Speed, impeller tip

The velocity head JT in a pipe flow is related to Hquid velocity hy H = I Qc The Hquid velocity in a mixing tank is proportional to impeller tip speed 7zND. Therefore, JTin a mixing tank is proportional to The power consumed by a mixer can be obtained by multiplying and H and is given... 

An example of liquid/liquid mixing is emulsion polymerization, where droplet size can be the most important parameter influencing product quality. Particle size is determined by impeller tip speed. If coalescence is prevented and the system stability is satisfactory, this will determine the ultimate particle size. However, if the dispersion being produced in the mixer is used as an intermediate step to carry out a liquid/liquid extraction and the emulsion must be settled out again, a dynamic dispersion is produced. Maximum shear stress by the impeller then determines the average shear rate and the overall average particle size in the mixer. 

Intensities of agitation with impeller m baffled tanks are measured by power input, hp/1,000 gal, and impeller tip speeds ... 

Another design parameter is impeller tip speed as this relates to pressure differences by changing fluid velocities. Tip speed is defined previously. ... 

The first dimensionless group on the right is the Reynolds number, the second represents the ratio of the gas velocity to the impeller tip speed, the third is the Weber number, and the fourth is the Froude number. 

Mild agitation is obtained by circulating the liquid with an impeller at superficial velocities of 0.1-0.2 ft/sec, and intense agitation at 0.7-1. Oft/sec. Intensities of agitation with impellers in baffled tanks are measured by power input, HP/1000 gal, and impeller tip speeds ... 

Figure 15.5 Measured and simulated turbulent kinetic energies (normalized with the impeller tip speed) at the impeller plane in a stirred tank reactor (From [17]).

For the same bioreactor mentioned above (operating at an impeller tip speed of 1.4 ms ), Dunlop et al. [57] predicted maximum Reynolds stresses in the impeller region of 32.4 Nm. However, if the energy is assumed to be uniformly dissipated throughout the vessel contents, then Eq. (5) will yield lower values. As calculated, the Reynolds stresses involve a length scale and the stress experienced by a particular entity will depend on its size. 

Both Vermeulen et al. (V3) and Calderbank (C3) conclude that the mean particle size is a function of impeller tip speed, whereas Rodriguez et al. (R7) find it to be a function of power input per unit volume. Jackson (J1) explains this apparent discrepancy on the basis that the System of Rodriguez et at. (R7) was more coalescing in nature than the systems studied by the others (C3, V3). In a coalescing dispersion there is frequent circulation and redispersion which requires impeller power. It is further pointed out (Jl) that, although the tip speed determines the mean particle size leaving the impeller, the particle size will also depend on the frequency of circulation which is a function of power input. 

Scale the agitator speed to maintain the same impeller tip speed. Thus, for an impeller of diameter d ... 

L T ), and v is the kinematic viscosity ofthe hquid (L" T ). Ihe dimensionless groups include N/v) = Reynolds number (Re) d N /g) = Froude number (Fr) and (Q/N d = aeration number (Na), which is proportional to the ratio of the superficial gas velocity with respect to the tank cross section to the impeller tip speed. 

For an animal cell culture, satisfactory results were obtained with a pilot fermentor, 0.3 m in diameter, with a liquid height of 0.3 m (clear liquid), at a rotational impeller speed N of 1.0 s (impeller diameter 0.1 m) and an air rate (30 °C) of 0.02 m min. The density and viscosity of the broth are 1020kg rn and 0.002 Pa s, respectively. The value can be correlated by Equation 7.36b. When k a is used as the scale-up criterion, and the allowable impeller tip speed is 0.5 m s , estimate the maximum diameter of a geometrically similar stirred tank. 

Ni, and Si, which typically had concentrations of <0.1 g/L. The test conditions that were varied included reaction temperature, impeller tip speed during reaction and crystallization, stoichiometry, and length of reaction and crystallization periods. The test conditions were varied as listed below and were based on information in the literature (Megy and Propst 1978) ... 

Reaction Temperature Impeller Tip Speed Stoichiometry Reaction Time Crystallization Time NaF Addition... 

The results of the tests on Zr-bearing waste acid showed that acceptable Zr removal could be achieved at 90Z stoichiometry (0.83 g NaF/g Zr). Zirconium removal averaged 85Z except at low impeller tip speeds during solid dispersal and reaction when it... 

Based on the results of these tests, recommended operating conditions for Zr precipitation in the pilot plant system include reaction temperatures of 20 C or 60 C, impeller tip speeds of 320 cm/s during solid dispersal/reaction vising a high efficiency axial flow impeller, addition of 0.83 g NaF/g Zr in solution, and crystallization periods of 24 hours. A filter press will provide acceptable solid/llquid separation even during process upsets without use of a precoat. A diaphragm pump functioned well during these tests. 

Table 7.6 shows as many as 12 stages in a single case. These machines are rated at either 10K or 12K ft/stage. The higher value corresponds to about 850 ft/sec impeller tip speed which is near the limit for structural reasons. The limitation of head/stage depends on... 

Power input per unit volume and impeller tip speeds are often used measures of the intensity of stirring, assuming correct proportions of the vessel and proper baffling. Appropriate ranges... 

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