About stepped channels and spillways
Investigation the Characteristics of Skimming Flow over Stepped Spillways
Stepped channels and spillways have been used since more than 3500 years. A stepped spillway can be defined as that hydraulic structure in which a series of steps of different shapes, dimensions, and arrangement is built into the spillway profile. These steps provide rough surface with extremely high turbulence which have the ability to slow down the rapid flow and dissipate significant amount of the overflowing energy (Chanson, 2002). The ease of construction and design simplicity have led this structure be more popular and important since 1980. The reduction of the flow energy, cavitation damage, and the dimensions of the downstream structure are the most principal engineering challenge they present. This essay seeks to introduce my PhD research about the characteristics of skimming flow over steep stepped spillways. This piece of work is divided into four main parts. Firstly, brief background information describes the skimming flow characteristics over stepped spillways. Secondly, an overview of the whole PhD task will be explained. Thirdly, possible results of this study are displayed. Finally, the practical and theoretical implications of the results are presented.
Initially, brief background information on the skimming flow over stepped spillways. In this part a summery of previous studies in this field is presented. It includes: the flow regimes over stepped spillways and the limits of skimming flow regime, skimming flow properties, and numerical model development of the skimming flow. First of all, flow regimes and the skimming flow limits. As Chanson (2002) stated, depending on the amount of the flow over a slopped spillway, three different regimes can be recognized; nappe, transition, and skimming regime. Rajaratnam (1990 in Carosi et al 2007) found that modern stepped spillways are designed to operate under large discharges pointing to the skimming flow regime. Yasuda et al (1999) proposed two equations for defining the upper limit of nappe flow and the lower limit of skimming flow regime. In this study, skimming flow in steep stepped spillways will be investigated. Now, we will discuss the skimming flow prosperities. Gonzalez et al (2004) demonstrated that very significant form losses and momentum transfer from the main stream to the recirculation zones are the main features of the skimming flows. Moreover, Carosi et al (2007) explained that in skimming flow regime, the flow is non-aerated at the upstream end of the chute. Downstream the free surface aeration, some strong air-water mixing occurs. From the recent investigations, it seems that the flow characteristics over stepped spillways are not clear and vary along the spillway, especially in steep slopes. In this study detailed characteristics of air-water flow will be studied under steep slope and skimming flow conditions along the spillway. Finally, we will explain the development of a numerical model. The prediction of skimming flow using numerical model approaches is widely used. Tongkratoke et al (2009) found that, the closest results to the experimental data can be predicted by using the combined linear realizable k-ε turbulence model and the non-equilibrium wall function as compared with the other linear models. Indeed, Xiangju et al (2006 in Tongkratoke et al 2009) showed that for the same stepped spillway, their results obtained by RNG model were more accurate than the results of Chen et al (2002 in Tongkratoke et al 209) obtained by using standard k-ε turbulence model. In this study and in order to explain the skimming flow characteristics over stepped spillways more accurately, a quasi 2D numerical model is developed on the basis of an existing finite volume 2D numerical model for free surface non-aerated flow.
Turning to explain an overview of the whole PhD task, detailed information of the air-water properties over a steep stepped spillway are presented in this study. For the provision of an accurate description of the flow behavior, this study is divided into two phases, physical model phase and mathematical and numerical model phase. The physical model is concerned with the laboratory experimental tests, whereas the mathematical and numerical model is related with the analytical solution of the phenomena using a computer programme.
The experimental tests of the physical model are conducted in a steep stepped flume assembled at the hydraulic laboratory of the Plymouth University. The stepped spillway physical model consists of four modes. In each mode a specific step shape is tested with respect to its energy dissipation efficiency: A horizontal step in the first mode, an upward slopped step in the second, a downward slopped step in the third one, and a 3D-overlay rectangular block equipped with a chamfer edge in the fourth mode. Furthermore, the number of the steps, the height and the length of the steps, the testing discharges regarding to skimming flow over the steps, and the slope of the stepped spillway for all modes are kept constant. A broad crested weir is selected for this study as an entrance condition for all modules with the existence of a stilling basin of a specific dimension at the toe. In addition, the experimental tests of each mode involve: firstly, examination the air-water flow structure, flow resistance, air concentration, air bubble sizes, characteristic flow depths and longitudinal flow velocity. For this purpose, an optical-fiber probe is used at several cross sections along the slope; secondly, estimation the forces on the steps. This can be accomplished by using and penetrating micro-pressure sensors on the horizontal and vertical faces of the steps in the fully developed flow region to measure the pressure applied on the steps; and finally, calculation the amount of the energy dissipation. Ultra-sound sensors can be used in this stage to measure the sequent depths of the forced hydraulic jump at the toe of the spillway. The measurements are also supported by digitized flow video sequences and high speed cameras. Dimensional analysis is applied in this study to analyze the experimental results and to correlate the parameters affecting the flow over stepped spillways.
As mentioned above, an accurate explanation of the flow characteristics requires a mathematical description of the flow. Therefore, a simple and realistic quasi-2D mathematical model is developed in this study to investigate the behavior of the aerated flow over the step shape that provides maximum energy dissipation efficiency on the basis of an existing finite volume 2D numerical model for free surface non-aerated flow. Now, I will highlight the results that this study may possibly show. Steps cause high turbulence especially, those having downward slopped and rectangular block shapes. Consequently, these shapes provide higher efficiency of energy dissipation than others. Indeed, high aeration can be observed some distance downstream the crest due to the air entrainment across the free-surface and leads both the reduction of water pressure close to the step surface and the appearance of white-waters. The pressure reduction is a good indication of the cavitation prevention. Similarly, the presence of air within the turbulent boundary layer reduces the shear stress as well. Moreover, parabolic relationships of velocity, pressure and air concentration can be obtained from the results. On the other hand, the mathematical and numerical model results may show realistic results regarding mixture depth, mean flow velocity, and air concentration of the free-surface flow and display good agreements with the experimental results of the physical model.
Finally, let's display the practical and theoretical implications of the present results. New empirical equations are proposed from the present investigation that can be considered as a guideline in the design of steep stepped spillways, especially for gravity dams, regarding the optimization of the shape and dimensions of the steps associated with both higher flow resistance and energy dissipation efficiency. Correspondingly, the amount of residual energy at the toe of the stepped spillway is a guideline for the design of the convergence walls and stilling basin downstream of the spillway. What is more, an extension knowledge of high velocity aerated skimming flows over different shapes of steep stepped spillways is contributed through the present experimental and numerical results to overcome the cavitation damage risk which faces most spillway surface during the overtopping period.
In conclusion, this essay introduces my PhD research about the skimming flow over stepped spillways. It does seem that the design of stepped spillways yields the dissipation of considerable amount of the flow energy, reduction of cavitation damage, and minimization the dimensions of the downstream hydraulic structures. Three different regimes appear over stepped spillways with respect to the amount of the discharge. The limits, conditions, flow properties and the numerical model development of skimming flow regime are presented in this essay. This research is divided into two phases, physical and numerical phases. In each phase, detail information is explained including the methodologies, instrumentation, and procedures. Probably, rectangular block and downward slopped steps provide higher energy dissipation efficiencies and flow resistance than other shapes. The empirical equations of this study can be use as a guideline in the design of stepped spillways and stilling basins of gravity dams.