Processing of experimental results for super-cavitating flow past cone by local polynomial regression (LOESS)

The aim of the study is to define the correlations describing the flow parameters during super-cavitating flow past an obstacle, often found in various elements of thermal power systems and units, as well as to offer a simple and reliable method for analysing experimental datasets for the flows in such systems. Full-scale modelling of cavitation processes was carried out using a circulating hydrodynamic set-up. The process of super-cavitation flow past cones with base diameters of15.45 and 21.75 mm and opening angles of 154° and 127°, respectively, in a working section having a diameter of 30 mm, was investigated. The obtained experimental data comprises a four-dimensional array that describes the dependence of the cavity length arising behind the obstacle and the pressure inside the cavity on the flow rate and temperature. Due to the complexity of processing and visual representation, this array was divided into two three-dimensional arrays. The approximation of the obtained data was carried out by locally estimated scatterplot smoothing (LOESS). The results demonstrated that the transition from vapour–gas to vapour cavitation is independent of the geometric dimensions of the obstacle. In addition, the dependence corresponding to the transition process to vapour cavitation was obtained by processing the experimental data. An empirical equation describing such a transition is proposed. Therefore, the method of smoothing a locally estimated scatter plot (local polynomial regression) illustrates the correlation between the processed data. The proposed empirical equation allows the critical length of the cavity to be determined that corresponds to the transition from vapour–gas to vapour cavitation and can be used for the design and operation of thermal power equipment.