Método da quadratura de momentos aplicado à simulação da distribuição de tamanho de bolhas em um biorreator pneumático por CFD

Abstract

Aeration is crucial for the functioning of pneumatic bioreactors, as injecting gas into the system allows to perform agitation of the medium and as well as to improve mass transfer with lower energy consumption. Bubble distribution and flow regime in these devices directly affect the performance of global parameters, such as the gas hold-up (εG) and the volumetric mass transfer coefficient (kLa). Thus, understanding their behavior and their interaction phenomena between the liquid and gas phases are important to evaluate the fluid dynamics and performance of these bioreactors. In this context, computational fluid dynamics (CFD) simulation stands out as an alternative tool for the study and evaluation of these global parameters under different operating conditions and geometries, allowing these evaluations to not be limited by the time and costs of building prototypes necessary for experimental evaluations. However, among the studies found in the literature, few are those that evaluate the influence of gas flow in the medium considering the existence of a bubble size distribution in its modeling, which is observable in practice. Such consideration is important so that coalescence phenomena and bubble breakage are accounted for in the problem, making it possible to refine the fluid dynamic behavior modeling of these devices. Therefore, this work aims to incorporate the bubble size distribution in CFD simulations of pneumatic bioreactors through population balance equations (PBE) using the Quadrature Method of Moments (QMOM), in order to evaluate the influence of this inclusion on the simulated response of the main performance global parameters. The simulations were performed using the Ansys Fluent software, versions 14.5 and 2022 R2, considering the Eulerian-Eulerian model for the description of the 3D air-water multiphase flow for the bubble column (CB) geometry studied by Mendes (2016). A Python routine was implemented and applied to assist in the simulations, with the goal of evaluating different coalescence and breakage models incorporated into the population balance. From this routine, the constants used in the 3D simulation for different collision frequency models were determined. Simulations were performed for specific airflow rates (ϕar) of 1 to 5 vvm, and contours for the bubble diameter and its Sauter mean diameter value were obtained. The results showed that the QMOM were able to describe the bubble size distribution and its evolution, with a maximum relative error of 9% obtained in the estimation of the Sauter mean diameter. It was also possible to estimate the value of kLa, with the lowest relative error obtained being 12% for ϕar equal to 1 vvm.