Overview of field conservation on mixing plane interfaces
Mixing plane interfaces (MPI) are a great way to model turbo machinery and general rotating machinery in steady state.
One the one hand, the averaging allows for the mitigation of clocking effects.
This means, that even though the rotor is not moving, the wake effects are mixed out over the circumference, which results in a more realistic downstream flow.
On the other hand, the MPI enables you to model only segments of your blade section against a different pitch of the next stage and therefore save cells.
If a direct internal interface had to be used, the segment of each row would need to fit the same angle, which results in modeling multiple blades per row.
Now both of these aspects require the same approximation;
An indirect connection of both regions, which averages all incoming flow quantities (from both sides of the interface) circumferentially.
This is done by calculating a series of circumferential bins (see User Guide for details on this).
The bins used by the solver cannot be made visible directly;
however the user can have a look at the resulting association to the boundary cells at the interface by using the field function "Boundary Circumferential Bin Index".
Now, you might expect that the averaged field functions, incoming and outgoing, should also be visible on the MPI, like in this example of a 360° MPI of a radial compressor;
But it is not possible to view the averaged fields on the interface boundary directly, since this is not the correct flow solution, because the cells next to the interface and beyond yield a different field. It would therefore be wrong to visualize the averaged flow field bands on the interface.
(Note that; in previous versions up until 15.02 the averaged fields were displayed - as in the picture above, while beyond this version only the actual cell values are shown - like seen below.)
To follow this example, we actually see the solution from the flow region volume cells to be reflected on the interface boundary faces, which looks like this:
We see the incoming wakes from the rotor on the upstream side as well as the changing pressure profile due to non-symmetry on the volute side, while still seeing the averaging effect.
Apart from this visual effect, we can also observe some inconsistencies for transport quantities on one side of the interface to the other.
If you measure a transport quantity in an average report and calculate the error in percent between both sides of the MPI.
For the above mentioned radial compressor, calculated for Temperature, Mass Flow and Total Pressure it may look something like this
The plot shows that there is an average error of ~3% for Total Pressure at the entire MPI, until at 500 iterations the CCA is turned off at which point the error drops to ~ 0.3%.
Please note, that this example is deliberately extreme, as the mesh on the interface is coarse and the described error is particularly prominent if the bins have a large circumferential dimension, i.e. long, thin bins like this 360° mixing plane.
On your average segment model, this effect is rather negligible.
This is due to two reasons adding together;
First the already mentioned approximation on an indirect interface.
Due to the constraints it is not possible to have a fully conservative interface, on which all transport quantities are conserved 100%.
The implementation of the MPI in STAR-CCM+ is such, that it targets to conserve mass first to the detriment of momentum and energy.
Therefore, it can be observed that there is a tiny error margin between integral values from one side of the MPI to the other.
Secondly, the solvers pressure correction step of Segregated Solver and Coupled Solver with CCA is carried out after solving the convective terms.
This enhances any discrepancy in the cell values of the pressure field between boundary-0 and boundary-1 of the MPI.
This means, that the solvers pressure correction step tries to ensure mass conservation on cost of pressure conservation.
So, how to counteract the effect described above?
If non-conserved quantities are a concern in your simulation, you want to follow through with;