A review on synergy of cavitation and

1 IntroductionHydraulic machineries (i.e., pump, turbine, and reversible pump-turbine) must be often operated in cavitation conditions. Cavitation is one of the major challenges limiting the safe and stable operation of electric power systems (i.e., pumps, turbines), especially in sediment-laden flows where the synergy of cavitation and sediment erosion will cause even more severe damages. According to the literature (Naidu, 2016; Sharma and Singh, 1987; Naidu, 1996; Wang et al., 2022), cavitation has shown to be the major cause of metal loss at pump/hydropower stations, particularly in South Asian countries belonging to Himalayan regions (such as India, China, and Nepal), where large contents of quartz exist in the sediment especially during the monsoon season (Singhal and Ratnendra, 2017). The synergy effects of cavitation and sediment erosion are important and result in more severe damage (Thapa et al., 2007; Teran et al., 2018), as shown in Figures 1, 2. In China, the total annual sediment yield of the main rivers was 4.77 × 109 tons in 2020 (Ministry of Water Resources of the People’s Republic of China, 2020), and pumps or turbines are prone to experience cavitation and thus even serious erosion due to the synergistic effects of cavitation and sediment erosion (Huang, 1991) when operated in sediment-laden rivers. This problem is a major concern in the case of small and mini hydropower plants, which have been developed quickly in recent years. According to the literature, 40% of the turbines in the built hydropower station in China experience serious synergistic effects of cavitation and sediment erosion (Yang, 2012), ultimately leading to economic losses (i.e., the efficiency and life reduction and operation and maintenance costs of the turbine).FIGURE 1. Erosion in the hydro turbine for (A) the needle with pure cavitation erosion, (B) the needle with synergy of cavitation and sand erosion, and (C) turbine runner with synergy of cavitation and sand erosion shown in the enlarged picture (Thapa et al., 2007).FIGURE 2. Erosion damage in the components of three Francis turbines: (A) hard-particle erosion in one of the covers, (B) cavitation damage at the trailing edge of one of the runner blades, and (C) synergistic damage of the hard particles and cavitation at the leading edge of the runner blades (Teran et al., 2018).Hydrodynamic cavitation generally occurs if the local static pressure drops below the saturated vapor pressure, and consequently, the negative pressures are relieved by means of forming gas-filled or gas- and vapor-filled cavities (i.e., evaporation) (Knapp et al., 1970; Arndt, 1981; Brennen, 1995). Vapor structures are transported into high static pressure areas by the flow, and the subsequent collapse of vapor regions will generate shock waves, which can cause vibrations and noise (Brennen, 1994). Near solid boundaries, the collapse of vapor structures often leads to severe damage of surface material, i.e., pitting or erosion (Knapp et al., 1970; Arndt, 1981; Brennen, 1994; Brennen, 1995). The synergism of cavitation and sediment erosion, which occurs in high-speed regions, including guide vanes and runner blade inlet of a turbine and pump in hydraulic machinery, generally consists of two interrelated processes: 1) high-speed impact on the solid walls of sediment particles carrying kinematic energy and 2) the collapse of cavitation bubbles, and their combined effects, such as cavitation-induced acceleration of the solid particles impinging the surface (Arndt et al., 1989; Kumar and Saini, 2010). Cavities in liquid flows will experience unsteady processes, i.e., cavity formation, growth, and collapse, which could significantly change the motions of nearby sediment particles, acting on the sediment erosion process known as cavitation enhancement. Meanwhile, the existence of sediment particles alters the cavity behaviors from cavity inception and development to the cavity collapse process, influencing the cavitation erosion. This is a challenging problem, and complex phenomena including gas/vapor-liquid-solid three-phase flows, mass transfer, compressibility, turbulence, unsteadiness, and material properties as well, where the physical understanding is very limited and requires further investigation. With the development of modern hydraulic machinery toward large-scale, large-capacity, high-speed, and high-performance directions, the synergistic effects of cavitation and sediment erosion are becoming a serious problem, and the lack of physics and mechanisms involved significantly limits the reliability, stability, and safe operation of hydraulic machinery in sediment-laden flows.2 Basic theory on synergy of cavitation and sediment erosionCavitation in sediment-laden flows is complex gas/vapor-liquid-solid three-phase turbulent flows. So far, despite plenty of research work on cavitation erosion (Tomita and Shima, 1986; Berchiche et al., 2002; Sreedhar et al., 2017) and sediment erosion (Padhy and Saini, 2008; Padhy and Saini, 2009), theoretical work on the synergy mechanism of cavitation and sediment erosion is very scarce. For example, Rao and Buckley (Rao and Buckley, 1984) reviewed erosion models for both long-term cavitation and liquid impingement proposed by different investigators, including the curve fitting approach and a power-law relationship. They also evaluated the importance of the different modeling methods using data from cavitation fields and a liquid impingement device. As for the prediction of synergy effects of cavitation and sediment erosion. Ni and He (Ni and He, 1994) theoretically investigated the impact of shock waves generated by the bubble collapse on the solid particles considering the liquid compressibility, and the maximum velocities of solid particles were obtained. The Gilmore equation was used to calculate the bubble radius and the particle motion was calculated by solving the Newton equation. Their study showed that the shockwave-induced speed of particles was large enough to cause damage to the concretes used in hydraulic structures. Duan (Duan, 1998) carried out experimental and theoretical work to investigate the erosion performance under different flow velocities, and found that when above certain flow rate, cavitation would protect the solid walls of flow passage from being eroded, thus weakening the erosion process. Inspired by this experiment, Li (Li, 2006) proposed a microscopic model based on the assumption that the particle near the cavitation bubbles will be trapped by the microjet of the collapsing bubble and accelerated to an extremely high velocity towards the solid walls, resulting in potential damage. That is,dVliquiddt≥V2L and dVparticledt≥V2L(1)here, V is the characteristic velocity of the flow and L is the characteristic length of the flow. The predictions by this microscopic model show that the acceleration rate is so high that the particle could acquire a velocity up to several hundred meters per second within microseconds. Following, this theoretical microscopic model was validated by the numerical simulation work by (Dunstan and Li, 2010).Recently, based on an effective-medium approach where the influence of effective suspension viscosity on bubble/particle dynamics and the impact energy of erosive particles were incorporated, (Su et al., 2021) developed a theoretical model to predict the synergistic erosion of cavitation and sediment particles by taking into account the dual effects of sediment particles (i.e., viscosity effect of small particles and inertial effects of large particles) in a large range of sediment sizes. Good agreement between the model prediction and experimental data was found. This theoretical model could predict the opposing effects of sediment parties on the cavitation erosion as well, and showed that the viscous effect of sediment-sized particles (STP, < 50 μm) could mitigate or even override the impact of impinging microjets and sand-sized particles (SDP, > 50 μm).μem=[1+2.5∅st1−∅sd+k(∅st1−∅sd)2]μm(2)andρem=ρp∅st+ρlm(1−∅total)1−∅sd(3)where μem and ρem are the effective viscosity and density of the STP suspension, respectively; ρp and ρlm are the
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