[SuperSonic Nozzle] Bondary conditions of external domain
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Hello everyone,
I am actually realizing a study of a supersonic nozzle. With the method of characteristic, I design the shape of the nozzle to obtain exit Mach number around 2. When I run the problem without the external domain, the convergence is very quick and I obtain what i want. Nevertheless, now I add the external domain, because I want to change the atmospheric pressure, to see if there are some shocks in different altitude. So, I make this domain (see picture 1 in attachments), to simulate the atmospheric pressure. Now, my question is : What kind of bondary conditions I have to use ? Pressure farfield ? Symetry ? Everything I tried went to divergence. Some informations about my problem. All my BC are extracted from my MATLAB program using characteristic method. BC 5 : Pressure Inlet Ptotal = Pi = 70e+04 Pa Ttotal = Ti = 500 K Pstatic = 625534 Pa Tstatic = 491 K BC 6: Wall BC 4: Axis BC 1, 2, 3 : I don't know what is the optimum kind of bondary conditions ? To be in optimum expansion condition, Pexit = Patm , my Pexit (static) is 77502 Pa. Thanks by advance if you have any idea or suggestions. Regards, m_f Note : Fluent 6.3 software 
Hy!
I'm also currently working on programming over and underexpanded jet flow behind a laval nozzle. I have the same problem with the boundary conditions that you had. Did you manage to solve your problem? If yes, which boundary conditions did you choose? Cheers! 
Did you tried pressure outlet for external BC 1,2,3

Hy,
since I use Matalb to solve my problem I don't really know what pressure outlet means ;) Does it mean that I have to define the static pressure at BC 1,2 and 3? Should this value then stay constant throughout the time steps? But what about the other flow properties, should I simply choose arbitrary values for them to start and extrapolate the values at the boundary from the interior? My approach was to use the characteristics to determine how many values should be variable at the boundary and how many should stay constant. For BC 1 which I assume to be subsonic this would mean that one characteristic plus the streamline goes inside my domain, hence I should keep 2 values constant and one variable. In my case the three variables would be the density, internal energy and velocity. I'm really confused about this right now... 
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Thanks for your help duri!
Now I applied the pressure outlet as BC 1 and I treated BC 2 as a free slip wall. Since BC 3 is a supersonic outlet I extrapolate the internal values. But it didn't work :( Can you tell me if it is right to apply a free slip boundary condition to BC 2? I'm also not sure if I apply this condition properly. For symmetry as well as free slip I put all normal gradients and the normal velocity component to zero. Now, does a zero gradient e.g. at a symmetry mean, that the value at the symmetry simply becomes the value of the next internal node parallel to it? 
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BC1 is too close to nozzle exit, which could result in convergence issue. Its better to move it far upstream so that pressure at the boundary is not influenced by nozzle exit pressure. Quote:

Ok, I will try to expand boundary 1 in the upstream direction.
Did I understand you right that I should switch the boundary conditions at boundary 3 depending on the Mach number at each node at the exit? This would mean that when the Mach number at a node is supersonic I extrapolate ALL values from the inside and when the Mach number at a node is subsonic I apply pressure outlet, hence the pressure becomes the specified static pressure and all other variables are extrapolated. Since I'm performing a time marching calculation using maccormacks technique this means that the boundary condition at the same node can change with time. is that right? 
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Update: I expanded my mesh in the outer region in the upstream direction and applied the following boundary conditions (see my attached figure for the labelling of my boundaries):
BC 1: Nozzle exit, all values are known and kept constant over time BC 2: pressure outlet BC 3: pressure outlet BC 4: pressure outlet BC 5: pressure outlet for nodes with subsonic speeds and simple extrapolation from the interior for supersonic nodes BC 6: symmetry BC 5 is the condition I'm most worried about. Since my simulation diverges something must be wrong. Can someone please tell me if this approach is appropriate, or what should I change? 
It seems you got confused a lot. Better try to solve this in softwares like fluent or cfx and understand what is happening before writing your own code.
This kind of BC2 and BC3 geometry is not much different from your old boundary. When you try to simulate a flow field try to match the geometry as close as possible. It seems you are not simulating the nozzle flow. If is just nozzle exit as one boundary, then problem is quite simple keep the boundary adjacent to nozzle exit (top one) as wall. Keeping pressure inlet and outlet at adjacent cells won't work. 
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5 = pressure outlet with the required static pressure 3 = pressure inlet with total pressure=static pressure = static pressure at 5 6 = axis 7 = do not specify any boundary other two boundaries should be pressure inlet and wall. 
subsonic to supersonic nozzle flow coding
hello everyone,
((subsonic to supersonic nozzle flow coding)) I want to write the nozzle length(x), area(a), density(r),velocity(v) and temperature(T) in non dimensional form (as the initial condition) in the MATLAB CODING.. please give me some hint to write these....... thanks in advance............ 
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