Calculations regarding a dust separation cyclone In an industrial fermentation system the fermentation broth is spray dried in order to recover the remaining yeast and residual biomass particles for feed. Due to the small size of the yeast and biomass, a lot of dust is formed in the ventilation system of the spray dryer. The engineers want to assess if an existing cyclone will be able to remove the two different dust particles from the air stream. The cyclone design is of the same geometry as shown in Figure 2 attached and described in Figure 7.22 (Kemiske enhedsoperationer: K. H. Clement, page 272). The B value according to Eq 7.35 for this cyclone is 0.27. The existing cyclone has a diameter (Dc) of 1 m. The total air flow out of the ventilation system is 2500 m3/h. The air has a density of 1.25 kg/m3 and a viscosity of 1.810-5 Pa.s. Both types of particles, yeast and residual biomass, are spherical and following characteristics are known:

a) At the given conditions, what will the removal efficiency of the cyclone be for each type of dust particle?

b) The removal of the larger particles is satisfactory. However, the removal efficiency of the yeast particles is too low for the requirements of the company. There is the option of increasing the air flow in the ventilation system and hence to the cyclone. One of the engineers suggest to do this in order to increase the removal efficiency of yeast in the cyclone. What air flow is required to remove 40% of the yeast particles?

c) It turns out that the ventilation system cannot provide the required air flow found in part b). The engineers decide to design a new cyclone with the same characteristic geometry as in part a) but with a different diameter (Dc). Using the original flow rate of 2500 m3/kg and a desired removal efficiency of 40%, what diameter cyclone is required?

\begin{tabular}{|l|l|l|} \hline & Yeast & Residual Biomass \\ \hline Particle size & 5m & 25m \\ \hline Particle density & 1100kg/m3 & 1220kg/m3 \\ \hline \end{tabular}