(165f) Experimental and Computational Studies of the Fluid Dynamic Behaviour of Liquid-Solid Mixtures in Agitated Vessels

Giovanni Meridiano, Weheliye Hashi Weheliye , Luca Mazzei, Panagiota Angeli

 Department of Chemical Engineering,
University College London, Torrington Pl, London WC1E 6BTA, UK

giovanni.merigiano.17@ucl.ac.uk; weheliye.weheliye.10@ucl.ac.uk; l.mazzei@ucl.ac.uk p.angeli@ucl.ac.uk, ,

Introduction

Mixing of solids in viscous liquids in
stirred vessels is a crucial step in many manufacturing processes; it is
regularly encountered in a wide range of industrial sectors like health-care, pharmaceuticals,
cement manufacturing and food processing. In many of these applications the
liquids have complex non–Newtonian behaviour (Paul, Atieno-Obeng and Kresta, 2004). In these industrial processes, obtaining a uniform
mixture is a difficult task, because there are no turbulent eddies to help
distribute the components.

The objective of this work is to understand and characterize the fluid
dynamics of uniform liquid-solid mixtures with both Newtonian and non–Newtonian liquid matrixes in stirred vessels.
For this purpose, we measured the power consumption and the velocity profiles
at different solid volume fractions and compared the results with those
obtained via Computational Fluid Dynamics (CFD) simulations.

Materials
and methods

The power required for stirring the suspensions as well as the internal
velocity fields obtained via Particle Image Velocimetry (PIV) were measured
experimentally at different solid volume fractions in a stirred vessel.

The measurements were carried out in a stirred tank specifically designed
to reproduce real industrial scale equipment. It consists of a transparent
cylindrical tank of internal diameter D_T= 50 mm equipped with two
baffles and a dual-blade impeller of diameter D = 37 mm. The height of the
fluid, H, in the tank was set equal to the tank diameter. The impeller was
located at the centre of the tank, 10 mm from the bottom, and was driven by a
variable speed motor that could operate in the range of 50–2000 rpm (IKA
Eurostar 20) (Fig. 1). As viscous Newtonian fluid, we employed a solution of
corn syrup and water, while, as non–Newtonian fluid, we opted for a solution of corn
syrup, water and xanthan gum. The solid in both cases is PMMA microspheres (32–37
µm).

Figure 1: Experimental
setup for the measurement of power consumption in the vessel

.

Power consumption measurements

A precise way to measure power consumption is to use an air bearing
system. A schematic of the air bearing system used in this work is shown in
Fig. 1. From the force that is required to stop the rotation of the rotational table
the power required to agitate the fluid can be calculated as follows:

where M_Idenotes the axial torque applied to the fluid
by the impeller and N is the impeller angular speed in rotations per
unit time. We recorded this force with a load cell (Omega LCM601-1) and a data
acquisition system and software (OmegaIN-USBH).

PIV measurements

Velocity field measurements were carried out
using Particle Image Velocimetry. For these experiments, we used the same
transparent tank used for the torque measurements, but in this case, the tank was
enclosed in a square transparent box. This box was made of acrylic and filled
with a refractive index matching fluid to avoid optical distortions on
the surface of the cylindrical vessel. The PIV set-up
includes a dual cavity Nd:Yag green laser (532 nm) (Litron Laser®, 15 Hz, 1200
mJ) and a straddling CCD camera with 1280 x 1024 pixels (TSI PowerView™ Plus) that
operates at a maximum frequency of 15 frames per second. The camera is equipped
with an AF Nikkor 50mm f/1.8D prime lens (Nikon®). A hall switch sensor was
used to capture images at the same phase angle. As tracers we used fluorescent
polymer particles (melamine resin based) coated with rhodamine B (20μm),
which absorb at 532 nm and emit at 610 nm. They are neutrally buoyant in the
fluids considered and, at the experimental conditions explored; their
relaxation time is negligible compared to the convection time. The laser and
the camera were synchronized by means of a Laser Pulse Synchroniser (Model
610035 TSI) and were controlled via the Insight 4G (TSI) software. The laser
beam passed through a collimator (Model 610026 TSI) and two cylindrical lenses
(25 mm, and 15 mm) to create a narrow plane of 1 mm thickness. The laser plane was
then reflected on a 45º silver coated mirror and entered the stirred vessel
from the bottom. A sketch of the setup is shown in Figure 2.

Figure 2: Sketch of the
main components of the experimental set-up for the PIV measurements

Computational fluid dynamics simulations

Computational Fluid Dynamics is a powerful tool that yields relevant
process information that can be used to design and assess the performance of
stirred vessels. A number of researchers have used CFD to study the behaviour
of different types of liquid-solid systems in mechanically stirred tanks with
different types of impellers (Blais et al., 2016) (Konz and Windhab, 2016) (Fradette et al., 2007). All the previous studies highlighted the importance of validating the CFD models against experimental data.

The model employed in this study follows a Eulerian–Eulerian approach.
This means that the transport equations are written in term of volume–averaged
quantities. For the mixture stress closure an experimental constitutive
equation is implemented that correlates the suspension viscosity to the solid
volume fraction. Therefore, the first step of our work focussed on the rheological
characterization of the two suspensions mentioned in Section 2 and on the
development of suitable rheological constitutive equations for the CFD model.

We compared the CFD findings against the
power measurements in the stirred vessels and the velocity fields for different
impeller speeds and solid loadings.

Preliminary
Results

We characterized the rheology of the Newtonian fluid–particles
system, at different solid volume fractions, using a HR-3 Discovery Hybrid
Rheometer (TA Instruments®). Some results are
shown in Fig.3.

Figure 3: Evolution of
viscosity with solid volume fraction F

As expected, the viscosity increases with the solid volume
fraction; moreover, the overall behaviour of the suspension remains Newtonian at
solid volume fractions below 0.2 while at higher solid volume fraction the
suspension shows a slightly shear-thinning behaviour. This phenomenon has been
widely documented in the literature (Stickel and Powell, 2005). In addition, the change in viscosity with volume fraction is well predicted by the Krieger–Dougherty equation, whose parameters
assume values similar to those found in the literature.

The power consumption for the Newtonian fluid alone has been
measured to calibrate the instruments and verify the reproducibility of the
results. Furthermore, we ran some simulation for the same system. In Fig. 4, we
report both the experimental and computational power numbers against the
impeller Reynolds number.

Figure 4: Power number
against Reynolds number for the Newtonian fluid–particles
system

We were able to recover the well-established relation
between the power number and the Reynolds number in the laminar regime (Paul, Atieno-Obeng and Kresta, 2004). Moreover, there is good agreement between the experimental and computational results.
 

Bibliography

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