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Explanation of the Advanced Resistance Model in Flotherm Version 2



Worked Example

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.:

and

We know:
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 Dialog Settings

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.