective boundary condition in openfoam? I am quite new in this area. Thank you.

The openfoam code is freely available on the internet. Do you have a specific question about the way it is implemented?

[calf.Z]

Originally Posted by LuckyTran

The openfoam code is freely available on the internet. Do you have a specific question about the way it is implemented?

Which BC code should be used to modify so that I can apply convective boundary BC in my simulation? Or are there any guide to introduce this boundary? I am new to this BC. Thank you.

[LuckyTran]

Originally Posted by calf.Z

Which BC code should be used to modify so that I can apply convective boundary BC in my simulation? Or are there any guide to introduce this boundary? I am new to this BC. Thank you.

For incompressible flows the advective BC should already be sufficient. For compressible flows additional treatment is needed to prevent unwanted reflection of acoustic waves. E.g. Pointsot & Lelef. Because of this, for incompressible flows you hear advective or outflow BC (and you don't normally call this non-reflecting, although it does prevent reflection of hydrodynamic waves). Non-reflecting BC usually implies acoustics.

[calf.Z]

Originally Posted by LuckyTran

For incompressible flows the advective BC should already be sufficient. For compressible flows additional treatment is needed to prevent unwanted reflection of acoustic waves. E.g. Pointsot & Lelef. Because of this, for incompressible flows you hear advective or outflow BC (and you don't normally call this non-reflecting, although it does prevent reflection of hydrodynamic waves). Non-reflecting BC usually implies acoustics.

Thank you for the helpful information !

In my case, the governing quations exclude acoustic interactions and compressibility effects from the full compressible Navier–Stokes equations. It is called Low-Mach Number equation. I think it is still a compressible flow but a littile special.

So I am confused if additional treatment of avective BC is needed to prevent unwanted reflection of acoustic waves? If so, which aspect should I modify? I will read the paper you gave later. Thank you.

[LuckyTran]

Since I can't see the actual governing equation, I can't say. If it truly remove acoustic waves then sure, then probably/maybe regular advective BC should work. But I don't know what types of Mach waves might be allowable in this model and if there are any, how the reflections need to be handled.

[calf.Z]

Originally Posted by LuckyTran

Since I can't see the actual governing equation, I can't say. If it truly remove acoustic waves then sure, then probably/maybe regular advective BC should work. But I don't know what types of Mach waves might be allowable in this model and if there are any, how the reflections need to be handled.

The actual energy equation:
∂(ρh)/∂t + ∂(ρUh)/∂x = ∂(k∂T/∂x)/∂x

I am also confused about Low-Mach assumption. It is said that pressure fluctuations can be eliminated due to it. But I am still not sure what influences can the assumption give. Thank you.

[FMDenaro]

Originally Posted by calf.Z

The actual energy equation:
∂(ρh)/∂t + ∂(ρUh)/∂x = ∂(k∂T/∂x)/∂x

I am also confused about Low-Mach assumption. It is said that pressure fluctuations can be eliminated due to it. But I am still not sure what influences can the assumption give. Thank you.

I suppose that you are considering a Taylor series for the pressure and density field around a base state that satisfies the gas law. This way you get an elliptic field for the pressure fluctuations having as source also the density fluctuations. The pressure BCs. are of Neumann type and you can use convective conditions at an outflow

[calf.Z]

Originally Posted by FMDenaro

I suppose that you are considering a Taylor series for the pressure and density field around a base state that satisfies the gas law. This way you get an elliptic field for the pressure fluctuations having as source also the density fluctuations. The pressure BCs. are of Neumann type and you can use convective conditions at an outflow

Yes I want to use the convective BC in outlet, which maybe is called advective BC in openfoam. And now I want to know which aspect I should notice to use this BC in compressible problem.

[FMDenaro]

Originally Posted by calf.Z

Yes I want to use the convective BC in outlet, which maybe is called advective BC in openfoam. And now I want to know which aspect I should notice to use this BC in compressible problem.

If you have the elliptic equation for the pressure, you have to set the proper Neumann BCs. that follow from the convective condition. That is if you set something like dU/dn = 0 the normal pressure gradient must be congruently prescribed.

[TurbJet]

why would incompressible flow has non-reflecting BC? I thought only compressible has one.

[LuckyTran]

Originally Posted by TurbJet

why would incompressible flow has non-reflecting BC? I thought only compressible has one.

It depends what is being non-reflected.

A hydrodynamic wave (i.e. vortex shedding) with a velocity (and pressure) fluctuation would be reflected backwards if you simply apply the du/dn = 0 constraint or pressure = some number.

However, the advective/convective/outflow BC is so widely implemented in most codes that we don't think of it as anything special. So it is common mis-belief that non-reflecting is only for compressible flows.