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Wedge boundary condition and the math behind it???????

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Old   April 21, 2017, 13:10
Default Wedge boundary condition and the math behind it???????
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Khamlaj
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Hello All,

I have been trying to understand the math and assumptions behind the wedge boundary condition that is implemented in OpenFoam to simulate axisymmetric flow usually expressed in cylindrical coordinates. I understand that they are employed since the NS equations implemented in OpenFoam are in Cartesian coordinates. Is there good documentation why this trick works?

I have verified results obtained using the wedge BC versus a full 3D simulation of an axisymmetric CD nozzle and as hoped, I got pretty decent agreement at a much lower computational cost. Now I am interested in implementing volume forces (for an actuator disk model) but I cannot wrap my head around how I need to implement them to play nicely with the wedge boundary condition and an axisymmetric assumption. I know how to compute the Cartesian components of the forces so am I just going to implement those? I would appreciate any insight anyone may have.

Thanks in advance,
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Old   April 22, 2017, 08:23
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I'm probably less experienced than many others here, but I might be able to add some small comment to this statement/question. The 3D Navier-Stokes equations are derived in many college textbooks in Cartesian coordinates. Usually in that same area of the book, they will go further to derive them in cylindrical coordinates. A classic, well known book that I know for sure has them, is Schlichting's "Boundary Layer Theory." I cannot say exactly how OpenFOAM uses them in its source code to complete the computations, since I'm not that well versed on the deeper inner workings of the code. But in terms of understanding the math that defines cylindrical NS equations, check out a fluids book; many have the cylindrical system derived therein.
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