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Simulation of air bearings

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Old   July 4, 2016, 08:08
Default Simulation of air bearings
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Daniel
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Hi everyone ,

I'm totally new here and i also have no experience with openFoam and C++ but I want to simulate the pressure distribution in an air bearing with OpenFoam.

I already simulated the lubrication gap with rhoSimpleFoam. These results are congruent with results I got by solving the Reynolds Equation for thin film flows with a Finite difference method in octave. So far so good, but because of the very thin gap my mesh needs to be very big to avoide highAspectRatioCells. To bypass this problem, i want to make an own solver which solves the Reynolds Equation in 2D.

\frac{\partial }{\partial x}(\frac{ \rho h^3}{12\mu}\frac{\partial p}{\partial x})+\frac{\partial }{\partial y}(\frac{ \rho h^3}{12\mu}\frac{\partial p}{\partial y})= u\frac{\partial \rho h}{\partial x}

h = Gap height

I tried to write it based on laplacianFoam. I think i declared all Fields correct
but I'm not sure how to discretize the Equation.

Here is what i have until now. ( Tried to do it incompressible first)

Code:
 
solve 
 (fvm::laplacian(pow(h,3) / (12 * nu) ,p)
      - Um&fvm::grad(h)
  );
Would be great if anyone could help me

Thanks,

Daniel

Last edited by evelknevel; July 4, 2016 at 11:58.
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Old   July 5, 2016, 09:19
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Daniel
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Hey guys,
I'm really desperate!
Can nobody can help me to discretize this PDE in OpenFoam?
I already read a lot about it, but all the other cases were quite different.

Greetings,

Daniel
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Old   July 8, 2016, 04:51
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Daniel
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Hi,
finally i got something that is compiling at least.
Code:
 
(...)    
    simpleControl simple(mesh);
    #include "createFields.H"
    // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
    Info<< "\nCalculating pressure distribution\n" << endl;
    while (simple.loop())
    {
        Info<< "Time = " << runTime.timeName() << nl << endl;
        while (simple.correctNonOrthogonal())
        {
   surfaceScalarField hls("hls", fvc::interpolate(hl) & mesh.Sf());
        solve (fvm::laplacian( h/ (12 * nu) ,p) == u*fvc::div(hls) );
        }
        #include "write.H"
        Info<< "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
            << "  ClockTime = " << runTime.elapsedClockTime() << " s"
            << nl << endl;
    }
    Info<< "End\n" << endl;
    return 0;
}
hl is a volVectorField I defined. hl = [ h 0 0 ]. And h is a volScalarField of the gap height.
My Case is diverging but the solution looks a little bit like i was hoping for.

Anyone got a Idea if I'm on the right way or is this just plain wrong ?

Many thanks,

Daniel
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