Influence of temperature on fouling removal for pipeline based on eco-friendly ultrasonic guided wave technology

When industrial pipelines are used to transport production materials, the scale can easily form on the inner wall of a pipeline due to long-term contact with the liquid medium. Scaling in industrial pipelines is a common problem that poses a great threat to the production process and environmental protection. In this paper, the influence of temperature on the fouling removal process in pipes is studied. A finite element simulation model was established for guided wave propagation in pipes with different temperatures to obtain the acoustic pressure distribution along the pipes, showing that when the temperature increases, the acoustic pressure value on the solid–liquid surface of the pipes increases, and the cavitation threshold decreases. The experimental system for pipe descaling at different temperatures was established, when the temperature is from 20 to 60 °C, the descaling rate in the inner wall of the pipe far from the transducer is increased from 77.49 to 93.71%, the descaling rate in the inner wall of the pipe near the transducer is increased from 87.01 to 97.02%. The experimental results showed that the descaling performance is better when the pipeline temperature is higher.Compared with the traditional technology, the pipeline descaling technology based on ultrasonic guided waves is highly efficient, safe and eco-friendly, which can remove the fouling inside pipeline online without affecting the transportation. The above conclusions could provide a reference for further popularizing the application of the descaling technology based on ultrasonic guided wave. LabVIEW program was written by computer to generate 10Vp-p sinusoidal continuous wave digital signal, and then the digital signal is converted into analog voltage signal by using a data acquisition card (DAQ), and then the analog voltage signal is amplified to 300Vp-p by input power amplifier. The amplified analog voltage signal is applied to the transducer, and the transducer converts the voltage signal into vibration signal to generate ultrasonic guided waves in the pipeline and remove dirt in the pipeline.


Introduction
With the progress of society and the improvement of people's living standard, the industrial environmental problems are getting more and more people's attention, and it is urgent to develop environmental management and cleaner production technology (Staniskis and Arbaciauskas 2003;Pukec and Dui 2022;Igor et al. 2010). Environmental management of industrial areas is also particularly important (Alnouri et al. 2014). Industrial facilities produce a large amount of waste and systems modeling and analysis methods can provide industrial decision makers with the ability to assess the sustainability status of industrial units so that the entire industrial area can be sustainable (Piluso and Huang 2009). Recently, there is high attention on Renewable energy and cleaner production. Clean technology and environmental policy issues involve various fields. Rational use of clean technology in industry can effectively improve process efficiency and plant energy saving and achieve sustainable development (Bulatov and Klemes 2009;Lee et al. 2019).
In industrial production, with the continuous increase of the scaling layer on the inner wall of pipelines, the flow cross section of the fluid in the pipelines gradually decreases, and the fluid flow resistance gradually increases, resulting in the reduction of pipeline transportation capacity (Bukuaghangin et al. 2016;BinMerdhah et al. 2010;Tang et al. 2017). And with the accumulation of time, this effect will become more and more obvious (Abu-Zaid et al. 2000) and even affect normal industrial production. Crystalline scale refers to the saturation state of dissolved inorganic salts in the fluid, usually existing in water-salt solution (Heath et al. 2013;Al-Janabi et al. 2010). Paakkonen et al. investigated the effect of parameters such as velocity and heat flow density on the crystalline scale and found that temperature variations on the surface of the equipment induced crystalline scale on the surface of the equipment (Paakkonen et al. 2012). Teng et al. studied the effect of solution concentration on calcium carbonate in a double-tube heat exchanger and showed that the solution concentration has a large effect on the formation of crystalline scale (Teng et al. 2017a, b). Bermudez found that the particles present in the suspension may also lead to pipe scaling and corrosion, and the thermal conductivity of the crystalline scale on the heat exchanger surface is very low (Bermudez et al. 2005;Teng et al. 2017a, b).
In terms of scale formation on the inner wall of pipelines, Chamra et al. studied the mechanism of particle deposition scale formation in pipelines and proposed a theoretical model based on inertia and diffusion mechanism (Chamra et al. 2005). Coletti et al. proposed a similar detailed modeling method, which studied the effect of scaling on the heat transfer performance of tubular heat exchangers in detail (Coletti et al. 2010). According to the formation mechanism, scaling in pipelines can be divided into large molecular particle deposition, biological scale, chemical reaction, corrosion scale, and crystalline scale (Lv et al. 2020). Niemczewski studied the influence of solution concentration of alkaline ultrasonic cleaning solution on cavitation intensity (Niemczewski 2009). Liu and Hsieh studied the influence of excitation dual-frequency or multi-frequency ultrasound on the cavitation effect and designed a new transducer that can generate dual-frequency ultrasound (Liu and Hsieh 2009 (Lais et al. 2019). Niemczewski studied the influence of bubble content in liquid, ultrasonic frequency, and ultrasonic power on cavitation and found that bubble content in the water has a great influence on cavitation (Niemczewski 2014).
In this paper, the propagation process of ultrasonic guided waves is firstly analyzed theoretically. And we mainly elaborate the cavitation effect due to the leakage of ultrasonic guided waves and analyze the main factors affecting the cavitation effect according to the cavitation threshold. Compared with the pipeline descaling technology based on ultrasonic waves, the technology with ultrasonic guided wave could cover a wider range of descaling. The influence of temperature on the calcium carbonate crystal fouling removal in pipeline using eco-friendly ultrasonic guided wave technology has been studied in this paper, in order to apply this technique better in the real-world scenarios.

Mathematical model
Ultrasonic guided waves are stress waves that propagate infinite media and are guided by its boundaries . UGWs consist of a variety of body waves, such as longitudinal and transverse waves, and when the UGWs propagate in a solid medium, the wave is affected by the medium boundary, where reflection, refraction, and waveform conversion between longitudinal and transverse waves occur (Rose 2002). The excitation and propagation principles of UGWs are shown in Fig. 1. The hollow pipe model is shown in Fig. 2, where a is the inner radius, b is the outer radius, and the pipe length is infinite. z is the axial direction of the pipeline, r is the radial direction of the pipeline, and is the circumferential direction of the pipeline. The boundary conditions are shown in Eq. 1.
According to the theory of elasticity, the Navier fluctuation equation of motion for the anisotropic elastic medium can be expressed as Eq. 2, where and are Lamé constants related to the material properties of the medium, � ⃗ u is the displacement vector,∇ is the three-dimensional Laplace operator, is the density of the isotropic elastic medium, and t denotes time.
The Helmholtz equation can be expressed as Eq. 3, where Φ is the scalar, and �� ⃗ H is the zero-dispersion vector.
(1) rr = r = rz = 0(r = a, r = b) Using Eq. 2 and 3 can be decomposed into the fluctuation equation expressed by the potential function Φ and �� ⃗ H . The fluctuation equations are Eq. 4 and 5, where c l denotes the longitudinal wave velocity, and c s denotes the transverse wave velocity.
When a longitudinal wave propagates in a solid, its wave velocity is expressed as Eq. 6, and when a transverse wave propagates in a solid, its wave velocity is expressed as Eq. 7, where and are Lamé constants, is the medium density, is the Poisson's ratio, and E is the modulus of elasticity.
The particles on the pipe satisfy the Navier equation of motion in elasticity. Gazis solved the equation and obtained the frequency propagation equation of the longitudinal guided wave in the hollow circular tube (Gazis 1959). The frequency propagation equation can be broken down into a product of several subdeterminants. The solution of the subdeterminant can be divided into longitudinal mode and torsional mode of guided wave.
Due to the ultrasonic guided wave is a mechanical wave, attenuation and loss of wave energy will inevitably occur when it propagates in waveguide medium. Ultrasonic guided wave will be caused by wave scattering, wave energy absorption and wave energy leakage and other reasons. For the pipe filled with fluid, the existence of (4) fluid changes the boundary conditions of the pipe, thus affecting the propagation characteristics of guided waves in the pipe. When the ultrasonic guided wave propagates in a liquid-filled pipeline, the liquid provides a path for the ultrasonic guided wave in the pipeline to leak energy, that is, there is energy leakage from the solid layer to the fluid environment, because the inner wall of the rigid body pipeline contacts liquid. The ultrasonic guided wave in the pipeline will leak into the liquid, and the ultrasonic guided wave in the pipeline provides energy for the cavitation of the liquid in the pipeline.
When the local pressure of the liquid is reduced, bubbles form inside the liquid or at the solid-liquid interface. In the process of bubble oscillation, the radius of the bubble increases at the moment of liquid thinning and decreases at the moment of liquid compression. For pipe descaling, the energy impact generated by the moment of bubble rupture in ultrasonic cavitation causes the scale layer to fall off from the surface. The nonlinear nature of a single spherical oscillating cavitation bubble (Lais et al. 2018) can be expressed as Eq. 8, where p(t) is the pressure inside the bubble, p ∞ (t) is the external pressure infinitely far from the bubble, L is the density of the surrounding liquid, R is the radius of the bubble, v L is the kinematic viscosity of the surrounding liquid, and s is the surface tension of the bubble.
The cavitation threshold P b can reflect the degree of difficulty of liquid cavitation, the greater the cavitation threshold, the more difficult it is for the liquid to cavitate.
Under isothermal adiabatic conditions, the cavitation threshold P b is equal to the sum of the liquid strength P c and the hydrostatic pressure P 0 . The liquid strength P c is expressed as Eq. 9, and the cavitation threshold P b is expressed as Eq. 10, where P v is the liquid saturation vapor pressure, is the liquid surface tension coefficient, and R 0 is the initial radius of the bubble.
As can be seen from Eq. 10, in other conditions the same, the temperature and cavitation threshold P b are inversely proportional, that is, when the temperature decreases, the cavitation threshold P b increases, and vice versa. The greater the hydrostatic pressure P 0 , the greater the cavitation threshold P b , the higher the difficulty of cavitation occurs.

Simulation models
To investigate the effects of temperature on the removal of calcium carbonate crystal fouling in pipes, a multi-physics field model was established and the propagation process of guided waves in pipes at different temperatures was simulated by using finite element analysis. As shown in Fig. 3a, a simulation model of pipe descaling is established, and the model is in full 3D model. The total length of the pipe is 1 m, the outer diameter is 42 mm, the wall thickness is 3 mm, and the material of pipe is set as structural steel. The wedge-shaped transducer consists of PZT-5H piezoelectric material and a square aluminum base. The base of the transducer is curved and coupled at one end of the pipe to ensure that the UGWs energy excited by the transducer can be effectively transmitted, as shown in Fig. 3b. The schematic diagram of the meshing of the model is shown in Fig. 3c.

Artificial fouling preparation
Carbonization and double decomposition are common methods for preparing calcium carbonate. Carbonation method requires CO 2 or CO 2 and air-mixed gas, which is complicated to operate, and the reaction process of double decomposition is difficult to control. To verify the influence of temperature on the removal of calcium carbonate crystal dirt in the pipeline, in this experiment, the thermal deposition method is used to carry out calcium carbonate crystal scaling in the pipeline. The thermal deposition method makes use of the phenomenon that the solubility of calcium carbonate decreases with the increase in temperature. At low temperature, the saturated calcium carbonate solution will precipitate calcium carbonate due to the increase in temperature. The advantage of the thermal deposition method is that it is simple to operate and can be maintained constant by controlling multiple variables to ensure that the thickness of calcium carbonate in the inner wall of different experimental pipelines can be similar when repeated scaling preparation experiments are carried out. The disadvantage is that the preparation time is relatively long. The solution is slowly circulated in the fouling experiment system, when the saturated calcium carbonate in the water tank flows through the experimental pipe with higher temperature, the original saturated solution will have calcium carbonate precipitated and deposited on the inner wall of the experimental pipe. The higher temperature accelerates the deposition of calcium carbonate on the inner wall of the experimental pipeline, and the surface temperature of the pipeline is maintained at 80 °C during scaling preparation. The schematic diagram of the pipeline calcium carbonate scaling preparation system is shown in Fig. 4. Due to the influence of gravity, calcium carbonate is easily deposited in the local position of the inner wall of the pipe, and the experimental pipe is rotated 180°every 8 h to make the calcium carbonate adhere to the inner wall of the pipe evenly. After 48 h to complete the calcium carbonate scaling of the pipe, remove the experimental pipe and pour out the solution inside the pipe. Until the calcium carbonate is completely dry, cut off the 4-mm rings at both ends of the experimental pipe, and sample the rings separately. Fouling reaction depends on the chemical Eq. 11.

Frequency selection
A PSV-500 Doppler scanning laser vibrometer is employed to achieve the pipe vibration character before the descaling experiment, as shown in Fig. 5a. To ensure that obtains a relativelygood cavitation effect, the test is conducted in the frequency range of 20-60 kHz, and the frequencycorresponding to the maximum point of displacement is selected as the excitation frequency. The graph of vibration test results is shown in Fig. 5b. When the frequency is 42.38 kHz, the displacement value is the largest, so 42.38 kHz is chosen as the excitation frequency for the experiment. Descaling experiment The experimental system of pipeline descaling at different temperatures is shown in Fig. 6, including the UGWs excitation system and temperature control system. UGWs excitation system equipment includes a computer, USB-6366 data acquisition card made by NI, HFVP-83A power amplifier, wedge-shaped transducer. The equipment for the temperature control system includes a WRN-291 thermostatic controller, a Pt100 thermocouple temperature sensor, and a glass fiber heating belt. The descaling experiment can maintain the temperature of the liquid in the pipeline at the preset temperature for a long time through the temperature control system. Three groups of scale removal experiments were set up at different temperatures. In each group of experiments, other experimental parameters were consistent except for the difference in the liquid temperature inside the pipeline. When the pressure inside the pipeline is 1 atm, the internal liquid temperature of the experimental pipeline is maintained at 20 °C, 40 °C, and 60 °C, respectively, and then, UGWs descaling is performed on the experimental pipeline.  The descaling experiment of the pipeline at different temperatures is shown in Fig. 7. The whole process of descaling is 30 min, and the dynamic process of the whole experiment is as follows, LabVIEW program was written by computer to generate 42.38 kHz and 10Vp-p sinusoidal continuous wave digital signal, and then the digital signal is converted into analog voltage signal by using a data acquisition card (DAQ), and then the analog voltage signal is amplified to 300Vp-p by input power amplifier. The amplified analog voltage signal is applied to the transducer, and the transducer converts the voltage signal into vibration signal to generate ultrasonic guided waves in the pipeline and remove dirt in the pipeline.
The graphs of the analytical results of the samples after the preparation of the experimental pipe scaling are shown in Fig. 8. Figure 8a shows the distribution of calcium carbonate in the inner wall of the pipe after scaling, and it can be found that the inner wall of the pipe is covered by calcium carbonate uniformly. Figure 8b shows the microscopic image of the scaling of the inner wall of the pipe after scaling with a magnification of 10,000 times. Figure 8c shows the result of energy spectrum analysis after the preparation of calcium carbonate scaling, in which it can be found that the scaling layer contains more calcium, carbon, oxide, and a small amount of iron, nickel, and chromium.

Simulation results
For quantitative analysis of sound pressure, the simulation frequency is set to 42.38 kHz. In the case of pipeline pressure of 1 atm, through the finite element simulation of the liquid temperature of 20 °C, 40 °C, and 60 °C, respectively, the distribution of sound pressure at the inner wall of the c The result of energy spectrum analysis after the preparation of calcium carbonate scaling pipe and the corresponding changes in the intensity of the sound field at different locations of the pipe, respectively, as shown in Fig. 9a, b and c. The simulation results show that the positive and negative pressure of the inner wall of the pipe is distributed alternately and axisymmetric on the pipe, and the sound pressure on the solid-liquid surface of the pipe increases with the increase of the temperature. In combination with Eq. 10, it can be seen that when the liquid temperature in the pipe increases, the cavitation threshold decreases under the condition that other liquid parameters remain unchanged. Therefore, according to the sound field simulation results and Eq. 10, it can be concluded that, with the increase of temperature, the pipe descaling effect becomes better.

Experiment results
After the descaling experiment was completed, 4-mm rings were cut at each end of the experimental pipe as samples, and then, the microscopic morphology of the inner wall Fig. 9 a The sound pressure distribution at a liquid temperature of 20 °C. b The sound pressure distribution at a liquid temperature of 40 °C. c The sound pressure distribution at a liquid temperature of 60 °C of the pipe after descaling was observed using an electron microscope, and the samples obtained during the experiment were analyzed for their chemical composition using an energy spectrometer. The electron micrographs of the pipes after descaling at temperatures of 20 °C, 40 °C, and 60 °C are shown in Fig. 10b, c and d, respectively (600 times magnification of the experimental samples), and the electron micrograph of the sample before descaling is shown in Fig. 10a. The results of the chemical element energy spectra of the descaling experiments at different temperatures are shown in Table. 1.  As can be seen from Table 1, the proportion of calcium elements in the inner wall of the pipe before descaling is about 30%, while the proportion of iron elements is less than 10%. After descaling, the elemental calcium content in the inner wall of the pipe decreases significantly and the elemental iron content increases significantly. When the liquid temperature is 60 °C, the calcium content in the inner wall of the pipe near the transducer is reduced from 39.24 to 1.17%, and the iron content is increased from 8.2 to 58.4% after descaling. According to the proportion of calcium elements, it can be inferred that the calcium carbonate in the inner wall of the pipe is removed.
The calcium content and descaling rate after descaling at different temperatures are shown in Fig. 11. It can be seen that when the temperature is from 20 to 60 °C, the descaling rate in the inner wall of the pipe far from the transducer is increased from 77.49 to 93.71%, the descaling rate in the inner wall of the pipe near the transducer is increased from 87.01 to 97.02%. The results show that with the increase in temperature, the content of calcium in the inner wall of the pipeline after descaling decreases, and the descaling rate increases. Therefore, it can be known that the temperature of the liquid in the pipeline will have a certain impact on the descaling effect, and the descaling effect is better when the temperature of the liquid in the pipeline is higher. Combining Eq. 10 with the finite element simulation results, it can be seen that the acoustic pressure value of the inner wall of the pipe is larger at a higher temperature, and the cavitation threshold is lower, so cavitation is easy to occur. Therefore, it can be concluded that the descaling effect is relatively better when the temperature is higher.

Conclusion
This paper studies the influence of different temperatures on the pipeline scale removal process based on the UGWs. A transducer was excited with a sinusoidal signal at a frequency of 42.38 kHz and 300Vp-p for 30 min at 20 °C. It can effectively remove the calcium carbonate scale in the pipe with a length of 1 m, an outer diameter of 42 mm, and a wall thickness of 3 mm. The descaling effect will be affected by the change of the temperature parameters of the liquid in the pipeline. When the temperature is 20 °C, 40 °C and 60 °C, respectively, the descaling rate of the inner wall of the pipe far from the transducer is 77.49%, 82.38% and 93.71%, respectively. When the temperature is 20 °C, 40 °C and 60 °C, respectively, the descaling rate in the inner wall of the pipe near the transducer is 87.01%, 91.01% and 97.02%, respectively. The descaling effect is better when the temperature of the liquid in the pipeline is higher. The research in this paper makes the ultrasonic waveguide wave technology can be better applied in practical application, which can better remove the scale on the inner wall of the pipeline by reasonably controlling the temperature in the pipeline without affecting pipeline transportation.