INTRODUCTION

The phenomenon of cavitation, in its most severe condition of occurrence, that is when the pressure surrounding the vapor cavities becomes higher than the vaporization pressure of the liquid, favoring the process of implosion of the bubbles formed, has been widely studied in what concerns the protection and integrity of hydraulic structures - spillways, dissipation basins, among others (Colgate, 1977; Quintela & Ramos, 1980; Tullis, 1982; Falvey, 1990; Bhate et al., 2021; Schleiss et al., 2023).

In addition to the characteristic hydrodynamic parameters – abrupt variations in pressure and fluid velocity – the presence of irregularities on the surfaces bordering hydraulic structures with the flow becomes a preponderant factor for the occurrence or even intensification of damage caused by the phenomenon of cavitation. Since, after being formed, the vapor cavities are fixed locally in the most evident roughness, thus imploding close to the contact surface. Extremely well-finished concrete surfaces admit flows with velocities greater than 30.0; 35.0 and up to 37.0 m/s, without the need for design changes. However, in spillways the presence of irregularities greater than the chamfer slope of 20:1 may cause damage due to the cavitation phenomenon with average speeds of 12.0 to 28.0 m/s (Ball, 1976; Falvey, 1990; Bhate et al., 2021; Mortensen, 2020; Abreu et al., 2023; Abreu, 2024).

Due the high complexity and particularities that the cavitation phenomenon imposes on the flow and surrounding surfaces make it unfeasible, under natural conditions of its occurrence, to study it in the field. In this way, the use of reduced models, totally dependent on scales, distortions and information from observable prototypes, are widely used to verify extreme pressures (maximum and minimum), flow velocities, of specifics flow discharges and cavitation indices characteristic of critical or limiting conditions for the action of the cavitation phenomenon (Sanagiotto, 2003; Amador et al., 2009; Conterato et al., 2015; Dai Prá et al., 2016; Osmar et al., 2018; Canellas, 2020; Priebe et al., 2021; Ferla et al., 2021; Matos et al., 2022).

There are also, in the laboratory, cavitation machines or devices that allow the effects of the phenomenon to be reproduced by favoring its critical conditions of occurrence, that is, high speed and pressures below the water vaporization pressure. These devices mainly aim to evaluate the resistance and quality of different materials when exposed to cavitation which cavitation ends up causing damage to their surfaces. Due to the complexity and high implementation costs, few research groups currently use cavitation devices, essentially those of the Ventury-type, which, through abrupt restrictions imposed on the flow, condition the occurrence of cavitation in a specific zone of the experimental apparatus.

The studies by Peterka (1953), USBR (Bureau of Reclamation, 1963), Gal’perin et al. (1971), Quintela & Ramos (1980) and Gikas (1981), despite having focused on the decades from 50’s to 80’s, until today are used as a reference on the subject, as they analyzed the wear caused on concrete surfaces, through cavitating flows with speeds that varied between 28 and 30 m/s. Gikas (1981) verified the effects of cavitation on specimens made of different materials (epoxy resin, common and special concrete), in order to establish relationships between the damaged materials and their resistance to the phenomenon. The duration of the tests varied from 140h, 60h and 30h at flow rates of 100 l/s and 150 l/s. The author concluded that correlations must be established between resistance to cavitation and the physical properties of hardness, rupture stress and coefficient of elasticity of materials. Peterka (1953) related different concentrations of air in the flow to the loss of mass in the specimens. Above air concentrations of 2%, the author concluded that there is a considerable reduction in the mass loss of concrete blocks due to the action of cavitation erosion.

Considering a Venturi-type cavitation device, characterized exclusively by the presence of a straight segment immediately after the abrupt constriction of the flow, the authors Dong & Su (2006) and Dong et al. (2007, 2008, 2010, 2023) evaluated the effects of aeration and the damage caused to concrete specimens by the action of cavitation. In their research, were analyzed flow velocities ranging from 20 to 50 m/s, average pressures and their variations, mass losses of different specimens, shapes of pressure waves and the interaction of the phenomenon with the presence of irregularities inside the device, with the insertion of different concentrations of air and sediments into the cavitating system. Dong & Su (2006) established correlations between the average flow velocity (V) and minimum air concentrations ($C_{mín.}$), necessary to avoid cavitation erosion. The authors carried out tests with concrete specimens with water/cement ratios (w/c) of 0.43; 0.70 and 1.5, cement/sand ratios (c/a) of 1.0; 0.25 and 0.21 and average compressive strength (fcm) of 15.4; 6.2 and 2.2 MPa, respectively.

In recent studies, Dong et al. (2023) verified the damage caused to specimens made of cement, lime, sand and water, without the presence of coarse aggregates, by a cavitating flow containing the presence of sand. The concentration of sediment added to the flow was 12kg/m³ with average particle sizes (d₅₀) of 0.08; 0.25; 1.0; 2.0 and 3.0 mm. The concrete samples were composed of w/c = 0.40, c/a (lime/sand) = 1.5 and f_cu,k (compressive strength on the day the specimen ruptures) of 17.8 kPa after 7 days of curing. The granulometry of the sand used in the concrete test specimens (CPs) was the same as that added to the water + sediment mixture. The authors concluded, through electron microscopy, that cavitation damage is intensified with the increase in sand particles, making the areas of damage and the number of cavities in the specimens larger with the gradual increase in the sand diameters d₅₀ evaluated (Dong et al., 2023). Although recent, the studies by Dong & Su (2006) and Dong et al. (2007, 2008, 2010, 2023) do not have direct representation with the “traditional” Ventury-type cavitation devices used by Peterka (1953), USBR (Bureau of Reclamation, 1963), Gal’perin et al. (1971), Quintela & Ramos (1980) and Gikas (1981), being presented here as references for an in-depth search on the topic.

Thus, the studies by Gal’perin et al. (1971) and Kudriashov (1983), considering flow aeration as a conditional parameter, for relative air demands (β) of 0; 4 and 8%, f_cm (average compressive strength of concrete between 20 ≤ f_cm ≤ 50 MPa) and flow velocities are widely used as criteria for the non-occurrence of cavitation damage in hydraulic structures (Figure 1). However, despite being a good tool for analyzing or mitigating damage arising from the cavitation phenomenon, the limits defined by Gal’perin et al. (1971) and Kudriashov (1983) are scarce, making their applicability restricted to the range compressive strength and flow velocity observed.

Due to the difficulty in obtaining experimental or prototype data, there are still gaps in information regarding the characteristics of concrete affected by cavitation – compressive strength, water-cement ratios, maximum height of damage, etc. In this way, this research aims to identify the limitations of using the methodology developed by Gal’perin et al. (1971) and propose new correlation functions that make it possible to expand its use to different boundary conditions from those established in their studies for non-aerated flows, considering concrete with a w/c (water/cement) ratio of 0.35; 0.45; 0.50 and 0.65, when exposed to flows with average speeds of 30 m/s.

The results and information obtained that make up this research are part of the Research and Development (P&D) project entitled: “Concrete Study for Hydraulic Surfaces”, financed by Foz do Chapecó Energia with the participation of Eletrobras-Furnas, the Laboratory of Hydraulic and of Concrete from the US Bureau of Reclamation (USBR), Desek Consultoria em Engenharia Civil and the Universidade Federal do Rio Grande (UFRGS) through the Instituto de Pesquisas Hidráulicas (IPH) - Laboratório de Obras Hidráulicas (LOH).

MATERIAL AND METHODS

The experimental installation used in the development of this study is located in the LOH/UFRGS, and was based on the characteristics of the installation and the cavitation device of the US Bureau of Reclamation, describes for article USBR (Bureau of Reclamation, 1963).

The contracted section of the cavitation machine, where the steam cavities are formed, is 6.75 mm high and 311.5 mm wide, providing an average speed of 30 m/s through an operating flow of 60 l/s. The average reference speed considered in this study was 30.0 m/s. However, during the tests with the presence of concrete blocks, average speeds higher than this were observed, around 8.0%. Possibly, due to the particularities of the experimental installation, control register activation limits, energy pulses inherent to the operation of the pumping load losses added by the block surfaces, etc. These may be some of the factors that contributed to the small changes in the average speed in the cavitation device.

The Figure 2 presents the schematic design and the constructed version implemented at LOH/UFRGS.

The tests at LOH/UFRGS were carried out by exposing the concrete blocks for a period of approximately 2 (two) hours to the effects of the cavitation phenomenon without the addition of air to the flow. For each trait, at least 3 (three) repetitions were performed for the same test condition. The contact surface of the blocks with the flow corresponds to an area of 220.0 cm², without any damage.

The characterization of the concretes used in tests with the LOH/UFRGS cavitation machine is presented in Table 1, with water/cement ratios (w/c) of 0.35 being evaluated; 0.45; 0.50 and 0.65.

The blocks were initially photographed and their surfaces scanned using an Artec brand 3D Scanner, EVA model. This equipment works based on successive superimpositions of images of the objects evaluated, thus building a digital model in 3 (three) dimensions of the solid in question. Using the equipment´s own software (Artec Studio 16 Professional), files were generated in extension .dwg compatible with the AutoCad® software, which allowed the extraction of level curves with a spacing of 0.5 mm from the eroded surface, where were estimated volumes and areas of the evaluated surfaces. This procedure was performed before and after exposing the concrete blocks to the LOH/UFRGS cavitation device, in order to allow the extraction of areas, and consequently, the maximum depths of damage (hmáx.) of each concrete block (Figure 3).

Considering the maximum depths of damage (hmáx.), extracted directly from the blocks after exposure to the cavitation phenomenon, comparative analyzes were carried out between the results found by Gal’perin et al. (1971) and the data extracted at LOH/UFRGS.

In this way, this research aims to identify the limitations of using the methodology developed by Gal’perin et al. (1971) and propose new correlation functions that make it possible to expand its use to different boundary conditions from those established in their studies.

A relevant aspect to highlight is that the relationships described by Gal’perin et al. (1971), reiterated by Kudriashov (1983), associate the occurrence of damage due to the action of the cavitation phenomenon to concrete surfaces. That has been exposed to high-velocity flow over a 48-hour period. In order for your data to be related to information also obtained in the laboratory, in which the analyzed concretes were exposed to cavitating flow for a period of 2 hours, adaptations were made to the data of Gal’perin et al. (1971) through the Equation 1 defined by Kudriashov (1983).

Where: $V_T$ are the average flow velocities linked to the structure's exposure time to the cavitation (m/s); $V$ are the average velocities used by Gal’perin et al. (1971), and $T$ is the new period of exposure of the structure to the cavitation (h).

RESULTS AND DISCUSSIONS

Initially, visual comparisons were made between the damage caused by the cavitation phenomenon in blocks with different water/cement ratios without the presence of air in the flow (Figure 4). The results presented in Figure 4 were obtained from tests with different durations, as some of the blocks with w/c ratios of 0.50 and 0.65 did not resist with the integrity necessary to maintain contact between the test piece and the cavitation device for them to complete the pre-established 2-hour exposure period.

As seen in Figure 4, the least significant material removal occurred on the surface of the block with the lowest water/cement ratio, w/c = 0.35. According to the increase in w/c ratios, concrete losses become increasingly significant, with the ratios showing 0.50 and 0.65 greater damage with removal of aggregates, essentially small for w/c = 0.50, and large for w/c = 0.65.

On the other hand, for the blocks with a/c ratio of 0.35 and 0.45, even though they were exposed to a longer period of time in the cavitation machine, only the most superficial coating layers of these concretes were extracted, represented by the mortar – cement + water + sand (Figure 4).

In parallel to the tests with the presence of concrete blocks in the LOH/UFRGS cavitation device, the compressive strengths of the concretes (f_cm,j) under study were determined by breaking the cylindrical specimens (CPs) in a hydraulic press, following the recommendations NBR – 5739 (Associação Brasileira de Normas Técnicas, 2018). The Table 2 and Figure 5 present the results of compressive strength for w/c ratios of 0.35; 0.45; 0.50 and 0.65 considering ages of 3, 7, 14, 28, 63 and 91 days of curing in a humid chamber.

As expected, we can see in Figure 5 that the lowest f_cm,j were found for the highest w/c ratios (0.50 and 0.65), essentially justified by the use of low cement levels in these mixtures, which reduces significantly improve the cohesion and resistance of these concretes.

Another relevant aspect verified, through the results of tests with concrete blocks with ratio w/c = 0.65 and f_cm,91 = 32.7 MPa, which made it possible to observe the most severe recorded effects of the cavitation phenomenon among all concrete evaluated, was the intense cavitation activity in the first 30 minutes of the tests. Where it is understood that material removal was favored mainly by the low cohesion of the particles that make up the concrete, and not by the presence of possible irregularities on the contact surface of the blocks with the cavitating flow (Figure 6).

From the already established erosion, the damage advanced in extent and depth, with the effects of cavitation visibly intensified by the increasing exposure of the coarse aggregates used in the concrete composition. This observation corroborates the theory that the cavitation process is intensified by the particle removal action itself, where there is an increase in irregularities until the erosion itself fully develops (Figure 6). Evidently, the results expressed in Figure 6 represent the most extreme possible conditions for the occurrence of damage than a concrete with low compressive strength. Therefore, concrete with a composition and w/c ratio of 0.65 should not, under any circumstances, be used in hydraulic structures, and especially on concrete surfaces subjected to high-speed flows, that is, flows greater than the limit of 15.0 m/s established by Ball (1976), Falvey (1990), Bhate et al., (2021) and Mortensen (2020).

Considering the maximum depths of damage (hmáx.) of the concrete blocks tested at LOH/UFRGS, resulting from surveys carried out using the 3D Scanner, and the average compressive strengths (f_cm,j), the hmáx. were indirectly estimated for the data described graphically by Gal’perin et al. (1971). Thus, Figure 7 presents the proposed modification made to the data obtained by Gal’perin et al. (1971) for β = 0%, considering the insertion of the speed limits to the f_cm,j, defined by these authors and adapted exposure time of 2 hours to the phenomenon. The hmáx. estimates of 5.2 and 4.4 mm for Gal’perin et al. (1971), were defined as the maximum and minimum limits considered by the authors, so that the irregularities formed by the cavitation process in concrete are considered as actual damage to the assessed concrete surfaces (Figure 7).

Adaptation to the time base presented in Figure 7 allowed the inclusion of hmáx. values for blocks with different f_cm,j, already tested at LOH/UFRGS. From the data on maximum erosion depths, an adjustment function was established (Figure 8) that allows estimating the maximum erosion depth for concretes with different average compressive strengths, when affected by cavitation.

According to Figure 8, the highest hmáx. (average) values found were 17.0 mm, defined for blocks with w/c 0.65. As compression resistances, damage depths reduce to values of the order of 12.50; 6.7 and 3.25 mm for w/c ratios of 0.50; 0.45 and 0.35, respectively.

According to the results presented in Figure 7, it was possible to identify that all concrete blocks characterized by f_cm,js of 47.9; 40.2 and 32.7 MPa, when exposed to cavitation without air additions to the flow, exhibit hmáx. >5.2 mm. Under these conditions, concrete with a w/c ratio of 0.45; 0.50 and 0.65 are subject to significant cavitation damage if exposed to the phenomenon for a period of less than 2 hours.

The blocks made up of f_cm,j = 64.5 MPa, where the hmáx. extracted were 1.5; 3.5 and 4.0 mm, after the same period of exposure to the cavitation device, performed better than the other w/c ratios mentioned above. This indicates that the w/c ratio of 0.35 did not develop erosions of relevant depth that would be classified as damage due to the cavitation phenomenon until t = 2h (Figure 7).

- The significant increase in maximum damage depths observed in concrete blocks, higher than the maximum limit of 5.2 mm identified by Gal’perin et al. (1971), allows us to infer that: Under project design conditions, considering concrete with composition and w/c ratio similar to those used in this study and flows with V = 30.0 m/s, without aeration, concrete with higher than 0.45 and f_cm,j < 47.9 MPa. Since significant cavitation damage has been observed on concrete surfaces with these characteristics, hydraulic structures that are designed with specifications different from those previously indicated must be experimentally justified by the designer;

- Already in pre-existing hydraulic structures, which may describe cavitation damage with hmáx. greater than 5.2 mm and characterized by the same concrete specifications and hydraulic conditions verified in tests with the cavitation device, would make it advisable to carry out repairs with materials of greater resistance and better finishing on the entire surface subjected to the action of the cavitation phenomenon.

Finally it is concluded that the results obtained through the tests at LOH/UFRGS, and the adaptations defined to the experimental data presented by Gal’perin et al. (1971), for flows with a time of 2h, corroborated the development of new limits associated with the maximum depths of damage, which also describe the evolution to be expected of the erosion pits formed by the action of cavitation in the analyzed concrete.

CONCLUSIONS

The adequacy of the data presented by Gal’perin et al. (1971), for β = 0% and t = 2h, allowed the estimation of the maximum and minimum limits, defined by the authors as the depths that would characterize the erosions arising from the phenomenon of cavitation. The depths (hmáx.) attributed to data from Gal’perin et al. (1971), were from 4.4 to 5.2 mm, above these limits the flow conditions and concrete resistance must be reviewed.

The results of hmáx. extracted from concrete of w/c 0.35; 0.45; 0.50 and 0.65, when subjected to flows without the presence of air in the flow, described cavitation damage above the limits established by Gal’perin et al. (1971). With the exception of concrete with w/c 0.35, which registered hmáx. which ranged from 1.5 to 4.0 mm.

Finally, we can conclude that the use of parameters pre-established by Gal’perin et al. (1971), when linked to hmáx., provide good tools for decision-making by the user to avoid or even control the damage due to the phenomenon of cavitation.

ACKNOWLEDGEMENTS

The authors are grateful to Instituto de Pesquisas Hidráulicas (IPH/UFRGS - Brazil), Foz do Chapecó Energia (Brazil) and Eletrobras for providing the conditions and financial support for the experimental works, to the team of engineers and technicians, especially the MSc. Eng. Josua Mortesen and Engª. Catherine Lucero of the hydraulics and concrete laboratories of the United State Bureau of Reclamation (USBR) and Dr. Selmo Kuperman – Desek Consultoria em Engenharia Civil for collaboration and information exchange. To CNPq (Brazil) and CAPES for granting scholarships.

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