Mixing impellers Scale

Figure 5-18. Laminar flow mixing. For known impeller type, diameter, speed, and viscosity, this nomograph will give power consumption. Connect RPM and diameter, also viscosity and impeller scale. The intersection of these two separate lines with alpha and beta respectively is then connected to give horsepower on the HP scale. By permission, Quillen, C. S., Chem. Engr., June 1954, p. 177 [15].

Such spatial variations in, e.g., mixing rate, bubble size, drop size, or crystal size usually are the direct or indirect result of spatial variations in the turbulence parameters across the flow domain. Stirred vessels are notorious indeed, due to the wide spread in turbulence intensity as a result of the action of the revolving impeller. Scale-up is still an important issue in the field of mixing, for at least two good reasons first, usually it is not just a single nondimensional number that should be kept constant, and, secondly, average values for specific parameters such as the specific power input do not reflect the wide spread in turbulent conditions within the vessel and the nonlinear interactions between flow and process. Colenbrander (2000) reported experimental data on the steady drop size distributions of liquid-liquid dispersions in stirred vessels of different sizes and on the response of the drop size distribution to a sudden change in stirred speed. 

Solution If power scales as NjDj, then power per unit volume scales as NjDj. To maintain constant power per unit volume, IV/ must decrease upon scaleup. Specifically, Nj- must scale as DJ2 3. When impeller speed is scaled in this manner, the mixing time scales as D2J3and the impeller pumping rate scales as D7/3. To maintain a constant value for t, the throughput Q scales as Dj = S. Results for these and other design and operating variables are shown in Table 4.1. 

The mixing time scales as Sn the pumping capacity of the impellor scales as SnS and the power to the impeller scales as Sjj. As discussed in Section 1.5, it is impractical... 

The reactor time scale, T(reactor), which is the largest macro-mixing time scale, T(macro-mixing), and typically of the order of seconds, can be the mean residence time in the reactor, T(residence), but in a reactor equipped with an impeller, the recirculation time, T(recirculation), rather than the mean residence time, should be used. The recirculation time can be defined as the mean time between successive encounters of a given fluid element with the impeller. Typically Ty< T(recirculation) < T(residence). 

Example 13-2 Scale Effects on Mixing in Stared Vessels. Determine whether the fast reaction from Example 13-1 will be affected by mixing on scale-up if the feed point is close to the impeller. Compute the values of the Corrsin mixing time, tm, at the impeller tip and the blend time, Tb. for (a) 1 L and (b) 20 (XX) L vessels stirred by a disk turbine (Np = 6) at power per unit volume of 0.36 kW/m. Use properties of water p = 1000 kg/m v = 10 m /s Sc = 2000 for a typical solute. 

The recircnlation rate, Qr, determines the frequency of cells entering the PFR, F, from a given scale-down STR, Vstr and Vpfr are volumes of the STR and PFR, respectively, and tR is the residence time in the PFR. The residence time of a flnid element in the PFR is considered to be analogous to the time that it would spent in the acid or alkali addition zone in a production scale fermenter. The STR represents the well-mixed impeller region. 

Gbewonyo, K., D. DiMasi, and B. C. Buckland (1987). Characterization of oxygen transfer and power absorption of hydrofoil impellers in viscous mycelial fermentations, in Biotechnology Processes, Mixing and Scale up, C. S. Ho and J. J. Ulbrecht, eds., AIChE, New York, pp. 128-134. 

Weetman, R. J. (1994). Development of an erosion resistant mixing impeller for large scale solid suspension applications with CFD comparisons, presented at the 8th European Conference on Mixing, Cambridge. 

Dimensionless Numbers. With impeller diameter D as length scale and mixer speed N as time scale, common dimensionless numbers encountered in mixing depend on several controlling phenomena (Table 2). These quantities are useful in characterizing hydrodynamics in mixing tanks and when scaling up mixing systems. 

These mixers are particularly suited for rapid mixing of powders and granules with liquids, for dissolving resins or solids in liquids, or for removal of volatiles from pastes under vacuum. Scale-up is usually on the basis of maintaining constant peripheral velocity of the impeller. 

Other scale-up factors are shear, mixing time, Reynolds number, momentum, and the mixing provided by rising bubbles. Shear is maximum at the tip of the impeller and may be estimated from Eq. (24-5), where the subscripts s and I stand for small and large and Di is impeller diameter [R. Steel and W. D. Maxon, Biotechnm. Bioengn, 4, 231 (1962)]. 

Constant Reynolds number is not used for fermentation scale-up it is only one factor in the aeration task. This is also true for considering the impeller as a pump and attempting scale-up by constant momentum. As mechanical mixing tends to predominate over bubble effects in improving aeration, scale-up equations including bubble effec ts have had httle use. 

For non-New tonian fluids, viscosity data are very important. Every impeller has an average fluid shear rate related to speed. For example, foi a flat blade turbine impeller, the average impeller zone fluid shear rate is 11 times the operating speed. The most exact method to obtain the viscosity is by using a standard mixing tank and impeller as a viscosimeter. By measuring the pow er response on a small scale mixer, the viscosity at shear rates similar to that in the full scale unit is obtained. 

The commonly used types of mixing equipment can be placed in the broad categories (1) mechanical agitators, (2) inline motionless mixers, (3) tank jet mixers, and (4) miscellaneous. The nature and type of agitator used depends upon the scale and type of mixing and upon the fluids being mixed. The broad classes of impellers are ... 

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