Impellers diameter ratio

A survey of the published literature indicates that the ratio of the maximum to mean energy dissipation rate in the vessel, Smax/ m can vary substantially but typically in the range 10 to 100 [85]. Recent measurements [100] of the turbulent flow properties with a range of impellers and vessel configurations indicate that the differences between the reported ratios of Smax/Cm re partly due to differences in the geometrical variables. For example, detailed factorial designs of experiments showed significant effects of impeller diameter to tank diameter ratio and off-bottom clearance to impeller diameter ratio on the value of emax/Cm-... 

FIGURE 12.1 Values of turbulent power number Np for various impeller geometries. Note W/D is actual blade-width-to-impeller-diameter ratio. 

Air oxidation of sodium sulfite solutions, containing a trace of cupric ion as catalyst, was first studied by Cooper et al. (C7). These workers found the reaction rate to be essentially independent of sulfite and sulfate concentrations and therefore especially convenient for their study. Most of their runs were made using a vaned-disk agitator (a flat disk with sixteen radial vanes on its lower face) in baffled vessels 6-17 in. in diameter. Tank-to-impeller diameter ratio was 2.5, and the impeller was 0.3 tank diameter off the bottom, in every case. Impeller speeds were 60-900 r.p.m. A few measurements were made with a simple flat paddle, with a total length one-fourth the vessel diameter, in 9.5- and 96-in. diameter tanks. Air was introduced from a single open-end pipe just below the center of the agitator. Superficial air velocities were 0.3-11 ft./min. 

Two studies have been concerned with measurement of the interfacial area obtained by agitation of liquid-liquid systems. Each of these investigations relied on the use of a photoelectric probe which measured the light transmission of the two-phase dispersion. Vermeulen and co-workers (V2) made measurements in two geometrically similar, baffled vessels of 10- and 20-in. diameter. They used a very simple four-blade paddle-like stirrer, with a tank-to-impeller diameter ratio of about 1.5, and a 0.25 blade-width/impeller-diameter ratio. The impeller was located midway between the top and bottom of the vessel, which had a cover and was run full. Impeller speeds varied from about 100 to 400 r.p.m. A wide variety of liquids was employed. Volume fractions of dispersed phase varied from 10% to 40%. The mean droplet diameters observed ranged from 0.003 to 0.1 cm. The results were correlated with a mean deviation of about 20% by an empirical equation relating the specific interfacial area near the impeller to several system and operating variables as follows ... 

The recommended sparge ring to impeller diameter ratio is 0.65-0.8, while the ring sparger orifice diameter is in the range of 2-10 mm, and the gas velocity through the orifice is between 15 and 30m/sec. Pressure drop across a perforated disperser or orifice is estimated by the conventional orifice equation ... 

In a mixing tank, the flow (Q) to impeller head ratio (H) is related to the tank diameter to impeller diameter ratio according to the relationship... 

Select the appropriate heat transfer coefficient correlation. From Table 14-3 (for the standard helix pitch/impeller diameter ratio P/D = 5, the appropriate heat transfer correlation is... 

The pumping number is a function of impeller type, the impeller/tank diameter ratio (D/T), and mixing Reynolds number Re = pND /p.. Figure 3 shows the relationship (2) for a 45° pitched blade turbine (PBT). The total flow in a mixing tank is the sum of the impeller flow and flow entrained by the hquid jet. The entrainment depends on the mixer geometry and impeller diameter. For large-size impellers, enhancement of total flow by entrainment is lower (Fig. 4) compared with small impellers. 

The Oldshue-Rushton (Mixco) extractor is similar in construction to the RDC in the fact that it is a relativelv open design, consisting of a series of compartments separated by horizontal stator baffles. The major difference from the RDC is that the height/diameter ratio of the compartments is greater, each compartment is fitted with vertical baffles, and the mixing is accomplished by means of a turbine impeller rather than a disc. 

Top-Entering Impellers For vessels less than 1.8 m (6 ft) in diameter, a clamp- or flange-mounted, angular, off-center fluidfoil impeller with no baffles should be the initial choice for meeting a wide range of process requirements (Fig. 18-14). The vessel straight-side-height-to-diameter ratio should be 0.75 to 1.5, and the volume of stirred liqiiid should not exceed 4 m (about 1000 gal). 

Axial-Flow Fluidfoil Impellers For vessel volumes of 4 to 200 m (1000 to 50,000 gal), a turbine mixer mounted coaxiaUy within the vessel with four or more baffles should be the initial choice. Here also the vessel straight-side-height-to-diameter ratio should be 0.75 to 1.5. Four vertical baffles should be fastened perpendicularly to the vessel wall with a gap between baffle and wall equal to Df/24 and a radial baffle width equal to Df/12. 

A basic stirred tank design is shown in Fig. 23-30. Height to diameter ratio is H/D = 2 to 3. Heat transfer may be provided through a jacket or internal coils. Baffles prevent movement of the mass as a whole. A draft tube enhances vertical circulation. The vapor space is about 20 percent of the total volume. A hollow shaft and impeller increase gas circulation (as in Fig. 23-31). A splasher can be attached to the shaft at the hquid surface to improve entrainment of gas. A variety of impellers is in use. The pitched propeller moves the liquid axially, the flat blade moves it radially, and inclined blades move it both axially and radially. The anchor and some other designs are suited to viscous hquids. 

The larger the ratio of impeller diameter to tank diameter, the less mixer power required. Large, slow speed impellers require a low er horsepow er for a given pumping capacity, and solid suspension is governed by the circulation rate in the tank. 

Helieal serews operate in tlie laminar range at normally high impeller to vessel diameter ratio (D /D ) with a radial elearanee equal to 0.0375 D. The impeller usually oeeupies one-third to one-half of the vessel diameter. They funetion by pumping liquid from the bottom of a tank to the liquid surfaee. The liquid returns to the bottom of the... 

Hicks et al. [8] developed a correlation involving the Pumping number and impeller Reynolds number for several ratios of impeller diameter to tank diameter (D /D ) for pitched-blade turbines. From this coiTclation, Qp can be determined, and thus the bulk fluid velocity from the cross-sectional area of the tank. The procedure for determining the parameters is iterative because the impeller diameter and rotational speed N appear in both dimensionless parameters (i.e., Npe and Nq). 

Geometric similarity requires all corresponding dimensions of a new system to have the same ratio with a test model which has proven acceptable. These dimensions should include vessel diameter and liquid level, baffle width and number in vessel, impeller diameter, number of blades and width ratio. For example, a tank four times the diameter of the original model also requires a turbine ten times the diameter of the original turbine. 

To select a turbine, there must also be geometric similarities for the type of turbine, blade width, number of blades, impeller diameter, etc. From the geometric similarity determination of the turbine diameter, the mixer speed can be established to duplicate. The Scale Ratio R, ... 

Referring to Figure 5-41, read the new approximate horsepower per unit volume ratio for the exponent X and the impeller ratio, D2/D1, where D2 is the larger impeller diameter. Calculate ... 

Let us define the ratio of tank diameter to impeller diameter ... 

Also, the ratio of the height of the liquid level to impeller diameter is ... 

Similarly, that is true for the rotational speed of large tank, which is related to a small tank with the ratio of impeller diameter of large and small tanks to the power of 2/3. 

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