A Study on the Optimization of Water Jet Decontamination Performance Parameters Based on the Response Surface Method

Abstract

The substrate that adheres between the teeth of the traveling track plate during the operation of a deep-sea polymetallic nodule mining vehicle affects the driving performance, so this study aimed to investigate the effect of the water jet on the cleaning and decontamination performance of the track under different conditions. An optimization design method based on response surface methodology (RSM) is proposed. Based on the Box–Behnken design, the optimization variables of jet pressure, jet target distance, and impact angle, and the target response of jet strike pressure on tracks, were selected, and the numerical simulation method was combined with the response surface method to establish the regression model of the response of each optimization variable to the jet strike pressure on tracks and to determine the optimal parameter combinations. The study findings indicate that the primary factor influencing the pressure of the jet striking the crawler is the jet pressure. The hierarchical order of influence on the pressure of the jet striking the crawler, under the interaction of the three factors, is as follows: jet pressure and impact angle, jet pressure and target distance of the jet, and target distance of the jet and impact angle. The maximum pressure of the jet striking the crawler occurs when the jet pressure is 0.983 MPa, the target distance is 0.14 m, and the impact angle is 89.5°. Overall, the proposed design serves as a systematic framework for parameter optimization in the cleaning and decontamination process, and the research method and results provide theoretical references for the optimal design of mining truck desorption efficiency, which is critical for increasing mining efficiency and lowering energy consumption.

1. Introduction

The deep seabed is known for its abundant mineral resources, prompting China to begin researching deep-sea mining technology in the early 1980s [1]. Polymetallic nodules, mineral resources located on the seafloor at depths between 3000 and 6000 m, contain valuable metals such as manganese, nickel, and copper, making them a promising source for commercial exploitation [2].

In deep-sea mining operations, the vehicle plays a critical role, as its performance when traveling on the seabed directly impacts the overall continuous operating performance of the mining system [3,4]. However, the soft nature of deep-sea sediments leads to sediment accumulation in the track gaps of the chassis during the vehicle’s operation on the seafloor. This accumulation reduces the effective working depth of the tracks and the vehicle’s maneuverability in soft sediment areas. Given the diverse and complex seabed topography, mining vehicle design and agility must adhere to rigorous standards [5]. To overcome this challenge, high-pressure water jet cleaning and decontamination technologies are necessary to clear material from the track gaps and improve the vehicles’ agility on the soft seabed substrate.

Tracked mining vehicles are commonly used in deep-sea operations due to their ability to carry heavy loads and provide a high traction power [6,7]. However, a major challenge lies in enhancing driving performance and removing sediments between the track teeth. Love [8] evaluated the effectiveness of different solutions and foams for decontaminating interior surfaces. In a study, researchers investigated the impact of track parameters on shear pressure between sediments by developing a numerical model for tracked mining vehicles [9]. Utilized extensively across several sectors, water jet technology can also aid in addressing the problem of adhesion cleaning [10]. In 2020, Li [1] investigated the reduction in viscosity and detachment of a traveling water jet, deriving the dimensionless equation for the crater’s radius and depth. Their findings revealed that the crater depth increased gradually with the radius before sharply rising, and it was influenced by water jet parameters, target distance, and the critical destructive force of the substrate. In 2020, Zhang [11] utilized EDEM–Fluent coupling to examine the impact of various key water jet parameters on soil, and the best effect on the soil was achieved with an 8 mm gap between the outlet pipes and a jet injection speed of 30 m/s but did not specify the effect of water jet flow and pressure on soil fragmentation. In 2023, Xiong [12] investigated the effects of jets impacting hull surfaces at various angles and speeds using the ALE algorithm, focusing on pressure and stress characteristics. The results revealed that contacting the target with the suitable injection angle can raise the kinetic energy of the high-pressure water jet and enhance the effect of cleaning the surface adherence. Furthermore, in 2020, Zhong [13] analyzed the flow field of a 300 m deep water jet for cleaning ground immersion filters, investigating the impact of different nozzle diameters, pressure drops, deflection angles, and target distances on fouling decontamination. The findings indicated that the maximum jet impact pressure and effective cleaning length increased by 22.15% and 905.46%, respectively, when the nozzle diameter is increased from 1 mm to 2 mm. A higher nozzle pressure drop also results in a higher jet impact pressure and better jet disinfection capability. In the domain of peri-implantitis treatment, there is a critical need for an effective yet non-destructive debridement technique to enhance the success rates of peri-implantitis interventions. Matthes [14] developed a new water jet device and a new cold atmospheric pressure plasma device to overcome these problems.

The rapid development of the finite element method (FEM) has provided an efficient means of numerical simulation for complex engineering problems, thereby avoiding the high cost and long cycle time associated with experimental methods [15]. Furthermore, computational fluid dynamics (CFD) technology has become a crucial tool for the analysis of fluid processes, particularly in situations where experimental measurements are unattainable due to various constraints that hinder their implementation. For example, Basson [16] used CFD to study ocular aqueous humor flow in the anterior chamber by inserting an Ahmed Glaucoma Valve and provided promising insights into improving patient prognosis and safety in glaucoma treatment. The response surface method offers the advantages of requiring fewer experiments and shorter cycle times [15,17]. It also demonstrates superior accuracy and convenience in comparison to alternative experimental methodologies [18]. Scholars in the field have utilized the response surface method to optimize the design of nozzle jet parameters by conducting numerical simulations on the hydrodynamic characteristics of water jet nozzles. In 2020, X. Wang [19] employed an orthogonal experimental design approach to optimize water jet nozzle geometry, aiming to maximize cutting capacity and minimize erosion rate. In 2017, Liu [20] examined the impact of various nozzle structures on flow field characteristics. In 2024, Sun [21] utilized an orthogonal experimental approach to determine the optimal parameters for nozzle structure and compared the cleaning effectiveness of different jet pressures and target distances on adherent compounds on car body surfaces. The author obtained three sets of pressure values of high-pressure water injection speed than before the optimization increased by 2%, while the input pressure was 10 MPa and the target distance 250 mm; the cleaning results were enhanced. In 2019, Wen [22] employed an orthogonal experimental design, numerical simulation, and water jet impingement testing to identify the optimal parameters for conical nozzles. However, it is evident from the review of the existing literature that previous scholars have not investigated the impact of multifactorial cleaning and decontamination indices on the adherence of contaminants to the surfaces within walking track gaps.

This research examined the adherent substrate located between the walking tracks of mining trucks as its primary subject of investigation. By combining the response surface and finite element methods, one can ascertain whether the parameter combination that has the biggest impact on the response value can be found within the range of values of the three influencing factors by analyzing the influence of each optimization variable on the pressure of the jet striking the crawler teeth. This allows one to determine the best combination of parameter values. The proposed design serves as a systematic framework for parameter optimization in the cleaning and decontamination process, and the research method and results provide theoretical references for the optimal design of mining truck desorption efficiency, which is critical for increasing mining efficiency and lowering energy consumption.

2. Methods

2.1. CFD Method

The finite element method (FEM) and computational fluid dynamics (CFD) are two numerical analysis methods commonly utilized in engineering and scientific research. The FEM focuses on solid mechanics problems such as structural stress and strain analysis, as well as electromagnetic and thermal field simulations. In contrast to the finite element method (FEM), computational fluid dynamics (CFD) method is better suited to simulating and analyzing fluid flows and their complicated interactions with heat transfer, mass transfer, and chemical reactions. CFD has numerous advantages for dealing with fluid dynamics problems, particularly in simulating multiphase flows, turbulence features, and free surface and interfacial difficulties. Its capabilities are demonstrated in the simulation of dynamic and transient flow problems, such as transient pressure fluctuations of fluids in piping systems, vibration response in fluid–structure interactions, and heat exchange efficiency analysis in thermal–fluid interactions. CFD is the preferred method when the problem involves fluid dynamics.

This study investigated the optimization of water jet decontamination performance parameters at a submergence depth of 5000 m. Therefore, computational fluid dynamics was chosen.

2.1.1. Geometric Model

Before numerical simulation, a geometric model was created in SOLIDWORKS (2024), followed by importing it into ICEM (v.19.0) for structured meshing, The mesh type was a hexahedral unstructured mesh. Subsequently, the simulation analysis was conducted using ANSYS Fluent software (2024 R1) to validate the accuracy and reliability of the simulation. The three-dimensional computational domain is shown in Figure 1. The model is accurately built based on the real dimensions of a deep-sea mining vehicle’s walking track teeth, and a previous simulation study showed that the jet velocity begins to decline rapidly at around 0.31 m for a 30 mm diameter linear nozzle. To handle the jet’s core efficacy region, the simulation analysis used a distance of 0.16 m between the nozzle injection point and the root of the tooth and the dimensions of the nozzle flow field measuring 1.8 m × 0.3 m × 0.3 m (length × width × height). This precise parameter selection was intended to maximize cleaning efficiency while optimizing energy consumption during the cleaning procedure.

2.1.2. Governing Equation

In numerical simulations of water jets, the fluid is typically considered a continuous and incompressible medium. The fluid flow process is governed by three fundamental equations: the continuity equation, the momentum conservation equation, and the energy conservation equation [23].

$$\begin{array}{c}{\displaystyle \frac{\partial {\rho }_{\mathrm{m}}}{\partial t}}+\nabla ·\left({\rho }_{\mathrm{m}}{\overrightarrow{\nu }}_{\mathrm{m}}\right)=0\end{array}$$

(1)

$$\begin{array}{l}{\displaystyle \frac{\partial }{\partial t}}\left({\rho }_{\mathrm{m}}{\overrightarrow{\nu }}_{\mathrm{m}}\right)+\nabla \cdot \left({\rho }_{\mathrm{m}}{\overrightarrow{\nu }}_{\mathrm{m}}{\overrightarrow{\nu }}_{\mathrm{m}}\right)=-\nabla p+\nabla \cdot \left[{\mu }_{\mathrm{m}}\left(\nabla {\overrightarrow{\nu }}_{\mathrm{m}}+{\overrightarrow{\nu }}_{\mathrm{m}}^{\mathrm{T}}\right)\right]\\ +{\rho }_{\mathrm{m}}\overrightarrow{g}+\overrightarrow{F}+\nabla \cdot \left(\sum _{\mathrm{k}=\mathrm{l}}^{\mathrm{n}}{\alpha }_{\mathrm{k}}{\rho }_{\mathrm{k}}{\overrightarrow{\nu }}_{\mathrm{d}\mathrm{r},\mathrm{k}}{\overrightarrow{\nu }}_{\mathrm{d}\mathrm{r},\mathrm{k}}\right)\end{array}$$

(2)

where $t$ is the time; ${\overrightarrow{\nu }}_{\mathrm{m}}$ is the velocity vector; $p$ represents the pressure on the fluid micro-element; ${\mu }_{\mathrm{m}}$ is the viscosity of the fluid; $F$ is the volumetric force; ${\alpha }_k$ is the volume fraction of the $k$th phase; and ${\overrightarrow{\nu }}_{\mathrm{d}\mathrm{r},\mathrm{k}}$ is the slip velocity of subphase $k$.

In a deep-sea environment, the nozzle jet used to flush sediments on the crawler is classified as a submerged jet. This jetting process involves two mediums, water and air, necessitating the selection of an appropriate multiphase flow model for analysis. Ansys includes three types of multiphase flow models: the mixing model, the VOF (Volume of Fluid) model, and the Euler model. The Volume of Fluid (VOF) model is applicable in scenarios where the phases are immiscible, share a common momentum equation, and are characterized by phase fractions. These phase fractions must be determined using a pressure-based solver. The Eulerian model possesses the capability to simulate multiphase-separated flows, as well as the interactions among different phases, which encompass liquids, gases, and solids. However, it is associated with high memory consumption and presents challenges in achieving convergence. The Mixture model, known for its ability to handle multiphase fluid flow with varying velocities of each phase, is preferred due to its ease of convergence in calculations, high accuracy, and computational efficiency. A variety of turbulence modeling solutions are accessible within the Fluent software. There are three types of k-ε models: the realizable k-ε model, the RNG k-ε model, and the standard k-ε model. The realizable k-ε model is used as the turbulence model due to the intricate nature of water jets, including high-speed flow, collision, entrainment, and other factors. This model can more correctly explain the diffusion velocity of the circular jet, and it meets the limits on the Reynolds stress, which can be kept consistent with the Reynolds stress of real turbulence.

2.1.3. Boundary Conditions and Solution Method Setup

To ensure the accuracy of numerical calculation results, it is crucial to define boundary conditions appropriately. In this study, the inlet of the jet was set as a pressure inlet, while the outlet was set as a pressure outlet. The wall surface was designated as a standard non-slip wall surface. Furthermore, the ambient pressure was established at 50 MPa, and the simulated inundation depth was set at 5000 m.

The numerical simulation’s parameter settings are as follows: the simulation focuses on pressure calculation and utilizes pressure–velocity coupling. The SIMPLE method is chosen for the solution system [24,25], the pressure term of the control equation is treated in the standard format, the gradient is treated using the least squares method, the volume transport equation is treated with a one-section windward difference, and the momentum, turbulent kinetic energy, turbulent dissipation, and continuity equations are treated with a second-order windward difference, with default settings for the rest of the parameters. The residual accuracy was set to 10⁻⁵, and 5000 iterations were performed after global initialization to enhance computational accuracy and convergence [26,27].

Figure 2 illustrates the entire computational flow, which aids in better understanding the CFD solution process.

According to Bernoulli’s principle, the relationship between fluid velocity and pressure can be simplified as follows:

$$\mathrm{v}=w\sqrt{{\displaystyle \frac{2P}{\rho }}}$$

(3)

where $\mathrm{v}$ is the fluid velocity, $w$ is the flow coefficient, $P$ is the inlet pressure, and $\rho$ is the fluid density. Under a 10–50 MPa injection pressure, Figure 3 compares the theoretical and simulated velocities of nozzles with different injection pressures and simulation plots of the jet velocity distribution at 50 MPa. The results reveal that theoretical and simulated velocities agree well, and numerical simulation results are accurate.

2.1.4. Mesh Delineation and Mesh-Independence Verification

In the computational fluid dynamics solution process, the impingement jet model utilizes the grid-blocking method for mesh division. The jet region is subdivided into key areas based on specific change rules, while the remaining grid areas are kept coarse. This approach considers the mesh requirements of different regions, reduces the total number of grid nodes, and ultimately enhances computational accuracy and efficiency. The primary regions of the jet, including the surface of the track tooth, the nozzle wall, and additional components, are subjected to mesh refinement.

Table 1. Verification of grid sensitivity.

Mesh	Mesh Size (mm)	Velocity (m/s)	Dynamic Pressure (Pa)
Mesh 1	1	45.21	1,020,234.4
Mesh 2	2	45.22	1,020,450.1
Mesh 3	4	45.3	1,024,043.9
Mesh 4	8	45.22	1,020,485.9
Mesh 5	16	44.97	1,009,342.6
Mesh 6	32	43.47	943,026.4
Mesh 7	64	43	923,008.8

displays the parameters of the model with varying mesh densities.

To validate the simulation results, the injection pressure is kept at 1 MPa with all other initial conditions unchanged. The same boundary conditions are applied, focusing on the nozzle’s axial linear velocity (Velocity) and the tracked tooth pressure (Dynamic Pressure) for analysis [28]. The results are presented in Figure 2.

The trends of axial velocity and pressure distributions for different grid sizes are consistent, as shown in Figure 4. To maintain accuracy and computational efficiency, 678,022 meshes were employed in the three-dimensional grid model for the jet calculation [28].

2.2. Response Surface Method

There exist three fundamental experimental design methodologies for investigating multifactorial and multilevel phenomena: orthogonal experimentation, uniform design, and response surface method. The orthogonal experimental methodology employs an orthogonal table to select a limited number of experiments that exhibit high representativeness, thereby facilitating optimal or improved conditions. This approach is characterized by uniform dispersion and clear comparability among the selected tests. The uniform design method produces complex statistics, fewer trials, and higher sampling error, and it is not appropriate in the presence of considerable experimental error. The response surface methodology (RSM) is a systematic approach employed to identify optimal parameter values utilizing experimental design and data acquisition. This process is subsequently followed by the formulation of regression equations that establish relationships between the optimized variables and the desired response [29,30]. It offers the advantages of intuition, comprehensiveness, and resource efficiency, as it can visually communicate the input–output relationship, comprehensively reflect the relationship and interaction of components, minimize the number of experiments, and enhance efficiency. This study utilized nozzle jet pressure $\mathrm{X}$, target distance ${\mathrm{X}}_2$, and impact angle ${\mathrm{X}}_3$ as independent variables. In the context of water jet cleaning and decontamination in deep-sea environments, the pressure of the water jet impacting the track tooth directly influences the de-attachment effect. Hence, the pressure of the jet hitting the track tooth was considered as the response variable, denoted as Y. The experimental ranges and levels of the independent variables are detailed in

Table 2. Response surface test factor levels.

Input Parameters	Variables Coded	Units	Level 1	Level 2	Level 3
Injection pressure	${\mathrm{X}}_1$	MPa	0.4	0.7	1
Target distance	${\mathrm{X}}_2$	m	0.14	0.16	0.18
Impact angle	${\mathrm{X}}_3$	°	60	75	90
Constant parameters
Nozzle type	Linear nozzle
Nozzle diameter	30 mm
Ambient pressure	50 MPa

. Based on the coded values in Table 2, 17 groups of numerical experiments with 5 center points were designed, with results presented in

Table 3. Results of the conducted experiments.

Run	${\mathbf{X}}_1$/MPa	${\mathbf{X}}_2$/m	${\mathbf{X}}_3$/°	Y/Pa
1	0.7	0.18	90	413,480
2	0.7	0.14	90	492,057
3	0.4	0.14	75	286,069
4	1	0.16	60	565,882
5	0.4	0.16	60	238,407
6	0.7	0.18	60	413,718
7	1	0.14	75	664,159
8	0.4	0.18	75	231,040
9	0.7	0.16	75	404,380
10	0.7	0.16	75	404,380
11	0.7	0.16	75	404,380
12	1	0.16	90	647,506
13	1	0.18	75	558,866
14	0.7	0.16	75	404,380
15	0.4	0.16	90	261,442
16	0.7	0.14	60	451,204
17	0.7	0.16	75	404,380

. Following the synthesis and analysis of the experimental results utilizing Design Expert software (v.13), a response surface model was developed employing the least-squares method [31].

$$Y={\beta }_0+{\sum }_{i=1}^k{\beta }_i{X}_i+{\sum }_{i=1}^k{\beta }_{ii}{X}_i^2+{\sum }_{\begin{array}{c}i,j\\ i<j\end{array}}^k{\beta }_{i,j}{X}_i{X}_j$$

(4)

where $Y$ is the response variable, $x$ is the design variable, ${\beta }_0$ is the linear term, ${\beta }_i$ is the slope of the variable $x_i$, ${\beta }_{ii}$ is the quadratic term of the variable $x_i$, and ${\beta }_{i,j}$ is the coefficient of the cross-product term of $x_i$ and $x_j$.

3. Results and Discussion

3.1. Regression Equation

Multiple regression analysis was carried out using Design Expert software, and the response surface quadratic function relationship was obtained as follows:

$$\begin{array}{c}\mathrm{Y}=\mathrm{404,400}+\mathrm{177,400}{X}_1-\mathrm{34,548.12}{X}_2+\mathrm{18,159.25}{X}_3-\mathrm{12,566}{X}_1{X}_2+\mathrm{14,647.25}{X}_1{X}_3-\mathrm{10,272.75}{X}_2{X}_3+\\ 8174X_1^2+\mathrm{22,479.5}{X}_2^2+\mathrm{15,755.25}{X}_3^2\end{array}$$

(5)

3.2. Analysis of Variance (ANOVA)

Table 4. ANOVA related to the RSM.

Source	Sum of Squares	df	Mean Squares	F-Value	p-Value
Model	2.7 × 1011	9	3 × 1010	274.31	<0.0001
${\mathrm{X}}_1$	2.52 × 1011	1	2.52 × 1011	2305.10	<0.0001
${\mathrm{X}}_2$	9.55 × 109	1	9.55 × 109	87.39	<0.0001
${\mathrm{X}}_3$	2.64 × 109	1	2.64 × 109	24.14	0.0017
${\mathrm{X}}_1{\mathrm{X}}_2$	6.32 × 108	1	6.32 × 108	5.78	0.0472
${\mathrm{X}}_1{\mathrm{X}}_3$	8.58 × 108	1	8.58 × 108	7.85	0.0264
${\mathrm{X}}_2{\mathrm{X}}_3$	4.22 × 108	1	4.22 × 108	3.86	0.0901
${\mathrm{X}}_1$2	2.81 × 108	1	2.81 × 108	2.57	0.1526
${\mathrm{X}}_2$2	2.13 × 109	1	2.13 × 109	19.47	0.0031
${\mathrm{X}}_3$2	1.05 × 109	1	1.05 × 109	9.57	0.0175
Residual	7.65 × 108	7	1.09 × 108
Lack of Fit	7.65 × 108	3	2.55 × 108
Pure Error	0	4	0
Cor. Total	2.71 × 1011	16

presents the ANOVA results of the model, with the p-value indicating the significance of the factor. A p-value less than 0.001 is highly significant, while one that is generally less than 0.05 is considered significant. The results in Table 4 reveal that the p-value of the regression model is less than 0.0001, signifying the high significance of the response surface model and the regression effect [18,32]. The single-parameter analysis demonstrates that the p-values of regression terms ${\mathrm{X}}_1$ and ${\mathrm{X}}_2$ are less than 0.0001, highlighting the highly significant effects of jet pressure and target distance on the pressure of the jet striking the track tooth. The p-value of ${\mathrm{X}}_3$ is 0.0017, indicating that the effects of jet angle on the pressure of the jet striking the track tooth are significant; the two-parameter analysis shows that the p-values of the combinations ${\mathrm{X}}_1{\mathrm{X}}_2$ and ${\mathrm{X}}_1{\mathrm{X}}_3$ are 0.0472 and 0.0264, respectively, which are distributed in 0.001 < p-value < 0.05, indicating that the effect of two two-parameter combinations on the jet striking the tracked teeth’s pressure is significant. From the F-value, it can be seen that the order of influence on the pressure of the jet striking the track tooth is ${\mathrm{X}}_1$ > ${\mathrm{X}}_2$ > ${\mathrm{X}}_3$. The quality of the regression model was assessed by the linear regression coefficient of determination, coefficient of variation, signal-to-noise ratio, and the sum of squares of forecasts [33]. The coefficient of variation CV = 2.45%, indicating that only 2.45% of the total variation cannot be explained by this model. The signal-to-noise ratio is 52.8. Refs. [32,34] indicates that when the model coefficient of variation is less than 10 and the signal-to-noise ratio is greater than 4, the model fits with a high accuracy and good reproducibility. The established response prediction model in this study is proven to be reliable in describing the response law of jet striking tracked teeth.

The model phase test results are presented in

Table 5. Model correlation tests.

R2	Adjusted R2adj	Predicted R2	C.V.	Adeq Precision
0.9972	0.9935	0.9548	2.45%	52.8

, showing a high correlation coefficient of R² = 0.9972 and a close-to-1 correction coefficient of R²_adj =0.9935. These values indicate that the predicted model exhibits a high degree of correspondence with the actual data, demonstrating a strong fit. Figure 5 presents a comparative analysis of the predicted and simulated responses of the jet impacting the tracked teeth. The graphical representation indicates that the predicted and simulated values closely follow the y = x line and neighboring positions, with experimental values predominantly corresponding with the predicted values. This further confirms the accuracy of the prediction model established in this article. Furthermore, distinct colored squares are used to distinguish between the actual values of the experiment and the expected values of the equation.

3.3. 3D Diagrams

This section analyzes 3D diagrams that show the pairwise relationships of variables concerning Y.

Figure 6 illustrates the relationship between the injection pressure, injection target distance, and strike pressure of the tracked teeth. The graph shows that the peak striking dynamic pressure occurs at 1 MPa and 0.14 m. Notably, the maximum striking dynamic pressure is achieved at 1 MPa. Moreover, when the spray angle is 75°, the strike pressure of the jet on the tracked tooth increases as the spray pressure rises, while the impact of the spray target distance on the strike pressure of the jet is less pronounced. The steepness and significant slope of the response surface suggest a strong interaction between jet pressure and jet target distance.

Figure 7 illustrates the impact of injection pressure and impact angle on the dynamic pressure of the strike track tooth. The graph indicates that the highest dynamic pressure occurs at 1 MPa and 90°. Furthermore, when the spray target distance is 0.16 m, raising the spray pressure positively influences the pressure of the jet striking the tracked teeth, with minimal impact from the spray angle. However, simultaneously elevating both the jet pressure and the impact angle leads to an increase in the jet strike pressure exerted on the monitored tooth.

The impact of the interaction between the impact angle and jet target distance on the dynamic pressure of the strike track teeth is illustrated in Figure 8. This figure demonstrates that the maximum dynamic pressure of the strike occurs at 0.14 m and 90°. Moreover, the graph indicates that at an injection pressure of 0.7 MPa, the pressure of the jet striking the tracked tooth rises with an increase in injection angle, decreases initially, and then increases with a decrease in injection target distance. The presence of circular contour lines indicates a weak interaction between the two variables, signifying that the relationship between jet pressure and jet target distance is negligible. Therefore, maintaining a constant pressure, the most effective way to enhance the pressure of the jet striking the track tooth is by adjusting the impact angle or reducing the jet target distance.

3.4. One-Dimensional Diagram

Figure 9 illustrates the correlation between the jet strike track tooth pressure and the injection pressure. The graph shows a linear increase in jet strike track tooth pressure as injection pressure rises. It is observed that the maximum jet strike tooth pressure occurs at a jet pressure of 1 MPa. The utilization of an elevated jet pressure improves the efficacy of cleaning and decontamination processes; however, it concurrently results in heightened energy consumption. Hence, selecting an appropriate jet pressure is crucial to achieving the desired jetting effect.

Figure 10 illustrates the relationship between jet strike tracking pressure and jet pressure. In Figure 10, it is evident that there is an inverse correlation between these two parameters. Specifically, increasing the distance to the jet target adversely affects the efficacy of jet cleaning and decontamination processes.

The relationship between jet strike track tooth pressure and impact angle is illustrated in Figure 11. The graph indicates that as the impact angle increases, the jet strike track tooth pressure also increases gradually. Although the maximum value is not explicitly depicted, it can be inferred from the trend that a higher impact angle (in the range of 0–90°) results in an increase in jet strike track tooth pressure.

3.5. Optimum Point

The mathematical optimization model for the nozzle jet performance is established based on the output of the response surface regression equations and diagrams. The objective is to maximize the pressure of the jet striking the track tooth while considering the range of the nozzle characteristic parameters, that is, to find the maximum value of the dependent variable Y that satisfies the constraints for a given range of values of the independent variable x.

$$\mathrm{find}\mathrm{x}=[{\mathrm{X}}_1,{\mathrm{X}}_2,{\mathrm{X}}_3{]}^{\mathrm{T}}$$

$$\max \mathrm{Y}\left(\mathrm{x}\right)$$

$$\mathrm{s}.\mathrm{t}.\left\{\begin{array}{c}0.4\mathrm{M}\mathrm{P}\mathrm{a}\le {\mathrm{X}}_1\le 1\mathrm{M}\mathrm{P}\mathrm{a}\\ 0.14\mathrm{m}\le {\mathrm{X}}_2\le 0.18\mathrm{m}\\ 60\text{°}\le {\mathrm{X}}_3\le 90\text{°}\end{array}\right.$$

Based on the results obtained from response surface methodology (RSM), it was determined that the water jet exhibited superior decontamination performance in track cleaning. Specifically, when the jet applied maximum pressure to the track teeth, the parameters were as follows: jet pressure of 0.983 MPa, jet target distance of 0.14 m, and jet angle of 89.5°, resulting in the jet striking the track teeth with 702,597 Pa. Through optimization using numerical modeling and simulation, it was found that the jet pressure on the track teeth was 702,875 Pa, with a relative error of 0.04%. This indicates the high predictive accuracy of the response surface model in assessing the impact of jet parameters on track pressure, highlighting the reliability and precision of the optimization approach.

4. Conclusions

This research employed numerical simulation and response surface analysis to investigate the impact of jet pressure, jet target distance, and impact angle on the efficacy of cleaning and decontamination processes for mining vehicles. The research focused on enhancing the performance of a water jet on a track for mining vehicles operating on soft-bottom substrates in deep-seabed environments. The study also optimized the influential parameters to improve overall performance. The optimal combination of parameters studied has far-reaching implications for water jet decontamination technology, which not only significantly improves the effectiveness and efficiency of decontaminating deposits on the surface of moving track teeth, but also plays an important role in promoting economic and environmental sustainability. Furthermore, this study presents a novel theoretical foundation for the development of water jet decontamination technology for deep-sea mining vehicles, as well as a practical solution with a high efficiency and low cost, which has significant implications for resource conservation and environmental protection. The main conclusions are as follows:

(1)

The experimental scheme and response values were obtained under different parameter conditions through response surface design and numerical simulation methods. The experimental results were statistically analyzed using Design Expert software. Additionally, a numerical model describing the influence of the affected parameters on the pressure of the jet striking track teeth was successfully established using the theory of least squares.

(2)

The ANOVA results and response surface plots indicate that the three factors have varying degrees of impact on the cleaning and decontamination performance of high-pressure water jets. Specifically, the jet pressure and jet target distance have a highly significant effect on the pressure of the jet’s striking track teeth, while the jet angle also has a significant effect. Furthermore, there is an interaction between the factors, particularly between jet pressure and jet target distance, as well as between jet pressure and jet angle, which has a substantial impact on the pressure exerted by the jet on the track teeth.

(3)

The optimal test parameters for evaluating the efficacy of water jet cleaning and decontamination performance on the track are identified as an injection pressure of 0.983 MPa, a target distance of 0.14 m, and an impact angle of 89.5°.

The independent variable in this study was chosen based on the real length of the tracking teeth of deep-sea mining vehicles, but due to the limited sample size, a comprehensive data analysis was not conducted. The response surface methodology did not fully consider the variable influencing factors in the study. When simulating the effect of influencing factors on track scouring at 5000 m in the deep sea, the extreme environmental conditions and a lack of relevant data in the literature may result in relative mistakes. Future research will investigate the effect of nozzle shape in optimizing the cleaning efficiency of water jets and confirm this experimentally to greatly enhance the decontamination performance and optimize experimental results.