## Cyclone Design Optimization

Cyclone design usually consists of choosing an accepted standard design or a manufacturer's proprietary model that meets cleanup requirements at a reasonable pressure drop. However, investigators have developed analytical procedures to optimize cyclone design, trading collection efficiency against pressure drop.

Leith and Mehta (1973) describe a procedure to find the dimensions of a cyclone with maximum efficiency for a given diameter, gas flow, and pressure drop. Dirgo and Leith (1985) developed an iterative procedure to improve cyclone design. While holding the cyclone diameter constant, their method alters one cyclone dimension and then searches for a second dimension to change to yield the greatest collection efficiency at the same pressure drop.

They selected the gas outlet diameter De as the primary dimension to vary. This variation changed the pressure drop. Then, they varied the inlet height a, inlet width b, and gas outlet duct length S, one at a time, to bring pressure drop back to the original value. They predicted the d50 for each new design from theory. The new design with the lowest d50 became the baseline for the next iteration. In the next iteration, they varied De again with the three other dimensions to find the second dimension change that most reduced d50. They continued iterations until the predicted reduction in d50 from one iteration to the next was less than one nanometer.

Ramachandran et al. (1991) used this approach with the efficiency theory of Iozia and Leith, Equations 5.16(8)-5.16(14), and the pressure drop theory of Dirgo, Equation 5.16(16), to develop optimization curves. These curves predict the minimum d50 and the dimension ratios of the optimized cyclone for a given pressure drop (see Figures 5.16.7 and 5.16.8).

To design a cyclone, the design engineer must obtain the inlet dust concentration and size distribution and other design criteria such as gas flow rate, temperature, and particle density, preferably by stack sampling. When a cyclone is designed for a plant to be constructed, stack testing is impossible, and the design must be based on data obtained from similar plants. Once the size distribution of the dust is known, the design engineer chooses a value of d50. For each size range, the engineer calculates the collection efficiency using Equation 5.16(13). The overall efficiency is calculated from the following equation:

Voverall

I fv

where fi is the fraction of particles in the ith size range. By trial and error, the engineer chooses a value of d50 to obtain the required overall efficiency. This d50 is located on the optimization curve (e.g., for H = 5D) of Figure 5.16.7, and the pressure drop corresponding to this d50 is found. Figure 5.16.8 gives the cyclone dimension ratios. The cyclone diameter is determined from the following equation:

PpzQz PpiQi

where D1, pp1, and Q1 are the cyclone diameter (0.254 m), particle density (1000 kg/m3), and flow (0.094 m3/sec) of the cyclone optimized in Figure 5.16.8; and pp2 and Q2 are the corresponding values for the system being designed. The following equation gives the design pressure drop:

QzDf2 QiD2

where AP1 is the pressure drop from Figure 5.16.7 corresponding to the chosen d50.

If the pressure drop AP2 is too high, then the design engineer should explore other options, such as choosing a taller cyclone as the starting point or reducing the flow through the cyclone by installing additional cyclones in parallel. These options, however, increase capital costs. The design engineer has to balance these various factors.