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Experimental research on the degradation of chemical industrial wastewater by combined hydrodynamic cavitation based on nonlinear dynamic model

  • Kai Zhang EMAIL logo , Huijun He , Lirong Liu , Junjie Zhang and Xiaobo Jiao
Published/Copyright: April 9, 2025
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Nonlinear Engineering
From the journal Nonlinear Engineering Volume 14 Issue 1

Abstract

Based on the self-developed combined hydrodynamic cavitation device composed of a Venturi tube with variable throat length-to-diameter ratios, a triangular orifice perforated plate and nonlinear dynamic model, the influences of factors such as the throat length-to-diameter ratio, cavitation number, orifice size, orifice quantity, initial concentration of raw water, and pH value on the degradation of chemical industrial wastewater by hydrodynamic cavitation were experimentally studied. Combined with the actual situation of chemical wastewater treatment, a nonlinear dynamic model of the hydraulic cavitation process was established, and the influence of different operating parameters on degradation effect was analyzed. The results showed that the extreme conditions generated during the collapse of cavitation bubbles could cause cavitation erosion damage to the refractory pollutants in chemical industrial wastewater. When the throat length-to-diameter ratio of the Venturi tube was L/R = 20, increasing the number of orifices (49 orifices) of the downstream perforated plate and reducing the orifice diameter (4.04 mm) were beneficial to the treatment of high-concentration wastewater. When the throat length-to-diameter ratio of the Venturi tube was L/R = 40 or 60, appropriately reducing the number of orifices (16 or 25 orifices) and increasing the orifice diameter (6.73 mm) could achieve the optimal degradation of high-concentration wastewater.

Keywords: hydrodynamic cavitation; chemical industrial wastewater; degradation rate

1 Introduction

According to the “Bulletin of China’s Ecological Environment Status in 2023” released by the Ministry of Ecology and Environment of the People’s Republic of China, wastewater pollutants from industrial sources include chemical oxygen demand (COD), total phosphorus, and permanganate index. In recent years, with the improvement of domestic wastewater treatment capacity and the increase in the number of wastewater treatment enterprises, the discharge volume of industrial wastewater has decreased to some extent, but there has been no significant change in the discharge structure. The wastewater discharge volume of the manufacturing of chemical raw materials and chemical products in the chemical industry still ranks first. The water quality components of chemical industrial wastewater are complex, with many by-products and high concentrations of organic substances. In particular, various toxic and harmful organic substances such as organic acids, alcohols, ketones, ethers, aldehydes, and epoxides in petrochemical wastewater will further oxidize and decompose in water, consuming a large amount of dissolved oxygen in the water. In addition, chemical industrial wastewater has a high salt content and a low B/C ratio (the ratio of biochemical oxygen demand to chemical oxygen demand), which increases the difficulty in cultivating secondary biochemical treatment bacteria and leads to unsatisfactory biochemical treatment effects [1]. At present, although the commonly used chemical industrial wastewater treatment technologies at home and abroad have achieved certain results, they also have many shortcomings and deficiencies. For example, the chemical method cannot completely oxidize all the pollutants in chemical industrial wastewater, and it is easy to cause secondary pollution to water bodies during the oxidation process. The biological method has a relatively slow treatment speed for chemical industrial wastewater, a long treatment cycle, and is greatly affected by external influencing factors such as reaction temperature and pH value. Although the advanced oxidation treatment technology has a high treatment efficiency, the operation cost of such reactors is relatively high, and there are strict requirements for reaction conditions [2,3,4,5]. Therefore, there is an urgent need for a new chemical industrial wastewater treatment process that is both efficient and economical.

The cavitation and cavitation erosion phenomena are accompanied by the formation, growth, and collapse of cavitation bubbles. The water vapor entering the cavitation bubbles undergoes splitting and chain reactions under high temperature and high pressure, generating hydroxyl radicals (˙OH) and hydrogen peroxide (H2O2). When the cavitation bubbles collapse, shock waves and microjets are generated, causing ˙OH and H2O2 to enter the entire solution. Volatile organic compounds can enter the cavitation bubbles to undergo pyrolysis reactions similar to combustion chemical reactions, organic compounds that are not volatile or are difficult to volatilize will have oxidation reactions with H2O2 and ˙OH on the gas–liquid interface of the cavitation bubbles or in the bulk solution. Meanwhile, during the cavitation process, a new fluid state that is different from gaseous, liquid, and solid states – supercritical water (SCW) is also formed. SCW has a low dielectric constant, high diffusivity, and fast transport ability, and it is an ideal reaction medium that is conducive to the increase in the rates of most chemical reactions. The ultrasonic cavitation technology was first applied in the field of water treatment. In 1927, the American scholar Richards first discovered that ultrasonic waves had the effect of accelerating the hydrolysis of dimethyl sulfate and the reaction of reducing potassium iodide by sulfurous acid [6]. Since the 1990s, the ultrasonic cavitation technology has achieved good progress in the application of degrading water pollutants. Sun et al. explored the optimal conditions for phenol degradation using acoustic cavitation and assessed its practical application through extensive pilot tests. Results from batch tests showed that low-frequency (15 kHz) ultrasonic cavitation effectively treated high concentrations of phenol (1,000 mg/L) [7]. However, the energy utilization rate of ultrasonic cavitation is relatively low, the cavitation action area is small, and its scaling up and expansion are restricted, making it difficult to achieve industrialization.

Generally, the phenomenon of generating cavitation in water bodies based on hydrodynamic methods is called hydrodynamic cavitation. In recent years, many scholars have carried out applied research on the treatment of refractory wastewater by hydrodynamic cavitation. Pandit and Joshi hydrolyzed castor oil and safflower oil by using cavitation technology for the first time, and hydrodynamic cavitation began to be applied in the field of water treatment [8]. Nong et al. measured the number of hydroxyl radical (˙OH) produced in the process of hydraulic cavitation by using the method of methylene blue ultraviolet spectrophotometer, and they found that the methylene blue spectrophotometer could successfully capture the hydroxyl radicals produced in the process of hydrodynamic cavitation, and the best hydrodynamic cavitation to produce hydroxyl radical was obtained from neutral water at 30°C when liquid flow rate is 800 L/h, gas flow rate is 0.15 L/h, and outlet pressure is 0.10 MPa [9]. The first author of this work degraded hydrophilic pollutants (nitrobenzene), hydrophobic pollutants (p-nitrophenol), and mixed hydrophilic and hydrophobic pollutants, respectively, through the cavitation and cavitation erosion effects of Venturi tubes, perforated plates, and different combinations of the two in the self-developed hydrodynamic cavitation devices. The experiment focused on studying the influences of factors such as combination modes, orifice sizes, orifice quantities, the relative length of the Venturi tube throat, and pollutant concentrations on the degradation rates of hydrophilic and hydrophobic pollutants. And the cavitation flow field was measured by testing instruments such as three-dimensional particle image velocimetry and high-speed cameras, and the action mechanism of removing refractory pollutants by cavitation and cavitation erosion of perforated plates and Venturi tubes was expounded [10,11,12]. Under the same conditions, the cavitation bubbles generated by the perforated plate are smaller and have a shorter collapse time. This can prompt hydroxyl groups to enter the liquid phase from the cavitation bubbles as early as possible, which is beneficial for pollutants to undergo chemical reactions. The Venturi tube with a relatively long throat can prolong the duration of the lowest water pressure and the expansion period of the cavitation bubbles, allowing the cavitation bubbles to grow for a longer time. This is conducive to pollutants entering the cavitation bubbles and undergoing pyrolysis when the cavitation bubbles collapse. Taking the actual chemical industrial wastewater as the treatment target, this study utilized a combined hydrodynamic cavitation device, which consists of Venturi tubes with variable throat length-to-diameter ratios and triangular orifice perforated plates. Through experiments, the impacts of multiple factors, including the cavitation number, throat length-to-diameter ratio, initial concentration of raw water, quantity of orifices, size of orifices, and pH value, on the COD degradation rate of the chemical industrial wastewater was investigated.

2 Experimental facility and measuring method

The experiment was carried out in the self-developed combined hydrodynamic cavitation device, as shown in Figure 1. The experimental device is a closed-circuit circulation system, which mainly consists of a water pump, a water tank, a working section combined with a Venturi tube and a perforated plate, a rotameter, a pressure gauge and a pipeline system. The Venturi tube is made of stainless steel plates, and the observation section as well as both sides and the top of the throat are made of plexiglass. The perforated plate is a stainless steel plate with a side length of 50 mm and a thickness of 5 mm, followed by a square observation section. The perforated plate is embedded at the entrance of the observation section, and its front and rear ends are connected to the pipeline system through square–round interfaces. Pressure measuring points are evenly arranged at the bottom of each pipe section.

Figure 1 Hydrodynamic cavitation device combined with Venturi tube and perforated plate. 1 – Water tank; 2 – Centrifugal pump; 3 and 4 – Pressure gauges; 5 – Combined cavitation working section; 6 – Rotameter; and V1–V6 – Control valves.
Figure 1

Hydrodynamic cavitation device combined with Venturi tube and perforated plate. 1 – Water tank; 2 – Centrifugal pump; 3 and 4 – Pressure gauges; 5 – Combined cavitation working section; 6 – Rotameter; and V1–V6 – Control valves.

Three types of Venturi tubes and four types of triangular orifice perforated plates have been designed. The Venturi tube mainly consists of three parts: the contraction section, the throat, and the diffusion section, as shown in Figure 2. The length-to-diameter ratios of the throat are L/R = 20, 40, and 60, respectively (where L is the length of the throat in mm and R is the hydraulic radius of the throat in mm), corresponding to 100–100–100 (the lengths of the contraction section, the throat, and the diffusion section, respectively, with the unit of mm for all), 100–200–100, and 100–300–100. The cross-sectional area of the throat is 20 × 20 mm2, and the detailed geometric parameters are shown in Table 1. The orifice sizes of the perforated plates are equilateral triangles converted from circular areas with d = 3 mm and d = 5 mm. The four perforated plates are as follows: a 16-hole triangular orifice perforated plate with a chessboard-like arrangement and an orifice side length of 6.73 mm, a 25-hole triangular orifice perforated plate with a staggered arrangement and an orifice side length of 6.73 mm, a 49-hole triangular orifice perforated plate with a chessboard-like arrangement and an orifice side length of 4.04 mm, a 25-hole triangular orifice perforated plate with a staggered arrangement and an orifice side length of 4.04 mm, as shown in Figure 3. The combination forms of the Venturi tubes and the perforated plates are shown in Table 2. Specifically, there are 12 combination forms: A1, A2, A3, A4, B1, B2, B3, B4, C1, C2, C3, and C4.

Figure 2 Venturi tube. d – Inlet diameter of the diffuser section; D – Outlet diameter of the diffuser section; L – Throat length; M – Contraction section and Diffuser section length.
Figure 2

Venturi tube. d – Inlet diameter of the diffuser section; D – Outlet diameter of the diffuser section; L – Throat length; M – Contraction section and Diffuser section length.

Table 1

Geometric parameters of the Venturi working section

Throat length L (mm) Hydraulic radius of the throat R (mm) Diffusion section length (mm) Throat length-to-diameter ratio L/R
100 5 100 20
200 5 100 40
300 5 100 60
Figure 3 Triangular orifice perforated plates. Plate 1, Plate 2, Plate 3, and Plate 4.
Figure 3

Triangular orifice perforated plates. Plate 1, Plate 2, Plate 3, and Plate 4.

Table 2

Combination forms of Venturi tubes and perforated plates

Venturi tube number Venturi tube specifications Perforated plate number Perforated plate specifications
A L/R = 20 1 16 holes with a side length of 6.73 mm in a chessboard arrangement
B L/R = 40 2 25 holes with a side length of 6.73 mm in a staggered arrangement
C L/R = 60 3 49 holes with a side length of 4.04 mm in a chessboard arrangement
4 25 holes with a side length of 4.04 mm in a staggered arrangement

The water flow rate was measured by the LZB-100 glass rotameter. The pressure in the hydrodynamic cavitation working section was collected in real time by the YE6263 pressure data acquisition system. The raw water samples were taken from the production wastewater of Zhejiang Transfar Chemical Group. The COD of the raw water was approximately 956 mg/L, the BOD₅ (the amount of free oxygen consumed by aerobic microorganisms in oxidizing and decomposing the organic matter in a unit volume of water within 5 days) was approximately 205 mg/L, and the initial pH was approximately 7.43. Gradient dilution was carried out using tap water, and the ratios of raw water (initial concentrations) V 0/V were 6.25, 12.50, 25.00, 50.00, and 75.00%, respectively, where V 0 is the volume of the raw water in the test water sample and V is the total volume of the test water sample. The test water samples were put into the water tank of the hydrodynamic cavitation device, and the water pump system was turned on to make the chemical industrial wastewater samples circulate and flow through the working sections of the Venturi tube and the perforated plate in sequence. The influences of factors such as the length-to-diameter ratio of the Venturi tube throat, the orifice size of the perforated plate, the number of orifices, the combination mode, as well as the cavitation number, the ratio of raw water and the pH value on the degradation of chemical industrial wastewater by cavitation and cavitation erosion were experimentally studied. The sampling times before and after the hydrodynamic cavitation action were 0, 30, 60, 90, and 120 min, respectively. Taking COD as the degradation index, it was measured by the 760CRT ultraviolet spectrophotometer. The degradation rate η of the wastewater is defined as:

(1) η = C 0 − C t C 0 × 100 % ,

where C 0 is the initial COD concentration of the diluted wastewater, mg/L; and C t is the COD concentration of the wastewater after the hydrodynamic cavitation action, mg/L.

3 Results and discussion

3.1 Influence of the throat length-to-diameter ratio on the degradation rate of chemical industrial wastewater

When the ratio of raw water V 0/V = 50%, taking the three combinations of A4, B4, and C4 as examples, the changing trend of the degradation rate of chemical industrial wastewater is shown in Figure 4. The combination of B1 (R/L = 20) shows an obvious degradation advantage, and the degradation rate of the wastewater is the highest. When the water flow passes through the contraction section of the Venturi tube, its speed increases and the pressure decreases. Cavitation bubbles are formed and cavitation occurs when the pressure drops to negative pressure at the throat. When the cavitation bubbles enter the diffusion section, their speed decreases and the pressure increases, causing the cavitation bubbles to collapse. The microjets and shock waves generated during the collapse of the cavitation bubbles will cause cavitation erosion damage to the refractory substances in the chemical industrial wastewater. It can be seen that the number of cavitation bubbles directly determines the effect of cavitation degradation. Cavitation bubbles are formed and develop in the Venturi area. If the length of the throat is too short (such as A1, R/L = 20), a large number of cavitation bubbles will enter the diffusion section before they have time to form, affecting the occurrence of cavitation. If the length of the throat is too long (such as C1, R/L = 60), the duration of the cavitation bubbles in it will be prolonged, resulting in a longer collapse cycle of the cavitation bubbles, a reduced collapse pressure, and a weakened ability to cause cavitation erosion on pollutants.

Figure 4 Influence of the throat length-to-diameter ratio on the degradation rate of chemical industrial wastewater.
Figure 4

Influence of the throat length-to-diameter ratio on the degradation rate of chemical industrial wastewater.

In addition, as the reaction proceeds, the degradation rate of COD tends to increase first and then gradually stabilize. During 0–60 min, the degradation rate increases rapidly and shows a linear growth. During 60–90 min, the degradation rate slows down, and during 90–120 min, the degradation rate basically levels off. Extending the cavitation action time can improve the degradation rate of chemical industrial wastewater. In particular, the first 60 min of the hydrodynamic cavitation reaction is the efficient degradation stage of COD. After that, as the reaction proceeds, a large number of cavitation bubbles escape due to the gradual increase in water temperature, which affects the effect of hydrodynamic cavitation.

3.2 Influence of orifice size and orifice quantity on the degradation rate of chemical industrial wastewater

The perforated plates of both combinations C2 and C4 have 25 orifices, with the orifice diameters being 4.04 mm and 6.37 mm, respectively. The upstream is a Venturi tube with R/L = 40. In the experiment, the ratio of raw water V 0/V = 50%, and the rest of the working conditions are the same. The change in the degradation rate of chemical industrial wastewater with the orifice size is shown in Figure 5: when the number of orifices is the same, appropriately reducing the orifice diameter is beneficial for improving the degradation rate of the wastewater. When the orifice diameter is relatively small, the flow velocity of the multiple jets passing through the perforated plate increases, intensifying the mixing and shearing among the jets, thereby increasing the turbulence intensity, which is conducive to the generation and collapse of cavitation bubbles, so the degradation rate increases.

Figure 5 Influence of orifice size on the degradation rate of chemical industrial wastewater.
Figure 5

Influence of orifice size on the degradation rate of chemical industrial wastewater.

Figure 6 discusses the influence of the number of orifices on the degradation rate of chemical industrial wastewater for combinations B1 and B2 (both with an orifice diameter of 6.73 mm and the number of orifices being 16 and 25, respectively). The results show that when the orifice diameter is consistent, increasing the number of orifices can improve the degradation rate of the wastewater. When the number of orifices increases, the number of jet strands increases, the mixing, entrainment, and turbulence shear stress among multiple jets intensify, and the pressure pulsation increases, strengthening the cavitation effect.

Figure 6 Influence of orifice quantity on the degradation rate of chemical industrial wastewater.
Figure 6

Influence of orifice quantity on the degradation rate of chemical industrial wastewater.

3.3 Influence of the ratio of raw water on the degradation rate of chemical industrial wastewater

Experiments were carried out on the 12 combinations under different ratios of raw water concentrations. The experimental results of hydrodynamic cavitation degradation for 120 min are shown in Figure 7, the degradation rate of the wastewater first increases and then decreases with the increase in the initial concentration. Each combination form corresponds to an optimal ratio of raw water concentration with the maximum degradation rate. Basically, all combinations have the maximum degradation rate when the ratio of raw water is 25 or 50%. By analyzing Figure 7, it can be known that the ratio of raw water corresponding to the maximum degradation rate for combinations A1 and A2 is 25%, and that for combinations A3 and A4 is 50%. Conversely, the ratio of raw water corresponding to the maximum degradation rate for combinations B1, B2, C1, and C2 is 50%, and that for combinations B3, B4, C3, and C4 is 25%. Due to the influences of the throat length-to-diameter ratio of the Venturi tube and the orifice parameters of the perforated plate, the number of cavitation bubbles generated and the degree of cavitation in the flow field of the cavitation working section are different for each combination. When the throat length-to-diameter ratio of the Venturi tube is R/L = 20, increasing the number of orifices (49 orifices) of the downstream perforated plate and reducing the orifice diameter (4.04 mm) are beneficial to the treatment of medium and high-concentration wastewater. When the throat length-to-diameter ratio of the Venturi tube is R/L = 40 or 60, appropriately reducing the number of orifices (16 or 25 orifices) and increasing the orifice diameter (6.73 mm) can achieve the effective degradation of medium and high-concentration chemical industrial wastewater. If the initial concentration of wastewater pollutants is too high, it is necessary to improve the degradation rate by increasing the flow velocity, prolonging the cavitation action time and other means.

Figure 7 Influence of the ratio of raw water on the degradation rate of chemical industrial wastewater. (a) Combination forms of A. (b) Combination forms of B. (c) Combination forms of C.
Figure 7

Influence of the ratio of raw water on the degradation rate of chemical industrial wastewater. (a) Combination forms of A. (b) Combination forms of B. (c) Combination forms of C.

3.4 Influence of the cavitation number on the degradation rate of chemical industrial wastewater

The degree of cavitation in hydrodynamic cavitation can be described by the cavitation number σ, and its expression is as follows:

(2) σ = p − p v ρ U 2 / 2 ,

where p is the absolute pressure, p v is the saturated vapor pressure of water, ρ is the density of water, and U is the orifice velocity or the throat velocity.

Taking four combinations, namely, B1, B2, B3, and B4 as examples, the temperature of the test water was 58°C, and the corresponding saturated vapor pressure was 17.312 kPa. The proportion of raw water was 50%, and the action time of hydrodynamic cavitation was 120 min. The YE6263 pressure data acquisition system was used to collect the pressure values at each pressure measuring point. The cavitation numbers at the throat and at each pressure measuring point downstream of the perforated plate are shown in Figure 8, and the influence of different combination methods on the degradation rate is shown in Figure 9. As can be seen from Figure 8, the cavitation numbers generated in the perforated plate section are smaller than those at the throat of the Venturi tube, and the cavitation numbers are basically stable at around 0.3. The cavitation phenomenon is more significant downstream of the perforated plate, and the degree of cavitation is more intense. It can be seen that combining the Venturi tube upstream of the perforated plate can extend the duration of the minimum pressure and the time of bubble collapse, and enhance the degree of cavitation in the perforated plate section. The combined reactor provides better hydraulic conditions for the formation, growth, and collapse of bubbles. Combining Figures 8 and 9, it can be seen that the staggered arrangement with 25 holes, which has a lower cavitation number, has a better degradation effect, and the degradation rate can reach 46% after treating pollutants for 120 min.

Figure 8 Changes in the cavitation number at each measuring point of the combined hydrodynamic cavitation reactor.
Figure 8

Changes in the cavitation number at each measuring point of the combined hydrodynamic cavitation reactor.

Figure 9 Influence of the cavitation number on the degradation rate of chemical industrial wastewater.
Figure 9

Influence of the cavitation number on the degradation rate of chemical industrial wastewater.

3.5 Influence of pH value on the degradation rate of chemical industrial wastewater

Taking the B3 combination as the analysis object, with the proportion of raw water being 25%, adjust the pH value of the water sample to 3.61, 7.12, and 10.36 in sequence, and run the experiment for 120 min to analyze the influence of the pH value on the degradation rate of chemical industrial wastewater. The test results are shown in Figure 10. As can be seen from the figure, compared with acidic and alkaline conditions, when the water sample is neutral, the degradation rate of the wastewater is the highest. The inhibitory effect of alkaline conditions on the hydrodynamic cavitation degradation of chemical industrial wastewater is greater than that of acidic conditions. Cavitation degradation occurs inside the bubbles or at the gas–liquid interface of the water pollutant solution. If the organic molecules in the water pollutant solution exist in the form of salts, their water solubility will increase and their volatility will decrease, resulting in a reduction in the concentration of organic substances inside the bubbles and at the gas–liquid interface, which is not conducive to cavitation degradation. Therefore, when performing cavitation degradation on organic acids and organic bases in the water pollutant solution, the pH value of the water sample should be adjusted to be neutral as much as possible to improve the hydrodynamic cavitation degradation rate, while avoiding the corrosive damage to the cavitation device caused by acidic or alkaline environments.

Figure 10 Influence of pH value on the degradation rate of chemical industrial wastewater.
Figure 10

Influence of pH value on the degradation rate of chemical industrial wastewater.

4 Conclusion

The following conclusions can be drawn from the degradation of chemical industrial wastewater by the combined hydrodynamic cavitation effect of the Venturi tube and the perforated plate.

  1. When the length-to-diameter ratio of the throat of the Venturi tube is L/R = 20, increasing the number of orifices (49 holes) of the downstream perforated plate and reducing the hole diameter (4.04 mm) are beneficial for treating medium and high-concentration wastewater. When the length-to-diameter ratio of the throat of the Venturi tube is L/R = 40 or 60, the number of orifices can be appropriately reduced (16 holes or 25 holes) and the hole diameter can be increased (6.73 mm) to achieve the optimal degradation of medium and high-concentration wastewater.

  2. For different combinations of the Venturi tube and the perforated plate, there are different optimal proportions of raw water for chemical industrial wastewater. Selecting a suitable volume ratio of raw water can make more efficient use of the cavitation effect to degrade pollutants.

  3. A lower cavitation number indicates a more intense hydrodynamic cavitation phenomenon. The cavitation number can be reduced by adjusting the parameters of the cavitation reactor to improve the degradation rate of chemical industrial wastewater.

  4. When using the hydrodynamic cavitation technology to degrade actual chemical industrial wastewater, it is necessary to adjust the pH value of the treated water sample to be neutral in order to achieve the best degradation effect, while avoiding the corrosion of the cavitation device caused by acidic or alkaline environments.

It should be pointed out that due to the limitations of the experimental conditions, the throat velocity and the orifice velocity are relatively low, and the corresponding cavitation number is relatively high. If the throat velocity and the orifice velocity are increased, the degradation rate of chemical industrial wastewater can be further improved.

Acknowledgments

The authors acknowledge the Special Project for University Teachers in Xinjiang Aided by the Department of Education of Zhejiang Province “Research on the Degradation Mechanism of Coal Chemical Wastewater by Cavitation and Erosion of High-Speed Water Flow” (Project No. Y202456896) and the National Natural Science Foundation of China (Grant: 51479177).

  1. Funding information: The authors acknowledge the Special Project for University Teachers in Xinjiang Aided by the Department of Education of Zhejiang Province “Research on the Degradation Mechanism of Coal Chemical Wastewater by Cavitation and Erosion of High-Speed Water Flow” (Project No. Y202456896) and the National Natural Science Foundation of China (Grant: 51479177).

  2. Author contributions: Conceptualization: Kai Zhang and Huijun He; methodology: Kai Zhang; experimental operation: Kai Zhang; data statistics: Lirong Liu, Junjie Zhang, and Xiaobo Jiao; writing – original draft preparation: Kai Zhang; writing – review and editing: Kai Zhang and Huijun He; funding acquisition: Kai Zhang, Huijun He, Lirong Liu, and Junjie Zhang. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: Authors state no conflict of interest.

  4. Data availability statement: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Received: 2025-01-22
Revised: 2025-02-26
Accepted: 2025-03-03
Published Online: 2025-04-09

© 2025 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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  102. Numerical simulation of damage mechanism in rock with cracks impacted by self-excited pulsed jet based on SPH-FEM coupling method: The perspective of nonlinear engineering and materials science
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https://doi.org/10.1515/nleng-2025-0103
Keywords for this article
hydrodynamic cavitation; chemical industrial wastewater; degradation rate
Creative Commons
BY 4.0

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