Vortex depth

Vortex Depth In an unbaffled vessel with an impeller rotating in the center, centrifugal force acting on the fluid raises the fluid level at the wall and lowers the level at the shaft. The depth and shape of such a vortex (Rieger, Ditl, and Novak, Chem. Eng. ScL, 34, 397 (1978)] depend on impeller and vessel dimensions as well as rotational speed. 

Since two geometrically similar tanks are considered, the ratio 8 = dS2/ds equals the ratio D2/D1 of the reactor diameters, and the vortex depths are in the same ratio if Re2 = Re 1 and Fr2 = Fr. It can be shown that, at constant v, these two conditions of dynamic similarity, respectively, yield the following scale-up prescriptions ... 

The vortex depth predictive methods included here are for (1) unbaffled vessels and (2) a 4BP impeller with lower half baffles. 

For any system the dimensionless vortex depth is a function of a Reynolds number (ratio of inertial to viscous forces) and the Froude number (ratio of inertial to gravity forces). Expressed mathematically. 

Vortex Depth in an Unbaffled Vessel with a 4BF Impeller... 

Let s design a 4BP impeller operating in an 80" diameter vessel with a batch depth of 80" to give a vortex depth that just reaches the impeller with lower half baffles. Let s try a 40" diameter 4BP impeller, 40" off the vessel bottom, operating at 100 rpm. 

Let s check the vortex depth in an unbaffled vessel operating at the same conditions. 

This indicates the reduction in vortex depth achievable using a partially-baffled vessel. 

Ws Weight of solid in a solid-liquid slurry, Ibm X Vortex depth from static liquid level to the bottom of the... 

In the case of more or less axially mounted stirrers in vessels without baffles, the liquid is set in rotation, and generates a liquid vortex. As long as the vortex is not so deep that gas can be entrained by the stirrer, the vortex depth has no influence either on the stirrer power or on the mixing process. Naturally, the power number Ne and the mixing number nO depend upon whether the stirred tank is provided with baffles or not (see Fig. 1.36 and 3.3). 

The vortex formation involves on the one hand a lowering of the liquid level, which is characterized by the vortex depth h on the stirrer shaft, and on the other hand a liquid level increase h" on the vessel wall, Fig. 1.21. The question concerning the relatively small liquid level increase h" at the vessel wall compared with the vortex depth h is irrelevant. 

The vortex depth h on the stirrer shaft depends, for a given stirrer type and for geometric installation conditions D/d, h/d) upon the stirrer diameter d, the stirrer speed n, the liquid height H above the stirrer at rest, the physical properties of the liquid (density p, kinematic viscosity v) and the acceleration due to gravity, g ... 

Zlokarnik [618] found in experiments in three differently sized vessels (D = 300 400 600 mm) the following process equations for the relative vortex depth h /d for the gate, turbine and propeller stirrer... 

The above expressions enable the determination of any vortex depths h. To determine the critical stirrer speed at which the vortex depth reaches the stirrer, h is set equal to H. In the case of slow stirrer speeds air is generally not entrained even for h = H. ... 

Markopoulos J., Kontogeorgaki E., Vortex depth in unbaffled single and multiple impeller agitated vessels, Chem. Eng. Technol. 18 (1995), p. 68-74... 

Rieger F., Ditl P., Novak V., Vortex depth in mixed unbaffled vessels, Chem. Eng. Sci. 34 (1979), p. 397-403... 

Vortex depth in nonbaffled agitated vessels has been investigated by Brennan (1976) and Rieger et al. (1979) both references present predictive methods. For... 

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