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Experimental observation of the erosion pattern, pits, and shockwave formation in a cavitating jet
Author’s Accepted Manuscript Experimental observation of the erosion pattern, pits, and shockwave formation in a cavitating jet Nobuyuki Fujisawa, Toshihiro Horiuchi, Kei Fujisawa, Takayuki Yamagata www.elsevier.com/locate/wear
PII: DOI: Reference:
S0043-1648(18)30639-2 https://doi.org/10.1016/j.wear.2018.10.014 WEA102524
To appear in: Wear Received date: 28 May 2018 Revised date: 24 August 2018 Accepted date: 12 October 2018 Cite this article as: Nobuyuki Fujisawa, Toshihiro Horiuchi, Kei Fujisawa and Takayuki Yamagata, Experimental observation of the erosion pattern, pits, and shockwave formation in a cavitating jet, Wear, https://doi.org/10.1016/j.wear.2018.10.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental observation of the erosion pattern, pits, and shockwave formation in a cavitating jet Nobuyuki Fujisawa a*, Toshihiro Horiuchi b, Kei Fujisawa c, Takayuki Yamagata a a
Department of Mechanical Engineering, Niigata University
b
Graduate School of Science and Technology, Niigata University Department of Mechanical and Aerospace Engineering, University of Florida *Corresponding author: [email protected] c
Abstract In this study, the erosion pattern, pits, and shockwave formation of a cavitating jet were experimentally observed to gain an understanding of the erosion mechanism of a cavitating jet discharging from a cavitator nozzle into a still water environment. The erosion pattern and formation of pits were visualized by direct imaging on the eroded material surface, while the shockwave initiation points were detected using the cross-schlieren visualization method, combined with two orthogonal high-speed observations near the wall. The experimental results indicated that the radial distributions of the erosion depth, number of pits, and shockwave initiation points were highly correlated. These results provided direct evidence of the cavitation erosion caused by the formation of pits that resulted from the shockwave generated by the periodic cloud collapse event near the wall. The results also demonstrated that the growth of the cavitation erosion volume is highly correlated with the number of pits formed rather than the diameters of the pits.
Keywords: Cavitation; Cavitating jet; Erosion; Cloud collapse; Shockwave; Cross-schlieren imaging.
1. Introduction A cavitating jet is a fundamental flow configuration of a submerged water jet and is discharged from a cavitator nozzle into a still water environment. This flow configuration is widely applied to the engineering, fabrication, cutting, and peening of metal materials owing to the highly erosive nature of the bubbles that are generated along the cavitating jet shear layer [1, 2]. The erosive nature of cavitating jets arises from the periodic cloud formation in the cavitator nozzle, which is caused by the flow instability through the orifice and periodic cloud formation downstream of the cavitator
1
nozzle [3-8]. The cavitation cloud from the cavitator nozzle eventually collapses in the relatively high-pressure region that is downstream of the nozzle and results in the damage of the target materials exposed to the cavitating jet [9-13]. The relationship between the behavior of the cavitation cloud and the erosion pattern on the wall material is a topic of interest for cavitation research [14-19]. This topic has been studied on the cavitating jet through high-speed observations of the cloud structure and the associated erosion pattern on the wall material [20-22]. The experimental results demonstrated that the cloud collapse occurred near the wall material, and additionally, the cloud collapse generated impulsive forces on the wall. Moreover, the erosion pattern on the material surface consisted of a number of pits, which were likely due to the generation of an impulsive force caused by the cloud collapse that occurred near the wall material. The pit formation on the material in the cavitating jet is likely caused by the liquid-jet mechanism produced at the instant of cloud collapse, which is similar to the bubble collapse behavior on a hydrofoil [14, 15]. The observation of pits on the wall material in the cavitating jet is essential for understanding the erosion characteristics of materials. The pits observation has advantages, such as the convenience of application, short experimental time requirements, and potential for understanding the erosion mechanisms of the cavitating jet [20, 21]. The most widely used pit sensors in literature [23-26] are thin metal films of aluminum, which can be adhered to the material surface. By observing the pits on the wall material, their spatial distribution can be evaluated over a small period of time, the timeframe of which is shorter than measuring the mass loss for characterization of the bulk erosion rate. Although the observation of pits enables the evaluation of the spatial distribution of the material erosion rate, a disadvantage of this method is that the pit sensor is often not capable of withstanding the central column of the liquid jet produced by the cavitating jet [21]. Therefore, this method is limited to lower injection pressures, or this method requires the sensor to be applied at a region that is distant from the nozzle. In order to avoid these challenges, one can observe the formation of pits directly on the erosive surface of the material, thus, permitting the application of a wide range of cavitating jet injection pressures [27-29]. However, this experimental technique has not been extensively studied in comparison to the former technique, which implements the thin film sensor. In order to further study the erosion mechanisms of the cavitating jet, simultaneous observations of the cavitation pits and cloud structure were obtained; high-speed observation techniques were implemented to view the formation of pits, and shadowgraph imaging was used to examine the cavitating jet [21]. The results indicated that the pit formation occurred at the instant of the cavitation cloud collapse in the cavitating jet. This is likely caused by the shockwave that is formed, and an impulsive force may occur at the instant of the cavitation cloud collapse, which is similar to the observation of the bubble-collapse generated by laser-induced cavitation [30-32]. During the bubble collapse event in the cavitating jet, several bubbles collapse simultaneously, 2
thereby generating shockwaves near the wall [33]. Furthermore, the impulsive forces that are generated on the wall material at the instant of the cavitation bubble collapse can be detected by piezoelectric polymer sensors that are made of polyvinylidene difluoride (PVDF), which has a high-frequency response [34-36]. In the present study, the spatial distribution of the erosion pattern, cavitation pits, and shockwave formation were investigated experimentally to examine the evidence of erosion mechanism of cavitating jet. The shockwave initiation points were detected by the cross-schlieren imaging method and high-speed observations.
2. Experimental method and procedure 2.1 Experimental setup Fig. 1(a) illustrates the experimental setup. Two test tanks were prepared: one for the erosion test and observation of the pits and the other for the visualization study of the shockwave formation in the cavitating jet. The former test tank had a square cross-section of 500 mm × 500 mm with a height of 600 mm, and the latter had a hexagonal cross-section with an opposite side length of 400 mm and height of 460 mm. It is noted that the latter test tank was constructed from a transparent acrylic resin to allow for the observation of the cavitating-jet behavior. The behavior was observed by the cross-schlieren method using two high-speed cameras. For this experiment, the temperature of the working fluid, water, was maintained at 25±1°C using a cooling unit. A cavitator nozzle was used for generating the cavitating jet and is shown in Fig. 1(b). The cavitator nozzle was located at a depth of 50 mm and was directed downward. The cavitator nozzle was made of a converging and diverging cross-section that was separated by an orifice with a diameter of 0.8 mm and a thickness of 2.4 mm [16, 17]. After issuing from the nozzle, the water of the cavitating jet spreads downward into the still water environment. The cavitation coefficients were evaluated from following equation, σ =2 (p - pv) / ρU2
(1)
They were σ =0.030, 0.019, 0.013 at pump pressures 8 MPa, 12 MPa, 18 MPa, respectively (where, p = pressure, pv = vapor pressure, U = injection velocity at orifice of nozzle, ρ = density of water). The jet flow through the nozzle was pressurized by a plunger pump and contained a filter to eliminate the particulate matter in the working fluid. The pump pressure, P, was maintained constant at values of 8 MPa, 12 MPa, and 18 MPa during the experiment, and each pressure corresponded to the injection velocities through the orifice of 82 m/s, 103 m/s, and 127 m/s, respectively. The mean velocity was evaluated directly from the measurement of the discharged flow rate. Additionally, the test specimen was made of aluminum (A1070) with a diameter of 40 mm and thickness of 8 mm. The specimen for the observation of the pits was processed by quench annealing to promote erosion damage. The specimen was heated for 1 hour in a heating furnace at 470 K and was then cooled in the furnace without further heating. The Vickers hardness of the specimen decreased from an initial 3
value of 36 prior to the annealing process to a value of 32 after the annealing process. Therefore, deeper pits were observed on the annealed specimen.
(a) Experimental test section for the erosion test
(b) Cavitator nozzle (units: mm)
Fig. 1 Experimental apparatus
2.2 Erosion characteristics The erosion characteristics of the test specimen produced by the cavitating jet were evaluated by measuring the mass loss characteristics of an aluminum (A1070) circular specimen. The test specimen had a diameter of 40 mm and thickness of 8 mm. The erosion test was conducted by placing the test specimen in the cavitating jet, which was operated at three nozzle pressures of 8 MPa, 12 MPa, and 18 MPa. The test specimen was located at varying distances between 10 mm and 60 mm from the nozzle with the aid of a traversing device. The mass loss measurement of the test specimen was conducted using a high precision weight meter with a resolution of 0.01 mg. The non-dimensional erosion rate, Vm, was then evaluated using Eq. (2) [37, 38]: Vm = dEv/ Qdt
(2)
where, Ev is the erosion volume per unit time, t, and Q is the volumetric flow rate of the cavitating jet. The non-dimensional erosion rate, Vm, was directly evaluated from the variation of erosion volume, Ev, with respect to the flow volume in a unit time of the cavitating jet, Qt. It is noted that the non-dimensional erosion rate, Vm, has been used in previous research for characterizing the erosion of the wall material using the liquid droplet impingement test [37, 38]. The radial distribution of the erosion depth was measured by traversing the laser displacement sensor over the specimen surface. The radial distribution of the mean depth was determined from the average of eight line measurements; a measurement was taken every 22.5° along the circular specimen through the center. The spatial resolution of the laser displacement sensor was 1 μm.
2.3 Observation of the cavitation pits 4
An observation of the cavitation pits on the wall material was conducted after the specimen was exposed to the cavitating jet. The imaging was performed using a digital camera with a spatial resolution of 3000 pixels × 2000 pixels, and the specimen was uniformly illuminated using a metal halide lamp. It should be noted that this technique is applicable to a wider range of injection pressures than that of a thin-film pit sensor [21]. The number of pits and pit diameters were evaluated from the image. A sample image is shown in Fig. 2(a), which was obtained at a pump pressure of 12 MPa and at a standoff distance of 30 mm. The image was analyzed using a Sobel filter to enhance the edges of the pits to evaluate the pit diameter, and the thresholding was applied prior to counting the number of pits present in the image, as shown in Fig. 2(b). The overlapping effect of the pits was not considered in this analysis. This is because the maximum number of pits was less than 800 when the operating time of the cavitating jet was a short duration (1 sec). The dimensions of the target images taken by the digital camera were 30 mm × 20 mm, and thus, the image spatial resolution was 10 μm/pixels. It is noted that the pit diameter smaller than 3 pixels (=30μm) are considered as an image noise in the experiment. An important consideration is the operating time of the cavitating jet, which was measured by a PVDF sensor that was attached to the specimen. Fig. 3(a) shows the structure of the pit sensor, where the PVDF film is fixed between the supporting rods of the specimen. The pit sensor is sealed with acrylic resin material to minimize the electrical noise. An example of the output signal from the pit sensor is shown in Fig. 3(b). This output signal was observed at a pressure of 12 MPa and a standoff distance of 30 mm. The result shows that a high frequency signal starts and ends at the initiation and conclusion of the pump operation, respectively. The pitting time, t, was estimated from the period of the high frequency pitting signal.
(a) Original image
(b) Post-processing image
Fig. 2 Observation of the cavitation pits
5
(a) Specimen with the pits sensor
(b) Example of the impulsive signal
Fig. 3 Structure of the pits sensor
2.4 Cross-schlieren imaging The relationship between the cavitation pits and shockwave formation in the periodic cloud behavior were obtained by evaluating the origins of the shockwaves using the cross-schlieren imaging method. This method is an extension of schlieren imaging technique, which was previously implemented [33, 39, 40]. This experimental technique obtains the three-dimensional distributions of the shockwave initiation points, where the collapsing of the cavitation bubbles is expected to occur. The main concept of cross-schlieren imaging is to evaluate the shockwave initiation points of the two orthogonal laser-schlieren images by simultaneously imaging the shockwave formation event. When the laser-schlieren imaging are simultaneously applied to the cavitating jet from the two orthogonal observations, the shockwave initiation points can be evaluated near the wall. Previous research has demonstrated that the shockwave formation generally occurs within 3 mm of the wall [33]. This new visualization technique for evaluating the shockwave center provides a powerful tool for obtaining the spatial distribution of the shockwave initiation points in the cavitating jet. Fig. 4 illustrates the experimental setup of the cross-schlieren imaging method, which consists of a CW Nd:YAG laser (5 W) and beam expander, a half mirror, two concave mirrors, and two complementary metal-oxide semiconductor cameras with a lens focal length of 200 mm. The concave mirror has a diameter of 150 mm and focal length of 1.2 m. Moreover, a slit-type darkfield illumination is placed as a knife edge in front of each camera to magnify the sensitivity of the laser-schlieren images. The details of the laser-schlieren imaging technique have been described in Ref. [33, 39, 40]. The observations of the shockwave formation from the two orthogonal directions were conducted with the two high-speed cameras synchronously operating at 400,000 frames/s. The two 6
cameras had spatial resolutions of 264 pixels × 384 pixels and 160 pixels × 264 pixels. The cameras were aligned with the laser beam, concave mirror, and slit-type dark field illumination. The exposure time of the camera was set to the shortest allowable time of the camera, 250 ns, in order to freeze the shockwave event, since a shorter exposure time is better suited for capturing sharper shockwave images. In order to obtain the shockwave initiation points from the two orthogonal cross-schlieren images, the shockwave was assumed to propagate spherically after initiation. Therefore, the shockwave initiation point was evaluated by fitting a circular trajectory to the shockwave image. Additionally, the two coordinates (x1, z1) were confirmed by the vertical height of the two shockwave trajectories. An example of the shockwave images is shown in Fig. 5, where the circular trajectories of the shockwave front can be observed in the two orthogonal images. After performing the thinning operation of the shockwave trajectories, the shockwave initiation point is obtained by applying a circular curve-fitting technique to the images. This operation allows the evaluation of the x1 and z2 coordinates of the shockwave initiation point, and these coordinates are obtained from camera 1 and 2, respectively.
Fig. 4 Experimental arrangement of the cross-schlieren imaging technique
7
(a) Camera 1 image
(b) Camera 2 image
Fig. 5 Examples of the shockwave images obtained by the cross-schlieren imaging method (P = 12 MPa, xs = 30mm) 3. Results and discussion 3.1 Erosion characteristics Fig. 6 shows a sample of the test specimen erosion characteristics in the cavitating jet at the operating pressures of 8 MPa, 12 MPa, and 18 MPa, where the standoff distances are maintained at 30 mm, 30 mm, 40 mm, respectively, which correspond to the distances that would provide the maximum erosion rate for each pressure. It is noted that the error bar shows the scattering of the data by the repeated experiment. The erosion volume, Ev, increases almost linearly with increasing exposure time, t, following the incubation period of 10 min from the start of the experiment. Additionally, the results indicate that the constant erosion rate in the terminal stage, dEv/dt, increases with an increase in the pump pressure, P, corresponding to the influence of the injection velocity of the cavitating jet. These erosion characteristics produced by the cavitating jet feature a steady-state period with a constant erosion rate, dEv/dt, after the incubation, acceleration, deceleration periods of cavitation erosion. The details of the cavitation erosion stage progression are described in Ref. [2]. Therefore, the non-dimensional erosion rate, Vm, defined by Eq.(2), in the steady-state period of cavitation erosion increases with increasing injection velocity of the cavitating jet. Fig. 7 shows the variation of the erosion rate, Vm, with respect to the standoff distance, xs, for the nozzle pressures of 8 MPa, 12 MPa, and 18 MPa. It is noted that the error bar shows the scattering of the data by the repeated experiment. These results indicate that the peak erosion rate increases with increasing nozzle pressures. Moreover, the erosion rate decreases at large standoff distances, independent of the injection pressure, thus, indicating the presence of an optimum standoff distance that maximizes the cavitating-jet erosion. The growth of the erosion rate with increasing standoff distances indicates that the erosion characteristics improve when the cavitating jet spreads in the radial direction; however, the erosion characteristics are weakened at longer standoff distances 8
due to the decrease in the jet velocity that occurs downstream. As a result, the erosion rate of the cavitating jet can be maximized at a given standoff distance, depending on the injection pressure. Additionally, the peak erosion rate increases with increasing injection pressure. Fig. 8 shows the variation of the local erosion rate, vm, in the radial direction from the jet centerline for the injection pressures of 8 MPa, 12 MPa, and 18 MPa. These data are obtained from the local erosion depth measurement by averaging the eight line measurements in the radial direction across the specimen at every 22.5° using the laser displacement sensor. The local erosion rate, vm, is defined by the variation of erosion depth in a unit time. It is noted that the error bar shows the scattering of the data by the repeated experiment. The results indicate that the local erosion rate increases with increasing injection pressures. Additionally, at higher injection pressures, the maximum local erosion rate shifts to the outer region of the cavitating jet, which indicates the radial growth of cavitating jet. On the other hand, the peak erosion rate near the centerline of the cavitating jet grows with increasing injection pressures, which demonstrates the influence of the jet velocity on the erosion rate. The maximum erosion rates occur at radial distances of 5 mm, 6 mm, and 8 mm for injection pressures of 8 MPa, 12 MPa, and 18 MPa, respectively, which demonstrates the radial growth of the cavitating jet with increasing injection pressures. Additionally, decreases in the local erosion rates were noted at radial distances of 6.5 mm, 7.5 mm, and 10.5 mm for the injection pressures of 8 MPa, 12 MPa, and 18 MPa, respectively. The decreases represent the negative growth of the local erosion rate that is expected to be caused by the plastic deformation of the wall material near the highly erosive region in the cavitating jet. On the other hand, the erosion rate near the jet axis increases at the highest injection pressure of 18 MPa. This may be caused by the influence of the direct contact of the liquid jet. This is because a similar erosion pattern is generated by the direct impingement of liquid jet in air using the present cavitator nozzle. Furthermore, the erosion rate increases with decreasing the standoff distance [21] due to the higher impact pressures near the nozzle.
Fig. 6 Time variation of the erosion volume, Ev 9
Fig. 7 Variation of the erosion rate, Vm, with standoff distance, xs
Fig. 8 Variation of local erosion rate, vm, with the radial distance, r 3.2 Observation of the erosion pattern and formation of pits Figs. 9 and 10 show the erosion patterns and pits that were observed on the test specimen for each of the cavitating jets. These results were obtained at the injection pressures of 8 MPa, 12 MPa, and 18 MPa at the maximum erosion rate condition with the standoff distances of 30 mm, 30 mm, and 40 mm, respectively. The observations of the erosion pattern have an exposure time of 40 min following the initiation of the cavitating jet, while the pit observations are made for approximately 1 sec following the cavitating jet initiation. Therefore, there is a substantial difference between these observation times. However, the two images have the common feature of indicating the amount of damage, and the images demonstrate the outward growth of the erosion pattern with increasing injection pressures. The results indicate that the cavitation erosion can be represented by the distribution of the number of pits. Additionally, the cavitation erosion is largely observed in the outer 10
region of the erosion pattern, where the dense pit patterns are observed. This eroded area consists of a number of pits having a magnitude on the order of millimeters in diameter (Fig.9). The diameter of the pits increases as the erosion mass loss grows with time. With increasing injection pressures, there is an increase in the number of pits and growth of the eroded area, which is similarly observed in the radial growth of the erosion pattern shown in Fig. 8. The smallest region of erosion loss is observed near the center of the cavitating jet, which is caused by the impingement of the liquid jet on the specimen. However, the corresponding pit patterns are not clearly observed in the images shown in Fig. 10. The liquid jet erosion does not follow the formation of pits due to its different erosion mechanism.
(a) 8 MPa
(b) 12 MPa
(c) 18 MPa
Fig. 9 Erosion pattern of the cavitating jet
(a) 8 MPa
(b) 12 MPa
(c) 18 MPa
Fig. 10 Observation of the pit patterns
Fig. 11 shows the number density distributions of the pit formation in the radial direction. The 11
number density distributions are obtained from the image analysis of the pits on the specimen for the injection pressures of 8 MPa, 12 MPa, and 18 MPa at the maximum erosion rate condition. The number of pits per unit time is obtained by an image analysis of the pit images for an exposure time of 1 sec. The exact exposure time was measured by the PVDF sensor that is attached to the specimen. These results indicate that the number density of the pits decreases near the jet centerline. On the other hand, the number density of pits grows in the outer region of the cavitating jet and reaches maximum values at radial distances of 5 mm, 6 mm, and 8 mm from the jet center for the injection pressures of 8 MPa, 12 MPa, and 18 MPa, respectively. The number density distribution of pits decreases gradually as the radial distance from the jet center increases. The number density distribution of the pits is higher at lower injection pressures, but the number of pits decreases at lower injection pressure (Fig.13). Therefore, the peak erosion rate decreases with decreasing injection pressure. These results agree qualitatively with the radial variation of the local erosion rate and the peak erosion rate variation with injection pressure that is shown in Fig. 8. Fig. 12 shows the pit diameter distribution for the injection pressures of 8 MPa, 12 MPa, and 18 MPa at the maximum erosion rate condition. The pit diameter distribution shows a sharp peak at lower pit diameter, which agrees with a feature of cavitation pits observed in literature [2]. Additionally, the pit diameter distribution is nearly independent of the injection pressure in the range of the present experiment. On the other hand, the observation of pits using the thin film sensor indicated that the pit diameters are rather small, having values of approximately 50 μm [16]. This difference in the average pit diameter can be caused by the different definitions of the pit diameters between these experiments. Fig. 13 shows the variation of the total number of pits, Pr, on the specimen with the standoff distance, xs, for the injection pressures of 8 MPa, 12 MPa, and 18 MPa. The total number of pits for each injection pressure is maximized at the standoff distances of 30 mm, 30 mm, and 40 mm, respectively. Furthermore, the maximum total number of pits increases with increasing injection pressures. These results are consistent with the variations in the erosion volume with respect to the standoff distance, which are shown in Fig. 7. Therefore, the main features of the erosion characteristics are well reproduced in the distributions of the total number of pits. Additionally, the growth of the erosion rate at higher injection pressures is likely due to an increase in the number of pits. However, the growth rate of the total number of pits is lower than that of the erosion volume. This may be due to the effect produced by the influence of the pit depth, because the pit depth increases at higher injection pressures [2].
12
Fig. 11 Number density distribution of the pits with respect to the radial distance, r
Fig. 12 Number density distribution of the pit diameters, Dp
Fig. 13 Variations of the number of pits with standoff distance, xs 13
3.3 Pit formation mechanism and shockwave In order to understand the pit formation mechanism, the relationship between the pits and shockwave initiation points was examined using the cross-schlieren imaging technique and image analysis. The results provide direct evidence of the pits and periodic cloud collapse event, which leads to the generation of impulsive forces in the cavitating jet. As previously mentioned, the shockwave initiation points are evaluated from the two laser-schlieren images taken from orthogonal directions near the wall. Fig. 14 shows the distribution of the shockwave initiation points that were obtained from the cross-schlieren imaging technique. This distribution was obtained at the maximum erosion rate of the cavitating jet with an injection pressure of 12 MPa and a standoff distance of 30 mm. It is noted that the results are obtained from 4 repeated experiments with each observation of 1 s. Then, total 800 shockwave pair images were analyzed to obtain the shockwave initiation points. The shockwave initiation points are distributed in a circular manner from the jet axis and have a lower density distribution near the jet center. Furthermore, the shockwave initiation distributions are densely observed at radial distances of 7 mm from the jet centerline. The features of the shockwave initiation points are in close agreement with the pit observation shown in Fig. 10(b), which indicates the similarity of the pits and shockwave initiation point distributions over the specimen. This result likely indicates that the pits are caused by the shockwave formation, which resulted from the periodic cloud collapse event in the cavitating jet. It should be mentioned that the shockwave image was not clearly observed at lower injection pressure 8 MPa, while it was too noisy at higher injection pressure 18 MPa due to an increase in the number of shockwaves to obtain the correspondence of the shockwave initiation points. In order to more closely observe the erosion pattern, pits, and shockwave initiation points, a comparison of the radial distributions at the same experimental conditions is shown in Fig. 15, that is P = 12 MPa, xs = 30mm. These results indicate a general agreement among the distributions, especially in the inner region of the erosion pattern, which suggests a correlation between the shockwave formation and the pit and erosion depth distributions. Furthermore, the peaks of these distributions generally agree and are located approximately 7 mm from the jet centerline. However, some deviations are observed in the outer region of the erosion. These results indicate that, to some extent, the distributions of the shockwave initiation points are well-correlated with the erosion and pit distributions except for the outer region. Thus, it can be concluded that the mechanism of the cavitating jet erosion is due to the shockwave emission accompanying a pit formation, which results from the periodic cloud collapse event, gas recompression during individual bubble collapse and bubble reentrant jets impacts [2, 22] in the cavitating jet. In addition, shockwaves could be emitted far from the wall, but they are not connected with the erosive event.
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Fig.14 Distribution of the shockwave initiation points (P = 12 MPa, xs = 30mm)
Fig. 15 Number density distribution of the pits and shockwave initiation points (P = 12 MPa, xs = 30mm)
4. Conclusions Observations of the erosion pattern, pits, and shockwave formation were conducted to determine the erosion mechanism in a cavitating jet. The results are summarized as follows: 1. The number of pits and their diameters are evaluated from the image analysis of the cavitation pits generated on the specimen subjected to the cavitating jet. The number of pits increased with increasing injection pressures of the cavitating jet, while the pit diameters do not show the same extent of change with respect to the injection pressure. 2. The influence of the standoff distance and injection pressure on the erosion rate is observed 15
when studying the variation of the number of pits in the cavitating jet, while the position of the maximum erosion rate shifts in the radial direction with increasing injection pressures. These results indicate the similarity between the number of pits and erosion depth distributions in the cavitating jet. 3. The shockwave initiation points near the wall is evaluated from the cross-schlieren imaging technique, and the results are compared with the erosion and pits patterns. The distribution of the shockwave initiation points highly correlates with the erosion depth and pit distributions in the inner erosion region, though they scatter in the outer region. It is considered that the cavitation erosion is associated with the pits and shockwave formation, which results from the periodic cloud collapse event, gas recompression during individual bubble collapse and bubble reentrant jets impacts in the cavitating jet. The shockwaves could be emitted far from the wall, but they are not connected with the erosive event.
Acknowledgements The authors are thankful for the financial support of this research from Niigata University and the cooperation of Mr. Y. Fujita and Mr. N. Sato from the Graduate School of Science and Technology of Niigata University for their assistance in conducting the experiments during the course of this study.
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distribution of cavitation activity within ultrasonic cleaning vessels, Ultrasonics 44 (2006) 73–82. [25] M. Dular, A. Osterman, Pit clustering in cavitation erosion, Wear, 265(2008), 811-820. [26] M. Dular, O.C. Delgosha, M. Petkovsek, Observations of cavitation erosion pit formation, Ultrasonics Sonochemistry, 20 (2013), 1113-1120. [27] T. Okada, Y. Iwai, S. Hattori, N. Tanimura, Relation between impact load and the damage produced by cavitation bubble collapse, Wear 184 (1995) 231-239. [28] J.-P. Franc, M. Riondet, A. Karimi, G.L. Chahine, Material and velocity effects on cavitation erosion pitting, Wear 274-275 (2012) 248-259. [29] K. Peng, S. Tian, G. Li, H. Alehossein, Mapping cavitation impact field in a submerged cavitating jet, Wear 396-397 (2018) 22-33. [30] A. Shima, K. Takayama, Y. Tomita, N. Miura, An experimental study on effects of a solid wall on the motion of bubbles and shock waves in bubble collapse, Acta Acoustica, 48 (1981) 293-301. [31] Y. Tomita, A. Shima, Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse, J. Fluid Mech. 169 (1986) 535-564. [32] J.-C. Isselin, A-P. Alloncle, M. Autric, On laser induced single bubble near a solid boundary: Contribution to the understanding of erosion, J. Applied Physics, 84 (1998) 5766-5771. [33] N. Fujisawa, Y. Fujita, K. Yanagisawa, K. Fujisawa, T. Yamagata, Simultaneous observation of cavitation collapse and shock wave formation in cavitating jet, Exp. Therm. Fluid Sci., Exp. Therm. Fluid Sci., (2018), pp.159-167. [34] T. Momma, A. Lichtarowicz, A study of pressures and erosion produced by collapsing cavitation, Wear 186-187 (1995) 425-436. [35] Y.-C. Wang, Y.-W. Chen, Application of piezoelectric PVDF film to the measurement of impulsive forces generated by cavitation bubble collapse near a solid boundary, Exp. Therm. Fluid Sci. 32 (2007) 403-414. [36] S. Hattori, T. Hirose, K. Sugiyama, Prediction method for cavitation erosion based on measurement of bubble collapse impact loads, Wear 269 (2010) 507-514. [37] F. J. Heymann, Conclusions from the ASTM interlaboratory test program with liquid impact erosion facilities, Proc. 5th Int. Conf. Erosion by Liquid and Solid Impact, 1979, 20-1–20-10. [38] N. Fujisawa, T. Yamagata, K. Hayashi and T. Takano, Experiments on liquid droplet impingement erosion by high-speed spray, Nucl. Eng. Des., 250 (2012) 101-107. [39] H. Kleine, H Groenig, K. Takayama, Simultaneous shadow, schlieren and interferometric visualization of compressible flows, Opt. Lasers Eng. 44 (2006) 170-189. [40] G.S. Settles, Schlieren and shadowgraph techniques, visualizing phenomena in transparent media, Springer Science & Business Media (2012) 111-122.
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Highlights ・Erosion pattern and pits formation of a cavitating jet were studied experimentally. ・Shockwave initiation points were evaluated from cross-schlieren imaging. ・Pits pattern showed similar behavior to erosion depth distribution. ・Shockwave initiation points were highly correlated with pits distribution. ・Cavitating-jet erosion was caused by pits resulting from shockwave formation.
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PII: DOI: Reference:
S0043-1648(18)30639-2 https://doi.org/10.1016/j.wear.2018.10.014 WEA102524
To appear in: Wear Received date: 28 May 2018 Revised date: 24 August 2018 Accepted date: 12 October 2018 Cite this article as: Nobuyuki Fujisawa, Toshihiro Horiuchi, Kei Fujisawa and Takayuki Yamagata, Experimental observation of the erosion pattern, pits, and shockwave formation in a cavitating jet, Wear, https://doi.org/10.1016/j.wear.2018.10.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental observation of the erosion pattern, pits, and shockwave formation in a cavitating jet Nobuyuki Fujisawa a*, Toshihiro Horiuchi b, Kei Fujisawa c, Takayuki Yamagata a a
Department of Mechanical Engineering, Niigata University
b
Graduate School of Science and Technology, Niigata University Department of Mechanical and Aerospace Engineering, University of Florida *Corresponding author: [email protected] c
Abstract In this study, the erosion pattern, pits, and shockwave formation of a cavitating jet were experimentally observed to gain an understanding of the erosion mechanism of a cavitating jet discharging from a cavitator nozzle into a still water environment. The erosion pattern and formation of pits were visualized by direct imaging on the eroded material surface, while the shockwave initiation points were detected using the cross-schlieren visualization method, combined with two orthogonal high-speed observations near the wall. The experimental results indicated that the radial distributions of the erosion depth, number of pits, and shockwave initiation points were highly correlated. These results provided direct evidence of the cavitation erosion caused by the formation of pits that resulted from the shockwave generated by the periodic cloud collapse event near the wall. The results also demonstrated that the growth of the cavitation erosion volume is highly correlated with the number of pits formed rather than the diameters of the pits.
Keywords: Cavitation; Cavitating jet; Erosion; Cloud collapse; Shockwave; Cross-schlieren imaging.
1. Introduction A cavitating jet is a fundamental flow configuration of a submerged water jet and is discharged from a cavitator nozzle into a still water environment. This flow configuration is widely applied to the engineering, fabrication, cutting, and peening of metal materials owing to the highly erosive nature of the bubbles that are generated along the cavitating jet shear layer [1, 2]. The erosive nature of cavitating jets arises from the periodic cloud formation in the cavitator nozzle, which is caused by the flow instability through the orifice and periodic cloud formation downstream of the cavitator
1
nozzle [3-8]. The cavitation cloud from the cavitator nozzle eventually collapses in the relatively high-pressure region that is downstream of the nozzle and results in the damage of the target materials exposed to the cavitating jet [9-13]. The relationship between the behavior of the cavitation cloud and the erosion pattern on the wall material is a topic of interest for cavitation research [14-19]. This topic has been studied on the cavitating jet through high-speed observations of the cloud structure and the associated erosion pattern on the wall material [20-22]. The experimental results demonstrated that the cloud collapse occurred near the wall material, and additionally, the cloud collapse generated impulsive forces on the wall. Moreover, the erosion pattern on the material surface consisted of a number of pits, which were likely due to the generation of an impulsive force caused by the cloud collapse that occurred near the wall material. The pit formation on the material in the cavitating jet is likely caused by the liquid-jet mechanism produced at the instant of cloud collapse, which is similar to the bubble collapse behavior on a hydrofoil [14, 15]. The observation of pits on the wall material in the cavitating jet is essential for understanding the erosion characteristics of materials. The pits observation has advantages, such as the convenience of application, short experimental time requirements, and potential for understanding the erosion mechanisms of the cavitating jet [20, 21]. The most widely used pit sensors in literature [23-26] are thin metal films of aluminum, which can be adhered to the material surface. By observing the pits on the wall material, their spatial distribution can be evaluated over a small period of time, the timeframe of which is shorter than measuring the mass loss for characterization of the bulk erosion rate. Although the observation of pits enables the evaluation of the spatial distribution of the material erosion rate, a disadvantage of this method is that the pit sensor is often not capable of withstanding the central column of the liquid jet produced by the cavitating jet [21]. Therefore, this method is limited to lower injection pressures, or this method requires the sensor to be applied at a region that is distant from the nozzle. In order to avoid these challenges, one can observe the formation of pits directly on the erosive surface of the material, thus, permitting the application of a wide range of cavitating jet injection pressures [27-29]. However, this experimental technique has not been extensively studied in comparison to the former technique, which implements the thin film sensor. In order to further study the erosion mechanisms of the cavitating jet, simultaneous observations of the cavitation pits and cloud structure were obtained; high-speed observation techniques were implemented to view the formation of pits, and shadowgraph imaging was used to examine the cavitating jet [21]. The results indicated that the pit formation occurred at the instant of the cavitation cloud collapse in the cavitating jet. This is likely caused by the shockwave that is formed, and an impulsive force may occur at the instant of the cavitation cloud collapse, which is similar to the observation of the bubble-collapse generated by laser-induced cavitation [30-32]. During the bubble collapse event in the cavitating jet, several bubbles collapse simultaneously, 2
thereby generating shockwaves near the wall [33]. Furthermore, the impulsive forces that are generated on the wall material at the instant of the cavitation bubble collapse can be detected by piezoelectric polymer sensors that are made of polyvinylidene difluoride (PVDF), which has a high-frequency response [34-36]. In the present study, the spatial distribution of the erosion pattern, cavitation pits, and shockwave formation were investigated experimentally to examine the evidence of erosion mechanism of cavitating jet. The shockwave initiation points were detected by the cross-schlieren imaging method and high-speed observations.
2. Experimental method and procedure 2.1 Experimental setup Fig. 1(a) illustrates the experimental setup. Two test tanks were prepared: one for the erosion test and observation of the pits and the other for the visualization study of the shockwave formation in the cavitating jet. The former test tank had a square cross-section of 500 mm × 500 mm with a height of 600 mm, and the latter had a hexagonal cross-section with an opposite side length of 400 mm and height of 460 mm. It is noted that the latter test tank was constructed from a transparent acrylic resin to allow for the observation of the cavitating-jet behavior. The behavior was observed by the cross-schlieren method using two high-speed cameras. For this experiment, the temperature of the working fluid, water, was maintained at 25±1°C using a cooling unit. A cavitator nozzle was used for generating the cavitating jet and is shown in Fig. 1(b). The cavitator nozzle was located at a depth of 50 mm and was directed downward. The cavitator nozzle was made of a converging and diverging cross-section that was separated by an orifice with a diameter of 0.8 mm and a thickness of 2.4 mm [16, 17]. After issuing from the nozzle, the water of the cavitating jet spreads downward into the still water environment. The cavitation coefficients were evaluated from following equation, σ =2 (p - pv) / ρU2
(1)
They were σ =0.030, 0.019, 0.013 at pump pressures 8 MPa, 12 MPa, 18 MPa, respectively (where, p = pressure, pv = vapor pressure, U = injection velocity at orifice of nozzle, ρ = density of water). The jet flow through the nozzle was pressurized by a plunger pump and contained a filter to eliminate the particulate matter in the working fluid. The pump pressure, P, was maintained constant at values of 8 MPa, 12 MPa, and 18 MPa during the experiment, and each pressure corresponded to the injection velocities through the orifice of 82 m/s, 103 m/s, and 127 m/s, respectively. The mean velocity was evaluated directly from the measurement of the discharged flow rate. Additionally, the test specimen was made of aluminum (A1070) with a diameter of 40 mm and thickness of 8 mm. The specimen for the observation of the pits was processed by quench annealing to promote erosion damage. The specimen was heated for 1 hour in a heating furnace at 470 K and was then cooled in the furnace without further heating. The Vickers hardness of the specimen decreased from an initial 3
value of 36 prior to the annealing process to a value of 32 after the annealing process. Therefore, deeper pits were observed on the annealed specimen.
(a) Experimental test section for the erosion test
(b) Cavitator nozzle (units: mm)
Fig. 1 Experimental apparatus
2.2 Erosion characteristics The erosion characteristics of the test specimen produced by the cavitating jet were evaluated by measuring the mass loss characteristics of an aluminum (A1070) circular specimen. The test specimen had a diameter of 40 mm and thickness of 8 mm. The erosion test was conducted by placing the test specimen in the cavitating jet, which was operated at three nozzle pressures of 8 MPa, 12 MPa, and 18 MPa. The test specimen was located at varying distances between 10 mm and 60 mm from the nozzle with the aid of a traversing device. The mass loss measurement of the test specimen was conducted using a high precision weight meter with a resolution of 0.01 mg. The non-dimensional erosion rate, Vm, was then evaluated using Eq. (2) [37, 38]: Vm = dEv/ Qdt
(2)
where, Ev is the erosion volume per unit time, t, and Q is the volumetric flow rate of the cavitating jet. The non-dimensional erosion rate, Vm, was directly evaluated from the variation of erosion volume, Ev, with respect to the flow volume in a unit time of the cavitating jet, Qt. It is noted that the non-dimensional erosion rate, Vm, has been used in previous research for characterizing the erosion of the wall material using the liquid droplet impingement test [37, 38]. The radial distribution of the erosion depth was measured by traversing the laser displacement sensor over the specimen surface. The radial distribution of the mean depth was determined from the average of eight line measurements; a measurement was taken every 22.5° along the circular specimen through the center. The spatial resolution of the laser displacement sensor was 1 μm.
2.3 Observation of the cavitation pits 4
An observation of the cavitation pits on the wall material was conducted after the specimen was exposed to the cavitating jet. The imaging was performed using a digital camera with a spatial resolution of 3000 pixels × 2000 pixels, and the specimen was uniformly illuminated using a metal halide lamp. It should be noted that this technique is applicable to a wider range of injection pressures than that of a thin-film pit sensor [21]. The number of pits and pit diameters were evaluated from the image. A sample image is shown in Fig. 2(a), which was obtained at a pump pressure of 12 MPa and at a standoff distance of 30 mm. The image was analyzed using a Sobel filter to enhance the edges of the pits to evaluate the pit diameter, and the thresholding was applied prior to counting the number of pits present in the image, as shown in Fig. 2(b). The overlapping effect of the pits was not considered in this analysis. This is because the maximum number of pits was less than 800 when the operating time of the cavitating jet was a short duration (1 sec). The dimensions of the target images taken by the digital camera were 30 mm × 20 mm, and thus, the image spatial resolution was 10 μm/pixels. It is noted that the pit diameter smaller than 3 pixels (=30μm) are considered as an image noise in the experiment. An important consideration is the operating time of the cavitating jet, which was measured by a PVDF sensor that was attached to the specimen. Fig. 3(a) shows the structure of the pit sensor, where the PVDF film is fixed between the supporting rods of the specimen. The pit sensor is sealed with acrylic resin material to minimize the electrical noise. An example of the output signal from the pit sensor is shown in Fig. 3(b). This output signal was observed at a pressure of 12 MPa and a standoff distance of 30 mm. The result shows that a high frequency signal starts and ends at the initiation and conclusion of the pump operation, respectively. The pitting time, t, was estimated from the period of the high frequency pitting signal.
(a) Original image
(b) Post-processing image
Fig. 2 Observation of the cavitation pits
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(a) Specimen with the pits sensor
(b) Example of the impulsive signal
Fig. 3 Structure of the pits sensor
2.4 Cross-schlieren imaging The relationship between the cavitation pits and shockwave formation in the periodic cloud behavior were obtained by evaluating the origins of the shockwaves using the cross-schlieren imaging method. This method is an extension of schlieren imaging technique, which was previously implemented [33, 39, 40]. This experimental technique obtains the three-dimensional distributions of the shockwave initiation points, where the collapsing of the cavitation bubbles is expected to occur. The main concept of cross-schlieren imaging is to evaluate the shockwave initiation points of the two orthogonal laser-schlieren images by simultaneously imaging the shockwave formation event. When the laser-schlieren imaging are simultaneously applied to the cavitating jet from the two orthogonal observations, the shockwave initiation points can be evaluated near the wall. Previous research has demonstrated that the shockwave formation generally occurs within 3 mm of the wall [33]. This new visualization technique for evaluating the shockwave center provides a powerful tool for obtaining the spatial distribution of the shockwave initiation points in the cavitating jet. Fig. 4 illustrates the experimental setup of the cross-schlieren imaging method, which consists of a CW Nd:YAG laser (5 W) and beam expander, a half mirror, two concave mirrors, and two complementary metal-oxide semiconductor cameras with a lens focal length of 200 mm. The concave mirror has a diameter of 150 mm and focal length of 1.2 m. Moreover, a slit-type darkfield illumination is placed as a knife edge in front of each camera to magnify the sensitivity of the laser-schlieren images. The details of the laser-schlieren imaging technique have been described in Ref. [33, 39, 40]. The observations of the shockwave formation from the two orthogonal directions were conducted with the two high-speed cameras synchronously operating at 400,000 frames/s. The two 6
cameras had spatial resolutions of 264 pixels × 384 pixels and 160 pixels × 264 pixels. The cameras were aligned with the laser beam, concave mirror, and slit-type dark field illumination. The exposure time of the camera was set to the shortest allowable time of the camera, 250 ns, in order to freeze the shockwave event, since a shorter exposure time is better suited for capturing sharper shockwave images. In order to obtain the shockwave initiation points from the two orthogonal cross-schlieren images, the shockwave was assumed to propagate spherically after initiation. Therefore, the shockwave initiation point was evaluated by fitting a circular trajectory to the shockwave image. Additionally, the two coordinates (x1, z1) were confirmed by the vertical height of the two shockwave trajectories. An example of the shockwave images is shown in Fig. 5, where the circular trajectories of the shockwave front can be observed in the two orthogonal images. After performing the thinning operation of the shockwave trajectories, the shockwave initiation point is obtained by applying a circular curve-fitting technique to the images. This operation allows the evaluation of the x1 and z2 coordinates of the shockwave initiation point, and these coordinates are obtained from camera 1 and 2, respectively.
Fig. 4 Experimental arrangement of the cross-schlieren imaging technique
7
(a) Camera 1 image
(b) Camera 2 image
Fig. 5 Examples of the shockwave images obtained by the cross-schlieren imaging method (P = 12 MPa, xs = 30mm) 3. Results and discussion 3.1 Erosion characteristics Fig. 6 shows a sample of the test specimen erosion characteristics in the cavitating jet at the operating pressures of 8 MPa, 12 MPa, and 18 MPa, where the standoff distances are maintained at 30 mm, 30 mm, 40 mm, respectively, which correspond to the distances that would provide the maximum erosion rate for each pressure. It is noted that the error bar shows the scattering of the data by the repeated experiment. The erosion volume, Ev, increases almost linearly with increasing exposure time, t, following the incubation period of 10 min from the start of the experiment. Additionally, the results indicate that the constant erosion rate in the terminal stage, dEv/dt, increases with an increase in the pump pressure, P, corresponding to the influence of the injection velocity of the cavitating jet. These erosion characteristics produced by the cavitating jet feature a steady-state period with a constant erosion rate, dEv/dt, after the incubation, acceleration, deceleration periods of cavitation erosion. The details of the cavitation erosion stage progression are described in Ref. [2]. Therefore, the non-dimensional erosion rate, Vm, defined by Eq.(2), in the steady-state period of cavitation erosion increases with increasing injection velocity of the cavitating jet. Fig. 7 shows the variation of the erosion rate, Vm, with respect to the standoff distance, xs, for the nozzle pressures of 8 MPa, 12 MPa, and 18 MPa. It is noted that the error bar shows the scattering of the data by the repeated experiment. These results indicate that the peak erosion rate increases with increasing nozzle pressures. Moreover, the erosion rate decreases at large standoff distances, independent of the injection pressure, thus, indicating the presence of an optimum standoff distance that maximizes the cavitating-jet erosion. The growth of the erosion rate with increasing standoff distances indicates that the erosion characteristics improve when the cavitating jet spreads in the radial direction; however, the erosion characteristics are weakened at longer standoff distances 8
due to the decrease in the jet velocity that occurs downstream. As a result, the erosion rate of the cavitating jet can be maximized at a given standoff distance, depending on the injection pressure. Additionally, the peak erosion rate increases with increasing injection pressure. Fig. 8 shows the variation of the local erosion rate, vm, in the radial direction from the jet centerline for the injection pressures of 8 MPa, 12 MPa, and 18 MPa. These data are obtained from the local erosion depth measurement by averaging the eight line measurements in the radial direction across the specimen at every 22.5° using the laser displacement sensor. The local erosion rate, vm, is defined by the variation of erosion depth in a unit time. It is noted that the error bar shows the scattering of the data by the repeated experiment. The results indicate that the local erosion rate increases with increasing injection pressures. Additionally, at higher injection pressures, the maximum local erosion rate shifts to the outer region of the cavitating jet, which indicates the radial growth of cavitating jet. On the other hand, the peak erosion rate near the centerline of the cavitating jet grows with increasing injection pressures, which demonstrates the influence of the jet velocity on the erosion rate. The maximum erosion rates occur at radial distances of 5 mm, 6 mm, and 8 mm for injection pressures of 8 MPa, 12 MPa, and 18 MPa, respectively, which demonstrates the radial growth of the cavitating jet with increasing injection pressures. Additionally, decreases in the local erosion rates were noted at radial distances of 6.5 mm, 7.5 mm, and 10.5 mm for the injection pressures of 8 MPa, 12 MPa, and 18 MPa, respectively. The decreases represent the negative growth of the local erosion rate that is expected to be caused by the plastic deformation of the wall material near the highly erosive region in the cavitating jet. On the other hand, the erosion rate near the jet axis increases at the highest injection pressure of 18 MPa. This may be caused by the influence of the direct contact of the liquid jet. This is because a similar erosion pattern is generated by the direct impingement of liquid jet in air using the present cavitator nozzle. Furthermore, the erosion rate increases with decreasing the standoff distance [21] due to the higher impact pressures near the nozzle.
Fig. 6 Time variation of the erosion volume, Ev 9
Fig. 7 Variation of the erosion rate, Vm, with standoff distance, xs
Fig. 8 Variation of local erosion rate, vm, with the radial distance, r 3.2 Observation of the erosion pattern and formation of pits Figs. 9 and 10 show the erosion patterns and pits that were observed on the test specimen for each of the cavitating jets. These results were obtained at the injection pressures of 8 MPa, 12 MPa, and 18 MPa at the maximum erosion rate condition with the standoff distances of 30 mm, 30 mm, and 40 mm, respectively. The observations of the erosion pattern have an exposure time of 40 min following the initiation of the cavitating jet, while the pit observations are made for approximately 1 sec following the cavitating jet initiation. Therefore, there is a substantial difference between these observation times. However, the two images have the common feature of indicating the amount of damage, and the images demonstrate the outward growth of the erosion pattern with increasing injection pressures. The results indicate that the cavitation erosion can be represented by the distribution of the number of pits. Additionally, the cavitation erosion is largely observed in the outer 10
region of the erosion pattern, where the dense pit patterns are observed. This eroded area consists of a number of pits having a magnitude on the order of millimeters in diameter (Fig.9). The diameter of the pits increases as the erosion mass loss grows with time. With increasing injection pressures, there is an increase in the number of pits and growth of the eroded area, which is similarly observed in the radial growth of the erosion pattern shown in Fig. 8. The smallest region of erosion loss is observed near the center of the cavitating jet, which is caused by the impingement of the liquid jet on the specimen. However, the corresponding pit patterns are not clearly observed in the images shown in Fig. 10. The liquid jet erosion does not follow the formation of pits due to its different erosion mechanism.
(a) 8 MPa
(b) 12 MPa
(c) 18 MPa
Fig. 9 Erosion pattern of the cavitating jet
(a) 8 MPa
(b) 12 MPa
(c) 18 MPa
Fig. 10 Observation of the pit patterns
Fig. 11 shows the number density distributions of the pit formation in the radial direction. The 11
number density distributions are obtained from the image analysis of the pits on the specimen for the injection pressures of 8 MPa, 12 MPa, and 18 MPa at the maximum erosion rate condition. The number of pits per unit time is obtained by an image analysis of the pit images for an exposure time of 1 sec. The exact exposure time was measured by the PVDF sensor that is attached to the specimen. These results indicate that the number density of the pits decreases near the jet centerline. On the other hand, the number density of pits grows in the outer region of the cavitating jet and reaches maximum values at radial distances of 5 mm, 6 mm, and 8 mm from the jet center for the injection pressures of 8 MPa, 12 MPa, and 18 MPa, respectively. The number density distribution of pits decreases gradually as the radial distance from the jet center increases. The number density distribution of the pits is higher at lower injection pressures, but the number of pits decreases at lower injection pressure (Fig.13). Therefore, the peak erosion rate decreases with decreasing injection pressure. These results agree qualitatively with the radial variation of the local erosion rate and the peak erosion rate variation with injection pressure that is shown in Fig. 8. Fig. 12 shows the pit diameter distribution for the injection pressures of 8 MPa, 12 MPa, and 18 MPa at the maximum erosion rate condition. The pit diameter distribution shows a sharp peak at lower pit diameter, which agrees with a feature of cavitation pits observed in literature [2]. Additionally, the pit diameter distribution is nearly independent of the injection pressure in the range of the present experiment. On the other hand, the observation of pits using the thin film sensor indicated that the pit diameters are rather small, having values of approximately 50 μm [16]. This difference in the average pit diameter can be caused by the different definitions of the pit diameters between these experiments. Fig. 13 shows the variation of the total number of pits, Pr, on the specimen with the standoff distance, xs, for the injection pressures of 8 MPa, 12 MPa, and 18 MPa. The total number of pits for each injection pressure is maximized at the standoff distances of 30 mm, 30 mm, and 40 mm, respectively. Furthermore, the maximum total number of pits increases with increasing injection pressures. These results are consistent with the variations in the erosion volume with respect to the standoff distance, which are shown in Fig. 7. Therefore, the main features of the erosion characteristics are well reproduced in the distributions of the total number of pits. Additionally, the growth of the erosion rate at higher injection pressures is likely due to an increase in the number of pits. However, the growth rate of the total number of pits is lower than that of the erosion volume. This may be due to the effect produced by the influence of the pit depth, because the pit depth increases at higher injection pressures [2].
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Fig. 11 Number density distribution of the pits with respect to the radial distance, r
Fig. 12 Number density distribution of the pit diameters, Dp
Fig. 13 Variations of the number of pits with standoff distance, xs 13
3.3 Pit formation mechanism and shockwave In order to understand the pit formation mechanism, the relationship between the pits and shockwave initiation points was examined using the cross-schlieren imaging technique and image analysis. The results provide direct evidence of the pits and periodic cloud collapse event, which leads to the generation of impulsive forces in the cavitating jet. As previously mentioned, the shockwave initiation points are evaluated from the two laser-schlieren images taken from orthogonal directions near the wall. Fig. 14 shows the distribution of the shockwave initiation points that were obtained from the cross-schlieren imaging technique. This distribution was obtained at the maximum erosion rate of the cavitating jet with an injection pressure of 12 MPa and a standoff distance of 30 mm. It is noted that the results are obtained from 4 repeated experiments with each observation of 1 s. Then, total 800 shockwave pair images were analyzed to obtain the shockwave initiation points. The shockwave initiation points are distributed in a circular manner from the jet axis and have a lower density distribution near the jet center. Furthermore, the shockwave initiation distributions are densely observed at radial distances of 7 mm from the jet centerline. The features of the shockwave initiation points are in close agreement with the pit observation shown in Fig. 10(b), which indicates the similarity of the pits and shockwave initiation point distributions over the specimen. This result likely indicates that the pits are caused by the shockwave formation, which resulted from the periodic cloud collapse event in the cavitating jet. It should be mentioned that the shockwave image was not clearly observed at lower injection pressure 8 MPa, while it was too noisy at higher injection pressure 18 MPa due to an increase in the number of shockwaves to obtain the correspondence of the shockwave initiation points. In order to more closely observe the erosion pattern, pits, and shockwave initiation points, a comparison of the radial distributions at the same experimental conditions is shown in Fig. 15, that is P = 12 MPa, xs = 30mm. These results indicate a general agreement among the distributions, especially in the inner region of the erosion pattern, which suggests a correlation between the shockwave formation and the pit and erosion depth distributions. Furthermore, the peaks of these distributions generally agree and are located approximately 7 mm from the jet centerline. However, some deviations are observed in the outer region of the erosion. These results indicate that, to some extent, the distributions of the shockwave initiation points are well-correlated with the erosion and pit distributions except for the outer region. Thus, it can be concluded that the mechanism of the cavitating jet erosion is due to the shockwave emission accompanying a pit formation, which results from the periodic cloud collapse event, gas recompression during individual bubble collapse and bubble reentrant jets impacts [2, 22] in the cavitating jet. In addition, shockwaves could be emitted far from the wall, but they are not connected with the erosive event.
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Fig.14 Distribution of the shockwave initiation points (P = 12 MPa, xs = 30mm)
Fig. 15 Number density distribution of the pits and shockwave initiation points (P = 12 MPa, xs = 30mm)
4. Conclusions Observations of the erosion pattern, pits, and shockwave formation were conducted to determine the erosion mechanism in a cavitating jet. The results are summarized as follows: 1. The number of pits and their diameters are evaluated from the image analysis of the cavitation pits generated on the specimen subjected to the cavitating jet. The number of pits increased with increasing injection pressures of the cavitating jet, while the pit diameters do not show the same extent of change with respect to the injection pressure. 2. The influence of the standoff distance and injection pressure on the erosion rate is observed 15
when studying the variation of the number of pits in the cavitating jet, while the position of the maximum erosion rate shifts in the radial direction with increasing injection pressures. These results indicate the similarity between the number of pits and erosion depth distributions in the cavitating jet. 3. The shockwave initiation points near the wall is evaluated from the cross-schlieren imaging technique, and the results are compared with the erosion and pits patterns. The distribution of the shockwave initiation points highly correlates with the erosion depth and pit distributions in the inner erosion region, though they scatter in the outer region. It is considered that the cavitation erosion is associated with the pits and shockwave formation, which results from the periodic cloud collapse event, gas recompression during individual bubble collapse and bubble reentrant jets impacts in the cavitating jet. The shockwaves could be emitted far from the wall, but they are not connected with the erosive event.
Acknowledgements The authors are thankful for the financial support of this research from Niigata University and the cooperation of Mr. Y. Fujita and Mr. N. Sato from the Graduate School of Science and Technology of Niigata University for their assistance in conducting the experiments during the course of this study.
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Highlights ・Erosion pattern and pits formation of a cavitating jet were studied experimentally. ・Shockwave initiation points were evaluated from cross-schlieren imaging. ・Pits pattern showed similar behavior to erosion depth distribution. ・Shockwave initiation points were highly correlated with pits distribution. ・Cavitating-jet erosion was caused by pits resulting from shockwave formation.
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