## OpenFOAM: STEADY STATE AIR FLOW THROUGH A SUGAR BEET CLAMP. UPDATE

THIS POST IS AN UPDATE ON A PREVIOUS POST IN WHICH THE WRONG KINEMATIC VISCOSITY WAS APPLIED IN THE SIMULATION.

In 2003, Lope G. Tabil and three co-authors decided that they would make my 2021 life much much easier by publishing the paper Airflow Resistance of Sugarbeet. This paper reports some very useful values for the fluid dynamic properties of piles of sugar beets. I’m not sure where they saw their work going, but my feeling is that a model such as mine was probably within their realms of imagination. So, thank you Prof. Tabil and friends.

From their work, it is possible to derive accurate estimates for the Darcy (D) and the Forchheimer (F) coefficients. For one of the experimental conditions they ran, I came up with values of around 100 000 and 370, respectively. Using a 5 m/s inlet velocity (from left), a mesh of around 15000 cells, and a clamp of 9m width at the base and 3m high, the results from a steady state simulation shown below were found. The results are stable after around 250 iterations, but the results after 1000 iterations are shown. The only difference in the images is the scale on which the results are divided.

Compared to the old, wrong, simulation, the rates of air flow are much higher, but the pattern is very similar. The much higher rates of air flow can be summarised as about half the clamp has an air speed of above 0.15m/s, and about half is below this. These values seem reasonable in light of some other systems. A “pile of stones from a mine” example has a similar ambient air velocity around a much larger and less porous pile and gets velocity values of a maximum 0.001m/s. An example of large (ca. 1/4 tonne?) bins of apples in a store room found air flow rates around 0.02 to 0.2m/s in the middle of the bins when the air velocity around the bins was between 0.8 and 1.4m/s. The variation came with the height of the bin in the store room.

**REFERENCES**:

Amos, R. T., et al. (2009). “Measurement of Wind-Induced Pressure Gradients in a Waste Rock Pile.” Vadose Zone Journal 8(4): 953-962.

Praeger, U., et al. (2020). “Airflow distribution in an apple storage room.” Journal of Food Engineering 269.

Tabil, L. G., et al. (2003). “Thermal Properties of Sugarbeet Roots.” Journal of Sugar Beet Research 40: 209-228.