Liu Shihe Liang Zaichao Hu Minliang
College of Water Consevancy and Hydro-eletric Power,
Wuhan
University, Hubei, 430072, China
Abstract:
Atomized flow widely exists in hydroelectric engineering. In this paper the
methods of numerical simulation, physical modeling as well as prototype
observation which were usually used to study the atomized flow were
systematically described. Furthermore, the harm and prevention of the atomized
flow were also briefly introduced.
Keywords: hydraulics, two-phase flow, atomized flow
In hydroelectric engineering if water discharges from the flip bucket at certain high speed, atomized flow would form owing to the spreading of the aerated jet and splashing as this aerated jet impinges with the water downstream. This atomized flow may threaten the safety of the hydroelectric engineering, sometimes even causes certain harm, since this flow might produce heavy rain as well as heavy fog in a certain area just downstream of the dam under the influence of upstream wind and downstream topography. In some hydraulic projects once flood discharges there exists a relatively large area downstream of the dam where violent wind and driving rain occurs, and the sky turns dark, thence normal operation of the hydraulic projects may be heavily affected, and sometimes power failure, building inundation and landslide even occur. The purpose to study the atomized flow is just to prevent its harm to hydraulic projects.
Atomized flow in hydroelectric engineering has been observed for a relatively long time, but only recently has been studied in detail [1][2]. This kind of flow is very complicated water-air and air-water two-phase flow, the characteristics of which can be affected by the flood discharge conditions, modulated by the down stream topography, and the meteorological conditions have certain effects also. Until now there are three methods to study this flow, i.e., theoretical analysis, physical modeling and prototype observation. Theoretical analysis is relatively difficult, and there are usually so many assumptions that the description is only qualitative. Large-scale physical modeling costs quite much, yet scale effect owing to the aeration can not be avoided too. Prototype observation is very important, yet until now prototype observation data of different projects is very difficult to be compared and extended with each other. Therefore we suggest the following method to study the atomized flow for a special hydraulic project. (1) By using theoretical analysis to establish a mathematical model. In this model the main factors which affect the atomized flow are all included. (2) By using splash model test and diffusion model test to gain deeper insight into the atomized flow phenomena for the hydraulic project and to determine the coefficients in the mathematical model. (3) To verify the numerical simulation results and slightly adjust the coefficients by feedback analysis of the prototype observation data, in which the projects with this prototype observation data is chosen to be of the same type as the predicted ones by fuzzy cluster analysis. Then the atomized flow of the project can be directly predicted by numerical simulation. This method has been used by us to study the atomized flow and the associated problems to ten projects in China including the Three Gorge’s Project and seems very useful. In this paper the simulation of atomized flow resulted by flip bucket energy dissipation is briefly described.
The typical pattern of the atomized flow is given in Fig.1. Considering that the characteristics of the atomized flow change rapidly downstream of the flip bucket in this paper the atomized flow is classified into the following three regions according to both morphological difference and physical mechanism. 1) Jet region which is composed of aerated jet. 2) Torrent rain region. 3) Atomized flow diffusion region.
Torrent rain is produced by the spreading and splashing of water droplets at the outer region of the aerated jet. The rainfall intensity in this region is much larger than that of the natural rain, thence this region is the most harmful region of the above three regions. According to the rainfall intensity the torrent rain region can be further divided into catastrophic rainstorm region and rainstorm region. Catastrophic rainstorm region is composed of the collision area between the aerated jet and the water downstream and the splash region near the collision area. The rainfall intensity in this region is larger than 100mm/h. Rainstorm region is near the collision area, and the rainfall intensity in this region varies between16 and 100mm/h.
In the atomized flow diffusion region, the water concentration is so high that the moving wind could not driven it anymore, those that exceed the transport capacity of the wind would turn down in the form of rain. The rainfall intensity in this region ranges from 0.5mm/h to 16mm/h, and according to the rainfall intensity this region can be further divided into heavy rain region, moderate rain region, light rain region and fog region. The fog region is composed of atomized water fog, where navigation, electric equipment might be affected to some extent.
Fig. 1 Typical pattern of the atomized flow resultedby flip bucket energydissipation in hydroelectric engineering.
The aerated jet could be classified into partly aerated jet, fully aerated jet and completely aerated jet based on its aerated extent. Using Hw to represent the length scale of the jet core (the region where no bubbles entrain in the sense of time averaging), for partly aerated jet Hw≠0, for fully aerated jet Hw =0, yet for completely aerated jet the air concentration is so high that the jet almost breaks into pieces, and the jet flow might be regarded as the fluid flow driven by the moving water droplets[3].
In this paper the natural coordinate system
along the jet axis was used to describe the aerated jet. For the detail of the
numerical model see Ref. [4,7]. The corresponding characteristics of the aerated
jet can be got by numerical simulation for the giving initial conditions at the
flip bucket, from which the collision conditions between the aerated jet and the
water downstream are determined.
When aerated jet impinges with the water downstream, water droplets form in large amounts. These water droplets move under the effect of the wind produced by the aerated jet and the upstream wind, and sometimes even break into pieces until impinging with the water or bank of the river downstream, which forms the splashing region.
Let α and ui be the impinging angle and impinging velocity of the aerated jet with the water downstream, and γ be the reflection angle of the water droplets, the reflection velocity u0 can be got by the consideration of momentum balance in the horizontal plane, i.e.,
whereγ is related to the impinging angle of the aerated jet, and e is a coefficient which depends on the hydraulic characteristics of the aerated jet just before impinging with the water downstream and the water depth at the impinging area. Both γ and e are suggested to determine by hydraulic model test. The motion of splashing droplets and the estimation of the splashing region were given in Ref. [2].
calculation of the atomization source
There are two types of atomization source produced by the aerated jet. One is the atomized part at the outer edge of the jet, the other is the impinging and reflecting atomization source resulted by the impinging of aerated jet with the water downstream and the following reflection of water droplets.
There exist small water droplets at the outer edge of the aerated jet. Some of them would move downstream with the surrounding air, yet the others return back to the surface of the aerated jet. By theoretical analysis the atomization source Q1 at the outer edge of the aerated jet is expressed as
Where q1 is atomization source per unit width at the outer edge of the aerated jet, which is expressed as
Where C1 is a coefficient, which is related to the aerated extent of the jet just before impinging with the water downstream, and q is the discharge per unit width of the aerated jet.
Generally speaking, the jet with few aeration would has relatively high penetration ability, and the associated atomized extent is also relatively less.
(1) impinging process of the water droplets with the water downstream
Water droplets would produce a series of deformation when impinging with the surface of the water. The vertical impinge of water droplets with water had been studied by Engle[8]. We also studied the vertical and inclined impinge of water droplets with water surface. By theoretical analysis the impinging and reflecting atomization source was got to be
Where H* and H* are used to represent the corresponding half jet height relative to the lower and upper layer of the aerated jet, and θm represents the impinging angle.
(2) distribution of the radius of reflected water droplets
The scale of the water droplets moving in the air depends strongly on its relative velocity with the air. It is estimated by theoretical analysis that the maximum diameter for a single water droplet stably moving in the air is about 0.38cm. Yet for the torrent rain in nature the diameter is about 0.3cm. In practical engineering the atomized flow is composed of various water droplets, some of the droplets even get together or break into pieces. Thence the droplet scale changes rapidly. In this paper we use Γ distribution to express the distribution of the radius of water droplets, i.e. ,
where the coefficient α and λ are determined by hydraulic model test and prototype observation data.
The flow in atomized flow diffusion region is air-water two-phase turbulent flow, and the main effect to the hydroelectric engineering is heavy rain when the atomized flow moves downstream. The estimation of the atomized flow in this region is given in Ref. [2].
As has been discussed above, atomized flow is very complicated two-phase flow, and this flow can not be completely modeled only by using theoretical analysis and numerical simulation. Thence the method of hydraulic model test and experiment in wind tunnel is needed. Yet atomized flow is not a simply two-phase flow, but is mainly composed of water-air two phase flow, impinge and splash flow as well as air-water two phase flow from the flip bucket downstream. Although it is not possible to model the whole process of atomized flow by a unified model similarity law both in theory and in practice, yet the atomized flow can be modeled by using several models each with different model similarity law which is corresponding to different regions.
The impinging and splashing phenomena of the atomized flow can be modeled with either whole model test or partial model test. Yet in the model test since aeration should be modeled completely thence the model is better to be as large as possible. To model the aeration process the Weber number similarity law should be obeyed at first. The expression for Weber number is
Where σ is the coefficient of surface tension, and V and r are the typical velocity and typical length of the jet respectively. The experimental results obtained now shows that the similarity in splash region might be the gravitational law if the Weber number in the model is larger than 500. In splash model test the splash extent, water concentration, and rain intensity are usually measured.
The flow in atomized flow diffusion region can be modeled in the wind tunnel. In this experiment the topography of the hydroelectric engineering is modeled by geometric similarity, and the water concentration, the distribution of the radius of water droplets and the driven velocity of the air are modeled by the corresponding similarity law. The rainfall intensity and the corresponding extent of the atomized flow can be determined by measuring the velocity distribution, water concentration as well as the rainfall intensity.
Prototype observation is an important method to understand the properties of atomized flow and to solve the engineering problems, and the prototype observation data is both the foundation of theoretical analysis and the method to test the results of numerical simulation. Of course, the prototype observation of atomized flow is very difficult to realize, and it is also not easy to obtain the accurate data. Although many observation data probably only give a rough estimate of the characteristics of the atomized flow, these data provide scientific basis for judging the reliability of the method to predict the atomized flow.
Although the atomized flow can be influenced by many factors, it is shown by the observation results obtained now that the most important factors are: the difference between the upstream and downstream water level, the discharge, the general arrangement of hydroeletric engineering and the downstream topography. The projects with almost the same factors above are called similar projects in atomization. We have carried out feedback analysis to the prototype observation data of Wujiangdu hydropower station, Dongjiang hydropower station, Fengtan hydropower station, Liujiaxia hydropower station and Manwan hydropower station in China. The results show that although the projects above are strongly different in engineering arrangements, flood discharge conditions and downstream topography, the predicted results are all in good agreement with the prototype observation data. Which means that the methods suggested in this paper have relatively high predictive power.
The atomized flow would do harm to hydroelectric engineering in many ways, and the electric power plant, navigation, stability of the side banks and traffic safety might be affected. The prediction of atomized flow should be completed at the plan and design stage of the hydroelectric engineering. If the properties of the atomized flow have been accurately predicted during the plan and design stage, then the constructions can be arranged at the outside of the effective range of the atomized flow, or in the effective range practicable engineering measures can be adopted. Thence the harm of the atomized flow can be avoided.
The harm of the atomized flow to electric power plant is in two ways. One is the safety operation of electric power plant. Generally speaking, the factory building of electric power plant and the substation should not be within the effective range of the atomized flow, otherwise heavy accident might be produced by the rain storm. The second effect is to the electrical equipment, since there might exist very small sediments in the atomized flow, these sediments would cause the pollution of the electrical equipment naked in the air, which might reduce the functions of the equipment.
The harm of the atomized flow to navigation is also in two ways. One is that the rainstorm produced by the atomized flow is unfavorable to navigation, the other is that the heavy fog in atomized flow diffusion region would largely reduce the visibility of navigation.
There are two possibilities if the side banks of the hydraulic projects are within the effective range of the atomized flow. One is that the heavy rainstorm would directly impinge upon the side banks, which might produce erosion and instability. On the other hand, if the time for flood release sustains too long, the stability of the side banks which is within the effective region of little rain and heavy fog of the atomized flow might also be affected, and the engineering measures of drainage and reinforcement should be adopted.
References
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