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Old   June 15, 2005, 11:04
Default Numerical Method
  #1
Andrew Hayes
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I have been working on a simple numerical program to calculate the velocity profile between two plates. I assume the initial Pressure, the exit Pressure=0, plate length,x, and distance between plates,h. I can then calculate an inlet velocity. If I solve the implicit finite difference model in steady state form I get a typical parabolic velocity profile. And, when I average the output velocities I get a velocity very close to the inlet velocity - some error due to small grid size. But, when I move to the time dependent model I cannot get the velocities to average to the inlet velocity any more. I do, however, get the velocity profile shapes (square in the beginning to parabolic). When I evaluate the dP/dx term in the NV equation I simply calculate the deltaP for the whole pipe and then multiply it by the distance at which the velocity profile is being evaluated [(P/x)*dx], then I divide that by the distance, dx. That worked with the steady state model, but doesn't work with the time dependent model.

Any suggestions would be very helpful.

thanks
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Old   June 15, 2005, 15:09
Default Re: Numerical Method
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Andrew Hayes
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NV should be NS..navier-stokes..sorry
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Old   June 16, 2005, 15:52
Default Re: Numerical Method
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Mani
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Provide some details on how you made your model time dependent. The flow itself is still supposed to be steady, since you use steady boundary conditions, correct?
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Old   June 17, 2005, 09:30
Default Re: Numerical Method
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Andrew Hayes
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it is developing flow between 2 plates, 1-d, no-slip boundary condition at the wall. I know the inlet Pressure, P, the length of the plates, x, and the distance between them, h. So, if I were to define a time-step and look at the velocity profile at the first time step it should be square in form, which I get. Then, as the time increases it becomes more parabolic. I get that too. But, I am under the impression that if I average the velocities at all the grid points at a certain time step I should come up with my Vin, which I don't get.

my equation: (standard Navier-Stokes equation)

(dUx/dt) = -(1/rho)(dP/dx) + nu(d^2Ux/dy^2)
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Old   June 17, 2005, 10:03
Default Re: Numerical Method
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Jim_Park
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The advection terms are negligible at steady state, as is the second of the momentum equations. I'd think that, during a startup transient, a lot of things are happening in the entrance region of the flow regime that are not 1-d.

In that case, the terms missing from your equation could screw things up during the startup. Put another way, you'll get that Uinlet = avg(Ux) when dUx/dt = 0 everywhere. Perhaps not before.

If you haven't done so, run your simulation out to convergence and see if that solves your problem.
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Old   June 17, 2005, 10:17
Default Re: Numerical Method
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Andrew Hayes
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I have run it at steady state (dUx/dt = 0) and have gotten the parabolic profile, and when I sum the velocities at each grid point I get the Vin. That was my only question; about the velocities at each grid point at each time step averaging to the Vin. The profiles look as the should, but the velocities do not average.

thanks
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