Mixing impeller Reynolds number

Not only is the type of flow related to the impeller Reynolds number, but also such process performance characteristics as mixing time, impeller pumping rate, impeller power consumption, and heat- and mass-transfer coefficients can be correlated with this dimensionless group. 

Power consuiTmtion has also been measured and correlated with impeller Reynolds number. The velocity head for a mixing impeller can be calculated, then, from flow and power data, by Eq. (18-3) or Eq. (18-5). 

Impeller Reynolds number and equations for mixing power for particle suspensions are in Sec. 5. Dispersion of gasses into liquids is in Sec. 14. Usually, an increase in mechanical agitation is more effective than is an increase in aeration rate for improving mass transfer. 

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)]. 

Impeller Reynolds Number a dimensionless number used to characterize the flow regime of a mixing system and which is given by the relation Re = pNDV/r where p = fluid density, N = impeller rotational speed, D = impeller diameter, and /r = fluid viscosity. The flow is normally laminar for Re <10, and turbulent for Re >3000. 

Other seale-up faetors are mixing time, Reynolds number, and shear. Shear is maximum at the tip of the impeller and may be determined by Equation 11-101 [17] ... 

Mixing achieved in the initial research and development processing must be in turbulent range. If the impeller Reynolds number is <2000, then mixing in the pilot tank was either inadequate or represented some other special case such as moderately viscous fluids. In these situations, another D/T ratio curve must be used. 

For normal mixing, the Pfaudler agitation-index (y) number for this low-viscosity fluid is 2 ft2/s3. Most stirrers are designed for impeller Reynolds numbers of 1000 or greater. For the impeller specified, the power number tjfn is 0.6 at high Reynolds numbers [2]. 

Another more general scale-up criterion is that of impeller Reynolds number, DzNp/fi. This approach, strongly recommended by Rushton (R8), is based on the observation that in many mixing operations the performance of the system can be successfully described by relations like Eq. (44) or (45), involving the familiar Nusselt or Sherwood numbers and the impeller Reynolds number. For geometrically-similar systems and constant material properties, these relations reduce to the forms... 

It is of interest here to discuss ideas proposed by Rushton and Oldshue (R12), on how to interpret observations of the influence of impeller diameter. Many mixing systems operate in an impeller Reynolds number range such that the power input P is proportional to NBDS ... 

The dimensionless mixing-rate constant, km, in standard baffled tanks, is a function of impeller Reynolds number (Npe) and geometry. For Nrc > 10,000, km is only a function of geometry, independent of Nrc. km is related to N, D, and T as follows (Fassano et al., 1994) ... 

Power numbers for different impeller types depend upon the impeller Reynolds number. Representative relationships of Power number versus Reynolds number for several types of impellers are given in Fig. 15-54. For additional information on a variety of impellers, see Sec. 6 and Hemrajani and Tatterson, Chap. 6 in Handbook of Industrial Mixing, Science and Practice, Paul, Atiemo-Obeng, and Kresta, eds. (Wiley, 2004). 

In designing blending systems, it is important to establish whether conditions will be turbulent, transitional, or laminar. Turbulent mixing occurs at impeller Reynolds numbers greater than Kf. ... 

Equation (9.45) underestimates the area in mixing vessels operated at high impeller Reynolds numbers, because additional gas is drawn into the liquid by surface aeration. Combining Eqs. (9.40), (9.44), and (9.45) leads to the following dimensional equation for gas holdup ... 

Initially it was studied the effect of various factors on the total volume of the reactor.Results showed that the main factors influencing its value were linear mixing velocity and suspension physical properties These variables were classified in form of impeller Reynolds number of the slurry (Re ).Its effect upon the reactor volume is illustrated in Fig.. The experimental values in the figure are interconnected by dotted lines.They were found to be represented well by a correlation of the Darcy type ... 

In stirred-tank reactors, the possibility of regulating the agitation speed and the selection of various impeller types and diameters allow control over the degree of mixing of different fluids, which is quantified by the impeller Reynolds number Re = D Sp/f D, impeller diameter S, speed of agitation p, fluid... 

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 power number depends on impeller type and mixing Reynolds number. Figure 5 shows this relationship for six commonly used impellers. Similar plots for other impellers can be found in the Hterature. The functionality between and Re can be described as cc Re in laminar regime and depends on p. N in turbulent regime is constant and independent of ]1. 

There are three types of mixing flow patterns that are markedly different. The so-called axial-flow turbines (Fig. 18-3) actually give a flow coming off the impeller of approximately 45°, and therefore have a recirculation pattern coming back into the impeller at the hub region of the blades. This flow pattern exists to an approximate Reynolds number of 200 to 600 and then becomes radial as the Reynolds number decreases. Both the RlOO and A200 impellers normally require four baffles for an effective flow pattern. These baffles typically are V12 of the tank diameter and width. 

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