Date of Award

Fall 2011

Document Type


Degree Name

Doctor of Philosophy in Chemical Engineering - (Ph.D.)


Chemical, Biological and Pharmaceutical Engineering

First Advisor

Piero M. Armenante

Second Advisor

Costas G. Gogos

Third Advisor

Basil Baltzis

Fourth Advisor

Norman W. Loney

Fifth Advisor

Maziar Kakhi


In many industrial applications, mixing vessels have a liquid height-to-tank diameter ratio, H/T, equal to, or larger than 1. However, there are many instances where this ratio is lower than 1, as in all those cases in which the vessel is either emptied or filled. Even when H/T<1, sufficient agitation must still be provided in order to attain the desired process objectives. When the impeller submergence is reduced as a result of lowering the liquid level, the fluid dynamics of even a single-phase stirred liquid can become quite complex, with different regimes possibly existing depending on the geometric characteristics of the system (such as impeller clearance, liquid height, or liquid submergence above the impeller). The objectives of this work were to study in detail the hydrodynamic changes that occur when H/T is decreased, and to determine the minimum liquid levels and the critical impeller submergence for different impeller off-bottom distances, impeller diameters and agitation speeds where adequate mixing process can still be achieved, both in a single liquid phase and in solid-liquid suspensions.

Flat-bottomed, baffled vessels (5L, 12L, 20L and 170L) equipped with a single disk turbine (DT) of four different sizes placed at five different impeller off-bottom clearances were used here to study the system's hydrodynamics and related mixing phenomena. A number of experimental tools were used to analyze the systems under investigation, including: Particle Image Velocimetry (PIV) for the experimental determination of the velocity profiles, and after the appropriate data manipulation, the impeller pumping capacity and its Pumping Number; a colorimetric system coupled with image processing to quantify mixing time; a strain gage-based rotary torque transducer system to measure the power dissipated by the impeller; and a visual observation method to determine the minimum agitation speed for complete solids suspension, Njs. In addition, Computational Fluid Dynamics (CFD) modeling was used to predict the behavior of the system in terms of its velocity profile, Power Number, Pumping Number, and mixing time. CFD predictions were obtained using a multiple reference frame (MRF) model coupled, when needed, with a Volume of Fluid (VOF) model, in order to study systems in which a vortex could be expected to form.

In general, good agreements between the experimental data and the predicted results for the velocities distribution, Power Number, radial Pumping Number, mixing time, and Njs were obtained. Results show that there is a critical impeller submergence ratio Sb/D below which: (1) the macroscopic flow pattern generated by the impeller changes substantially, transitioning from either a "double-loop" recirculation flow or a "single-loop" recirculation flow (depending on the impeller clearance off the tank bottom) to an upward "single-loop" recirculation flow; (2) the Power Number and radial Pumping Number drop significantly; (3) solid suspension cannot be attained at any agitation speed; (4) mixing time increases suddenly; (5) vortex formation occurs, air entrainment is significantly facilitated, and impeller flooding typically results. This is the first time that such hydrodynamic regime change has been reported and characterized. When this flow regime transition occurred, it was observed that the average velocity field and turbulence intensity close to the tank bottom decreased substantially; this was identified as the reason why solid suspension became unachievable. Furthermore, the critical impeller submergence ratio resulting in the establishment of the newly described flow regime was not affected by dynamic variables such as agitation speed. Impeller flooding was observed only when the new regime was established and when the vortex depth reached the impeller disk. This phenomenon was correlated to critical values of the Froude number. Additionally, by decreasing the impeller off-bottom clearances the operating window within which the stirred vessels could be operated effectively became wider. However, for low impeller off-bottom clearances (Cb/T<0.05) and low impeller submergence ratios (Sb/D<0.37, corresponding to H/T<0.16) even the lower recirculation loop was suppressed (tank bottom effect) and an unstable flow system was observed with no clear recirculation, implying that effective mixing could not achieved.

The results from this work show that mechanically stirred vessels can be effectively operated only within certain ranges of the operating variables without compromising their mixing effectiveness. These operating ranges were quantified. It is expected that this knowledge will help practitioners avoid operating their equipment in regions where the desired mixing effects are not achievable. Furthermore, in this work, the establishment of a previously unreported hydrodynamic regime at critical impeller submergences was described. This regime is not only associated with reducing mixing effectiveness, but can also explain why phenomena such as air entrainment and loss in impeller pumping capacity occur at low H/T ratios.