Reynolds number impeller

For a given impeller and tank geometiy, the impeller Reynolds number determines the flow pattern in the tank ... 

Figure 6-40 shows power number vs. impeller Reynolds number for a typical configuration. The similarity to the friction factor vs. Reynolds number behavior for pipe flow is significant. In laminar flow, the power number is inversely proportional to Reynolds number, reflecting the dominance of viscous forces over inertial forces. In turbulent flow, where inertial forces dominate, the power number is nearly constant. 

Impeller Reynolds Number The presence or absence of turbulence in an impeller-stirred vessel can be correlated with an impeller Reynolds number defined... 

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). 

Heat Transfer In general, the fluid mechanics of the film on the mixer side of the heat transfer surface is a function of what happens at that surface rather than the fluid mechanics going on around the impeller zone. The impeller largely provides flow across and adjacent to the heat-transfer surface and that is the major consideration of the heat-transfer result obtained. Many of the correlations are in terms of traditional dimensionless groups in heat transfer, while the impeller performance is often expressed as the impeller Reynolds number. 

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. 

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. 

Figure 21. Discharge co cient for 45° pitched blade turbine V5. impeller Reynolds number.

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). 

The next step in the analysis is to calculate the impeller Reynolds number achieved during this original compounding using Equation (12). The impeller Reynolds number must be >2000 to proceed with analysis (3). 

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. 

Equation 13 is the empirical relationship obtained by the linear regression between D/T and terminal pumping numbers (4). It is important to note that a family of curves exists for each D/T ratio when Nq (pumping number) is plotted versus the impeller Reynolds number (5). In the turbulent range (iVRe > 2000), the Nq curves flatten out and thus are independent of the Reynolds number. 

Then the value of the impeller Reynolds number was obtained by plugging known values into Equation (5). 

Figure 1 Pumping number versus impeller Reynolds number for turbine and marine type propeller agitators.

Figure 10.7. Flow number as a function of impeller Reynolds number for a pitched blade turbine with AE = 1.37. D/T is the ratio of impeller and tank diameters. [Dickey, 1984, 12, 7 Chem. Eng., 102-110 26 Apr. 1976)].

The dimensionless group in the left-hand side of Eq. (9.53) is known as power number NP, which is the ratio of drag force on impeller to inertial force. The first term of the right-hand side of Eq. (9.53) is the impeller Reynolds number NRe. which is the ratio of inertial force to viscous force, and the second term is the Froude number NFr which takes into account gravity forces. The gravity force affects the power consumption due to the formation of the vortex in an agitating vessel. The vortex formation can be prevented by installing baffles. 

Figure 9.6 shows Power number-Reynolds number correlation in an agitator with four baffles (Rushton et al., 1950) for three different types of impellers. The power number decreases with an increase of the Reynolds number and reaches a constant value when the Reynolds number is larger than 10,000. At this point, the power number is independent of the Reynolds number. For the normal operating condition of gas-liquid contact, the Reynolds number is usually larger than 10,000. For example, for a 3-inch impeller with an agitation speed of 150 rpm, the impeller Reynolds number is 16,225 when the liquid is water. Therefore, Eq. (9.54) is simplified to... 

The complex flow field created by the impeller does not allow the direct calculation of shear rate (6,8). It is assumed that the dimensionless power number (pNo) is inversely proportional to the impeller Reynolds number (Re,) for Newtonian fluids in a laminar flow regime in which the RE, is <10 ... 

For the impeller ribbon viscometer technique, the power number of an impeller is inversely proportional to the impeller Reynolds number (Eq. 1). As the impeller rotational speed increases, the flow will gradually change from laminar to turbulent, passing through a transition region. Parameter c can be obtained from the calibration fluids. If the same value for c is assumed to apply to a non-Newtonian fluid, then Eq. 4 can be used to calculate the apparent viscosity of that fluid. The range of the impeller method is determined by the minimum and maximum torques that can be measured (5). 

He) impeller Reynolds number based on impeller diameter 4.11... 

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