Let us consider the case where we have a grille with
the geometry shown in figure 1, and we want to represent this as a planar
resistance in a system level Flotherm model.
Figure 1 Grille Arrangement and Detail Showing the Dimensions
The first thing we have to do is determine
the pressure drop versus velocity profile for the detailed grille. To
do this we use Flotherm as a computational wind tunnel; we build a two
dimensional model of a representative section of the grille. The representative
section we can use is shown in figure 1, indicated by the dashed lines.
The Flotherm model and the grid used is shown in figure 2. The model is
completed by ensuring that both of the y domain boundaries are set to
symmetry, and both of the x domain boundaries are set to open. A Fixed
Flow Device is used to set the approach velocity to the grille. By creating
a two-dimensional model we can use a fine grid and perform a number of
runs giving us a series of pressure drop versus velocity points.
Figure 2 Flotherm Model
of the Grille Detailed
The results from the analysis are then entered
into a spreadsheet and a curve fitted to the data. I used Microsoft Excel,
fitting a second order polynomial trendline, and fixing the intercept
to zero. This data is shown in Figure 3.
Figure 3 Results from
the 2D Analysis of the Detailed Model of the Grille
We need to equate the equation of the trendline
to the equation we arrived at for the Advanced Resistance model. Recall
that this equation was:
If we set a equal
to zero we get a second order polynomial for velocity:
We can now equate the coefficients in this
equation with those in the curve fitted trendline; e.g.:
m = 1.84e-5 Nsm-2
r = 1.1614 kgm-3
l is arbitrary so we can set this to 1m, this gives:
a = 645130 and b = 90.33
These values can now be put into the advanced
resistance model, the dialog settings are shown in figure 4.
Figure 4. Advanced Resistance
Before we use these settings in out model
we should run the resistance model in the same wind tunnel as we ran the
detailed model. This was done and the results are shown in table 1.
Table 1 Comparison of
Pressure Drop Through both the
Detailed and Advanced Resistance Models
As we can see the comparison is good and
we can now use this advanced resistance formula in our system level simulation
with the confidence that it is valid for the full velocity range.