Effect of output parameters of electromagnetic anti-fouling technology

Abstract

Magnetic induction intensity and current are crucial factors to determine the effect of electromagnetic anti-fouling technology (EAFT). For getting the current value in the coil which was tightly wrapped around the PVC pipe, the inductance and equivalent resistance of the coil was measured by LCR meter, and the current in the circuit of the anti-fouling system was obtained by Ohm’s law. The magnetic induction intensity in the solenoid centre can be calculated by Faraday’s law. The purpose of the experiment was to find the optimal output parameters of EAFT and explored the anti-fouling effect. Therefore, we established an experimental platform to optimize the output parameters and explore the effect of different output frequency on solution conductivity and particle diameter. Through experiments, it’s found that current in the coil was reduced with increasing frequency, the number of turns and the diameter. As the frequency and diameter increase, the magnetic induction intensity reduced, and the turns basically no impact on the magnetic induction intensity. The hardness solution of 10 mol ⋅ m⁻³ (as CaCO₃) is treated by four different frequencies electromagnetic field shows that the lower the frequency, the greater decrease in conductivity and the greater increase in particle size, that phenomenon verifying that the higher current and stronger magnetic field intensity has a better anti-fouling effect.

Keywords

Electromagnetic anti-fouling technology current magnetic induction conductivity particle diameter

1. Introduction

Water is an important heat transfer medium in heat exchangers [1]. When the hard water flows in the heat transfer equipment, the slightly soluble salt is crystallized by the decrease in thermal solubility and adsorbed on the heat exchange surface form scale [2]. Calcium carbonate precipitation is one of the most common forms of scale [3]. When scale formed in the heat transfer equipment surface, at least two inevitable problems associated with scales occur. One is that the heat transfer efficiency will be greatly reduced in the heat transfer equipment, the other is that it will greatly increase the pressure drop in the pipe and even cause a safety accident [4–6].

There are many ways to deal with scale which can be attributed to chemical and physical methods [7]. There is no doubt that the chemical anti-fouling method has high cleaning efficiency and obvious effect by adding acidic agent to the circulating water. However, acidic agent corrosion not only shortens the life of heat transfer equipment but also causes second pollution and other unavoidable shortcomings [8–10]. For these reasons, physical methods such as electromagnetic anti-fouling technology have been developed recently [11]. EAFT as a physical anti-fouling technology has a good development prospect due to its non-polluting and low consumption characteristics [12]. Generally, the EAF system is composed of a control unit and a solenoid coil tightly around the PVC pipe. The EAF control unit supplies the alternating current in the coil, the alternating current generates induced alternating electronic field in the pipe, and in the meanwhile, the alternating electronic field generate induced magnetic field in the pipe, which can be explained by Ampere circuital theorem and Faraday’s law. The electromagnetic field increases the molecular agitation of the scaled ions in the circulating water, which not only increases the probability of scale formation, but also the generated scale is soft and poor adhesion ability and easy to be washed away by the water flow within the pipe. Thus, it mitigates precipitation fouling in heat exchangers [13,14].

Liu et al. [15] explored how the output frequency, the number of turns and the diameter of the pipe affect the current in the electromagnetic coil and the magnetic induction in the carbon steel tube. He found that the alternating current and magnetic induction decrease with increasing frequency, and the rate of decline is getting slower and slower. To evaluate the effectiveness of scale inhibitors. Drela et al. [16] provided a method based on measuring the conductivity of a solution, which he found to determine the quantitative relationship between the concentration of the scale inhibitor and the relative supersaturation of the scale compound. It is shown that the conductivity in the solution can reflect the efficiency of CaCO₃ precipitation. Zhang et al. [17] studied calcium carbonate crystals by scanning electron microscopy, and then he observed that the EAFT-treated crystals were cubic crystals, indicating that the EAFT-treated calcium carbonate crystals were calcite crystals, and he found that the crystal size was larger than that of without EAFT.

In summary, the current and the magnetic intensity are the most important factors affecting the anti-fouling effect of electromagnetic field. Meanwhile, the output frequency, the turns of coil and pipe diameter are the main parameter affect the current and the magnetic induction intensity. So, we investigate the variation of current and the magnetic intensity with the frequency, the number of turns and diameter to optimize the antifouling effect. The first three experiments were to investigate the effect of frequency, turns and diameter on the current and magnetic induction intensity, which provide the basis for finding the optimal output parameters of EAFT.

Accordingly, this paper provides a measurement and calculation method to get the current in the coil and the magnetic intensity in the solenoid centre and find the optimal output parameter to investigate the anti-fouling effect, and we have established an electromagnetic anti-fouling experimental platform to explore the effect of different output frequency on solution conductivity and particle diameter, both of which provide the basis for finding the optimal output parameters of EAFT.

2. Experimental

2.1. Material

The schematic diagram of the experimental structure was shown in Fig. 1, which contains an LCR meter, a solenoid coil, series resistance, a PVC pipe and supersaturated water. The type of the wire was polyvinyl chloride insulated flexible cables with copper core meeting Chinese National Standard which conductor was 5.3 mm in diameter and 0.8 mm in insulation thickness. The two ends of the winding coil were directly connected with HIOKI IM3523 LCR METER, and the basic precision of measurement was 0.05%. The model of the oscilloscope was TBS1102 produced by Tektronix, and it was 100 MHz in bandwidth, ±3% in vertical precision.

Fig. 1.

Schematic drawing of the experimental device.

In this paper, calcium carbonate was used to simulate hard water because it was not easy to dissolve in water, and it was also the common form of scale in the cooling water system. At the same time, 111 g calcium chloride and 168 g sodium bicarbonate were added to the 100 L of distilled water with the mass ratio of 1:2, which the hardness of the solution was 1000 ppm, and the temperature of the water tank was maintained at 25 °C by the thermostat. Pipes with different diameters such as 100 mm, 200 mm and 315 mm were used in the experiment. And we assumed that the diameter of solenoid coil was the diameter of the pipe. Water in the water tank entered the test section through the pump and then flowed back to the water tank after EAFT treatment. The solution in the water tank was replaced and all the experimental equipment was cleaned to prevent the scale from forming in the water tank and the inner pipe, which can affect the next experimental results.

If the use of the magnetic conductive material would affect the distribution of induced magnetic field [17], because the magnetic conductive material will affect the distribution of electromagnetic field, PVC pipe was chosen in this experiment.

In addition, the last experiment was carried out to verify the effect of output frequency on the change of conductivity and particle size in solution. Figure 2 showed the experiment platform schematic diagram of winding pulse electromagnetic field treatment system for circulating water. After the water pump was turned on, the solution to be tested passes through the test section from the water tank in the direction of the arrow and returns to the water tank. In the experimental group, the voltage across the solenoid coil was set to 9.6 V by the EAFT control unit, output frequency in the experimental groups are 5 kHz, 10 kHz and 20 kHz respectively. The control group was set up in this paper; that is to say, there is no use of EAFT in this group.

Fig. 2.

Experiment platform schematic diagram of winding pulse electromagnetic field treatment system for circulating water.

In this paper, the model of the conductivity tester and pH tester was Seven Excellence^{^TM} from Mettler Toledo Company. The test range of conductivity tester was 0.1–9999 μS/cm, and the measurement accuracy is ±0.5%. Temperature compensation of conductivity tester was 25 °C. At the same time, the particle diameter in solution was detected by laser particle size analyzer, its model was Winner 2308 from Winner Particle Instrument Company of China, its range was 0.1–2000 μm, and the accuracy and repeatability errors were all less than 3%.

2.2. Methods

Figure 3 represents the equivalent circuit diagram of the experiment. The output frequency of the EAFT control unit is much less than 1 MHz, while the solenoid coil can be equivalent to the inductor L and the resistor R in series [18], so the solenoid coil in Fig. 3 was converted into the equivalent the resistor R with the inductor L being in series. The output control unit, the RL measurement and the scope in Fig. 3 together represent the LCR meter.

Fig. 3.

Schematic diagram of experimental device equivalent circuit.

The EAFT control unit outputs the square wave that maximizes the anti-fouling effect [18]. Therefore, in this experiment, the output waveform of the LCR meter was square wave. The inductance value and the equivalent resistance of the winding coil under alternating current can be measured directly through the LCR measuring instrument. This experiment set the output frequency of the LCR meter and EAFT control unit can change from 1 kHz–30 kHz. The 30 turns and 90 turns solenoid coil are tightly wrapped around each PVC pipe. The diameter of the three different PVC pipes was 100 mm, 200 mm and 315 mm. The total impedance of the winding can be obtained by formula: $\begin{eqnarray}\displaystyle Z=\sqrt{(2{\pi}fL)^{2}+\boldsymbol{ R}^{2}}. & & \displaystyle\end{eqnarray}$ (1)

Where L is the inductance value, R is the equivalent resistance value.

The current value in the winding can be obtained by Ohm’s law: $\begin{eqnarray}\displaystyle I=\frac{U}{Z}. & & \displaystyle\end{eqnarray}$ (2)

Where U is the voltage across the solenoid coil, Z is the total impedance of the winding coil. In this study, the output voltage is set to 9.6 V by the EAFT control unit.

The current value can obtain by the formula (2), so the magnetic induction intensity in the solenoid centre can be calculated by: $\begin{eqnarray}\displaystyle B=\frac{{\mu}_{0}nI}{2}\frac{l_{0}}{\sqrt{\left(\frac{l_{0}^{2}}{4}+r_{0}^{2}\right)}}. & & \displaystyle\end{eqnarray}$ (3)

Where μ₀ is magnetic permeability of solution, l ₀ is the length of solenoid coil, r is the radius of solenoid coil, n is the number of turns of solenoid coil.

The different inductance and equivalent resistance can be obtained by changing the output frequency, winding turns and diameter. Therefore, we can get different current and magnetic induction intensity by changing the frequency, the number of turns and pipe diameter. Thus, we can optimize the output parameters based on the rule of current and magnetic induction as a function of frequency, the number of turns and pipe diameter.

When measuring the conductivity and particle size in solution, we took 200 ml of the water sample from the sample point every 2 hours for measurement, and we should measure three times to average; and after the end of the experiment, we measured the size and distribution of the particle size in solution.

2.3. EAF mechanisms

When the circulating solution flow in the pipe, the EAF control unit produce time-varying current in the solenoid coil to create a time-varying magnetic field in the pipe, meanwhile, the time-varying magnetic induce an electric field in the pipe, that can explain by Faraday’s law: $\begin{eqnarray}\displaystyle \int \mathbf{E}\cdot ds=-\frac{\partial }{\partial t}\int \mathbf{B}\cdot d\mathbf{A}. & & \displaystyle\end{eqnarray}$ (4)

Where E is induced electric field intensity vector, s is circumferential vector, B is the magnetic field strength vector, and A is the cross-sectional area.

Fig. 4.

Schematic diagram of the induced electromagnetic field working to ions motion in the solution.

The process of the charged ions influenced by the induced electromagnetic field to form the particle is shown in Fig. 4. The Lorentz force increases the molecular agitation of the scaled ions in the circulating water, which not only increases the probability and efficiency of scale formation, but also the generated scale is soft and poor adhesion ability and easy to be washed away by the water flow within the pipe. Thus, it mitigates precipitation fouling in heat exchangers [13,14].

The movement of charged particles in the electromagnetic field is affected by the Lorentz force; the force can be calculated by: $\begin{eqnarray}\displaystyle F=\int V(pE+J\times B)dr. & & \displaystyle\end{eqnarray}$ (5)

Where V is the volume of the integral, p is the charge density, J is the current density, and r is the body element.

The induced electromagnetic field provides molecular agitation to charged calcium ions and bicarbonate ions collide and precipitate forming CaCO₃ nuclei, see Fig. 1. $\begin{eqnarray}\displaystyle \text{Ca}^{2+}+2{\text{HCO}_{3}}^{-}\rightarrow \text{CaCO}_{3}\downarrow +\text{H}_{2}\text{CO}_{3}. & & \displaystyle\end{eqnarray}$ (6)

Cho et al. [1] find that the supersaturated solution forms a large number of nuclei before entering the heat exchanger under the EAF treatment, which reduces the supersaturation of cooling water before entering the heat exchanger, and generating calcium carbonate is calcite with low adhesion and can discharge with the cooling water, therefore, the EAF treatment can achieve the purpose of scale inhibition.

According to the mechanism, the electromagnetic field increased the probability and efficiency of calcium ions and bicarbonate ions collide and precipitate forming CaCO₃, So the electromagnetic field strength stronger, the more CaCO₃ is formed, the anti-fouling effect is better. Since only calcium ions and carbonate ions form precipitation in the solution, the conductivity can be used to indicate changes of calcium ions, and the particle diameter is the CaCO₃ diameter, so we verified the optimal parameters of EAFT by conductivity and average particle diameter.

3. Results and discussion

Figures 5–7 represents variation in current and magnetic induction intensity as function of frequency, turns, and diameter. Figures 9–10 showed the change of conductivity and particle diameter in solution concerning time under different output frequencies.

Figure 5(a) represents variation in alternating current as function of frequency at different turns and diameters. As the frequency of PVC tubes with different numbers of turns and diameters increases, the rate of alternating current decreases more and more slowly. For example, in the case of 30 turns coil winding around the diameter of 200 mm PVC pipe, when the frequency increased from 2 kHz to 30 kHz, the current decreases from 5.23 A to 0.36 A, and the current reduced 93.8% with the frequency increased from 2 kHz to 16 kHz. Drop amplitude of the alternating current became slower as the increase of frequency. And when the turns kept constant, as the diameter increased, the alternating current decreased in the coil. The alternating current in the coil decreased with the increase of turns when the diameter was unchanged. As the frequency increases, the self-inductance of the coil increases, causing the current in the coil to decrease.

Figure 5(b) represents variation in magnetic induction intensity as function of frequency at different turns and diameters. From Fig. 5(b), we can get that the trend of magnetic induction intensity with frequency was similar to the trend of current with frequency. And when the turns kept constant, the magnetic induction intensity decreased with the increased diameter. The magnetic induction intensity decreased with the increase of turns when the diameter was unchanged. Changing the output frequency results in the change of self-inductance resistance in the solenoid coil, so changing the frequency only changes the current and the others condition unchanged, because when the others condition unchanged, the magnetic induction intensity was liner with the current. Therefore, the trend of magnetic induction intensity with frequency was similar to the trend of current with frequency.

Fig. 5.

(a) Variation of current with frequency; (b) Variation of magnetic induction with frequency.

Figure 6(a) represents variation in current as function of turns at different diameters and frequencies. At the same turns, the alternating current decreased with the increase of frequency and diameter. And when the output frequency kept constant, the alternating current in the coil decreased with the increase of diameter. The alternating current in the coil decreased with the increased of turns when the diameter was unchanged. The main reason is that as the number of turns and diameter increased, the total impedance in the coil increased, which could result in a decreased in the current of the circuit. It can be seen from Fig. 6(a) that the current and the number of turns was not a simple linear relationship, so the number of turns is not liner with the inductance resistance when other parameters unchanged.

The variation of magnetic induction intensity as function of turns at different diameters and frequencies was shown in Fig. 6(b). When the output frequency kept constant, magnetic induction intensity decreased with the increase of diameter. And the number of turns basically had no effect on magnetic induction intensity when the diameter did not change, and it showed the same trend in different diameter and the output frequency. The current value in the coil, radius of solenoid coil and the number of turns determined the magnetic induction intensity. The length and current value of the winding coil were functionally related to the number of turns. The number of turns and the current were the main parameters affect the magnetic induction intensity. Although the current decreased as the number of turns increased, the magnetic induction intensity basically had not changed under the joint action of the two parameters.

Fig. 6.

(a) Variation of current with the number of turns. (b) Variation of magnetic induction with the number of turns.

Figure 7(a) represents variation in current as function of diameter at different frequencies and turns. From Fig. 7(a), it can be seen that the alternating current in the coil wrapped around the diameter of 100 mm was largest compared with the other diameters, and when the diameter was 100 mm, the alternating current in the coil with 5 kHz and 30 turns was about 5.14 A, which was always largest than other groups. And the alternating current in the coil decreases as the diameter of the pipe increases. For example, on the condition of 5 kHz and 30 turns, the alternating current in the coil decreases from 5.14 A to 0.95 A as the diameter of the pipe increases from 100 mm to 315 mm. The reason for the change was that with the increase of coil diameter, the total resistance of the coil increases and the current in the coil decreases.

Figure 7(b) represents variation in magnetic induction intensity as function of diameter at different frequencies and turns. From Fig. 7(b), it can be seen that the magnetic induction intensity in the 100 mm diameter pipe was larger than the others, and the magnetic induction decreased as the diameter of pipe increased. For example, on the condition of 5 kHz and 30 turns, the magnetic induction intensity in the coil decreased from 1.76 × 10⁻⁴ T to 0.35 × 10⁻⁴ T as the diameter of the pipe increases from 100 mm to 315 mm. In other words, although the induced magnetic was determined by many factors, the magnetic induction intensity as function of diameter with different output frequency and the number of turns show that the induced magnetic field decreases as the diameter of the pipe increases. The main reason is that although the inductive reactance of the coil is the only function of frequency, as the diameter of the tube increases, the fixed resistance of the coil increases, so the magnetic induction decreases as the diameter of the tube increases.

Fig. 7.

(a) Variation of alternating current with diameter; (b) Variation of magnetic induction with diameter.

In order to prevent the current overload in the circuit, the resistance was connected in series in the original circuit. In order to verify the accuracy of the current in the circuit that obtained by measuring the inductance and the equivalent resistance, in this paper, series resistance was used to measure the current in the circuit of the EAFT. The two ends of the coil were connected to the EAFT control unit. When the resistance was connected in series, the current change trend of the circuit remains unchanged, and because the series resistance was negligible compared with self-inductance resistance, the series resistance basically no effect when analyzing the variation. The voltage at the two ends of the series resistance was measured by an oscilloscope, and then the current value in the loop was obtained by Ohm’s law.

The external resistance inevitably affects the current in the circuit. For protecting circuit and reducing the effect of series resistance on the circuit, this experiment resistor was 1.18 Ω. Meanwhile, the output frequency of the power supply basically had no effect on the fixed resistance, so the fixed resistance assumed to be a constant value. This paper only discussed the main factors affecting the intensity of electromagnetic field by experiment in three common pipes. Further theoretical analysis and numerical simulation will be used to find the best combination parameters.

Figure 8 showed that the verified current value was obviously smaller than the current value obtained by LCR meter when the output frequency was low and the number of circuits kept unchanged. For example, when the output frequency was 2 kHz and the number of circuits was 90 turns, the verified current value in the diameter of 100 mm was about 2.65 A, at the same time the current value obtained by LCR meter in the diameter of 100 mm was about 3.55 A. But with the increase of output frequency, the current value in circuit obtained by the two methods was basically equal. For example, when the output frequency was 27 kHz, the number of circuits was 90 turns, the current value obtained by the two methods was about 0.48 A. At the same time, we can see from Fig. 5 that the similar change of the current value in circuit obtained by the two ways concerning the output frequency when the pipe diameter was 200 mm and the number of circuits kept unchanged.

The reason for this phenomenon was that the introduction of series resistance wound inevitably reduced the current value in the circuit, which series resistance in the closed loop would share a part of the total current according to the Ohm’s law. But with the increased of output frequency, the total resistance of the winding coil increased, which was equivalent to the proportion of series resistance decreased and the current value of series resistance in the closed loop becomes smaller, resulting in that the effect of the series resistance of the circuit gradually become smaller and negligible finally. So as the output frequency increased, the current value in circuit obtained by the two methods was basically equal finally, which confirmed the accuracy of the current value obtained by LCR meter. Compared to the current value in the circuit obtained by the two methods in this experiment, we can find that the way of series resistance in the closed loop was effective, and the experimental data were reliable.

Fig. 8.

Validation of experimental data.

From the analysis of the first experiment, we can find that when the number of turns of the coil was 30 turns and the diameter of the pipe was 100 mm, and the current and magnetic induction in the coil reaches the maximum. Therefore, we used coil turns of 30 and pipe diameter of 100 mm in the next output frequency versus conductivity and particle size measurement experiments.

Figure 9 showed that conductivity in solution decreases more and more slow as time, and conductivity in solution was barely changed after 72 hours. At the same time, as the frequency was lower, the decrease in conductivity was relatively larger. For example, the range of conductivity was 3791 μm/cm to 3795 μm/cm at the beginning of the experiment, after 72 hours conductivity in solution without EAFT, was gradually stabilized at 3118.3 μm/cm, while the frequency was 5 kHz, conductivity in solution was 2850.3 μm/cm as it was stable, which was 268 μm/cm lower than that in solution without EAFT.

The concentration in the initial solution was supersaturation, so conductivity in solution was high. With pulsing voltage inputting in the test section, there would be a time-varying electromagnetic field provided necessary molecular agitation to charged mineral ions such that calcium and bicarbonate ions collide and precipitate, which could result that conductivity in solution decreases finally. At the beginning of the experiment, the number of charged particles in the solution was large, so the collision frequency was higher, and the formation of precipitation was faster. As time goes on, the number of charged particles in solution decreased, and the rate of the scale ions collision and precipitation slowed down, so the reduction of conductivity was slower relatively.

Fig. 9.

Variation of conductivity along with time under different frequency.

The range of particle diameter was 7.950 μm to 8.038 μm at the beginning of the experiment. As shown in Fig. 10, after 72 hours of circulation the average of particle diameter were 8.556 μm without EAFT, 11.884 under the frequency of 20 kHz, 13.055 μm under the frequency of 10 kHz and 14.648 μm under the frequency of 5 kHz. The positive and negative ions moved out of order without EAFT, which had little difference between the rate of dissolution and precipitation. But with the electromagnetic, the scale ions such as calcium ions and carbonate ions in solution was accelerated to move. And the calcium and carbonate ions were equal in charge and opposite in polarity, they moved in opposite directions in the electromagnetic field, so the rate of collision and the precipitation was quicker under the action of electromagnetic field, which caused the rate of crystal nucleation was greater than that without EAFT.

In addition, we have found from the analysis of the first two sections that the induced current in the coil decreased as the output frequency of the power supply increased, so the induced electromagnetic field force generated in the coil also decreased. Since the electromagnetic field force generated at a lower frequency was large, calcium ions and carbonate ions in the solution were subjected to a large force to accelerate the movement. The particle size of the solution at the final low frequency was larger than the particle size under the high frequency.

Fig. 10.

(a–d) Particle diameter distribution in solution after 72 hours, (a) Without EAFT; (b) Under the frequency of 5 kHz; (c) Under the frequency of 10 kHz; (d) Under the frequency of 20 kHz.

4. Conclusions

In this paper, an experiment platform was built to explore the variation of peak current and magnetic field intensity with frequency, number of turns and diameter. In order to increase the credibility of the experimental results, the current measurement results were compared with the calculated results. Besides, we established an experiment platform to investigate the frequency on the anti-fouling effect by conductivity and average particle diameter. The main conclusions of the experiment are as follows:

As the frequency increased, the alternating current and the magnetic induction intensity decreased, and the rate of decline was getting slower and slower. As the number of turns increased, the current in the coil decreased, but the magnetic induction intensity remained essentially constant as the number of turns increased. The current and magnetic induction intensity decreased as the diameter increased. When the frequency is 2 kHz, the number of turns is 30, and the diameter is 100 mm, the current and magnetic field intensity is the biggest.

Compared to the current value in the circuit obtained by the calculation and measurement in this experiment, we can find that the way of series resistance in the closed loop was effective and the experimental data were reliable.

EAFT can effectively reduce the conductivity and increase the average particle diameter in solution. The lower the frequency, the greater the decrease in conductivity and the greater the increase in particle size, indicating that the higher current and stronger magnetic field intensity has a better anti-fouling effect. So, the frequency is 2 kHz, the number of turns is 30, and the diameter is 100 mm is the optimal parameters in this experiment.

Footnotes

Acknowledgements

This work is supported by National Key R&D Program of China (2017YFB0603300).

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