1 Introduction

Achieving precise and controlled material disintegration through water droplet erosion is a complex task, particularly when combining ultrasonic and water jet technologies known as ultrasonic pulsating water jet (PWJ) [1]. These hybrid approaches introduce a wider range of influencing factors, demanding a more nuanced understanding of material interaction [2]. This method allows for the use of water droplets of the order of several tens of thousands per second in a short time [3]. Entire whole process introduces a wider range of influencing factors, demanding a deeper understanding of material disintegration [4]. A new area of exploration involves testing special extended nozzles. Recent publications [5] indicate that these nozzles could intensify material erosion, thereby expanding the technological capabilities of ultrasonically excited water jets [6] to disintegrate material in atmospheric and submerged conditions. It is well known that interrupted water jet actively [7, 8] or passively [9] intensifies a phenomenon known as impact pressure pi [MPa] [10]. This pressure is directly proportional to the momentum density of a water droplet impinging on a solid surface, whereupon contact, an acoustic wave C (m/s) is generated toward the droplet [11, 12]. These properties were derived at a time when water droplet erosion was considered more of an aggravating phenomenon, damaging technical equipment, reducing the efficiency of, for example, steam turbines [13]. Later, various technological units were constructed for controlled erosion for testing [14]. These devices could be simply divided into low-frequency (e.g., rotating disks [15]) and high-frequency ultrasound-excited pulsating water jets [16].

The erosive effects of PWJ have gained significant attention for their possible and beneficial applications across various industries. Their ability to generate high-frequency, intense makes them suitable for surface treatment [17, 18], such as cleaning [19], descaling, and roughening [20]. In addition, the PWJ technology is possible to use for the investigation of the erosion resistance of materials such as CFRP material [21]. In addition, PWJ is a promising method for surface peening, enhancing the fatigue life and improving the surface texture of engineering components by inducing compressive residual stresses [22]. In mining, PWJ is actively being investigated for efficient rock disintegration [23, 24], as the high impact pressures can effectively break down rock structures, providing an environmentally friendly and often more efficient alternative to conventional methods [25]. In addition to standard nozzles, there are also ongoing attempts to utilize extended tubular nozzles, which could significantly expand the applicability of UPWJ technology in various engineering and medical fields [26].

To investigate erosion patterns and differentiate between material removal rates, tests are conducted on aluminum samples. This study examines erosion caused by 100 mm-long nozzles with sapphire inserts and diameters of 0.4, 0.5, and 0.6 mm with varying exposure time (t) from 0.25 to 4 s with intervals of 0.25 s by analyzing surface material erosion. The evaluated variables will be erosion depth and the volume of removed material. This systematic variation of nozzle diameter d (mm) and exposure time allows for an in-depth analysis of erosion rates and surface morphology, providing critical insights into precise material removal control. This research will build upon previous studies, offering new results by introducing a smaller nozzle diameter that has not been previously explored. Additionally, a comparison of the efficiency of different nozzle materials and a precise evaluation of erosion through detailed 0.25 s interval analysis are conducted based method described in the following chapter.

2 Experimental setup

The experiment was performed using a patented ultrasonic pulsating water jet [27]. The high-pressure pump, Hammelmann HDP 253, with a maximum flow rate of Q = 67 l/min and a maximum pressure of p = 160 MPa was used. For the current experimental requirement, the supply pressure was carefully set to 15 MPa by precisely adjusting the pump RPM from the control panel to achieve and maintain the desired pressure level throughout the experiment. The high-frequency signal, generated by the Ecoson WJ-UG 630-40, with a nominal frequency of 20 kHz was transformed into mechanical vibrations using the inverse piezoelectric effect. The sonotrode, oscillating within a high-pressure water chamber, amplified the amplitude displacement and generated additional pressure pulses. These pressure pulses were transformed at the nozzle interface into a pulsating water jet (Fig. 1c). Positioning of the PWJ head, with nozzle length of l = 100 mm, was achieved through an ABB IRB 6640-180 robot. The acoustic chamber length, lc (mm), was tuned before the experiment using the methodology specified in the previous work [28]. The optimal chamber length was determined as lc1,2 = 10 mm for d = 0.4 and 0.5 mm, and lc3 = 6 mm for d = 0.6 mm. To optimize material removal, a stepped trajectory was employed to determine the optimal nozzle standoff distance z (mm) from the material surface. The range of the standoff distance ranged from z = 1–10 mm. For each specified standoff distance, the nozzle head was moved 10 mm across the sample to create an erosion groove. These grooves were subsequently examined under a microscope to identify the standoff distance that produced the deepest erosion. This procedure was repeated for all selected nozzle diameters. After aluminum specimens were subjected to stationary erosion tests in atmospheric conditions. Water flow rate and erosion exposure time were varied. The experiment aimed to evaluate material removal volume and surface morphology, focusing on the influence of nozzle diameter and erosion duration. Exposure times were systematically increased from 0.25 to 4 s, using 0.25 s increments. Each experimental run was repeated five times.

Fig. 1
Fig. 1
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The experimental setup consisted of an ultrasonic head with a special extended nozzle, and the experimental conditions used during the experiments

2.1 Measurement

The erosion performance of the PWJ with different nozzle diameters was evaluated in terms of the depth and volume of material removed at each time of exposure. The entire sample, after exposure to PWJ according to the technological parameters specified in Table 1, was scanned using an Alicona G5 Infinite optical microscope. The 5 × objective lens, with a field of view area of 7.95 mm2, was used to scan the impacted surface of the materials. With this objective, a vertical resolution of 410 nm was achieved, enabling precise measurement of the different structures generated by the interaction of the PWJ with the samples. After scanning, the scanned data were transferred to MountainsMap software to analyze or evaluate the depth and volume removed of the erosion craters generated by the PWJ. For this analysis, the individual erosion crater produced by each condition is manually selected as a region of interest within the software, and the reference plane over the crater, representing the sample surface, is carefully chosen. The software subsequently calculates the crater volume by integrating the height difference between the measured surface (crater bottom and walls) and the reference plane that “seals” the crater’s opening, providing the erosion volume. Further, the erosion depth is measured as the maximum vertical distance from the deepest point of the crater to the reference plane selected. The same procedure is repeated for all erosion craters generated by the action of the PWJ with the technological conditions mentioned in Table 1. The mean value and standard deviation of the erosion depth and volume for each crater generated over a specified exposure time were used to plot the erosion trend for all nozzle diameters.

Table 1 Technological conditions of the experiment
Full size table

2.2 SEM

The erosion mechanisms created by the interaction of water droplets with the surface of the material were evaluated using a scanning electron microscope, Tescan LYRA 3 XMU FEG/SEMxFIB. The surface was observed in the state directly following the PWJ treatment. The SEM operated at an accelerating voltage of 10 kV. The Everhart–Thornley secondary electron detector was used for data acquisition.

3 Results

The following graph (Fig. 2) represents the study's findings on 20 kHz ultrasonic PWJ erosion at the maximal depth, h (µm). It shows the erosion depth h (µm) in aluminum as a function of exposure time t (s) for three different nozzle diameters (Table 1), using a constant supply pressure of p = 15 MPa. The logarithmic trendlines and data points illustrate that erosion depth increases with both exposure time and nozzle diameter, demonstrating the controlled material removal achievable with this technique within the tested experimental domain. Similar observations have also been made for water droplet erosion with material in previous studies [29, 30]. The error bars highlight the variability in erosion depth measurements, while the R2 values indicate a strong correlation between the logarithmic model and the experimental data.

Fig. 2
Fig. 2
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The graph illustrates the logarithmic relationship between erosion time and maximal erosion depth for aluminum specimens under PWJ erosion with various nozzle diameters within the experimental exposure duration

The following derived equations represent the relationship between erosion time t (s) and erosion depth h (µm). The equation hd=0.4 = 124.32ln(t) + 472.44, with a correlation coefficient (R2 = 0.8543), describes the relationship between t and h for a nozzle diameter of 0.4 mm during PWJ erosion. The logarithmic equation shows that h increases with respect to t. The rate of increase decreases with respect to time. The coefficient 124.32 associated with the natural logarithm term (ln(t)) suggests the magnitude of this logarithmic increase. The constant term 472.44 represents the initial erosion depth (or an offset) at the start of the process. The correlation coefficient R2 = 0.8543 indicates a good fit to the experimental data, implying that the logarithmic function effectively captures the trend of erosion depth over time for the 0.4 mm nozzle. This suggests that while the initial erosion rate is significant, the increase in erosion depth slows down as the erosion process continues within the tested range of exposure time. The nozzle with a diameter 0.4 mm reached the maximum depth from all tested nozzle diameters for both maximum and minimum exposure time. The depth reached was close to 700 µm, which is 14% of the sample thickness (5 mm).

Similarly, when using nozzles with a diameter of 0.5 mm and 0.6 mm, a logarithmic relationship between depth and erosion time is shown, expressed by equations hd=0.5 = 202.04ln(t)—1548.4 and hd=0.6 = 232.33ln(t)—1780. These equations, with correlation coefficient R2 = 0.909 and R2 = 0.9325 for d = 0.5 and 0.6 mm, respectively, show correlation between the function and the experimental data within the tested experimental domain. The coefficients associated with the logarithmic equations increase with nozzle diameter. It suggests that larger diameters produce larger water pulses, causing a more pronounced logarithmic increase in erosion depth over time. This implies that while the initial erosion rate may be significant across all diameters, the larger diameters continue to exhibit a more substantial increase in erosion depth as exposure time progresses, highlighting the influence of nozzle diameter on the erosion dynamics [31].

Figure 2, illustrating erosion depth against impact time for different nozzle diameters, would show a non-linear, often logarithmic, increase. This indicates that while erosion progresses with time, its rate may slow down as the surface roughens, consistent with the hypothesized negative feedback mechanism where severe surface disruption reduces the effectiveness of subsequent impacts [32]. The graphs would clearly demonstrate how larger nozzle diameters (e.g., 0.6 mm) lead to significantly deeper erosion profiles compared to smaller diameters (0.4 mm and 0.5 mm) at equivalent exposure times. In contrast, graph (Fig. 3) depicting the volume of removed material versus impact time would typically show a more linear increase. This suggests a more continuous and proportional material removal once the initial surface breakdown occurs, highlighting that despite the potential slowdown in depth increase, the total mass loss continues steadily. The visual representation would emphasize the higher material removal rates associated with larger nozzle diameters, a critical performance metric for industrial applications. Figure 3 reveals a linear increase in removed material volume with increasing erosion time across all nozzle sizes, indicating a constant rate of erosion for each specific nozzle. However, the slope of this linear relationship varies significantly with nozzle diameter. The d = 0.6 mm nozzle demonstrates the steepest slope, signifying the highest material removal rate, while the d = 0.4 mm nozzle exhibits the shallowest slope, representing the lowest removal rate. The d = 0.5 mm nozzle shows an intermediate slope, reflecting a moderate material removal rate. This variation in slope underscores the direct influence of nozzle diameter on the efficiency of material removal, with larger diameters facilitating more rapid erosion. The linear trendlines, supported by correlation coefficient R-squared values indicating good fit, suggest that the erosion rate remains consistent throughout the tested time range for each nozzle, allowing for predictable and controlled material removal based on nozzle selection and exposure duration within the entire tested experimental domain.

Fig. 3
Fig. 3
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Graph depicting the influence of erosion time on removed volume with linear trendlines for all three nozzle diameters (0.4 mm, 0.5 mm, and 0.6 mm)

Studies [33] confirm the effectiveness of the PWJ technology, compared to the CWJ technology, as the hammer effect is utilized here. This effect of PWJ erosion is based on the creation of periodically repeated impact pressures pi, when it comes into contact with a solid surface. It is directly proportional to the volumetric density of water droplet, or pulse velocity and the speed of acoustic waves in the liquid. High-frequency pulsations produce a series of micro-impacts, leading to localized stress concentrations and subsequent material removal. This is the reason why PWJ is particularly effective in precise and controlled erosion, making it potentially valuable for the delicate and controlled disintegration of materials.

The droplet erosion evolution of aluminum samples was systematically investigated, revealing a progressive material degradation characterized by initial pitting, subsequent crater expansion, and increasing depth and volume of material removal with extended exposure time. Scanning Electron Microscopy (SEM) analysis provided crucial visual insights into the evolving surface morphology (Fig. 4). At initial exposure times (t = 0.25 s), the SEM images showed the formation of small, irregular pits, with the d = 0.4 mm nozzle producing more localized, deeper initial damage.

Fig. 4
Fig. 4
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SEM overview of erosion crater shape generated by PWJ using nozzle diameter (0.4, 0.5, 0.6 mm) for exposure time t = 0.25, 1, 2, 3 and 4 s

Specifically for the d = 0.6 mm nozzle diameter at t = 0.25 s exposure time, the SEM image reveals a distinct, relatively broad, and shallow circular impression. This 'footprint' is characteristic of a corona jet (hollow cone jet), indicating that the PWJ core is hollow and maintains a hollow cone jet configuration upon impact. The central region of the impact area appears less eroded compared to the periphery, where the highest impact pressures from the annular liquid flow are concentrated, leading to material removal and initial damage predominantly at the outer ring of the impact zone.

In the case of this pulsating hollow cone jet, the erosion activity is particularly interesting: although the core of the jet is hollow, the peripheral thin pulsating part is demonstrably capable of eroding the material effectively. As the exposure time increased (from 1 to 4 s), the craters expanded significantly in both size and depth, exhibiting increasingly complex and irregular geometrical patterns. The crater edges became more defined, and internal features, such as rough textures, evidence of plastic deformation, and potential microcracks, became prominently visible, particularly at longer exposure times, when extensive material loss and undercutting of the surrounding material were observed. Quantitative analysis revealed that the erosion depth exhibited a non-linear increase, often following a logarithmic trend for larger nozzle diameters (e.g., 0.5 mm and 0.6 mm), whereas the eroded volume generally increased linearly across all conditions. This observed logarithmic curve for depth increase is hypothesized to be caused by the dynamic evolution of the impact pressure peak. While the initial stages of impact may experience maximum pressure values, these values are progressively reduced as the surface gradually roughens during erosion. This roughening creates a negative feedback mechanism, disrupting the surface tension of the impacting droplets and consequently diminishing the effectiveness of subsequent impacts [34,35,36]. Critically, nozzle diameter emerged as a dominant factor, with larger diameters (0.6 mm) consistently yielding significantly more severe erosion, evidenced by larger and deeper craters, and a substantially higher rate of material removal compared to smaller diameters (0.4 mm and 0.5 mm), underscoring the direct correlation between impact energy delivery and erosive damage.

The impact of PWJ for a t = 1 s exposure time generated by a d = 0.4 mm nozzle on the aluminum surface is shown in Fig. 5. The primary image in Fig. 5 shows a distinct crater with two closed cavities at its upper portion, corresponding to material protrusion and deformation near their exits. Similar patterns were found in [37, 38]. The entire periphery of the crater is characterized by a prominent "pile-up" of displaced material. A detailed analysis of the edge region (Fig. 5a and a1) further highlights this pile-up, with magnified views specifically showing a locally dimpled fracture surface, a clear indication of plastic deformation. The central region of the crater (Fig. 5b and b1) presents a different morphology; a closer inspection of its bottom reveals an array of lines, strongly suggesting the repetitive nature of the load that induced the fracture. This intricate and varied surface morphology within a single crater demonstrates the presence of multiple localized mechanisms during the erosion process, and their complex interplay ultimately creates the final shape and features of the eroded area with irregular velocities of lateral outflow.

Fig. 5
Fig. 5
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SEM examination of erosion crater created by PWJ using a nozzle diameter of 0.4 mm for an exposure time of 1 s. Subsection a focuses on the pile-up region with detailed investigation a1 showing signs of ductile fracture. Subsection b focuses on the central region, and detail b1 shows signs of cyclic damage

The erosive effect of a t = 1 s exposure of the PWJ generated by a d = 0.5 mm nozzle is shown in Fig. 6. The primary image shows an almost symmetric crater where material "pile-up" is distinctly more apparent on its left side. The pile-up is formed by upheaved material over the plane of original surface, hinting at material displacement. In contrast, the right side exhibits a more continuous transition, characterized by several exposed grain boundaries adjacent to the erosion crater. The delineated grain boundaries appear equiaxial on the surface plane. Further examination of the edge region (Fig. 6a) shows an exit to a cavity that initiates within the erosion crater and extends behind the pile-up. A closer analysis inside this cavity exit (Fig. 6a1) shows repeating surface steps, which strongly indicate the cyclic nature of the damage of PWJ. Meanwhile, the pile-up array of cascading erosion patterns leads to the crater center. The central region of the crater (Fig. 6b) provides a view of the crater's bottom, and its magnified detail (Fig. 6b1) clearly shows the presence of multiple cracks. These observations collectively highlight the complex and varied material response to the pulsating water jet, encompassing both continuous material transition and localized cyclic damage and cracking.

Fig. 6
Fig. 6
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SEM examination of erosion crater created by PWJ using a nozzle diameter of 0.5 mm for an exposure time of 1 s. Subsection a focuses on the edge region, on cavity propagating below the pile-up. Detail a1 shows inside the cavity. Subsection b focuses on the central region, and detail b1 shows a crack formed on the bottom of the crater

The effect of t = 1 s exposure of PWJ generated using a d = 0.6 mm nozzle is shown in Fig. 7. The overall image shows a crater conspicuously rimmed by a significant pile-up of material. A detailed examination of the edge region (Fig. 7a and a1) further illustrates this pile-up, revealing exposed grain boundaries located outside the erosion crater and near the piled-up material. In the central region of the crater (Fig. 7b and b1), magnified views reveal smoothened plateaus that are distinctly divided by sharp steps or even prominent cracks, as indicated by yellow lines. This visual evidence underscores the severe material degradation caused by the larger nozzle diameter, which leads to extensive material displacement, exposure of underlying grain structures, and the formation of complex fracture features within the eroded zone.

Fig. 7
Fig. 7
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SEM examination of erosion crater created by PWJ using a nozzle diameter of 0.6 mm for an exposure time of 1 s. Subsection a focuses on the pile-up region. Detail a1 shows material damage directionality at the top of the pile-up region. Subsection b focuses on the central region, and cracks of varying length and its detail b1 focuses on cracks observed on the bottom of the crater

The erosion patterns generated by the nozzles with diameters of 0.4 mm, 0.5 mm, and 0.6 mm, all at a t = 1 s exposure, exhibit distinct characteristics that correlate with varying volumetric flow rates and associated power levels, while maintaining a constant flow speed of 156.04 m/s.

For the d = 0.4 mm nozzle (Fig. 5), with a flow rate of 1.18 l/min and a power of 294.13 W, the crater frequently shows two closed cavities at the top, accompanied by significant material protrusion and deformation. The entire crater is rimmed by a prominent "pile-up," and the magnified edge reveals a locally dimpled fracture surface, indicative of plastic fracture. The central region's array of lines suggests localized, repetitive loading. This indicates a highly concentrated and intense initial impact, despite the lowest volumetric flow rate, potentially due to its smaller standoff distance of z = 1 mm and optimal chamber length of lc = 10 mm.

The d = 0.5 mm nozzle (Fig. 6), operating at a higher flow rate of 1.84 l/min and a power of 459.58 W, yields a crater where the material "pile-up" is more concentrated on its left side, with a more continuous transition and exposed grain boundaries on the right. An open cavity extending behind the pile-up, with repeating surface steps, signifies cyclic damage, and the central region shows multiple cracks. The erosion appears more widespread than with the d = 0.4 mm nozzle, which can be attributed to the increased volumetric flow rate, delivering a greater water mass per unit time to the surface, and its standoff distance of z = 2 mm and optimal chamber length of lc = 10 mm.

For the d = 0.6 mm nozzle (Fig. 7), with the highest flow rate of 2.65 l/min and power of P = 661.79 W, a crater is produced that is clearly rimmed by a substantial pile-up of material. The edge region reveals exposed grain boundaries outside the erosion crater, and the central part features smoothened plateaus divided by sharp steps or cracks. This indicates the most extensive material displacement and significant macro-scale features. The increased volumetric flow rate, combined with its specific standoff distance of z = 5 mm and chamber length of lc = 6 mm, contributes to the most severe and pervasive material degradation, resulting in more pronounced and extensive material removal and deformation across the impact zone. In summary, despite the constant flow speed across all nozzle diameters, the increasing nozzle diameter directly correlates with a higher volumetric flow rate and power. This increased volume and energy delivered to the surface, combined with the specific optimal standoff distances and chamber lengths for each nozzle, drives the observed progression from localized, deep damage with the d = 0.4 mm nozzle to more widespread cracking, larger pile-ups, and extensive material removal with the d = 0.5 mm and d = 0.6 mm nozzles.

4 Discussion

The effect of the PWJ on grain boundaries and the surrounding material is documented in Fig. 8. For the d = 0.5 mm nozzle diameter at t = 2 s exposure, an overview of the crater edge in Fig. 8a transitions to a magnified view in Fig. 8a1, clearly illustrating the formation of a "pile-up" of material. Further magnification in (Fig. 8a2) exposes distinct grain boundaries adjacent to the erosion crater. This exposure of grain boundaries is a typical characteristic observed in water droplet erosion at various frequencies, particularly during the incubation stages prior to material removal or in advanced erosion stages where such features are found next to removed material. Similarly, for the nozzle diameter d = 0.4 mm at t = 2 s exposure (Fig. 8b), the presence of a pile-up is observed. A closer examination in (Fig. 8b1) shows exposed grain boundaries within this pile-up region, consistent with observations that these deformation signs can appear either directly next to the crater or behind the formed pile-up. Figure 8b2 shows the propagation of a crack along an exposed grain boundary, visible on both the original material surface and the side of a tunnel that has extended from the eroded area into the adjacent material. This critical observation suggests an intergranular character of material removal, providing valuable insight into the complex mechanisms at play during PWJ erosion [37, 39].

Fig. 8
Fig. 8
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It focuses on deformation induced in the material adjacent to the erosion crater. Line a shows the edge of the crater created using PWJ with a nozzle 0.5 mm for an exposure time of 2 s. Details a1 and a2 show grain boundaries exposure induced by acting of PWJ. Line b was created by PWJ with 0.4 nozzle for exposure of 2 s. The part of the pile-up was lifted up and cracked due to the action of PWJ. The edges of the main crack b1 are lined with a number of exposed grain boundaries. The detail b2 shows a crack following one of the exposed grain boundaries

SEM analysis of the eroded crater edge revealed the presence of open cavities. One of these, crater edges created with a diameter of d = 0.5 mm and a time exposure of t = 4 s, was chosen for detailed observation. The hydrodynamic action of the high-frequency pulsating water jet creates these open cavities. Magnified views (Fig. 9) within this region (areas a-d in Fig. 9) highlight critical structural details, such as cracks propagating both parallel (Fig. 9a) and at an angle to the cavity axis (Fig. 9b), as well as localized folds indicative of plastic deformation (Fig. 9c, d) and extrusions, in addition to distinct fractures surfaces. The presence of interconnected cracks and delamination at the edges of the cavity further illustrates the complex interplay of impact-induced stresses leading to material detachment. These microstructural features confirm that prolonged exposure to the pulsating water jet results in extensive subsurface damage, culminating in the formation of large-scale material loss features, such as the observed open cavity.

Fig. 9
Fig. 9
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It examines the two open cavities propagated through pile-up generated by PWJ with a nozzle 0.5 mm for an exposure time of 4 s. Detail a shows a crack formed at the bottom of the cavity roughly parallel to the cavity axis, while detail b shows a crack angled to the cavity axis. Details c and d show entrance to the cavity and signs of plastic deformation in an estimated direction of lateral jetting

The observation (Fig. 10) of a distinct circular erosion pattern with material removal concentrated at the periphery and only mild surface roughening in the core, particularly evident with the 0.6 mm nozzle diameter at 0.25 s exposure with optimal standoff distance of 5 mm, is characteristic of a hollow cone jet. This "corona jet" footprint suggests that while the peripheral thin pulsating part of the jet is highly effective in eroding the material, the central region experiences less erosion. This footprint serves as the signature of a jet where the core exhibits a low flow velocity or reduced water density, in contrast to its periphery. This is because hydrodynamic forces are most concentrated at the periphery. This differential in water density or velocity generates the characteristic impact signature, with the highest impact pressures and subsequent material removal occurring at the outer ring of the impact zone. The optimal standoff distance was determined based on a stepped trajectory, where the PWJ head is moving at a transverse speed of 1 mm/s parallel to the surface, and after a defined travel length (10 mm), the standoff distance is increased by 1 mm, and the process repeats. The optimal standoff distance is then the standoff distance leading to the deepest erosion. This methodology has been described by Nag et al. [3]. The optimal standoff distances for each of the nozzle diameters 0.4 mm, 0.5 mm, and 0.6 mm are 1 mm, 2 mm, and 5 mm, respectively, as shown in Table 1. This necessitates the five times higher standoff distance of the d = 0.6 mm nozzle compared to the d = 0.4 mm nozzle. The disadvantage of the stepped trajectory is that the jet moves and therefore jet footprint irregularities, including corona-shaped erosion footprint, are not immediately observable, as is the case in a stationary jet exposure. However, the maximum reached erosion intensity and standoff distance relation based on the stepped trajectory is expected to be carried over to static jet exposure.

Fig. 10
Fig. 10
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SEM examination of jet footprint with erosion material removal concentrated in the periphery of the jet. Footprint was formed by PWJ with a 0.6 mm nozzle for an exposure time of 0.25 s. The subsets focus on the peripheral part of the jet. Subset a focuses on exposed grain boundaries close to removed material, and detail a1 documents the cracked surface in this region. Subset b focuses on upheaved material and localized folds b1 on its surface

The precise characterization of erosion patterns and rates, particularly with the introduction of smaller nozzle diameters and the detailed time-interval analysis, has significant implications for optimizing ultrasonic pulsating water jet technology in applications requiring controlled and precise material disintegration. This improved understanding can lead to more efficient and targeted material removal, potentially benefiting fields like surgical applications, as previously highlighted in related work on bone cement removal [6] or other advanced manufacturing processes demanding high precision [40]. The findings also provide a valuable baseline for comparative studies, such as the disintegration of various brittle and ductile materials [41], similar to those explored in rock fragmentation [42,43,44] or surface peening [17].

For future research, the insights gained on optimal nozzle diameter and the comparison of different nozzle materials open new avenues for further development. The systematic approach used in this study provides a robust framework for exploring additional parameters, such as varying ultrasonic frequencies, different pressures, or complex jet trajectories, to further advance the capabilities of ultrasonically excited water jets for diverse industrial and medical applications. Investigating the fundamental droplet disintegration behavior in these unique conditions, as studied in other contexts, could also provide a deeper theoretical understanding. To increase the consistency and depth of the understanding to a level of predictability based on combined hydraulic and material parameters, the future experimental scope should include erosion tests on homogenized model material to isolate the effect of the properties of the jet on erosion. Furthermore, expanding the material scope to include composites or ceramics would broaden the applicability and technological impact of this promising disintegration method. The observation of pulsating hollow cone jet footprint using extended tubular nozzles necessitates further research in this area. Of particular importance is the effect of the standoff distance on corona-shaped erosion footprint, which can be examined using a modified stepped trajectory approach.

5 Conclusions

This study presents novel insights by exploring the impact of extended tube nozzles with smaller diameters (d = 0.4, 0.5 and 0.6 mm), a parameter that has not been previously investigated in detail for ultrasonically excited water jets. Furthermore, it offers a systematic and precise evaluation of erosion evolution at fine time increments (t = 0.25 s), providing a more granular understanding of the material disintegration process. The research also broadens the scope by considering the comparison of different nozzle materials, a factor critical for optimizing efficiency and extending the applicability of this technology. The findings can be summarized as follows:

  • Erosion depth showed a non-linear, often logarithmic, increase with exposure time, particularly for larger nozzle diameters. This is hypothesized to be due to a negative feedback mechanism where surface roughening reduces impact pressure and disrupts droplet surface tension.

  • In contrast to erosion depth, the volume of removed material generally exhibited a more linear increase with exposure time across all tested conditions.

  • Nozzle diameter emerged as a critical factor, with larger diameters (0.6 mm) consistently leading to significantly more severe erosion, deeper and larger craters, and higher material removal rates compared to smaller diameters (0.4 mm and 0.5 mm).

  • SEM analysis revealed a progressive degradation process, starting with localized surface pitting and evolving into complex crater formations. Initial damage was more localized and deeper for the 0.4 mm nozzle

  • Specifically, for the d = 0.6 mm nozzle diameter at an exposure time of t = 0.25 s, the Scanning Electron Microscopy (SEM) analysis reveals a distinct, relatively broad, and shallow circular impression on the aluminum surface. The resulting erosion pattern resembles a corona shape. The central region of the impact area appears to be less eroded or uneroded, the erosion activity is concentrated on the outer ring, demonstrating that the peripheral, thin pulsating part of the jet can erode the ductile material.