Agitated vessels flow number

This chapter reviews the various types of impellers, die flow patterns generated by diese agitators, correlation of die dimensionless parameters (i.e., Reynolds number, Froude number, and Power number), scale-up of mixers, heat transfer coefficients of jacketed agitated vessels, and die time required for heating or cooling diese vessels. 

Power is defined for a well-agitated vessel with a mechanical stirrer then read power number for turbulent flow from Figure 6.6, Chapter 6 ... 

Fig. 13. Spatial distributions of bubble size in three vessels agitated by different impellers a classical Rushton turbine (DT), a hydrofoil impeller (A315) manufactured by Lightnin, and a Pitched Blade Impeller (PBT). The gas flow numbers in these simulations are in the range 0.01-0.02. These simulation results have been obtained by using GHOST Reproduced with permission from Bakker (1992).

A criterion for the prediction of minimum stirrer rotation speeds for the suspension of coarse-grain particles (Archimedes number > 40) is derived by Molerus and Latzel (1987). They showed that the minimum stirrer rotation speeds can be predicted by the evaluation of two diagrams the drag of fluidized particles as a function of concentration, and the pressure-head volumetric flow-rate characteristics of the agitated vessel. The latter can be obtained using the similarity of fluid-kinetic machines and can be expressed as lAav = /([Pg.48]

Another important design parameter for miscible liquids is the power consumption, which can be obtained from Fig. 24. For viscous liquids, flow is in most part laminar. When the agitated vessels contain baffles, turbulence is achieved at a lower Reynolds number. Once the flow becomes turbulent, the power number attains a constant value. 

For an open system, the homogenization can only be achieved if the pumping capacity of the stirrer is greater than the liquid flow rate through the vessel. This pumping capacity expressed in a dimensionless form Q = q /Nd3 is a function of the Reynolds number and the vessel geometrical parameters (d-f/dy) and HJdt. In turbulent flow (Re > 103), Q is independent of the Reynolds number. The nature of the relationship also depends upon the nature of the stirrer and the agitated vessel. 

Gas flow has little effect on heat transfer in a mechanically agitated vessel containing power-law fluid. While for turbine stirrers the heat-transfer coefficient for a power-law fluid can be obtained from Eq. (7.7), a more generalized form Nu = a[Re /(m)]2/3 Pr1/3 should be preferred. Here the expression given by Metzner and Otto (1957) for Re /(m) should be used and the viscosity in Prandtl number must be the constant viscosity value at high shear rates. 

The power dissipated by an impeller rotating in a homogenous, single-phase liquid in a baffled vessel is a function of the type of impeller, the flow regime in which the impeller operates (laminar vs. turbulent), which is, in turn, a function of the impeller Reynolds number. Re = plAD /p, and a number of geometric ratios. For an agitated vessel, the impeller power dissipation, P, and the power dissipation per unit liquid mass, , can be calculated, respectively, from ... 

For axial-flow impellers such as pitched-blade turbines or marine propellers, q is the discharge rate in a vertical direction as measured immediately below the impeller. The flow number Nq may be considered constant. For the design of baffled agitated vessels the following values are recommended ... 

Indeed, judging from the modified Reynolds number, A/jt, which extends from 10 to 10 regarding the experimental condition for the data points in Fig. 8, the liquid flow in the agitated vessel (Fig. 1) is in a transient region between laminar and turbulent. 

The exact scale-up of crystallizers is not possible because it would be necessary to preserve similar flow characteristics of both liquid and solid phases together with identical temperatures and supersaturations in all equivalent regions. The scale-up of simple agitated vessels containing a liquid phase alone has long been recognized as a difficult problem. The two dimensionless numbers most frequently encountered in the analysis of stirrers and agitators are the Reynolds number, Re, and the Froude number, Fr ... 

The ungassed power number (Np ) represents the ratio of the pressure differences producing flow to the inertial forces of the liquid dispersion and it is analogous to a fiiction factor or drag coefficient. Np is usually based on the power input by the impeller for agitated vessels and takes the form ... 

An agitator acts like a centrifugal ptimp impeller without a casing and gives a flow at a certain pressure head. This circulation rate Q in m /s from the edge of the impeller is the flow rate perpendicular to the impeller discharge area. Fluid velocities have been measured in mixers and have been used to calculate the circulation rates. Data for baffled vessels have been correlated using the dimensionless flow number Nq (Ul). 

BTU/hr. sq.ft. over a wide range of viscosities and rotational speeds. This is equivalent to the thermal resistance of a fluid film equal to about 1/2 the clearance between the helical agitator and the vessel wall. This represents Reynolds numbers in the range of 10 to 10. This is the region of creeping flow where, with no inertial effects, there is little displacement of the fluid adjacent to the wall. 

The revolutions required for a volume of liquid equal to the vessel volume to pass under the agitator can be calculated from a knowledge of the geometry and the thickness of the layer passing under the agitator. This number would be misleading, however, since the fluid in this wall layer is displaced only slowly by the secondary (top-to-bottom) flow. 

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