I am running a simple laminar pipe flow problem in CFX-5.7. I put in a
developed parabolic velocity profile at the inlet to the pipe. I have using an additional variable
to model a diffusive scalar.
My boundary condition for the additional variable at the inlet is 1 (uniform). My boundary condition for the additional
variable at the outer pipe wall is zero.
I would expect that the flux of additional variable into the wall (or the corresponding normal flux), would decrease
down the length of the pipe as would the value of the additional variable.
I observe the following behavior:
1. For high diffusivities of the additional variable, the behavior is as expected.
The normal flux of the additional variable at the wall decreases continuously with pipe length.
2. For low diffusivities, however, I see a initial region where the normal flux increases with pipe length
before it reaches a maximum value and decreases thereafter. If I look at the conservative value
of the additional variable at the pipe wall, I see that it has a high value initially before decreasing to
zero. The hybrid values of the additional variable at the wall are always zero. The region of non-
zeroconservative additional variable wall values corresponds to the region where the normal flux
increases with pipe length.
The behavior described is caused by an inconsistency between the additional variable boundary
conditions at the wall and at the inlet.
At the inlet, you have set a boundary condition for the additional variables of 1.
At the wall, you have set an additional variable boundary condition of 0.
The inlet boundary touches the wall boundary which means there is a conflict at the nodes which lie on the
inlet-wall intersection which CFX-5 resolves by assuming the inlet value overrides the wall value.
This puts a clump of additional variable at the wall. For higher diffusivities, this clump diffuses radially
quickly and you don't see its effect.
For low diffusivities in laminar flow, the transport equation for the additional variable becomes
almost hyperbolic or wavelike, and that initial clump of material next to the wall persists farther
down the wall. This causes the near wall value of the additional variable to be non-zero which
reduces the gradient and the normal flux. This causes the pattern that you see where as the diffusivity
of the additional variable decreases, there is a progressively longer region where the normal flux increases
before reaching a maximum and then decreasing therafter.
One way to reduce the effect would be to use a step function so that your inlet condition
for the additional variable goes to zero at the wall. It can still be 1 at the last non-wall node at the
inlet but should be zero at the wall node.
A problem set up in this manner shows the expected behavior: i.e., the additional variable normal fluxes
at the wall decrease continuously with increasing length down the pipe.