Penyusunan Model Elemen Hingga Interaksi Persamaan Aliran dengan Persamaan Sebaran Udara

Abstract

Aeration process is one of water treatment processes. The process consists of two physical phenomena, flow, and spreading of air bubble. This research has developed a finite element model for three-dimensional flow and spreading of air bubble. The flow equation employs Navier-Stokes equation. The spreading of air bubble is modeled as convection-diffusion equation. The Navier-Stokes and the spreading of air bubble equation are combined by Navier-Stokes equation with additional new term, which shows the accelerated flow caused by the air bubble moves. The Navier-Stokes equation was solved in four stages, i.e., Taylor Galerkin convection approximation, viscous prediction, pressure correction and velocity correction stages. Galerkin Standard method was used to solve the spreading of air bubble equation. Quadratic brick finite elements with 20 nodes were used on the geometry. To show performance model, comparison to the result of air bubble investigation was carried out. The numerical model that has been obtained is capable of simulating the phenomena of air bubble spreading and flow. The numerical stability analyses showed that the numerical scheme of convection and diffusion equation based on Galerkin is stable for Courant Number £ 0.01 and Peclet Number <125.