In nature and engineering, when the water flow velocity reaches a certain high level, a series of special water flow phenomena such as cavitation erosion, strong air entrainment, splashing, severe fluctuations, and severe scour and abrasion may occur. High-velocity hydraulics is a hydraulic research area that targets these special flow phenomena.

In hydraulic and hydropower engineering projects, these flow phenomena are often concentrated due to high flow velocity, complex boundaries, and free surfaces, posing a particularly prominent threat of destruction. In this book, these water flow phenomena are studied at the mesoscale level in the context of hydraulic and hydropower engineering, aiming at better application of high-velocity hydraulics in engineering guidance.

1.1 Definition of Mesoscale

In terms of research methods, high-velocity hydraulics has undergone two research stages, namely, a stage combining theoretical analysis and physical experimentation and a stage combining theoretical analysis, physical experimentation, and numerical simulation. The theoretical analysis is mainly based on fluid mechanics and hydraulics theory (Pope 2001), the physical experimentation includes mechanism testing, scale model testing, and engineering prototype testing (Brennen 2005), and the numerical simulations are based on the Navier–Stokes equations and take advantages of numerical methods and modern computing technology (Lee et al. 1990; Bernard and Wallace 2002).

In terms of research scale, the past high-velocity hydraulics is mainly categorized as macroscale research, which is characterized by the description of the motion of water flow with macroscopic parameters such as flow rate, water depth, flow velocity, pressure, and concentration (Boes and Hager 2003; Hager 2013). In the early stage, the concept of total flow was largely adopted, using the integral forms of the continuity equations, equations of motion, and momentum equations as the main theoretical tools and supplemented by a large amount of experimental measurements and analyses (Hibbeler 2007; Crowe et al. 2011). In the late stage, with the development of measurement and computing technologies, detailed descriptions of the flow field became possible, the differential forms of the water flow equations started to play an increasingly prominent role, and the detailed spatiotemporal distribution of the macroscopic parameters could be obtained through physical experimentation and numerical simulation (Xu et al. 2002).

In theory, high-velocity hydraulics problems are actually multiscale problems ranging from the macroscopic to microscopic scale. The microscale here refers to the molecular scale of water and the medium interacting with water (Crowe et al. 1998). For example, the main energy dissipation in water flow follows the cascade of the mean flow, large vortex (energy-containing vortex), small vortex (energy-dissipating vortex), smaller vortex, and the so-called minimum vortex, which is unable to overcome the viscous effect of the water flow. Eventually, the energy is dissipated by the minimum vortex into the thermal energy of the water body through the viscous effect of the water flow, that is, the thermal motion of molecules. Another example is the dissolution and evaporation in the air–water two-phase flow at the microscopic scale, regardless of air bubbles in the water or water droplets in the air. A third example is the formation of cavitation erosion and scour, which, at the microscopic scale, is ultimately attributed to the breaking of bonds between molecules in solid materials under water flow. From this perspective, as research methods continue to advance, the study of high-velocity hydraulics may eventually expand to the microscale in the future.

It has become increasingly difficult to meet current engineering needs by relying only on macroscale research (which is especially unsatisfactory for revealing underlying mechanisms), while the necessity of microscale research has not yet been fully justified. Therefore, mesoscale research has become an area that urgently needs to be explored. The mesoscale here refers to the scale of cavitation bubbles, air bubbles, water droplets, particles, and small vortex blobs between macroscopic flow and microscopic molecules. The role of mesoscale research is to more clearly reveal the underlying mechanism and trends of the special hydraulic phenomena of high-velocity water flow and to better predict the occurrence and development of these phenomena in order to better provide theoretical and methodological guidance for engineering applications.

1.2 Necessity of Mesoscale Research

Although various mechanical phenomena specific to high-velocity water flow exhibit remarkable macroscopic characteristics on the surface, they are essentially the macroscopic aggregation of mesoscopic phenomena. Cavitation is the process of the generation, development, movement, and collapse of cavitation bubbles (Rayleigh 1917; Plesset 1949). Cavitation erosion is the result of cavitation bubbles acting on a solid surface (Knapp et al. 1979). Aerated water flow is a result of water entraining air bubbles and water droplets spalling into the air (Ervine and Falvey 1987). Aeration and erosion protection is the interaction between cavitation bubbles, air bubbles, and a solid surface (Russell and Sheehan 1974). Flood discharge atomization is the diffusion of water droplets or clusters of water droplets in the air (Ibrahim and Przekwas 1991). Energy dissipation is the process by which small vortex blobs eventually dissipate the energy of water flow into thermal energy (Kolmogorov 1962).

Therefore, if we only study the various mechanical phenomena specific to high-velocity flow from the macroscopic scale, it is inevitably difficult to clarify the complex underlying mechanisms. In fact, the in-depth understanding of cavitation erosion so far has been mostly originated from research on bubble dynamics, which itself is mesoscopic research. Nevertheless, the previous studies on bubble dynamics have mostly focused on cavitation bubbles but have rarely involved the effects of factors such as the two-phase flow that is of concern to hydraulics. The first thing to understand regarding aerated water flow is the mechanism of air entrainment in water flow, which is the basis for revealing the concentration distribution pattern. Although the previous understanding of this aspect has been limited by experimental techniques, the research on aerated water flow has consistently been committed to forming a complete chain ranging from the origin of aeration to prediction methods. Aeration and erosion protection is a more typical example. Due to the lack of a direct experimental basis for understanding the mechanism of aeration and erosion protection, there have been a variety of explanations for this mechanism for a long time. In addition, mesoscale analysis plays a very important role in the study of the calculation methods and the scale effect of flood discharge atomization as well as the local vortex structures of flood discharge and energy dissipation.

The development of contemporary experimental and computing techniques provides a powerful basis for the mesoscale analysis of high-velocity hydraulics. The early film-based high-speed cameras have been replaced by digital counterparts, which not only have faster shutter speeds and higher image quality but also reduce the cost of image analysis and improve the analysis efficiency. The development and popularization of many pieces of specialized equipment such as the spark-induced cavitation generating device, laser-induced cavitation generating device, and ultrasonic cavitation device have greatly facilitated the mesoscopic study of cavitation erosion. Various advanced light source systems also enable more in-depth and detailed mesoscale observations. Additionally, the development of numerical simulation techniques not only opens up a new path for mesoscale analysis but also provides an effective means for clarifying the mechanics behind the phenomena because of its complete and detailed simulation results.

1.3 Main Contents of Mesoscale Research

Overall, mesoscale research mainly includes mesoscopic mechanisms, mesoscopic trends, and mesoscopic predictions.

The study of mesoscopic mechanisms aims to answer the “what” questions. Traditional macroscale studies fail to provide definitive answers to the mechanisms for many well-known high-velocity hydraulic phenomena. A typical example is aeration and erosion protection. Cavitation reduction by aeration has been verified in engineering practice for decades and has even become the last line of defense for the reduction of cavitation damage in hydraulic and hydropower projects. However, there is still a lack of direct evidence-based answers to the most fundamental question of why aeration can reduce cavitation damage. Consequently, multiple explanations coexist, which affects the establishment of basic principles and critical control conditions for the design of aeration and erosion protection facilities in engineering. A similar problem has also occurred in the study of self-aerated water flow, that is, how high-velocity water flow is self-aerated. Only by accurate exposure of the mechanism for self-aeration of high-velocity water flow can various self-aeration theories be unified in order to lay a solid and reliable foundation for the research on self-aerated water flow.

The research on mesoscopic trends are expected to answer the “why” questions. The study of mesoscopic trends is intended to expand and quantify the study of mesoscopic mechanisms. Still taking the aeration and erosion protection as an example, research on mesoscopic trends aims to further reveal the physical factors that influence the effects of aeration and erosion protection as well as the conditions of aeration and erosion protection based on the study of the mesoscopic mechanisms. The same is also true for the example of the self-aeration of high-velocity water flow as described above, that is, how the various factors of high-velocity water flow interact with each other and what level these interactions need to reach to lead to self-aeration. There are many other similar examples. For instance, for cavitation caused by the flow around a convex body, why is cavitation damage to the solid surface induced under some conditions while there is no cavitation damage under other conditions? In this situation, it is certainly difficult to provide an accurate answer by relying only on the incipient cavitation number and flow cavitation number of a convex body, as adopted in macroscopic studies. Another example is the local vertical vortex occurring in flood discharge and energy dissipation. Why is cavitation damage sometimes induced on the floor, but on other occasions, no cavitation damage is induced at all? All of these questions need to be answered through the research on mesoscopic trends.

The core of research on mesoscopic predictions is to answer the “how” questions. Aeration and erosion protection is again taken as an example. To predict aeration and erosion protection, not only the flow field calculation method but also the coupling of the flow field calculation and bubble calculation are needed so that the aeration concentration distribution and the bubble movement can be predicted. Similarly, for self-aerated water flow, it is necessary to establish a systematic calculation method for self-aerated water flow on the basis of elucidating the self-aeration mechanism and conditions of the high-velocity water flow. Obviously, calculation methods (including theoretical calculations and numerical simulations) play very important roles in mesoscopic prediction research.

Specifically, the mesoscale analysis of high-velocity hydraulics in this book includes the following six parts, namely, cavitation erosion, aeration and erosion protection, air–water two-phase flow, energy dissipation and scour, flood discharge atomization, and flash flood and sediment disasters, which have clear mesoscopic characteristics and correspond to Chaps. 2–7 of the book.