عنوان مقاله [English]
نویسندگان [English]چکیده [English]
One of the hazards which almost always threaten dam spillways is the cavitation phenomenon which is caused by high-velocity flow hydrodynamic effects on the structure. Presence of air in high-velocity flow can prevent the dangers of cavitation or at least reduce them. Stepped spillways with considerable applications have been economically justified the downstream of RCC weight dams. Superiorities over smooth spillways include high rate of energy dissipation along the spillway and reduction in stilling basin dimensions.
The most important indexes of the flow passing the stepped spillways are the high level of turbulence and the way air enters the flow. Turbulence fluctuations near the water-air free surface (two-phase flow) create air bubbles. Generally, turbulent flow is present in the vicinity of boundary layer which begins from the crest, develops downstream and crosses the water surface. When outer edge of the boundary layer reaches the free surface, turbulence occurs and causes a natural aeration of the flow. Air entrance location is called the inception point. In the downstream, the flow is fully developed and there is accelerated aeration in the free surface.
In these spillways, aeration length which is defined as the distance between the crest to the inception point can be exposed to cavitation. The boundary layer thickness has been estimated by different researchers for spillways without any step but it is not accurately determined for stepped ones. The reason is due to the complexity of flow conditions in these kinds of spillways.
Inception point location in most cases is obtained by observation. Therefore, the specifications and coordinates presented for this point by different researches have a wide range of discrepancy. Classically, this point conforms to a cross section of the step in which the water flow has a white or milky color. In this experimental study, three models were used at Water Research Institute of Ministry of Power. Plexiglas was applied in the models for stepped spillways with 18.44, 38.81 and 50.2 degrees tangents. The step numbers were 59, 61 and 65 and they had 1.33, 1.5 and 2.12 meters width, respectively.
The objective was to investigate the distance between the crest and the inception point along the spillway tangent, so the inception point was determined by passing different amount of mass flow rates on different experimental models. It is worth mentioning that the minimum and maximum amount of mass flow rate, required to record the flow inception point, are not the same for the three models since they are based on model width and its tangent. By increasing the tangent and its width, the mass flow rate will be higher for a continuous flow to be established.
According to the results obtained, increasing the spillway tangent would bring the inception point closer to the crest. In other words, it would delay the flow. Considering the model specifications of this study, an equation is extracted which is applicable for a wide range of angles. To do this, taking the Froud number (F_*) and spillway tangent as variables, the following relation is obtained:
l_i/k_s =11.08 ?F_*?^0.675 ?(tan???)??^(-0.2114) R^2=0.87 (1)
This equation is valid for the range of ?18?^°????52?^°.
A comparison between above equation with the Wood’s relation for ogee spillways in model number 2 with mass flow rates in the experiments showed that the length without air in stepped spillways was less than the length in ogee spillways. Consequently, the inception point was closer to the crest. Also, a comparison was performed between the recommended relation and Chanson and Boes relations. The reason of selecting these two relations was the wide range of angles they conclude. Results showed that the presented equation had the smaller standard error with respect to the abovementioned relations.
Generally, the results show that a stepped spillway will bring the inception point closer to the crest in comparison with smooth and ogee spillways i.e. l_i will be smaller in these kinds of spillways. Implementing a quantitative comparison between the Wood's relation and the equation obtained in this study shows that l_i can be reduced up to 5-10%, depending on the mass flow rate. Increasing the mass flow rate in these spillways which promotes the Froud number (F_*), will increase the aeration length and cause a delay in aeration process. This means that F_* has a direct relationship with l_i. Results also show that increasing the spillway tangent will reduce l_i and bring the inception point closer to the crest. Consequently, equation 1 which verifies the abovementioned discussion was derived with an acceptable correlation coefficient.