When we get the mass flow rate from different cross section in a flow field, they are different. Are they not mass conservation? How will you explain it?

must be same, when you do not have any sources/sinks. how did you obtain the mass flow rate?

There is no rule that says mass flow rate must be the same through any cross-section in the interior of the domain. The sum of mass flow rates must only be zero when taken from ALL domain BOUNDARIES.

you are absolutely right - it depends on the geometry! when you have a straight pipe with one inlet and one outlet the mass flow rate is equal in every cross section. I just considered an too easy problem.

err...to be more precise, it depends on the flow field... imagine taken cross-sections parallel to and perpendicular to the streamlines.

Draw a control volume around any part of your simulation. Now if you take the sum of the mass flows through that control volume and add any sources/sinks, they must equal zero.

If the two planes you created cut through the entire flow (ie. there are only walls between them and no other inlet/outlets/passages) and there are no sources/sinks, the mass flow rates should be equal. If they are not, either your solution is not converged or your post-processor is introducing interpolation errors (if it uses ip mass flows, the results should be exact).

Although mass flows should equal across all boundary conditions, this is not sufficient a conservation criteria as the solver may be enforcing mass flow conservation at the boundary to accelerate convergence in the computational domain.

Regards, Robin

Even a pipe flow does not have equal mass flow in any section at one time-step or iteration if the flow is compressible and transient. You have to look for the time averaged values.

If the flow is compressible and transient, you will have to account for the accumulation of mass within the control volume, but mass is still conserved.

-Robin