Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 9, No. 2, 2024 

89 

Research	on	the	Characteristics	of	Stirring	Flow	Field	of	
Flotation	Separator	Based	on	PIV	Technology	
Sijin Yu, Xiangyong Liao, Qiu Jing 

School of Mechanical Engineering, Sichuan University of Science & Engineering, Yibin 643000, China 

Abstract: In order to explore the distribution characteristics and characteristics of the internal flow field of the flotation 
machine, and to understand the variation law of the flow field parameters in the process of the internal flow field of the flotation 
machine, particle image velocimetry was used to measure the flow field of the flotation machine, and four groups of sections 
were designed, each group of sections had four different revolutions, and there were 16 experimental groups in total. The results 
show that the vertical plane of the flow field of flotation machine can be roughly divided into four areas. The flow field level of 
the flotation machine can also be divided into three areas. The effect of rotating speed on the average circulating speed of flotation 
machine was studied. This paper analyzes the statistical law of vorticity distribution in the internal flow field of flotation machine 
and the relationship between average speed and rotating speed, and establishes the probability model and influence analysis 
model related to it. 

Keywords: PIV; Flotation machine; Velocity field; Vorticity. 

1. Introduction
Flotation technology is based on adjusting the physical and 

chemical properties of mineral particles, separating useful 
minerals from ores, attaching them to bubbles, and then 
floating with bubbles to become foam products, so as to 
achieve the separation of useful minerals from other minerals 
[1][2]. Since the development of flotation cells, they can be 
roughly divided into four categories according to the different 
separation methods: pneumatic type, mechanical agitation 
type, reaction-separator and flotation column. In the past 100 
years, despite the rapid development of flotation machines, 
mechanical stirring flotation machines still dominate the 
industry due to their maturity and practicability [2][3]. In this 
paper, in order to study the distribution characteristics and 
flow field characteristics of the flotation cell during stirring, 
the speed characteristics of the stirring flow field of the LZFD 
flotation cell were tested by laser PIV technology, and the data 
fitting of the flow field was carried out according to the 
experimental data, so as to provide a basis for the selection of 
the operating speed of the impeller and the improvement of 
the structure. 

2. Experiment

2.1. Experiment quipment 
The test device is a three-dimensional PIV measurement 

device produced by Dantec Dynamics in Denmark, which 
mainly includes four parts: light source system, image 
acquisition system, PIV synchronization system and image 
analysis system [4], as shown in Figure 2-1. The container 
containing the solution in the experiment is a hollow 
rectangular body assembled and glued together by transparent 
plexiglass, and the specifications are: In the experiment, the 
tracer particles were rhodamine B fluorescent polymer 
particles, which had good tracerability, scattering and follow-
up properties of the convective field. The depth of the mixing 
solution is 430 mm. The motor selects a stirring motor with a 
rated power of 100W. One stepper motor speed controller. 
LZFD flotation machine (built-in stirring impeller with a 

diameter of 45mm). 

Figure 1. Schematic diagrams of experiment 

2.2. Protocol 
Select the vertical cross-section of the centerline of the 

horizontal section of the rectangular container as the reference 
cross-section, as shown in Figure 2-2, make it a 0-0 cross-
section, and then extend it downwards to a depth of 20mm, 
40mm, and 60mm for the shooting cross-section. Figure 2-3 
shows that the PIV shooting area is 70 mm away from the 
bottom surface of the liquid, 60 mm from the left wall, and 
240 mm high. In order to obtain the changes of the flotation 
machine at different speeds of the same shooting cross-
section, the speed of the stirring impeller was preliminarily 
proposed to be 800、1200、1600、2000 four gears for 
recording and observation. As shown in Figure 2-4, the 
impeller axis is set to L2, the left side of the axis is set to L1, 
and the right side of the axis is set to L3 at 120mm. 

Figure 2. Schematic diagram of the horizontal section of the 
flotation machine box 



 

90 

 
A-LiquidB-Camera 

Figure 3. Schematic diagram of the PIV shooting area 
 

 
C-impeller 

Figure 4. Schematic diagram of axis selection 

3. Results 

3.1. Plots and Models 
In order to further explore the characteristics of flow field 

motion, the vorticity is analyzed.Figures 3-6 and 3-7 have two 
cross-sections closest to the impeller region, and there are 
four main vortices in the figure. The four vortices are centered 
symmetrically with respect to the position of the impeller, and 
with the increase of the number of revolutions, the fluid flow 
velocity increases, the turbulence intensifies, and the 
formation range and value of the vortex gradually decreases 
while the position of the vortex remains the same. 

As shown in Fig. 3-8 and Fig. 3-9, the vortex range 
gradually decreases as the number of revolutions increases, 
but the vorticity value gradually increases in the cross-section 
away from the impeller. The farther away from the impeller 
cross-section, the more disordered the vortex becomes, and 
the range is unstable, and the direction of movement changes 
from transverse to longitudinal. 

 

 
Figure 5. 0-0 Cross-section vorticity 

 

 
Figure 6. 20-20 Cross-section vorticity 

 

 
Figure 7. 40-40Cross-section vorticity 

 

 
Figure 8. 60-60Cross-section vorticity 



 

91 

 
A histogram of the percentage of vorticity intensity in the 

0-0 section is established, and it can be seen from Figure 3-10 
that the vorticity value is symmetrical with respect to the 
vorticity intensity S=0. 

 

 
Figure 9. 0-0Percentage histogram of cross-section strength 

 
The distribution curve was fitted to obtain the trend of 

"normal distribution curve", and the function was selected for 
curve fitting, and the function fitting formula is as follows: 

 

      (1) 

 
The trend of the fitting curves is consistent with the 

experimental data, and they all show a "normal distribution", 
with a relative frequency fitting curve for the vorticity at 0-0 
cross-section and rotational speed, as shown in Fig. 10. 

 

 
Figure 10. Lorentz curve 

 

The data  ,  ,  ,   were analyzed and fitted, 

where the third-order polynomial was used for fitting and the 
formula was as follows: 

 

        (2) 

 
For linear fit, the formula is as follows: 
 

              (3) 

  
After the data fitting of the computer software, the 

 parameters of the function are the functions about 
the variables, where is the rotational speed of the impeller, 
and the fitting function of each parameter in the 0-0 section is 
as follows: 

 
  (4) 

 
 (5) 

 

        (6) 

 
 (7) 

 
Finally, the relationship between the vorticity in the 0-0 

cross-section with respect to the speed of the impeller is 
obtained: 

 

 

 

3.2. The influence of rotational speed on the 
circulating flow rate of the flotation cell 

In order to explore the circulating flow rate of the LZFD 
flotation cell, the data point analysis was carried out at the 0-
0 section that is convenient for the measurement data, and the 
extracted data curve was analyzed in the Origin 2021 software 
to obtain the average curve, and the definite integral median 
value theorem was used. 

The formula for the median value of the definite integral: 
 

          (8) 

 
In the experimentally extracted data,

， The 

curves are integrated to obtain the area and average velocity. 



 

92 

Further fitting the obtained average velocity data with respect 
to the number of revolutions, the function adopts a second-
order polynomial: 

 

            (9) 

 
The fitting result of the fluid velocity function is: 
 

  (10) 

 

 

Figure 11. The average speed varies with the number of 
revolutions 

 
Figure.11 shows the fitting curve. The volume flow 

function of the LZFD flotation cell with respect to the number 
of revolutions is obtained: 

 

       (11) 

 
Where Ra is the radius of the circulating flow region 

containing bubbles,Ra=116.7mm. 
The measured nominal volume flow results are shown in 

Table 1. 
 

Table 1. Date processing result 
Rotate speed(r/min) 800 1200 1600 2000 

Area(m2·10-2) 2.3094 4.07366 4.51102 3.86828 
average velocity(m/s) 0.0221 0.03898 0.04317 0.03702 

volume flow rate(m3/h) 3.4039 6.0043 6.64894 5.70159 
 
According to Eq. (10), the number of revolutions 

corresponding to the maximum value of the number of 
revolutions: 

 

  (12) 

 
Put（ ）into (10) and (11): 

 

 

In this experiment, the theoretical optimal speed of the 
impeller of the LZFD flotation cell can be selected as 1500 
r/min. 

As shown in Table 1, the impeller speed has a maximum 
volume flow rate of , which contributes to the 

efficiency of flotation of minerals. However, in the selection 
of flotation machine speed, it must also be considered that the 
greater the speed of the flotation engine impeller, the greater 
the resistance during its rotation, and under the condition of 
maintaining the maximum flow rate, it is necessary to choose 
a more economical engine output power, save more electrical 
energy, and reduce production costs. Therefore, it is possible 
to select a speed slightly lower than the maximum flow rate. 

4. Conclusion 
By studying the characteristics of the stirring flow field of 

the flotation cell, the following main conclusions are drawn: 
(1) In the LZFD flotation machine, the vertical surface of 

the flow field can be divided into four areas from the bottom 
to the top according to the flow of the flow field.

  is a mixed area of ore grains, and the 

fluid in this area is mainly horizontal;  
is the mixing collision zone, which is close to the impeller 
mixing center area, where the ore particles and air bubbles 
collide violently;   is the bubble entry 
area, and the flow form of this area is dominated by the 
circulating flow of bubbles.  It is a 
foam stratosphere, and the flow velocity in this area is 
minimal. 

(2) The flow field of the flotation cell can also divide the 
flow area into three zones from the periphery of the flow field 
to the center of the impeller agitation. The part close to the 
impeller is the collision area of upper and lower convection; 
Slightly away from the impeller area is a mixed area of 
circulating and rotary flow; The area away from the impeller 
exists in the form of a rotational flow and an upwelling flow. 

(3) The calculation of the flow rate of the flotation cell and 
the fitting of the average speed of the impeller can 
theoretically select the optimal speed for the flotation 
machine and provide the best flow field for the flotation of the 
flotation machine is 1500 r/min. 

Acknowledgment 
Supported by The Innovation Fund of Postgraduate, 

Sichuan University of Science & Engineering. (Y2022050) 

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