Ultrasonic phased array parameters determination for the gas bubble size distribution control formation in the iron ore flotation |
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16/07/2014 2:59pm
A method for the effective control of the pulp gas phase composition in the flotation process using dynamic effects of high energy ultrasound on the base of phased array technology and determination of its parameters are described. Key words: phased array, ultrasound, pulp, control, flotation Ultrasonic phased array parameters determination for the gas bubble size distribution control formation in the iron ore flotation Vladimir Morkun
Natalia Morkun
Andrey Pikilnyak
Introduction.Flotation is the most widely used separation process in the processing industries and is the most complete and versatile mineral processing operation. Materials and methods.To form the required gas bubble size distribution function, which would conform with the pulp solid phase particle size distribution in the flotation process, it is proposed to affect on the pulp flow with high-energy ultrasonic wave with given frequency and amplitude, resulting in a gas bubbles concentration change, and redistribution of their size. Character of redistribution depends on the size of the bubbles themselves, the frequency and amplitude of the incident radiation. Increasing the frequency and amplitude to the values at which the transition cavitation starts, bubble size will decrease due to crushing of larger bubbles. When decreasing the amplitude and frequency the bubbles will rise due to coalescence of smaller bubbles [4]. To solve this task, let’s form the control action based on the dynamic effects of high-energy ultrasound using phased array technology, the main feature of which is computer-controlled driving pulses amplitude and phase of the individual piezoelectric elements in multi-element transducer to control the parameters of the ultrasound beam, for example, angle, focal length, focal spot size [5,6].Taking into account the above in the proposed method using the ultrasonic phased array mounted on the external wall of the flotation machine chamber, in the working area, at each current moment of time we generate the high energy ultrasound effect with a given frequency 0.7 - 2.5 MHz, (because the value lower than 0.7 MHz does not give a stable effect of bubble size changes, which is caused by the extreme nature of cavitation, and a value above 2.5 MHz is not affect the change of necessary indicators) and the pressure amplitude of 102 -5×106 Pa, (because the value lower 102 Pa not sufficient to effectively control the gas phase, and the values above 5×106 Pa not give quality indicators growth), wich focused on the window in the interchamber septum. The gas bubbles which formed in the aeration step, after impeller dispersing are exposed to focused ultrasound, which leads to variations in their concentration and desired size redistribution in the pulp flow. To focus precisely on the window in the interchamber septum it is necessary to calculate the parameters of a phased array and to construct its directivity pattern. The acoustical pressure of the array was calculated by modeling every element of the array as an independent simple source and summing the contribution of each simple source at each point in the field. The acoustic pressure p(x,y,z) at a specific point (x,y,z) in the field due to a simple source was calculated using the Rayleigh-Sommerfeld equation [7,8] , (1) where W - is total acoustical power output from the array, ρ – is density of the medium, c – is speed of sound in the medium, A – is active transducer aperture, f – is frequency, S – is area formed by source, d – is distance from the source to the point (x, y , z), φ – is phase of oscillation, λ – is wavelength, and α – is attenuation in the medium. The active aperture (the total length of the array) is calculated by the following formula [6]. , (2) where A - is active aperture; g – is gap between nearest elements; e – is width of one element (typically e <λ / 2); n – is number of elements. Active aperture projection onto a plane seen along the refracted rays (effective active aperture Аeff) is given by , (3) Recommended passive aperture is determined by probe frequency and the focal depth range as follows , (4) Its contribution to the focal depth (near-field length) is given (for nonfocused probes) by formula (5) , (5) Array pitch of p is determined by the formula: , (6) where g – is the element gap; e – is the element width. The maximum width of a single element, which is determined by the maximum beam refracted angle by electronic control emax can be represented as follows , (7) Note that the beam width is dependent on the focal length and the angle of entry. A focused beam is characterized by the focusing factor or normalized focus depth , (8) with 0 < Sac < 1 and Fac < N0, andFac – is the actual focal depth. An optical focus point is defined by , (9) where R - lens curvature radius. The optical focusing factor is defined by , (10) The net pressure due to all the elements was determined by summing the effects of each simple source: . (11) The net power deposition at point (x,y,z) was the result of the attenuation [5] , (12) The total energy at a point (x, y, z) is given by [8,9] , (13) where - intensity at the point (x, y, z), W∙m -2 The phase of each element of the array was determined by , (14) where φi is phase of element i in degrees, di is distance from the center of element i to the focus, d0 is the focus depth, n is an integer used to maintain 0 <= φi <= 360°.
Results.Normalized directivity pattern for a rectangular array with Z = 16 elements equally spaced from each other d = 0,6 mm in the plane (Fig. 1) used in the simulation with software and hardware tools TAC (Transducer Array Calculation) [10] is presented on Fig. 2.
Figure 1. Phased array configurationFigure 2. Directivity pattern of a rectangular phased array with Z=16, j=0°
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