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Bjorn B January 10, 2006 04:24

Outlet boundary conditions for unsteady flow
Hi all,

I'm currently constructing a C++ program that's supposed to simulate onedimensional pipe flow (turbulent) of liquid helium. I use a finite volume approach and follow the SIMPLE algorithm outlined in the book "Numerical heat transfer and fluid flow" by Patankar.

I think I've got the steady simulation to work. There I used the inlet temperature, inlet velocity and outlet pressure as boundary conditions (I was planning to use the inlet pressure instead but for some reason it didn't work, any ideas why not?). Quantities that was not specified at a boundary (for example outlet temperature & outlet velocity)I calculated by setting the gradient to zero.

Now, my question is about the case of unsteady flow. Can I still use the boundary conditions of zero gradient for non specified quantities? I've heard that this can cause problems when used at unsteady simulations. Can anyone suggest a better boundary condition?

Thanx in advance,

Bjorn Backman

TITAN Algorithms, Staff January 10, 2006 07:01

Re: Outlet boundary conditions for unsteady flow

The typical selection of boundary conditions for subsonic incompressible flow can lead to a variety of stability related issues. In general, a reasonable application is to apply a fixed Dirichlet P boundary at the outlet and a zero velocity Neumann gradient boundary, i.e. GRAD(V) * en = 0. The inlet is defined by a fixed velocity BC with a floating Neumann BC for pressure (pressure at the inlet adusts via the Neumann BC. The fixed outlet pressure boundary will tend to minimize pressure wave reflections (numerical) which are traversing the system. The continuative or Neumann velocity BC, while destablizing, will allow unsteady flows to be simulated.

The following model demonstrates this. I have created a simple example that demonstrates vortex sheading. The BCs do in fact support the unsteady flow.

See the example posted at the following link (top of page)

Kind Regards,


Bjorn B January 10, 2006 08:49

Re: Outlet boundary conditions for unsteady flow
OK, thanx a lot for your reply.

The flow is subsonic alright, but what I forgot to mention is that I simulate compressible flow NOT incompressible (since Helium is very much compressible). How does this affect the boundary conditions for unsteady simulation?

And in the case of steady state, do the boundary conditions I use (fixed inlet velocity & temperature, fixed outlet pressure + zero gradients elsewhere) go well together with compressible flow? I hope so since I have managed to find a steady solution that doesn't look too bad to me...

Thanx in advance,

Bjorn Backman

TITAN Algorithms, Staff January 11, 2006 06:42

Re: Outlet boundary conditions for unsteady flow

You should be able to apply the local density (evaluated from the EOS in your simulation) that resides next to the control surface you are creating the Neumann pressure boundary condition for.

Example: lower face of the flow field (fixed wall, no slip) has a GRAD(P).en defined by the following:

GRAD(P).en = rho(-GRAD V{V}.en + mu DELTA(V).en + g.en)

en = -ey

DELTA(V).en ~ GRAD^2(V).-ey = - GRAD^2(v) (3 space curvature)

g.en = -gy

-GRAD V{V}.en = 0 (advection term, zero becuase V=0 on wall)

Note that it is generally advisable to apply 3 point forward operators on the curvature terms DELTA(V) and higher order forward first order derivatives.

After you have solved for dP/dy at your control surface, the solver would then update P on the surface based on the first CV into the domain.

(Pi - P_CS) / dy/2 = dP/dy (from notation above)

As indicated, local fluid properties are maintained, just apply the local density (and viscosity values) in the adjoining control volume i.



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