# Interesting Inlet Boundary Conditions April 10, 2015 By: Hsin-Hua Tsuei

Inlet boundaries are where flow enters a flow domain of interest in a CFD analysis. The inlet boundary condition usually describes the total amount of mass flow rate, total pressure and total temperature that the fluid carries.  If no additional flow source is added, the inlet total quantities are the highest level that these flowfield quantities can attain anywhere in the flow domain.  For example, if the inlet total pressure is 20 psi, then both static pressure and total pressure have to be less than 20 psi everywhere in the domain.  If there is a stagnation point in the domain, then the total pressure will be close, but not equal to 20 psi, given the fact the fluid will experience some loss in the system.  If the CFD result indicates that there are regions of pressure, static or total, greater than 20 psi, then the results may not be believable.  The model has to be checked carefully to identify if any potential error (mesh, BC, numerical settings, convergence, etc.) exists that might increase the pressure to more than 20 psi artificially. If there is mechanical work being added to the fluid, like flow through a compressor or a pump adding work through blade rotation, then both the total and static pressure can be greater than 20 psi.

When looking at the total inlet mass flow rate, we have to remember that it has to be conserved throughout the flow domain, because we are solving the continuity equation for mass conservation. Mass cannot be created or destroyed in the flow domain unless a mass source is present. Therefore, the conservation of mass is the first check of a CFD analysis.  If the total inlet mass flow rate is 1 kg/s, and the total exit mass flow turns out to be 0.8 kg/s with no mass injection or suction in the flow domain, then where and why did 20% of the mass flow disappear?  The results are not valid in this case because the most fundamental principal in fluid dynamics, conservation of mass, has not held true. The colorful plots, no matter how pretty they are, are misleading, and shouldn’t be used for any purpose. Thus, the total inlet mass flow rate serves as a basic check point for a CFD analysis. In general, the criteria used to check mass conservation is 1% or less, given the fact numerical dissipation often plays a role in mass conservation.  However, any CFD solver should be able to conserve the mass flow to a tighter tolerance, if the model is generated appropriately. If your CFD solver of choice has difficulty achieving this goal regardless the mesh resolution, numerical settings, convergence, etc., then it’s time to think hard about using this particular solver.  After all, not all solvers are created equal and not all color plots are meaningful.

In analyses with heat transfer and/or compressible flow, the total temperature at the inlet must be specified.  Similar to inlet total pressure, it is the highest level of temperature that should exist in the flow domain when no additional heat source is present. It’s another useful check to identify the solution accuracy.  For example, in systems that need to avoid a high temperature “hot spot”, like in many HVAC applications, we need to make sure that the total temperature will not exceed the inlet quantity.  Otherwise, the hot spots that show up in the results may be a consequence of modeling errors or an inadequate solver.

So, the inlet boundary conditions defined in a CFD analysis not only define how the flow enters the domain, but also serve several meaningful purposes for checking if the final outcome is valid or not.  I want to reiterate again – if the solver cannot achieve the fundamental requirements to conserve total inlet quantities of a CFD analysis, it’s time to bolt.