Experimental Analysis of Cavitation Erosion: Parameter Sensitivity and Testing Protocols

Abstract

The scientific goal of this study was to investigate the effects of various parameters on cavitation-induced erosion, with the aim to enhance the understanding and assessment of cavitation resistance in hydraulic systems. Cavitation erosion poses significant challenges to the durability and efficiency of hydraulic components, such as those found in hydropower plants and pumping stations. Prompted by the need to improve the reliability of cavitation testing and material assessment, this research conducted a comprehensive sensitivity analysis of a cavitation jet apparatus (CJA). This study employed an experimental platform that consisted of a vertical cylindrical test tank, a submerged nozzle, and an aluminum sample. By examining a range of orifice diameters, this research identified that smaller diameters led to increased erosion intensity, with the most pronounced effects observed at a diameter of 2 mm. Furthermore, various standoff distances (SoDs) were tested, which revealed that shorter distances resulted in greater erosion, with the highest impact noted at an SoD of 5 cm. This study also evaluated different nozzle geometries, where it was found that a 132° conical sharped edges nozzle, combined with an orifice diameter of 2 mm and an SoD of 5 cm, produced the most severe erosion. Conversely, chamfered edges nozzles and a commercial nozzle (MEG2510) with an SoD of 10 cm or greater showed reduced erosion. These results highlight that by standardizing the testing duration to 1200 s, the CJA could reliably assess the cavitation resistance of materials. This study established a clear relationship between increased pressure and higher impact forces, which led to more severe erosion. The findings underscore the effectiveness of the CJA in evaluating material resistance under various cavitation conditions, thus addressing a critical need for reliable cavitation testing tools.

1. Introduction

Cavitation erosion is one of the remarkable catastrophic consequences of cavitation. It is a complex phenomenon since it includes both hydrodynamic and material aspects. From a hydrodynamic point of view, vapor structures are produced in low-pressure regions of a cavitating flow. They are entrained by the flow and may violently collapse when entering regions of pressure recovery, which causes the erosion of solid walls [1,2]. Based on the material aspects, the erosion caused by cavitation is defined as a material mass loss due to aggressive cavity collapse near a surface. The literature contains numerous studies focused on understanding material performance under cavitation and on developing new materials resistant to cavitation. For instance, Fe-based alloys were investigated for their application in repairing eroded areas of hydropower runners [3,4,5], while brass was studied for its use in ship propellers [6]. Additionally, surface treatments, such as plasma nitriding, were explored to enhance the cavitation resistance of materials [7].

The collapse of these cavities induces high mechanical loads and stress levels on the adjacent surface that often exceeds the material’s yield or fatigue stress, which makes material removal inevitable. In 1754, Euler was the first to propose that cavitation poses a significant risk of damage to hydraulic machinery [8]. Consequently, cavitation erosion is a critical factor in the design of hydraulic structures and machinery (such as spillways, hydropower systems, and pumps), as it impacts their operational lifespan [9,10,11,12,13,14,15,16,17]. This is illustrated in Figure 1, which shows brighter areas that were previously repaired by depositing stainless steel onto the carbon steel base metal. Vaz et al. [5] described this type of repair as a routine procedure in hydropower-worn runners. The severe erosion not only leads to substantial damage in fluid machinery but also considerably drives up repair and maintenance expenses. Consequently, the problem of cavitation erosion has garnered significant attention within both academic research and industrial practice.

While cavitation is typically undesirable in most hydraulic machinery, it is intentionally harnessed in submerged cavitation jets for various applications. The destructive power of cavitation bubbles is utilized in tasks such as organic wastewater treatment [19,20,21,22], marine pipeline cleaning, enhancing the drilling rate in petroleum wells by breaking rocks [23,24,25,26], and performing shotless peening [27,28,29,30]. Additionally, cavitation can cause flow obstruction and choking, thus severely impairing the functioning of systems. The implosion of cavitation bubbles can lead to erosion damage, which compromises the durability and increases the maintenance demands of critical equipment. However, in the context of fuel injection systems, cavitation plays a dual role. While it can have negative impacts, such as disrupting jet formation, cavitation can also positively influence the stability and atomization of fuel jets. These effects are essential for optimizing the combustion process, which directly affect the engine performance and reduce emissions [31,32]. Furthermore, microbubble-enhanced high-intensity focused ultrasound (HIFU) has significant relevance in tumor ablation, particularly for brain and liver cancers [33,34,35]. A comprehensive review by Soyama investigated the aggressive intensity of cavitating jets and cavitation peening in terms of the erosion rate and peening intensity [28,29]. During cavitation peening, cavitation forms as fluid passes through a Venturi or orifice nozzle. When imploding bubbles collide with the workpiece, they provide energy for the peening process. Studies by Takahashi et al. [36] and Sonde et al. [37] examined cavitation-peening and shot-peening methods in terms of improving the surface hardness, surface finish, fatigue strength, and corrosion resistance.

Research into the mechanisms of cavitation erosion explored both the micro-scale and macro-scale hydrodynamic processes that lead to aggressive collapse events [1,38,39,40,41,42,43,44]. Micro-scale mechanisms include shock wave emission and micro-jet formation [28,29,38,42,45]. Shock waves are emitted following the collapse of spherical bubbles [46]. For instance, Fujikawa and Akamatsu [47] demonstrated through experiments and simulations that spherical bubble collapse can generate shock waves with pressures that can deform surfaces due to the mechanical load.

Fortes-Patella et al. [48] showed that solid deformation aligns with the non-dimensional pit profile observed in experimental pitting tests. Another micro-scale mechanism is micro-jet formation, which occurs during non-spherical bubble collapses near a surface. Non-uniform pressure fields around the bubble result in high-speed micro-jets impacting the surface, thus potentially removing material if the jet velocity is sufficiently high [1,49].

At the macro-scale, numerous studies investigated the hydrodynamic mechanisms of erosive collapses [50]. Various mechanisms that influence the erosiveness of collapsing cavities were described by Bark et al. [51], who developed analysis models based on a kinematic analysis of cavity dynamics and erosion patterns from paint tests and high-speed video (HSV) observations [11,52]. These models are based on the energy cascade concept, which involves energy transfer between macro-cavities and smaller cavities collapsing near the surface during macro-scale erosive cavity collapse [51].

Efforts to study the impact of cavitation on solid surfaces led to the development of various evaluation methods. For example, Zhao et al. [53] proposed a cavitation rotary abrasive flow polishing method that utilizes multiple Venturi cavitation channels to create a rotary abrasive flow above the solid specimen. The ASTM G134 test method, which uses cavitation liquid jets, is effective for evaluating cavitation damage in stainless steel, though it requires at least 4 h to achieve measurable erosion. However, it is not suitable for assessing the wear of elastomeric coatings, composites, or other non-metallic aerospace materials. Additionally, ASTM G134 does not define the optimal standoff distance (SoD) [54]. The ASTM G32 is a test method that evaluates cavitation damage by subjecting a specimen to high-frequency vibrations in a liquid, which causes the formation and collapse of cavities that result in material erosion. Although the cavitation mechanism differs from that in ASTM G134, which simulates cavitation in flowing systems, the material damage process is considered similar. ASTM G32 offers a controlled, small-scale method to compare the cavitation erosion resistance of different materials, with standardized conditions and guidelines that typically involve a 20 kHz ultrasonic transducer and a specially designed horn for the specimen.

Liu et al. [8] conducted an extensive study on cavitation erosion across a range of pressure conditions, specifically 0.1, 3, 6, and 10 MPa. The study focused on three metallic materials: copper, 17-4PH stainless steel, and tungsten, which were selected as representative test specimens. Figure 2 presents field-emission scanning electron microscope (FESEM) images that reveal the morphology of cavitation-induced erosion pits on these materials under varying pressures.

The influence of the cavitating jet nozzle geometrical parameters was consistently emphasized in studies, with results demonstrating a strong correlation between the nozzle geometry and erosion rates [55,56,57]. Yamauchi et al. [56] conducted erosion experiments on aluminum plates using three distinct nozzle types: conical, cylindrical, and Venturi (horn-shaped). In these experiments, the targets were positioned perpendicularly to the jet nozzle, with an upstream pressure of 30 MPa.

Subsequent studies [55,57] experimentally investigated the impacts of various geometrical parameters on cavitation erosion by utilizing a high-speed submerged cavitating jet on copper samples. Convergent and divergent nozzles were employed, and the discussions focused on the erosion rates and the extent of eroded areas. Notably, the nozzle in this equipment remains stationary, thus lacking both forward and backward mobility. To address this limitation, the SoD was adjusted by modifying the thickness of the solid samples, with the upstream pressure consistently maintained above 16 MPa. Among the factors that influence cavitation erosion, the nozzle geometry is paramount, as it dictates critical parameters, such as the pressure and velocity [57].

Soyama [29,58] further evaluated erosion across standoff distances that ranged from 14 to 22 mm, where the SoD is defined as the distance from the upstream edge of the nozzle throat to the sample surface. This contrasts with the common practice of measuring the SoD from the nozzle outlet to the solid surface. In Soyama’s experiments, an upstream pressure of 30 MPa was utilized. Consequently, there remains a need for testing across varying pressures to identify a test rig capable of operating at lower pressures, while ultimately aiming for a cost-effective solution, such as employing a weaker plunger pump.

Despite significant advancements in pressurized flow devices for cavitation erosion evaluations, such as those extensively employed in submerged systems [22,28,29,53,59,60], there remains a critical gap and need for devices that can assess cavitation erosion within free-surface hydraulic structures. Current methodologies often focus on pressurized environments, which leaves a need for more accessible and versatile apparatuses that can effectively simulate and measure erosion in free-surface conditions, which are prevalent in many hydraulic structures.

To bridge this gap, this paper introduces the cavitation jet apparatus (CJA), which is a straightforward and effective experimental platform designed to evaluate cavitation-induced erosion in free-surface hydraulic environments, where samples are placed in a free-surface tank flow. The CJA generates controllable cavitation across various scenarios, including different orifice diameters, standoff distances, and nozzle geometries. Through a comprehensive sensitivity analysis, this research aimed to establish optimal conditions for cavitation erosion testing, thereby advancing our understanding of cavitation phenomena, particularly in unsteady cavitation contexts within tanks and submerged jets.

2. Materials and Methods

Figure 3 illustrates a mind map outlining the sequential steps detailed in the materials and methods section of this paper. The diagram begins with an explanation of the experimental setup, followed by a description of the various nozzle parameters, including the orifice diameter, standoff distance, and nozzle geometry. It further elaborates on the procedures for preparing the test samples and measuring cavitation erosion. Our research methodology rigorously adhered to the specifications established in previous studies and conformed to ASTM G134 for cavitation erosion testing. This standard provides extensive guidelines on the design and operational parameters of the test equipment, which we diligently followed to ensure that our results are both valid and comparable. Finally, the mind map encompasses the statistical analysis methods employed in the research, specifically the interquartile range (IQR) method, standard deviation, coefficient of variation, and coefficient of determination.

2.1. Experimental Setup

The experimental methodology employed in this study involved the generation of a submerged cavitating jet, which impinged on a stationary solid specimen submerged in a fluid medium, as depicted in Figure 4c. This interaction led to the formation and subsequent collapse of cavitation bubbles on the surface of the specimen, which resulted in erosive effects. To assess the cavitation erosion characteristics of solid materials, a specialized apparatus known as the cavitation jet apparatus (CJA) was utilized, as shown in Figure 4a,b,d.

The CJA system comprised a triplex plunger pump (PROMINAS BPS-327-025-MP) (1), capable of operating at a maximum pressure of 15 MPa with a maximum flow rate of 29 L/min (4.84 × 10⁻⁴ m³/s). The pump was powered by a 12.33 hp electric motor (2) that ran at 1200 rpm and was connected to a three-phase power source at 220 V. The pump outlet was linked via a conduit (3) to a stainless steel nozzle (4) positioned within a vertical cylindrical test tank, which had a diameter of 68 cm and a height of 74 cm. The tank was equipped with three circular glass observation windows (5) with a diameter of 12 cm, which enabled visual monitoring of the experiments.

The tank was further designed with a top drain (6) of diameter $\mathsf{\Phi }=6.35$ cm for fluid discharge and a bottom drain (7) of diameter $\mathsf{\Phi }=1.27$ cm to facilitate maintenance. A solid sample (8) was placed at the bottom of the tank, which was subsequently filled with tap water through the top drain.

To monitor pressure oscillations, a pressure transducer (HBM, model: K-P8AP-231B-17A5, measurement range: 0–20 MPa) with an accuracy of $\pm 1\%$ was strategically placed upstream of the nozzle. Additionally, an impact force transducer (HBM, model: WAGEZELLE/Load Cell-Z6FD1, class D1, TC2207) with an accuracy of $\pm 0.1\%$ was installed on the external bottom layer of the tank in indirect contact with the solid sample. Both sensors were connected to a PC-based data acquisition system (Spider 8), with the data processed using Catman^® Express V4.5 software. The pressure and impact force were measured and recorded at a sampling rate of 200 Hz.

A digital infrared thermometer (MESTEK^®, model: IR02C) was used to measure the water temperature at one-minute intervals during the experiment. The average water temperature recorded during the tests was approximately 26 °C, with a margin of uncertainty of 0.1 °C.

To assess the gas content in the system, water samples were collected before and after the measurements, and the dissolved oxygen levels were measured using an oxygen sensor (RDO PRO-X Probe). Given the substantial volume of the water tank, no significant changes were detected in the oxygen levels. Throughout the series of experiments, the average dissolved oxygen concentration remained consistent at $8.25\mathrm{mg}/\mathrm{L}$, with minimal variation.

It is important to note that the upstream pressure, nozzle orifice diameter, nozzle geometry, and SoD were adjustable to achieve the desired experimental conditions.

2.2. Different Parameters of Nozzle

It was necessary to scrutinize the key parameters related to the nozzle, such as the orifice diameter of the nozzle (D), standoff distance (SoD), and nozzle geometry.

2.2.1. Orifice Diameter of Nozzle (D)

To examine the influence of the nozzle orifice diameter on the pressure and, subsequently, the extent of erosion, this research employed five different orifice diameters (2, 2.5, 3, 3.5, and 4 mm). A previous study [61] demonstrated that using orifice diameters of 1.5 mm or smaller resulted in the failure of the control valve and connections within the cavitation apparatus. In this study, the pump pressure was set to its maximum, and the variations in the upstream pressure for nozzles with different orifice diameters were measured, along with the corresponding cavitation erosion associated with each orifice size.

2.2.2. Standoff Distance (SoD)

As depicted in Figure 5, the standoff distance is defined as the distance from the nozzle orifice downstream to the surface of the specimen.

A body of research established that the SoD exerts an inverse influence on cavitation erosion (e.g., Refs. [62,63,64,65]). Brennen et al. [64,65] conducted an in-depth analysis of the likelihood of material damage to proximate solid surfaces, as well as the generation of noise. His findings revealed that both erosion and noise are consequences of the transient high pressures that arise when the contents of a collapsing bubble are abruptly compressed. The flow induced in the liquid by the volumetric displacement of a growing or collapsing cavity led to the conclusion that the pressure ($P_a$) is inversely related to the SoD, as described by Equation (1) [65,66]:

$$P_a={\displaystyle \frac{\rho }{4\pi \left(SoD\right)}}{\displaystyle \frac{d^{2}V}{d{t}^2}}$$

(1)

In this equation, $P_a$ represents the radiated acoustic pressure, while SoD and $\rho$ denote the standoff distance and fluid density, respectively.

In the present study, the erosive impact of the cavitating jet on the aluminum specimens was evaluated by varying the SoDs to 5, 10, and 15 cm (with a tolerance of ±5 mm). These specific SoDs were selected to comprehensively assess the relationship between the SoD and cavitation erosion intensity.

2.2.3. Nozzle Geometry

To maximize the cavitation erosion, various nozzle geometries were tested, including a 20° conical nozzle, a 132° conical nozzle, a circular nozzle with a radius of 12.5 mm, and the MEG2510 WashJet^® Spray Nozzle (with a spraying angle of 25° and a flow rate capacity of 65 × 10⁻⁵ m³/s at a pressure of 300 kPa). These designs were selected to identify the most effective geometry for inducing cavitation erosion. For each nozzle type, two models were constructed: one that featured internal sharped edges and the other with internal chamfered edges (except for the MEG2510). The configurations of these nozzle models are illustrated in the sketches provided in Figure 6a–f. This comparative approach aimed to determine the nozzle geometry most susceptible to producing cavitation erosion, thereby providing insights into optimizing the nozzle design for such applications.

2.3. Test Specimen and Measurement of Cavitation Erosion

A comprehensive review of previous studies revealed that aluminum samples were predominantly employed for evaluating pitting and measuring cavitation erosion [27,36,59,67]. While these studies did not specifically focus on the erosion characteristics of aluminum itself, they utilized aluminum as a medium to record the intensity of cavitation bubble collapses. The rationale behind this choice lay in the material’s ability to undergo permanent deformation upon exposure to implosions intense enough to cause damage, thereby serving as a reliable indicator of cavitation erosion.

In line with the aforementioned research, an aluminum sample fabricated from alloy 6351-T6 was selected for the current study. The sample, with a diameter of 15 cm and a thickness of 6.5 mm, was positioned at the bottom of the tank to serve as a solid test specimen. The mechanical and physical properties, as well as the chemical composition of the aluminum alloy, are detailed in

Table 1. Mechanical and Physical Properties of Al 6351-T6 [68].

Density (g/cm3)	2.71
Hardness, Brinell	95
Hardness, Knoop	130
Modulus of elasticity (GPa)	68.9
Fatigue strength (MPa)	89.6
Poisson ratio	0.33
Tensile strength, ultimate (MPa)	310
Tensile strength, yield (MPa)	283
Elongation at break (%)	14
Shear modulus (GPa)	26
Shear strength (MPa)	200
Thermal conductivity (W/m.K)	176

and

Table 2. Chemical Properties of Al 6351-T6 (wt.%) [68].

Al	95.9–98.5
Cu	$<=$0.10
Fe	$<=$0.50
Mg	0.40–0.80
Mn	0.40–0.80
Other, each	$<=$0.05
Other, total	$<=$0.15
Si	0.70–1.3

, respectively. Additionally, a scanning electron microscope (SEM) image of the aluminum sample is presented in Figure 7, which provides further insight into its surface morphology.

To assess the cavitation-induced erosion, a concentric ring pattern of intensively cavitation-impacted and moderately cavitation-impacted regions was observed surrounding the centrally damaged area on the aluminum sample. These regions are illustrated in Figure 8, which depicts the erosion pattern formed using a circular sharped edges nozzle with an orifice diameter of 2 mm and an SoD of 5 cm.

To quantify cavitation erosion, a trinocular stereoscopic microscope (Opton Microscope, zoom range $1\times$ to $4\times$, magnification $10\times$ to $160\times$) was employed to count the number of pits formed in the intensively cavitation-impacted region of the polished aluminum surface. The severity of cavitation wear was determined by counting the number of pits per square centimeter in the intensively cavitation-impacted area. To further validate the pit-counting methodology, a comparative analysis was conducted by cross-referencing the mass loss of the aluminum sample with the pit-counting results. This validation experiment was performed using a ${132}^{°}$ conical sharped edges nozzle, an SoD of 5 cm, and an orifice diameter of 2 mm. The mass loss induced by the cavitation erosion under these specific conditions was measured and compared with the pit density obtained from the microscopy analysis. For this purpose, a high-precision analytical balance (Sartorius, model: PRACTUM224-10BR, accuracy e = 1 mg, resolution d = 0.1 mg) was used to determine the mass loss, which offered an additional perspective on the material degradation induced by the cavitation. This dual approach—which combined a pit-counting analysis with a mass loss measurement—provided a comprehensive understanding of the erosive effects and ensured the reliability of the experimental findings.

2.4. Statistical Analysis

The dataset initially underwent a thorough cleansing process to eliminate any errors or records affected by measurement failures. Outliers were identified and removed using the interquartile range (IQR) method. Subsequently, statistical analyses were conducted on the refined dataset, including the calculation of the standard deviation ($\sigma$), coefficient of variation (CV), and coefficient of determination ($R^2$).

2.4.1. Outlier Removal Using the Interquartile Range (IQR) Method

The interquartile range (IQR) method is a robust statistical technique employed to detect and exclude outliers from a dataset. Outliers, which are observations that deviate significantly from the bulk of the data, can distort statistical analyses and modeling results. The IQR method identifies outliers based on the spread of the data around its median, which makes it particularly effective for skewed distributions.

The IQR is a measure of statistical dispersion that captures the range of the middle 50% of the data, which is defined as the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$):

$$\mathrm{IQR}=Q_3-Q_1$$

(2)

To detect outliers using the IQR method, the following steps are implemented:

• Calculate the first and third quartiles: compute the first quartile ($Q_1$) and the third quartile ($Q_3$) of the dataset.
• Determine the IQR: calculate the IQR by subtracting $Q_1$ from $Q_3$.
• Define the outlier boundaries: establish the lower bound (LB) and upper bound (UB) for outlier detection as follows:

  $$\mathrm{LB}=Q_1-k\times \mathrm{IQR}$$

  (3)

  $$\mathrm{UB}=Q_3+k\times \mathrm{IQR}$$

  (4)

  where k is a constant multiplier, typically set to 1.5 or 3, depending on the sensitivity required for outlier detection.
• Identify and remove outliers: any data points that fall below the lower bound (LB) or above the upper bound (UB) are identified as outliers and can be excluded from the dataset.

The IQR method is particularly advantageous for handling skewed distributions and is less affected by extreme values compared with other outlier detection techniques, such as the Z-score or modified Z-score methods [69,70].

2.4.2. Standard Deviation ($\sigma$)

The standard deviation is a fundamental statistical metric used to quantify the dispersion or spread of a dataset relative to its mean. It measures the average deviation of data points from the mean, and thus, provides insight into the variability within the dataset. A lower standard deviation indicates that the data points are closely clustered around the mean, while a higher standard deviation suggests greater spread.

For a dataset, the standard deviation is defined as

$$\sigma =\sqrt{{\displaystyle \frac{1}{N}}\sum _{i=1}^N{(x_i-\mu )}^2}$$

(5)

where N is the total number of data points, $x_i$ represents each individual data point, and $\mu$ is the mean of the data.

For a sample, the standard deviation s is calculated using

$$s=\sqrt{{\displaystyle \frac{1}{N-1}}\sum _{i=1}^N{(x_i-\overline{x})}^2}$$

(6)

where $\overline{x}$ represents the sample mean [71].

2.4.3. Coefficient of Variation (CV)

The CV is a dimensionless measure that assesses the relative variability of a dataset in relation to its mean. It is particularly useful for comparing the variability of datasets with different units or scales. The CV is defined as the ratio of the standard deviation ($\sigma$) to the mean ($\mu$), which is expressed as a percentage:

$$\mathrm{CV}=\left({\displaystyle \frac{\sigma }{\mu }}\right)\times 100\%$$

(7)

A lower CV indicates that the data points are closely grouped around the mean, which implies low variability, whereas a higher CV signifies greater dispersion [72].

2.4.4. Coefficient of Determination (R²)

The coefficient of determination is a statistical metric used in the context of regression analysis to evaluate the goodness of fit of a model. It is a key indicator of how well the independent variables explain the variability in the dependent variable.

Mathematically, R² is defined as the ratio of the explained variation to the total variation in the dependent variable. This can be expressed as

$$R^2=1-{\displaystyle \frac{{\mathrm{SS}}_{\mathrm{residual}}}{{\mathrm{SS}}_{\mathrm{total}}}}$$

(8)

where ${\mathrm{SS}}_{\mathrm{residual}}$ is the sum of the squares of the residuals, which represents the variation in the dependent variable that is not explained by the model. ${\mathrm{SS}}_{\mathrm{total}}$ is the total sum of the squares, which represents the total variation in the dependent variable.

R² values range from 0 to 1:

• An R² of 0 indicates that the model does not explain any of the variance in the dependent variable.
• An R² of 1 indicates that the model explains all of the variance in the dependent variable.

In scientific research, a high R² value suggests that the model provides a good fit to the data, which means that a large portion of the variability in the dependent variable can be explained by the independent variable(s). Conversely, a low R² value indicates a poor fit, which suggests that the model fails to capture much of the variability in the data [73].

3. Results and Discussion

In this study, the CJA was utilized to assess the erosion of solid surfaces induced by cavitation. The intensity of the cavitation bubble collapse was quantified by counting the number of pits in the most intensely cavitation-impacted areas. To ensure the accuracy of the pit-counting method, its results were validated by comparing them with corresponding mass loss measurements in selected cases.

The experiments were conducted in multiple stages to identify the optimal experimental conditions, with each test replicated at least three times using similar samples to ensure precision. The mean values from these repetitions are presented in this section. Outliers were identified through statistical analysis using the interquartile range (IQR) method. Furthermore, the standard deviation and coefficient of variation were calculated to evaluate the accuracy of the measurements, while the coefficient of determination was employed to assess the reliability of the results. These statistical evaluations are crucial for quality control, compliance with standards, and process improvement.

3.1. Orifice Diameter of Nozzle

The CJA was investigated with various orifice diameters, as mentioned in Section 2.2.1. For this purpose, we used a nozzle with ${132}^{°}$ sharped edges. The pressure valve of the rig was adjusted to the maximum capacity of the plunger pump, which was approximately 15 MPa. By utilizing the maximum pressure capacity of the pump, different orifice diameters produced varying pressures, which were measured by a pressure sensor located upstream of the nozzle. The maximum upstream pressure for each orifice diameter is illustrated in Figure 9.

As depicted in Figure 9, the nozzle with an orifice diameter of 2 mm generated a mean upstream pressure of approximately 15 MPa, which was the highest recorded in this study. When the orifice diameter was increased to 2.5, 3, 3.5, and 4 mm, there were corresponding decreases in the upstream pressure by roughly 69%, 32%, 18.4%, and 9%, respectively, where the rate of pressure decrease was nonlinear.

Multiple studies examined the relationship between cavitation erosion and varying nozzle pressures [63,74]. Their findings indicate that a reduction in pressure leads to a decrease in cavitation erosion. Consistent with these findings, our observation of pressure reductions associated with increasing orifice diameters (Figure 9) suggests that a larger orifice diameter results in reduced cavitation erosion.

Consequently, the orifice diameter of 2 mm, which produced the highest pressure, was expected to lead to the most significant cavitation erosion among the tested diameters. Therefore, this orifice size was selected for further investigation in the subsequent stages of this research.

Due to the inherent characteristics of triplex plunger pumps, a slight fluctuation in the pump pressure was observed, which also affected the upstream pressure and the concentration of cavitation bubbles within the tank. To assess these parameters, we measured the upstream pressure using a pressure sensor. Additionally, the impact force at the bottom of the tank, which corresponded to the force that impacted the aluminum sample, was recorded using an impact force sensor. Both parameters were recorded at a frequency of 200 Hz. The comparison of the impact force and upstream pressure over different time periods is illustrated in Figure 10. The results demonstrate a direct correlation between the impact force and upstream pressure. Furthermore, during stable periods, the quantity of pits and the volume loss increased proportionally with the impact energy, as previously reported by Okada et al. [75]. Similarly, Sarkar et al. [76] observed that a liquid jet directed toward a solid wall generates multiple shock waves due to its impact with the bubble surface and, ultimately, with the solid wall.

As previously mentioned in the Section 1, Liu et al. [8] performed tests on cavitation erosion across various pressure conditions, which focused on three metallic materials. Although the materials examined differ from the aluminum sample in our study, their findings (Figure 2) support our observations regarding the relationship between pressure, impact force, and erosion severity. Specifically, their results confirm that increased pressure leads to a greater impact force, which, in turn, exacerbates erosion. This corroboration enhances the validity of our results and highlights the consistent nature of pressure-induced cavitation erosion across various metallic materials.

3.2. Standoff Distance

The effectiveness of the CJA was significantly influenced by the standoff distance. To investigate this dependence, a sensitivity analysis was conducted with various SoDs while maintaining a constant nozzle geometry. In this phase, a 20° conical sharped edges nozzle with an orifice diameter of 2 mm was employed. The results of these tests are depicted in Figure 11, Figure 12, Figure 13 and Figure 14, with detailed statistical analysis results presented in

Table 3. Statistical Evaluation of Compressive Strength, Including Standard Deviation ($\sigma$) and Coefficient of Variation (CV).

SoD (m)	Time (s)
	60		120		180		240		300		1200
	$\mathit{\sigma }$	CV	$\mathit{\sigma }$	CV	$\mathit{\sigma }$	CV	$\mathit{\sigma }$	CV	$\mathit{\sigma }$	CV	$\mathit{\sigma }$	CV
0.05	2.71	7.73	5.57	8.03	13.45	14.59	15.92	13.21	22.68	10.02	33.42	10.21
0.10	1.36	7.84	4.53	11.90	7.64	14.48	9.17	12.10	10.70	12.56	17.83	11.01
0.15	0.63	6.25	2.74	12.31	5.05	15.46	5.85	16.39	7.16	13.93	11.15	17.95

.

To comprehensively understand the effects of the SoD on the cavitation erosion, we examined the erosion variations over time up to 1200 s for different SoDs of 5, 10, and 15 cm. The results, as illustrated in Figure 11, highlight that the wear was most pronounced with an SoD of 5 cm, which achieved a maximum erosion of 35.01 pits/cm² within the first 60 s. As the SoD increased, the erosion decreased, with SoDs of 10 and 15 cm resulting in erosion quantities of 20.78 pits/cm² and 10.10 pits/cm², respectively.

Throughout the testing period, the erosion trends exhibited a pronounced increase until approximately t = 300 s, after which a knee-shaped pattern was observed, which was characterized by a sharp rise in the erosion rate, followed by a gradual slope. This observation aligns with the ASTM G134 recommendations, which suggest that testing should continue until a knee-shaped curve is detected to ensure a reliable erosion measurement.

Our findings, which are consistent with ASTM G134 and corroborated by Zhuang et al. [54], indicate that reduced SoDs enhance the cavitation impact force, and thus, lead to increased erosion. Conversely, a longer SoD reduced the erosion rate due to diminished jet power. Figure 12 illustrates that the highest erosion was recorded at an SoD of 5 cm, with 327.22 pits/cm², which was approximately five times higher than the erosion at 15 cm, which was 62.13 pits/cm².

Figure 13 provides a visual representation of the erosion patterns at different SoDs, thus demonstrating significant plastic deformation and material detachment due to shock waves and micro-jet cavitation effects. Figure 14 depicts the erosion evolution over time for a 5 cm SoD. Based on these observations, it was concluded that cavitation erosion inversely correlated with the SoD. This finding is consistent with previous research by Kodama [62], Trummler [63], Reisman [64], and Brennen [65].

In summary, Figure 11, Figure 12 and Figure 13 confirm that an SoD of 5 cm resulted in the most significant damage. Therefore, this distance was utilized in subsequent stages of testing with different nozzle geometries.

3.3. Nozzle Geometry

The final phase of our experimental study examined the impact of seven distinct nozzle geometries on cavitation erosion. In these experiments, the SoD was maintained at 5 cm, and the orifice diameter was fixed at 2 mm. The diameter of the intensively cavitation-impacted area was measured as 4 ± 0.2 cm. The tested nozzle geometries are detailed in Section 2.2.3 and illustrated in Figure 6.

Figure 15 presents the evolution of cavitation erosion on an aluminum sample over a period of 1200 s (at 60, 120, 180, 240, 300, 600, 900, and 1200 s). The statistical analysis results of the erosion data are summarized in

Table 4. Statistical Analysis of Cavitation Erosion for Different Nozzle Geometries, Including Standard Deviation ($\sigma$) and Coefficient of Variation (CV). Parameters: Orifice Diameter = 2 mm, SoD = 5 cm, Intensively Cavitation-Impacted Diameter = 4 cm (N.G.—Nozzle Geometry, A—20° Conical Sharped Edges, B—132° Conical Sharped Edges, C—Circular Sharped Edges, D—MEG 2510, E—20° Conical Chamfered Edges, F—132° Conical Chamfered Edges, G—Circular Chamfered Edges).

N.G.	Time (s)
	60		120		180		240		300		1200
	$\mathit{\sigma }$	CV	$\mathit{\sigma }$	CV	$\mathit{\sigma }$	CV	$\mathit{\sigma }$	CV	$\mathit{\sigma }$	CV	$\mathit{\sigma }$	CV
A	4.78	17.72	8.80	18.13	10.44	14.34	13.20	13.87	14.46	8.08	21.38	8.27
B	9.75	15.95	12.58	17.61	11.95	13.27	16.98	11.15	22.01	9.18	147.16	5.96
C	5.34	15.35	9.12	15.20	11.19	13.59	12.45	9.41	18.86	9.20	28.29	6.11
D	1.26	10.10	3.14	13.70	9.43	25.51	10.06	16.41	12.58	13.97	10.06	8.02
E	5.03	18.91	8.80	18.77	11.00	14.51	13.71	13.68	15.72	11.47	18.86	8.07
F	2.20	11.82	4.40	16.47	9.75	17.45	10.44	14.51	12.58	10.99	12.58	8.58
G	3.14	14.20	5.03	15.27	9.56	19.10	10.69	13.80	12.83	10.92	15.72	9.03

.

The results reveal that the 132° conical sharped-edges nozzle caused the most significant erosion. Specifically, after 60 s, the erosion rate was 61.12 pits/cm², which increased to 71.43, 90.04, 152.29, 239.81, 520.45, 677.12, and 790.73 pits/cm² at 120, 180, 240, 300, 600, 900, and 1200 s, respectively. The erosion caused by other nozzles was ranked in decreasing order of intensity as follows: circular sharped-edges nozzle, 20° conical sharped-edges nozzle, 20° conical chamfered edges nozzle, circular chamfered edges nozzle, 132° conical chamfered edges nozzle, and $MEG2510$.

The erosion effects of various nozzle geometries at t = 1200 s are illustrated in Figure 16. This figure shows that the 132° conical sharped edges nozzle caused the highest damage, which resulted in 790.73 pits/cm², which is equivalent to 12,576 pits in the intensively cavitation-impacted region. The circular sharped edges nozzle followed with 462.77 pits/cm², while the 20° conical sharped edges and 20° conical chamfered edges nozzles recorded 258.55 and 233.77 pits/cm², respectively. Other nozzle geometries produced erosion rates below 200 pits/cm², which indicates their reduced efficacy in cavitation jet applications. Additionally, the erosion increased proportionally with time up to t = 1200 s. The sharped edges nozzles generally performed better at enhancing erosion compared with the chamfered edges nozzles. The commercial $MEG2510$ nozzle exhibited the least wear. This was attributed to the sharped edges nozzle’s ability to rapidly decrease the pressure and increase velocity, and thus, significantly enhance the erosion [23]. Moreover, a larger convergent angle within the nozzle and a smaller divergent angle outside the nozzle are associated with increased erosion rates on solid samples [57]. Consequently, the 132° conical sharped edges nozzle is recommended as the optimal configuration for the CJA.

To validate the accuracy of pit counting, we conducted tests using a nozzle with a 132° conical sharped edges geometry. In these tests, both the SoD and the nozzle orifice diameter were held constant at 5 cm and 2 mm, respectively. Erosion was assessed by measuring the cumulative mass loss of the samples at intervals of 60, 120, 180, 240, 300, 600, 900, and 1200 s. As illustrated in Figure 17, the trend observed in the cumulative mass loss aligned with the pit-counting results shown in Figure 18, which demonstrates the reliability of the pit-counting method. This methodology provided a thorough validation of the pit-counting technique, thus affirming its reliability in evaluating cavitation-induced material degradation. It is important to note that the cumulative mass losses at $t$ = 60, 120, and 180 s should not be identical. However, our measurements showed values of 0.1 mg due to the limitations of the balance’s precision. This discrepancy was attributable to the fact that the mass of the aluminum sample exceeded the maximum capacity of more precise balances.

Thus, the application of the 132° conical sharped edges nozzle with an SoD of 5 cm and an orifice diameter of 2 mm was validated as the calibrated parameters for the CJA. Consequently, the relationship between the erosion and processing time could be described by the linear regression equation, as presented in Figure 18, for the CJA under these settings. The coefficient of determination $R^2$ was calculated to be $0.9722$. Figure 18 depicts the cavitation erosion as a function of time under the optimized test conditions, where it demonstrates a highly positive correlation ($R=0.986$) between the erosion intensity and time. Given the precise calibration of the nozzle geometry, SoD, and orifice diameter used in the CJA, it is advisable to avoid using alternative nozzle configurations or SoDs without conducting further calibration tests.

Additionally, the heavily cavitation-impacted ring and the less damaged areas of the aluminum sample were analyzed throughout all stages of the study (see Figure 8). The diameter of the intensively cavitation-impacted region was measured for various nozzle geometries and SoDs. The results are summarized in

Table 5. Representation of Jet Amplitude With Different Nozzle Geometries and SoDs.

Nozzle Geometry		SoD (cm)	Intensively Cavitation-Impacted Diameter (cm)
Sharped edges	20° conical	$15\pm 0.5$	$5.5\pm 0.2$
		$10\pm 0.5$	$5\pm 0.2$
		$5\pm 0.5$	$4\pm 0.2$
	Circular
	132° conical
Chamfered edges	20° conical
	Circular
	132° conical
MEG 2510

, which provides the associated intensively cavitation-impacted areas used to quantify the cavitation erosion (pits/cm²). The findings indicate that increasing the SoD led to a larger intensively cavitation-impacted diameter, thereby reducing the extent of wear. Conversely, varying the nozzle geometry did not significantly affect the diameter of the cavitation-impacted area.

4. Conclusions

Understanding the impact of cavitation on solid surfaces is of paramount importance for mechanical and civil engineers, as the structures they design are frequently exposed to high-speed fluid flows, which leads to significant erosion. This research introduced the cavitation jet apparatus (CJA) as a cost-effective experimental platform for identifying cavitation-induced erosion.

The results of this study establish a clear relationship between pressure, impact force, and the severity of erosion. Notably, increasing the standoff distance resulted in a larger diameter of the intensively cavitation-impacted region, which, in turn, reduced the extent of wear on the material surface. In contrast, variations in the nozzle geometry were found to have a minimal impact on the diameter of the cavitation-impacted area.

Furthermore, this study concluded that the rate of cavitation erosion, as measured using the CJA, increased with processing time up to 1200 s, after which it stabilized. The increased standoff distance not only enlarged the intensively cavitation-impacted diameter but also contributed to a decrease in overall erosion. However, different nozzle geometries did not significantly alter the concentration diameter of the cavitation-impacted region.

The conclusions regarding optimal conditions for utilizing the CJA based on our current data were as follows:

• Use of a nozzle with an orifice diameter of 2 mm;
• Adjustment of the standoff distance to 5 cm;
• Implementation of a 132° conical sharped edges nozzle;
• Setting a testing duration of 1200 s to ensure standardized results.

However, it is important to note that our experiments were constrained to a minimum nozzle orifice diameter of 2 mm and a shortest standoff distance of 5 cm. The data obtained within these limited conditions may not fully substantiate the conclusions on optimal conditions. Future research should explore a broader range of nozzle diameters and standoff distances to more comprehensively determine the optimal conditions for using the CJA. Expanding the experimental range will provide more robust data and may refine the conclusions regarding the most effective conditions for evaluating cavitation erosion.

The findings from this study provide a foundational understanding and effective reference for future investigations into cavitation erosion. Further studies, including numerical simulations and experimental work with varied conditions, will enhance our knowledge of cavitation’s effects and improve the accuracy of predictive models.