Estimation of the depth of penetration in a plunging hollow jet using artificial intelligence techniques

Purpose: Experimental investigations assessment and comparison of different classical models and machine learning models employed with Gaussian process regression (GPR) and artificial neural network (ANN) in the estimation of the depth of penetration (Hp) of plunging hollow jets. Design/methodology/approach: In this analysis, a set of data of 72 observations is derived from laboratory tests of plunging hollow jets which impinges into the water pool of tank. The jets parameters like jet length, discharge per unit water depth and volumetric oxygen transfer coefficient (Kla20) are varied corresponding to the depth of penetration (Hp) are estimated. The digital image processing techniques is used to estimate the depth of penetration. The Multiple nonlinear regression is used to establish an empirical relation representing the depth of penetration in terms of jet parameters of the plunging hollow jets which is further compared with the classical equations used in the previous research. The efficiency of MNLR and classical models is compared with the machine learning models (ANN and GPR). Models generated from the training data set (48 observations) are validated on the testing data set (24 observations) for the efficiency comparison. Sensitivity assessment is carried out to evaluate the impact of jet variables on the depth of penetration of the plunging hollow jet. Findings: The experimental performance of machine learning models is far better than classical models however, MNLR for predicting the depth of penetration of the hollow jets. Jet length is the most influential jet variable which affects the Hp. Research limitations/implications: The outcomes of the models efficiency are based on actual laboratory conditions and the evaluation capability of the regression models may vary beyond the availability of the existing data range. Practical implications: The depth of penetration of plunging hollow jets can be used in the industries as well as in environmental situations like pouring and filling containers with liquids (e.g. molten glass, molten plastics, molten metals, paints etc.), chemical and floatation process, wastewater treatment processes and gas absorption in gas liquid reactors. Originality/value: The comprehensive analyses of the depth of penetration through the plunging hollow jet using machine learning and classical models is carried out in this study. In past research, researchers were used the predictive modelling techniques to simulate the depth of penetration for the plunging solid jets only whereas this research simulate the depth of penetration for the plunging hollow jets with different jet variables.