Chapter 3
Materials and Methods
3.1 Vessel and Impellers
The vessel used was of diameter, T=150mm. The vessel is constructed of perfect borosilicate glass. The vessel was immerged in a glass rectangular tank filled with the same investigation fluid, in order to minimize the errors due to the refraction of the water and curved glass of the inner vessel. The vessel was equipped with four baffles, of width B=T/10, made from 3 mm thick Perspex. The liquid height was the same as the diameter of the vessel, T. The impeller was operated with a clearance C= T/4, the blade thickness was ~1 mm and the diameter D=0.45 T.
A schematic summary of the geometry of the system is illustrated in Figure 3.1.
The problem of air entrainment never occurred; the impeller was operated until 800 rpm, without capturing air from the surface.
The power input was evaluated in order to carry out the PIV experiments in with the same power input adjusting the rotational speed of the impeller. (see paragraph related to the power number). The impeller speed was controlled via an integrated motor unit (Eurostar, PowerVisc, IKA, Bremen Germany).
The impellers used were up-pumping and down-pumping six-bladed pitch blade turbines, respectively PBT-Up and PBT-Down. Due to the limitation of the torque meter to measure the torque only clockwise, two impellers were made having respectively the blades angled at 45 degrees respect to the shaft axe and the other one with the blades oriented at 135 degrees, both rotating clockwise, in order to obtain the two flow configurations. The two impellers made of Perspex are illustrated in Figure 3.2. Due to the material of which the impellers were constructed, no reflection on the camera was observed for the power of the laser adopted during the analysis.
¾ T = 150 mm ¾ H/T = 1 ¾ D/T = 0.45 ¾ C/T = 0.25 ¾ B/T = 0.1
Figure 3.1: Schematic representation of the vessel
a) b)
3.2 Measure of the power number
The measure of the power number is essential to characterize an impeller, as described in the previous chapter, but also to provide a common base of comparison for the two impellers.
Experiments to measure the power draw were performed over a sufficiently wide range of Reynolds numbers (NRe). For every measure the mechanical losses were recorded, performing the experience without liquid in the vessel. Then for the same N adopted in the measure of the mechanical losses, the same measurement was carried out with liquid and in order to obtain a more precise measure of the exact value of the torque and provide good confidence with the measurement. The power transferred to the fluid from the impeller was measured with the torque meter, Coesfeld ViscoMix unit (Coesfeld, Dortmund, Germany) and recorded by a chart recorder from Concept Instuments (Stone lane Kinver, Stourbridge, West Midlands UK).
The energy input for the two different impellers has been measured over a wide range of N, thus NRe. In order to identify the different conditions of impeller rotation speed, to obtain the same power input. Every measurement of the torque has been repeated several times, until the results agreed on the same value.
3.3 Vessel configuration and PIV
Basically a PIV equipment (see Figure 3.3), is composed of a dual head Nd:YAG laser (New Wave Research, Fremont, CA), single frame-straddling CCD (TSI PIVCam 10-30, TSI Inc.) capturing the images, with a resolution of 1024x1024 pixel, a DELL Precision 620 workstation running INSIGHT 5.1 (TSI Inc.) for image processing. The seeding particles used were hollow 10μm diameter silver coated particles and the synchronizer was a TSI LASERPULSE 610030 (TSI Inc., Shoreview, MN).
The camera was mounted on a computer controlled traverse, able of controlling movements of the order of 0.5 mm.
The frame capture delay was chosen in function of the maximum displacement that a particle could travel in the interrogation window.
t
Δ
t
Δ was calculated as follows:
tip u Iw M t< Δ
Where M is the magnification, Iw is the pixels dimension of the interrogation window and utip is the tangential velocity at the tip of the blade.
The position of the baffles generally adopted for this analysis is symmetrical with the laser. To be more precise, the laser sheet entering the vessel between the two baffles, usually forms one angle of 45° with each one. Since the impossibility to match the refractive index of Perspex and water, the baffle covering the laser appeared in the images captured by the CCD thus in the flow field, hiding part of the first recirculation loop and part of the discharge. In order to obtain the maximum information on the flow field, thus reduce the information hided by the baffle, the baffles were rotated and the angle formed between the laser and the closest baffle was of 5° (as shown in Figure 3.4).
Figure 3.3: Vessel during acquisitions of the images.
Figure 3.4: Baffle-laser configuration
Image analysis and vector fields
Two dimensional PIV data were obtained for each vessel configuration, processing the images with a recursive Nyquist grid, 32x32 was the dimension in pixels of every
interrogation window for the first pass, while a dimension of 16x16 pixels has been adopted for the second pass. A 50% overlap between adjacent interrogation areas was adopted in order to obtain an increment in the information on the flow of twice as many point for every coordinate. This effect does not have to be mistaken with an increment of the spatial resolution which remains dependent to the magnification and to the 16x16 interrogation window size.
500 couples of images were recorded for every acquisition. The missing points on the same number of flow field obtained were interpolated using 9x9 grid points in order to provide good confidence with the values calculated. Every vector obtained by the image analysis, was compared to the velocity tip vector, and only those with value below were accepted. A filter on the standard deviation was also applied, however, since the very large tolerance, practically every vector passed. This routine filtering step, was performed by the TSI Insight® software.
3.4 Angle resolved measurements
The experiments regarding the measure of the flow characteristics at certain angles of the blade were carried out with the aid of a trigger especially designed to guarantee an angle resolution of less than half of a degree. Figure 3.6
The degree of separation of the acquisition between two subsequent angles was chosen having in mind that the flow field obtained form one acquisition is actually a 2D measure over a volume determined by the thickness of the laser sheet. And thus, a compromise between the acquisition of the complete flow field, having the end of the overlapping for r=T/2, and a degree of separation which would leave behind too many information on the flow filed was needed.
Figure 3.6: Trigger to obtain acquisitions at the same
angle
The compromise was found for a 3° angle. In this way were obtained 20 acquisitions for each blade passage. Also in the angle resolved analysis, 1000 images for every acquisition were recorded, which lead to 500 vector fields.
