Air Entrainment in Central Jet Dropshafts: Theoretical Formulation and Experimental Implementation

Vertical dropshaft is a hydraulic structure, typical for hydro power-plants or sewer plants, which may be affected by air entrainment. Air entrainment phenomenon can be responsible of high risk for both the hydraulic machinery and the sewer conduit, since large air pockets dynamics may cause overpressures. Therefore entrained air rate evaluation is essential to check both the structure working conditions and their correct design. A meaningful parameter is the air/water flow rates ratio, called b. In literature, application of dimensional analysis to this phenomenon leads to the conclusion that physical parameters that affect the phenomenon are the jet length H, the hydraulic head in the tank h and the diameter of the dropshaft D all suitably divided by the orifice diameter d, and moreover the impact Froude number Fri, the impact Weber number Wi and the impact Reynolds number Rei. Moreover, always in literature, some equations are provided to obtain the b parameter in specific cases, often starting from experiments carried out on little dimension (far from real plants dimensions) physical models. In this paper a large dimension plant was tested in which viscosity played no more any role and consequently Rei could be discarded. Moreover dimensional analysis was rearranged to show the dependence of b on only four parameters: practically the three already considered ratios (suitably rearranged) and a new Froude number (Plant Froude Number) varying only with the shaft diameter. Experimental results of tests carried out on that plant (characterized by a well defined Plant Weber Number) relative to all possible combinations within suitable ranges of the three mentioned ratios are reported and are used to calibrate a physically based mathematic model. This investigation could be usefully followed by others similar experiments carried out changing the Plant Froude Number.