Impeller flow number

Chudacek, M.W. Impeller power numbers and impeller flow numbers in profiled bottom tanks. Ind. Eng. Chem. Des. Dev. 1985, 24, 858-867. 

Using the continuity relation (7.20), the radial component of the velocity can be expressed as a function of the impeller flow number ... 

Revill (1982) recommends an impeller flow number, FI, defined as Q/ND, of 0.75 for Rushton turbines in a fully turbulent system. Thus the impeller pumping capacity, Q, will increase with scale ... 

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. 

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. 

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 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. 

Note The respective impellers used are a classical Rushton turbine (DT), a hydrofoil impeller (A315) manufactured by Lightnin, and a Pitched Blade impeller (PBT). The cases 1 through 4 all relate to a superficial gas rate of 3.6mm/s only, with impeller speeds varying between 5 and 10/s (gas flow numbers between 0.01 and 0.02) cases 2 and 3 differ in sparger size and position. 

The vendor shall provide eomplete performance curves, ineluding differential head, typieal efficieney, water NPSHR, and power expressed as funetions of capacity. The curves shall be extended to at least 120 percent of capacity at peak efficiency, and the rated operating point shall be indicated. The head curve for maximum and minimum impeller diameters shall be ineluded. The eye area of the first-stage impeller and the impeller identification number shall be shown on the curves. If applieable, the curves shall indicate viscosity corrections. Minimum flow (both thermal and stable), preferred and allowable operating regions, and any limitations of operation shall be indicated. 

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 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). 

Maxflo T Wide-blade, high-efficiency impeller Blending, np and Nq varY with tjP an9le and Transitional flow, number of blades Simultaneous gas dispersion and solid suspension (like mining),... 

Determine the power number at process and operating conditions. Turbulence in agitation can be quantified with respect to another dimensionless variable, the impeller Reynolds number. Although the Reynolds number used in agitation is analogous to that used in pipe flow, the definition of impeller Reynolds number and the values associated with turbulent and laminar conditions are different from those in pipe flow. Impeller Reynolds number NRe is defined as... 

Compute the process-side heat-transfer coefficient. The correlations for inside (process-side) heat-transfer coefficient in an agitated tank are similar to those for heat transfer in pipe flow, except that the impeller Reynolds number and geometric factors associated with the tank and impeller are used and the coefficients and exponents are different. A typical correlation for the agitated heat-transfer Nusselt number (ANu = htT/k) of a jacketed tank is expressed as... 

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