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Computing gas and liquid interactions based on interfacial force models require a proper turbulence model that accurately resolve the turbulent scales such as turbulence kinetic energy and turbulence dissipation rate with cheap computational resources. The  k −    ε  turbulence model can be a good turbulence predictive tool to simulate velocity components in different phases and approximately picture the turbulence eddy structure. However, even this average turbulence method can be expensive for very large domains of calculation, particularly when the number of phases and spices increases in the multi-size structure Eulerian approach. In this study, with the ability of artificial learning, we accelerate the simulation of gas and liquid interaction in the bubble column reactor. The artificial learning method is based on adaptive neuro-fuzzy inference system (ANFIS) method, which is a combination of neural cells and fuzzy structure for making decision or prediction. The learning method is specifically used in a cartesian coordinate such as Eulerian approach, while for the prediction process, the polar coordinate is applied on a fully meshless domain of calculations. During learning process all information at computing nodes is randomly chosen to remove natural pattern learning behavior of neural network cells. In addition, different    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$r$$\end{document}   rand    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\theta$$\end{document}   θare used to test the ability of the learning stage during prediction. The results indicate that there is great agreement between ANFIS and turbulence modeling of bubbly flow within the Eulerian framework. ANFIS method shows that neural cells can grow in the domain to provide high-resolution results and they are not limited to the movement or deformation of source points such as Eulerian method. In addition, this study shows that mapping between two different geometrical structures is possible with the ANFIS method due to the meshless behavior of this algorithm. The meshless behavior causes the stability of the machine learning method, which is independent of CFD boundary conditions.

Bubbly flow prediction with randomized neural cells artificial learning and fuzzy systems based on k–ε turbulence and Eulerian model data set