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# Accurate Boundary Condition Assignment for CFD Analysis  March 13, 2015 By: Hsin-Hua Tsuei

The governing equations for a CFD analysis are the Navier-Stokes equations, which describe how the velocity, pressure, temperature, and density of a moving fluid are related.  They require proper specification of boundary conditions  in order to properly determine the flowfield when performing a CFD analysis.  In other words, boundary conditions “tell” the flow how to behave in a system, providing bounding values that the flow should not exceed.  For example, in an internal flow system, if the inlet total pressure and outlet static pressure are specified, then the total pressure anywhere in the flow passage should be in between these two values, assuming no external work has been added to the system. And, in a conjugate heat transfer analysis, without the addition of a heat source or sink, the steady-state fluid temperature should lie in-between the specified boundary temperatures.  If the flowfield temperature is outside these bounds, the validity of the solution has to be examined.

In a CFD analysis, if a boundary condition is specified incorrectly, it is impossible to expect a correct answer in return.  Different sets of boundary conditions represent different flow results.  For example, let’s say the mass flow rate for a system is 1.0 kg/s and we are trying to compute the pressure drop.  If the mass flow is mistakenly specified with the incorrect units as 1.0 lb/s, then the calculated pressure drop will compare poorly with the design point.  There is no numerical secret or black magic that can correct boundary condition mistakes.

The other important piece is to specify an appropriate boundary condition for the analysis you’re working on.  For example, let’s look at the fuel-air mixing system shown above.  Ideally, we want to start the mixing analysis at station 1.  At this station, fuel and air enter the mixing chamber at separate locations, where we can specify their corresponding boundary conditions, such as flow rate with a uniform or parabolic velocity distribution, inlet pressure and temperature, species composition, etc. The analysis will then calculate how fuel and air are propagating through their inlet region, then mix later downstream.

If we want to start the mixing analysis at station 2, then we need to think about what happens at this location, and how to specify appropriate boundary conditions.  At station 2, fuel and air still remain in their separate paths, prior to the mixing chamber.  So, we know the annulus region is where air enters, while fuel injected from the internal tube.  This knowledge allows us to specify fuel and air species boundary conditions.  However, when air and fuel reach this station, they have already gone through a diffusion or turning process, which will lead to non-uniform, distorted pressure, temperature and velocity distributions for both fuel and air at this location. Thus, a uniform inlet boundary condition is no longer appropriate if we start the analysis at station 2.  Instead, we need to know these profiles at this station, either from test data or from an existing, similar inlet manifold, in order to properly specify boundary conditions at this location.

To complicate things further, if we’d like to start the analysis at station 3, then all the assumptions we made above are no longer valid.  At this location, the fuel and air have already gone through the mixing process to form a mixture prior to entering the downstream segment (perhaps a combustor). At this station, pressure, temperature, velocity, as well as species composition are all non-uniform. So, we need to know all of this information before we can assign a proper boundary condition at this station to start the analysis for the subsequent process.  If we use a uniform profile for any of the inlet conditions, then the fuel-air mixing condition is not properly represented for the analysis starting at station 3.  Incomplete mixing can lead to much lower temperature than measured data.

Therefore, for every CFD analysis, accurate boundary conditions paramount to the accuracy and outcome of the results.