3
Experimental Equipments and Techniques
3.1 Multiphase System
3.1.1 Stirred Vessel Configuration
PIV measurements of instantaneous radial and axial velocity components were performed in an open, flat-bottom, cylindrical vessel made of Perspex. An aspect ratio of 1 was used, i.e. the liquid height (H) in the vessel was equal to the tank diameter (T), where T = 100 mm. Figure 3.1.1.1 shows the geometry of the mixing vessel:
Figure 3.1.1.1: System geometry
In order to minimize optical distortion of the laser beams due to index of refraction mismatch, the vessel was placed within a larger, water-filled
square tank made of glass. The tank was equipped with four fixed baffles (width B = T/10) placed at 90° intervals to each other.
The impeller clearance was C = 0.33T, where C was defined as the distance from the vessel bottom to the middle plane of the impeller disc. A pitched-blade turbine with six 45° inclined blades in the down- and up-pumping mode was chosen, basically because it is more efficient than Rushton turbines for processes requiring solid suspension (Zwietering, 1958).
The impeller diameter was equal to D = 0.48 T, that is 48 mm. The blade height was W = T/10 = 10 mm.
The working fluid was distilled water with density ρ = 1000 kg/m3 and dynamic viscosity µ = 0.001 Pa·s. As solid phase we used glass ballotini with diameter DP= 500 µm and specific gravity ρs = 2855 kg/m3.
Measurements were conducted at four different velocities as it is reported in table 3.1.1.1: N (rpm) Re Tip Speed (m/s) 483 18550 1.214 609 23390 1.531 696 26730 1.749 767 29450 1.928
Table 3.1.1.1: Re and Tip Speed
where Re is calculated from (Perry & Green, 1997): µ ρ N D2 Re= (3.1.1.1)
In one case, i.e. N = 483 rpm in upward pumping, although most of the particles were entrained by the liquid, the impeller pumping capacity was not able to ensure a condition of “fully” suspended solid as defined by Zwietering( 1958): “When no deposits remained on the bottom for more
3.1.2 Particle Image Velocimetry
The local investigation of velocity fields of the two-phase system was carried out using a non intrusive optical technique called Particle Image Velocimetry (PIV). TSI Incorporated provided the system.
This technique involves seeding the flow with neutrally buoyant reflective particles that are illuminated by a laser light sheet in a well defined slice of the vessel; many couples of pictures (50 couples as it has been suggested by Sharp and Adrian ( 2001)) were taken at very short time intervals by a CCD camera (two cameras are used for 3 D measurements).
The laser was a double-pulsed Nd:Yag laser: it requires two signals to create a laser pulse; the first one triggers the flash lamp and the second signal opens the Q-switch that pulses the laser. The Q-Switch is fired twice during a single flash lamp discharge. The double pulse laser has the advantage to be easier to align than a two laser system.
A light arm facilitates delivering the pulses of light from the Nd:Yag lasers to the experimental region of interest.
Figure 3.1.2.2: Q-Switch
Figure 3.1.2.3: Light arm
The laser beam is then transmitted through a cylindrical lens to diverge the beam in the height direction and a spherical lens is used to control the thickness of the light sheet. The camera is focused near the light sheet waist, at the focal length of the spherical lens.
Figure 3.1.2.4: Optical lens
The camera used in this study was PIVCAM 10-30 CCD camera with a resolution of 1000 x 1016 pixels.
The Synchronizer provides the pulse delay to allow the first laser pulse to be located at the very end of a video frame. The second laser pulse image is then captured on the next frame. At the same time, the camera signals the INSIGHT software to capture the pair of frames.
Figure 3.1.2.5: Synchronizer
The CCD camera converts light energy into electrical energy and sends an electrical image to the Frame Grabber in the computer. The Frame Grabber in the computer reads the camera image and passes the information to the computer system for processing.
Measurements were taken just behind or just in front of the baffle, depending on the rotating direction of the impeller, in a plane shown in figure 3.1.2.6.
Figure 3.1.2.6: laser plane
Each particle is recorded as a white dot and by comparing the position of each dot in the first frame and in the second frame the software, Insight 6.0 (provided by TSI with the whole system), is able to identify the particle displacement field.
This identification is made by dividing the image in small cells (32 x 32 pixels) and by analyzing every cell with a cross correlation method that uses two-dimensions Fast Fourier Transforms (2 D FFTs).
The software compares particles displacements with the time interval between the two frames and calculates the whole velocity field for the area of interest.
Figure 3.1.2.8: Vectors
However is quite common obtaining images with some “wrong” vector as it can be seen in figure 3.1.2.8. These vectors are calculated by the software and might be noises or reflections so a very important point is the processing of the images and the following validation (made usually by statistical methods) of the obtained vectors.
At a first step we used a Range Filter to remove vectors with velocity values greater in magnitude than the tip speed, after that we used a Mean Filter to filter and interpolate within holes in the vector field.
As well as the validation parameters other factors has to be considered in order to obtain the “proper” velocity field, such as the frequency of the laser and the delay between two frames. The delay time (dT) is directly linked to the speed within the flow: for a proper processing of the images the maximum displacement of each particle has to be not greater than eight pixels.
A simple equation is usually used to calculate the maximum delay:
vmax⋅dTmax ≤8⋅M (3.1.2.1) where: vmax should be the maximum velocity achievable by the fluid
and usually it’s chosen as the tip speed
M is a Magnification Factor that takes account of the conversion between pixels and millimetres
In this work the delay varied between 250 and 300 µs.
After the processing a statistical analysis can be done with a graphical software, Tecplot 8.0, provided with Insight. It offers comprehensive fluid flow data visualization to be presented in many options.
Particular attention has to be paid to the seeding particles employed during the experiments.
First of all the system was calibrated with the classical silver coated hollow glass spheres (10 µm in diameter and density of 1.1 gr/cm3). Because this
type of seeding particles had already been used in previous experiments in The Department of Chemical Engineering of the University of Birmingham we used them to test new fluorescent tracers provided by TSI (3 µm in diameter and density of 1.05 gr/cm3).
This new particles, made of polystyrene, emit a bright and distinctive red colour when illuminated by light of shorter wavelengths than the emission wavelengths (see fig 3.1.2.9), and have been usefully used by other workers in opaque systems (Northrup et al. 1993; Peurrung et al. 1995; Hagiwara et al. 2002).
Figure 3.1.2.9: Excitation and emission wavelength
In such systems there is the problem of capturing at the same time the liquid and the solid reflections. Fluorescent tracers allow to measure fluid flow field just by putting a wavelength filter that blocks the reflections due to the solid phase. Removing the filter the solid flow can be captured.
In our experiments we used a filter that allowed passing only wavelengths greater than 545 nm while the solid phase emitted at the laser wavelength, i.e. 532 nm.
3.1.3 Refractive Index Matching Technique
In Section 2.1.2 we explained some previous works and attempts made in order to discriminate the different phases.
In our experiments we tried to combine without success the use of fluorescent tracer with refractive index matching. Here is a brief description of the methodology followed with some possible explanation why it didn’t work.
The first solid phase employed was constituted by spherical glass beads 130 µm in diameter and with specific gravity ρs = 2950 kg/m3.
A preliminary test with this particles showed that the limiting value of the solid phase concentration that allowed PIV measurements for the total field of view was 0.3 % by weight.
To obtain optical access to a solid-liquid mixture, first of all, the solid material should be transparent and this can be done by matching the refractive index of the liquid (usually by using a mixture) with the refractive index of the solid phase.
Virdung and Rasmuson ( 2004) used a mixture of benzyl alcohol and ethanol in order to match refractive index of glass spheres (r.i. =1.52), Zachos et al. ( 1996), with glass spheres of r.i. = 1.513 used a mixture of Tetraline (1,2,3,4-tetrahydronaphthalene) and clear coal oil, Wang and Khalili ( 2002) used a mixture of organic liquids with Duran glass beads with an index of refraction of 1.471.
As it has been pointed out all these authors employed mixture of organic liquids but the available fluorescent tracers couldn’t be suspended in such liquids due to possible degradation.
Other workers, Chen et al. ( 1994), Chen and Kadambi ( 1995) used a different kind of matching liquid, i.e. a solution of sodium iodide, 50% by weight, in water and a different kind of solid particles, i.e. silica gel with
r.i. = 1.4429. With this solution a wide range of r.i. could be obtained (1.333-1.487).
All the matching techniques started from knowing the refractive index of the solid phase and trying to match it by varying concentration and temperature of the liquid phase, but in our experiments we didn’t know the
r.i. of the solid particles employed. A different approach had to be found.
Measuring the r.i. of a solid material is quite easy if it is available as a thin and transparent slice but it’s such a difficult thing with spherical or other three-dimensional geometries. The latter happens quite often in mineralogy and this was the right way to approach the problem.
The measurements of the indices of refraction of small particles is well described in the literature (see for example Stroiber & Morse, 1994; Mazzi & Bernardini, 1988)
The refractive index of a cubic crystal or a homogeneous non-crystalline material such as glass or a fluid does not vary with the direction of light propagation. Therefore, these substances are isotropic with respect to the propagation of light. The single refractive index n of an isotropic solid may be determined by observing refraction effects when small grains of the solid are placed in liquids of known refractive indices.
A set of such liquids was prepared by using mixtures benzyl alcohol-ethanol of different composition and solutions of sodium iodide in water and by evaluating their r.i. with a refractometre connected with a water bath in order to keep the temperature constant at T ≅ 293 K.
Due to their wide range of achievable r.i. the former were employed in order to know particles refractive index and the latter during PIV experiments.
Figure 3.1.3.1 and 3.1.3.2 shows respectively the values obtained for alcohol mixtures and for sodium iodide solution.
Refractive Index of Benzyl Alcohol-Ethanol Mixtures
volumetric fraction of Ethanol
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 R.I. 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56
Figure 3.1.3.1: Refractive Index of benzyl alcohol-ethanol mixtures
The red line represents the correlation proposed by Tasic et al. ( 1992) for binary liquid mixtures with no volume change in mixing. The linear shape underlines the fact that these mixtures can be considered as ideal mixtures.
The set prepared contained mixtures with refractive index differences of 0.001.
Refractive Index of Sodium Iodide Solutions
% by weight of sodium iodide
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 R.I. 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48
Figure 3.1.3.2: refractive index of sodium iodide solutions
We used two different microscopic techniques: the oblique illumination method and the Becke line method.
In the former the normal illumination system of the microscope is used except that a piece of cardboard is placed beneath the condenser system to block half of the light and thus to create a half illuminated field.
Placing a particle at the border between the bright and the dark part of the field, it is only illuminated on one half. The side of the crystal which appears clear depends on the relative value of the refraction indices of the immersion liquid and the crystal. If nsolid is greater than nliquid than the
bright side of the crystal is oriented towards the bright side of the field. The reverse is true if nsolid is lower than nliquid.
Figure 3.1.3.4: n liquid < n solid n liquid > n solid
Because r.i. is also wavelength depending (it decreases when light wavelength increases) a wavelength filter was placed above the light source in order to get the match at the laser wavelength.
In the other method the Becke line is a bright halo of light that appears around the perimeter of a particle when the indices of refraction of the particle and surrounding medium are different and when the microscope is
defocused (by convention, the microscope is defocused by increasing the distance between objective and sample).
The Becke line results from the concentration of light either inside or outside of the image of the particle, depending ob whether the particle or the medium has the larger index of refraction. This refraction of light at the boundaries creates an optical halo. The Becke line will move toward the region with higher index of refraction.
With these two methods we found that the glass ballotini employed had a
r.i. higher than that of benzyl alcohol (1.5411) and therefore impossible to be obtained with a solution of sodium iodide and water (1.333 – 1.487). Another attempt was done using silica gel particles (150 – 250 µm in diameter) instead of glass beads and we found a refractive index of 1.450 achievable with a solution of sodium iodide 51.3 % by weight.
A match was found as it can be seen in figure 3.1.3.7.
Figure 3.1.3.6: Silica gel particles in benzyl alcohol (Becke line external)
Figure 3.1.3.7: Silica gel particles in matching solution
As soon as we tried we these particles and with the matching liquid during PIV experiments no appreciable improvements were obtained and we couldn’t increase the solid concentration.
Possible explanations for this fact are the problematic temperature control in working at the microscope (as soon as the testing medium was placed above the plate glass the light source warmed it up quickly therefore the matching temperature was unknown), the impurities and inhomogeneities within particles and their irregular shape.
The problem was in part solved by changing particle size: instead of 130 µm in diameter we employed 500 µm glass beads and this allowed achieving solid concentrations of 0.7 % by weight without blocking the laser light sheet in the total field of view and up to 1.2 % by weight considering the righter part of the vessel.
3.2 Study of Turbulence
3.2.1 Stirred Vessel Configuration
Experiments were performed in a flat-bottom cylindrical vessel made of glass. An aspect ratio of 1 was used, i.e. the liquid height (H) in the vessel was equal to the tank diameter (T), where T = 202 mm. Figure 3.2.1.1 shows the geometry adopted both for Rushton turbine and for PBT:
Figure 3.2.1.1: System geometry
In order to minimize optical distortion of the laser beams due to index of refraction mismatch, the vessel was placed within square water-filled glass jacket. The tank was equipped with four fixed baffles (width B = T/10) placed at 90° intervals to each other. The impeller clearance was C = T/2
with C being defined as the distance from the vessel bottom to the middle plane of the impeller disc.
As it has been previously mentioned two different impeller were used, a Rushton turbine and 45° 6-blade Pitched Blade Turbine. All the details are reported in table 3.2.1.1:
Rushton 45° 6 blade-PBT
Diameter D (mm) 73 67.41 Blade Width W (mm) 14 10.55 Blade Thickness (mm) 2 1.66
Table 3.2.1.1: Impeller details
Measurements were conducted at different velocities corresponding, for both impellers, to power input/unit mass ε of 0.25, 0.5, 1 W/kg.
Rushton PBT N (rpm) Re Tip Speed (m/s) ε N (rpm) Re Tip Speed (m/s) 337 29930 1.288 0.25 534 40440 1.885 425 37750 1.624 0.5 673 50970 2.375 535 47520 2.045 1 848 64220 2.993
Table 3.2.1.2: Impeller speeds
Due to impediments in the laboratory the laser-sheet plane was placed in between the baffles but not exactly in the centre plane as can be seen in figure 3.2.1.2 and 3.2.1.3.
Figure 3.2.1.2 Laser plane above
Figure 3.2.1.3: Laser plane front
However this setup was not limiting since the region of interest was the impeller swept region.
3.2.2 High Frame Rate PIV
This new device provided by TSI follows exactly the same general principles reported in section 3.1.2, i.e. illuminating a well defined slice of the fluid containing seeding particles, taking two or more picture of the sheet at short time interval, calculating the displacements of the particles, plotting the instantaneous velocity field of the liquid.
The innovations are the new POWERVIEWTM PIV Cameras that offer image
capture rates from a few hundred hertz to more than 10 kHz, making it possible to obtain unique information about the motion of structures and to measure the frequency spectrum in the flow field. Because of the high laser power required these camera have a unique masking arrangement that protect the camera CCD sensor from damage.
The lasers used can also vary the laser pulse rate from few hundred hertz to more than 10 kHz.
TSI developed a new master control unit for use with the high-update-rate cameras and lasers. This new Synchronizer offers 1 nanosecond time resolution to ensure the utmost precision in timing control and the most accurate time resolved measurements available.
A memory bank, external to the computer, is required in order to store the large number of images captured by the camera.
In our experiments 250 couples of images were taken within a capturing time of about 0.25 seconds allowing the measurements of the fluid flow field for small angular revolution of the impeller.
In table 3.2.2.1 are shown some parameters of the experiments:
Impeller
Type Rushton 45° 6-Blade PBT
Rpm 337 425 535 534 673 848 dT (ms) 450 N° of Pictures 250 Capturing Time (s) 0.25 Impeller Revolution 1.4 1.8 2.2 2.2 2.8 3.5 N° of Pictures between to consecutive blades 30 24 19 19 15 12 Angle between 2 consecutive pictures 2° 2.6° 3.2° 3.2° 4° 5.1°
Table 3.2.2.1: Experimental parameters
The seeding particles used were the same silver coated hollow glass spheres described in section 3.1.2 and image analysis involved a first processing in which the images were divided in cells of size of 32 x 32 pixels and a second processing with smaller cells of 16 x 16 pixels.
A Range Filter followed by a Mean Filter were adopted in order to discriminate “wrong” vectors from real vectors.
