Simplified modeling and fast simulation for oxygen transfer in aeration by bubbles using Gaussian plume equation, MAC and Crank-Nicolson methods for control and environmental treatment purposes

In an attempt to simulate the bubbling aeration process in a fast and efficient manner, we propose a simplified model based on theoretical concepts and equations that represent the phenomenon. The computational domain considered for the calculations is a rectangular channel with water flow crossed by air bubbles. The mass transport equations are discretized in time and space using the Crank-Nicolson technique, whereas the momentum transport equations are solved using the Marker and Cell (MAC) method. The profile of the bubbles' plume is modeled using a Gaussian equation for two-dimensional dispersion. The novelty of this approach lies in the coupling of these three equations and techniques, which has not been reported before. The contribution of this work is the convenience of obtaining fast and robust responses for the concentration of dissolved oxygen, which can be useful for preliminary guidance and dynamic modeling for process control and environmental treatment purposes.