4.1 Multiphase System 4 Results

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4 Results

4.1 Multiphase System

4.1.1 Initial experimental validation of the fluorescent tracers

Because fluorescent particles have never been used for this kind of experiments an accurate comparison with usually employed silver coated tracers was necessary.

The system was the same described in section 3.1 and the regions analyzed were the discharge zones of impeller (see figure 4.1.1.1): i.e. the zone just above the impeller for upward pumping and the zone just below it in downward pumping. Tests were conducted in up- and down- pumping flow, both at the four impeller speeds reported in section 3.1, i.e. 483 rpm, 609 rpm, 696 rpm, 767 rpm.

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We chose to compare the discharge regions of the impeller because they are critical ones. In fact the mean difference between the two tracers is the diameter (3 µm for fluorescent particles and 10 µm for silver coated particles) and this could influence particles behaviour in high turbulence zones. In fig. 4.1.1.2 is reported, as example, the flow pattern for 696 rpm up-pumping.

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The two figures on previous page show clearly how the two kinds of particles behaved in the same way and this was also featured by a statistical analysis reported below.

Values were averaged over each zone of those of figure 4.1.1.1.

rpm 450 500 550 600 650 700 750 800 Ve lo ci ty Ma gn itud e / T ip Sp ee d 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55

Fluorescent mean velocity/tip speed Silver Coated mean velocity/tip speed Fluorescent max velocity/tip speed Silver Coated max velocity/tip speed

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rpm 450 500 550 600 650 700 750 800 Vel oci ty Ma gn itude / T ip Sp eed 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Fluorescent mean velocity/tip speed Silver Coated mean velocity/tip speed Fluorescent max velocity/tip speed Silver Coated max velocity/tip speed

Figure 4.1.1.4: Fluorescent VS Silver Coated up pumping

In figures 4.1.1.3 and 4.1.1.4 mean and maximum overall velocities normalized with the tip speed are reported. It was expected to find the same almost constant curves for both tracers and this is what happened. Even in high turbulence zones the difference in the diameter is so small that there’s no influence of inertial force.

Thus, the results obtained allowed using fluorescent particles as liquid tracer during the following experiments in multiphase flow.

However, it was found that fluorescent microspheres were much more sensitive to the camera focus and even a small degree of out of focus caused a complete lost of vectors during image processing.

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4.1.2 Multiphase flow

In order to fully understand the influence of the solid phase on the liquid behaviour, measurements were carried out at seven different concentrations, up to 0.7 % by weight, in addition to single phase flow. This was the maximum value achievable without the laser-sheet to be obscured by the particles. Solid amounts are reported in table 4.1.2.1.

Weight % of Solid Solid Amount (gr)

0.1 0.831 0.2 1.663 0.3 2.497 0.4 3.333 0.5 4.171 0.6 5.010 0.7 5.851

Table 4.1.2.1: Solid amount

Due to massive reflections at the bottom of the tank the measurement area was located at a distance of 6 mm from the bottom but it was large enough to enable a deep insight into the main circulation loop generated by the impeller both in up- and down- pumping flow.

In figure 4.1.2.1 and 4.1.2.2 are shown the flow patterns at 609 rpm in downward pumping for the liquid phase at 0.1% and 0.5% by weight of solid respectively.

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Figure 4.1.2.1: Liquid flow pattern 0.1% 609 rpm down pumping

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The two figures on previous page shows a remarkable decrease even at these low concentrations in the overall velocity in the impeller discharge region, while in the bulk the liquid flow was less influenced by the presence of the solid phase. This effect is not obvious to explain.

The decrease could be realistic, i.e. solid particles, in high turbulence regions, generated a high drag force on the liquid phase that tended to be slowed down. On the other hand, because of the large amount of particles, there could have been a lot of light scattering that caused the liquid phase to be tracked with less accuracy.

This difference can also be observed by looking at the axial profiles of the mean radial and axial velocities.

Both velocities are reported normalized with the tip speed; positive values goes upwards for axial velocity while goes further from the centre for radial velocity. All lengths are reported dimensionless and the reference length is the tank diameter for radial coordinates and the liquid height for axial coordinates (H=T, therefore is exactly the same).

r/T=0.21 z/H 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Vz/VTIP -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 liquid only liquid solid r/T=0.21 z/H 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Vz/VTIP -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 liquid only liquid solid

Figure 4.1.2.3: 609 rpm down pumping: axial profile of the mean axial velocity, 0.4% by weight (left) and 0.7% by weight (right)

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For r/T = 0.21 the decrease in axial velocity for the liquid phase was observed only below the impeller. In this zone, as well as above the stirrer, the solid phase was always ahead.

r/T=0.21 z/H 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Vr / VTIP -0.2 -0.1 0.0 0.1 0.2 0.3 liquid only liquid solid r/T=0.21 z/H 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Vr / VTIP -0.2 -0.1 0.0 0.1 0.2 0.3 liquid only liquid solid

Figure 4.1.2.4: 609 rpm down pumping: axial profile of the mean radial velocity, 0.4% by weight (left) and 0.7% by weight (right)

In the impeller swept region, because of the blades not being transparent, it was not possible to acquire particle and liquid tracer displacements, thus

at r/T=0.21 no measurements are reported between z/D=0.27 and

z/D=0.39.

Both for axial and radial velocities the effect of an increase of solid amount from 0.1% to 0.7% by weight was unimportant, except for the impeller jet region but, as it has been already pointed out, this could be due to an increase of light scattering.

In the following figures axial and radial profiles are reported for 609 rpm in down pumping flow for concentrations of 0.4% and 0.7% and for r/T=0.31 and r/T=0.45.

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In downwards flow (r/T=0.31) particles led the fluid while in upwards flow (r/T=0.45) they lagged it.

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Again, even for radial velocity, the influence of the particle was higher in the impeller jet stream (r/T = 0.21 and z/H < 0.3) than in the bulk of the flow (r/T = 0.31 and r/T = 0.45) and no more decrease was observed with increasing the concentration.

The experiments were carried out for all the impeller speeds, both in down and up pumping flow but, for the sake of brevity, only few graphs, for up pumping, will be reported. Furthermore, because radial and axial velocity

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are reported dimensionless, the slope of the curves is almost the same for all speeds. r/T=0.21 z/H 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Vz/VTIP -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 liquid only liquid solid r/T=0.21 z/H 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Vz/VTIP -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 liquid only liquid solid

Figure 4.1.2.9: 609 rpm up pumping: axial profile of the mean axial velocity, 0.4% by weight (left) and 0.7% by weight (right)

Concerning r.m.s. values nothing could be predicted before the experiments. In fact the ratio of the particle diameter to the integral length scale le is a critical parameter in explaining the increase or decrease of

turbulence intensity caused by the addition of particles (Gore & Crowe, 1989). Kresta and Wood ( 1993) assumed for a pitched blade turbine

le=0.1 D where D is the impeller diameter. As a consequence in our case

1 . 0 ≅ e P l D

that is exactly the demarcation value above which there’s an increase in r.m.s. and below which there’s a decrease (Gore & Crowe, 1989).

Figures 4.1.2.10 and 4.1.2.11 shows the contour plot of the overall r.m.s. both in up and down pumping.

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Figure 4.1.2.10: r.m.s. 696 rpm down pumping: liquid only (left) and 0.5% by weight (right)

Figure 4.1.2.11: r.m.s. 767 rpm up pumping: liquid only (left) and 0.4% by weight (right)

Virdung and Rasmuson ( 2004) reported an increase of turbulence levels with increasing solid concentration; they used solid particles greater in diameter than the ones employed in our study ( 1 mm against 0.5 mm) thus the ratio DP/le in their geometry was 0.2.

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On the contrary Guiraud et al.( 1997) with particles of 253 µm of mean diameter didn’t observe any remarkable increase except for the region close to the vertical wall.

In the present work a decrease in r.m.s. values with increasing solid amount was observed in the impeller swept region, both in up- and down-pumping, but whereas in the former it was not so noticeable, in the latter it was as remarkable as it was for axial and radial velocities.

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4.2 Study of Turbulence

Because our main challenge was the development of a new technique and because data concerning flow structure and velocity fields are largely present in the literature both for Rushton Turbines and Pitched Blade Turbines, we did not focus our attention on such subjects.

4.2.1 Angle Identification

Due to the not availability of a shaft encoder the position of each image in respect to the narrow blade had to be determined. According to what reported in table 3.2.2.1 the number of images acquired between two blades was roughly known, thus the issue was just the identification of the frame in which a blade was at 0° in respect to the laser-sheet plane. This was done by looking at each image and by measuring the dimensions of the blade: when they matched the real dimensions then the 0° was found. Since more images referred to the same angle position they were averaged and the initial number of 250 frames decreased to values near those reported in table 3.2.2.1.

4.2.2 Vortex Identification

Trailing vortices were visualized by the software Tecplot 8 in terms of vorticity values and colours, blue or red, to discriminate the direction of rotation between clockwise and counter-clockwise respectively (figure 4.2.2.1 shows upper and lower vortex for Rushton turbine rotating at 337 rpm and for an angle from the laser plane of 4.3°).

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Figure 4.2.2.1: Vortex Identification

The vortex centre was chosen as the centre of the blue or red zone showed in figure 4.2.2.1. An attempt was done by setting a threshold value for the dimensionless vorticity ζ following the work of Derksen et al. ( 1999) but it revealed not so much more accurate then the simple optical observation of the images. In fact as it can be seen in the figure above the coloured contour of the vortices is enough well defined.

Thus, each image as figure 4.2.2.1 refers to an axial cross section and the vortex centre had to be figure out by trigonometric calculations.

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Figure 4.2.2.2: Trigonometry

If NTOT is the number of images taken between two blades (60°) the angle

between two consecutive images is 60°/NTOT. Once the position at 0° has

been found, assuming N the number of images passed from the one at 0°, the angle α (see figure 4.2.2.2) can be determined from:

TOT N N⋅ 60 = α (4.2.2.1)

Concerning the axial position it was exactly the measure obtained from the images since no trigonometric projections were required.

4.2.3 Rushton Turbine

Following the guidelines reported in previous paragraphs, radial and axial position of the trailing vortices axis, both upper and lower, where determined. Results are reported with all lengths normalized by the tank diameter T.

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Rushton: 337 rpm 0.00 0.25 0.50 0.00 0.25 0.50 0.00 0.25 0.50 0.00 0.25 0.50 0 30 60 90 120 150 180 210 240 270 300 330 upper lower Blades Baffles

Figure 4.2.3.1: Rushton 337rpm radial position

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Figure 4.2.3.3: Rushton 535rpm radial position

It appeared that although the path of the two vortices is almost the same, the lower vortex seems to be a bit further from the centre; this fact was also noted by Escudiè et al. ( 2004)

Concerning the axial position, due to the presence of the blade, it was not possible to locate properly the vortex centre in the Z-plane for the first angles. However, the radial position was detected by looking at the upper edge of the vortex just above and below the blade (see figure 4.2.3.4):

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In fact, assuming for the vortex cross-section a circular shape, the upper or the lower edge (respectively for the upper and the lower vortex) should have the same radial coordinate as the vortex centre. Experimental results and comparison with data present in the literature confirmed this assumption.

Axial positions are reported in the following figures. z/T = 0 is taken as the disc of the blade.

Rushton: 337 rpm Angle 0 10 20 30 40 50 60 70 80 90 100 110 120 130 z/T -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 upper lower Blade

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Rushton: 425 rpm Angle 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 z/T -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 upper lower Blade

Figure 4.2.3.6: Rushton 425 rpm axial position

Rushton: 535 rpm Angle 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 z/T -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 upper lower Blade

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For both vortices the centre moved up with increasing θ, except the upper vortex at the highest impeller speed that seemed to be at the same height in the vessel. This was probably due to difficulties in the vortex location at high turbulence level when the vorticity contours were not so well defined. Van’t Riet and Smith ( 1975) reported that the position of the vortex axis is independent of Re at Re > 5000. Figure 4.2.3.8 compares the axis of upper vortices for the three velocities: no displacement was observed.

Rushton: upper trailing vortex

0.00 0.25 0.50 0.00 0.25 0.50 0.00 0.25 0.50 0.00 0.25 0.50 0 30 60 90 120 150 180 210 240 270 300 330 337 rpm 425 rpm 535 rpm Blades Baffles

Figure 4.2.3.8: Rushton radial position and Reynolds

Even for the axial position no differences were found with increasing Reynolds as can be noted in figure 4.2.3.9.

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Rushton: axial position Angle 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 z/T -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 337 rpm upper 337 rpm lower 425 rpm upper 425 rpm lower 535 rpm upper 535 rpm lower

Figure 4.2.3.9: Rushton axial position and Reynolds

4.2.4 Pitched Blade Turbine

Concerning the 45° 6-blade PBT, data analysis was carried out exactly in the same way previously described. Compared to those of Rushton turbine images were much clearer and well defined, probably due to the axial flow instead of the radial one that didn’t create much turbulence around the vortex.

Thus, other measurements were carried out in addition to those reported for Rushton turbine.

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45° 6-PBT 0.00 0.25 0.50 0.00 0.25 0.50 0.00 0.25 0.50 0.00 0.25 0.50 0 30 60 90 120 150 180 210 240 270 300 330 534 rpm 673 rpm 848 rpm Blades Baffles

Figure 4.2.4.1: PBT radial position

45° 6-PBT Angle 0 10 20 30 40 50 60 70 80 90 100 110 120 z/T -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 534 rpm 673 rpm 848 rpm

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As well as for Rushton turbine even for the PBT Reynolds number had no influence on the vortex axis location, both radial and axial. It is worth of note that, with PBT, vortex axis didn’t move away from the centre while with a Rushton it was affected by the radial discharge flow.

In the case of the PBT, because the images were much more clear it was also possible measuring the vortex radius and the maximum vorticity within it.

Vortex radius is reported in figure 4.2.4.3 normalized with distance from the blade along the vortex axis.

45° 6-PBT Angle 0 10 20 30 40 50 60 70 80 90 100 110 120 r/Y 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 534 rpm 673 rpm 848 rpm

Figure 4.2.4.3: 45° PBT variation of vortex radius with blade angle

Maximum vorticity values were also measured within the vortex cross-section and reported normalized with the ratio between the tip speed and the tank diameter as suggested by Derksen et al. ( 1999) and Escudiè et al.

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45° 6-PBT angle 0 5 10 15 20 25 30 35 40 45 50 55 60 D ime ns io nl ess Vort ici ty 0 2 4 6 8 10 12 14 16 18 20 22 24 26 574 rpm 673 rpm 848 rpm Re

The peak was located between 8° and 11°, thus quite close to the blade, while, with increasing the angle, ζ tends to a constant value between 6 and 12.

Reynolds number also influenced the shape of the curves that tended to become flatter with increasing impeller speed.