Critical impeller speed

Critical speed the mixer shaft speed which matches the first lateral natural frequency of the shaft and impeller system. Excessive vibrations and shaft deflections are present at this speed. 

Much of the literature correlations for solids suspension are based on the so-called critical impeller speed. Attempts to duplicate experiments between various investigators often yield deviations of 30-50% from the critical speed shown by other investigators. Because power is proportional to speed cubed, power varies on the order of 2 to 3 times, which is not sufficiently accurate for industrial full-scale design. Therefore, many approximate, conservative estimates have been made in the literature as general guidelines for choosing mixers for solids suspension. Table IV is one such guideline for solid particles of a closely sized nature. 

The studies of Juvekar (1976) and Ramanarayanan and Sharma (1982) with a 0.2 m i.d. multistage contactor with d,/dx = 0.5 showed that both aL and kLaL are independent of superficial gas velocity above the critical speed of agitation, and they vary linearly with impeller speed. Both aL and kLaL were independent of the number of stages under otherwise identical conditions of dfdj, N, ug, and gas-liquid system. Thus, the results for a single stage are applicable to multistage systems. This conclusion needs to be verified for larger-diameter columns. 

The optimum stirrer, from the point of view of energy efficiency, is the one that requires the least power at the critical speed of rotation. In terms of a dimensionless relation, this can be expressed as the condition where Ne Fr3/jj is minimum. For a propeller stirrer with Ne = 0.50 and a turbine stirrer with Ne = 10.0, and with the values of b already given for the two stirrers, the propeller stirrer requires only 20% of the power needed by the turbine stirrer. Mixing Equipment Co, CA, has recently introduced a new impeller design that consists of a pitched blade turbine (three blades). At the tips of the... 

A typical formula for calculating the first natural frequency (critical speed) of an agitator shaft considers the shaft stiffness, the shaft length, the weights of impellers and shaft, and the rigidity of the shaft mounting ... 

Apart from its effect on critical speed, such an impeller will affect horsepower requirements. Furthermore, the speed change may require a new gear reducer. 

The critical-speed problem may in some cases be solved hand in hand with a common problem related to dynamic loads. One source of dynamic loads on an agitator shaft is the waves and vortices that occur when an impeller operates near the liquid surface, such as when a tank fills or empties. 

Adding stabilizer fins to the impeller blades will help reduce some of these loads. Such fins also permit the agitator to operate closer to critical speed, perhaps at 80 percent rather than 65 percent. 

Another alternative to avoid critical-speed problems is the use of a shorter shaft. Reducing the shaft length and impeller extensions by 10 in (0.25 m) reduces equivalent weight to... 

Pavlushenko et al. (P2) studied the suspension of screened fractions of sand and iron ore in a variety of liquids, with a 1-ft. diameter unbaffled vessel filled to a depth of one foot. Square-pitch three-blade propellers of 3-, 4-, and 5-in. diameter were used, and most of the observations were made with a 1 to 4 weight ratio of solids to liquid. Thief samples were taken at various levels in the vessel. In some cases, the contents did not become uniform at any impeller speed in other cases the contents became uniform at some impeller speed and remained so at higher speeds in a third type of behavior, the upper part of the vessel reached the over-all vessel average and then exceeded it as impeller speed was increased. Using the observations from the second and third types of behavior, a critical speed was defined as the lowest impeller speed at which the solids concentration at each level, or in the upper layers of the liquid, was equal to the over-all average solids concentration. This critical speed Nc in revolutions per second had the following relation to the operating variables ... 

Tank diameter (T) and acceleration of gravity (g) are in this equation as a result of dimensional analysis. Tank diameter was not varied during the experiments. The values for p and p. are those of the liquid medium. A series of tests with one solid showed that this correlation applied over a range of solid-to-liquid ratios of to J. The critical speed decreased with solids concentration below a weight ratio. A vortex was present during these experiments, and Eq. (42) did not apply if the vortex was deep enough to reach the impeller. 

Henry s constant for component x (kmol/m )/(N/m ) reaction rate constant for CO2 hydrolysis (m /kmol/s) gas-liquid mass transfer coefficient (1/s) solid-liquid mass transfer coefficient (m/s) term defined by Equation (CS10.13) (-) molecular weight of component i (kg/kmol) speed of rotation of impeller (rps) critical speed for complete dispersion (rps)... 

Critical speeds of agitator Critical impeller speed for solid suspension The speed shonld be adequate to keep the particles suspended. The critical speed for snspension in the presence of gas, Nj q, is calcnlated from the following correlation (Rewatkar and Joshi 1991d) ... 

Although the effect of the mass of the impeller is easy to take account of in air, little notice has been paid to m, , the associated added mass of liquor, which is the amount of liquid that effectively vibrates with the impeller, so increasing its inertia and reducing its natural frequency (and thus critical speed). The general subject of added mass is researched in, and applied to impellers in. The added mass of an impeller has been determined as a coefficient multiplied by the mass of liquid contained within a cylinder of diameter equal to the impeller diameter and of length equal to the projected blade width ... 

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