Penetration depth of plunging liquid jets – A data driven modelling approach

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In the case of impinging water jets or droplets, air entrainment processes are crucial to the casing design of hydraulic impulse turbines in the micro-hydro sector. To initiate first steps towards a precise prediction of the complex, multi-phase casing flow of impulse turbines, single aspects such as the penetration depth of impinging liquid jets have to be separated and fully understood. Existing investigations determining penetration depths are related to a very small range of flow rates and therefore show an underestimation of the penetration depth being applied to the casing flow of impulse turbines, which are generally operated at higher flow rates. For a more general description of the air entrainment process, investigations of plunging water jets within an extended flow rate range are conducted and the penetration depth is modelled using a data driven artificial neural network (ANN) approach and a non-linear regression model.At low flow rates, experiments results are in accordance with existing studies, whereas penetration depths up to 170cm are measured at higher flow rates. For the mathematical models to achieve a wide range applicability, a large data base is used, including published and measured data. The modelled penetration depths can be precisely verified by the performed measurements and show correct physical behaviour, even in areas without underlying data. Calculation rules, weight matrices and biases of the trained ANN are published to achieve high transparency and scientific improvement in neural modelling of penetration depths of impinging liquid jets.