CFD analysis of viscous fingering in Hele-Shaw cell for air-glycerin system

Abstract

In this research paper, a numerical study has been done on the viscous fingering instability for the air-glycerin system in the 2D horizontal Hele-Shaw cell. The air and glycerin are immiscible fluids and the viscosity of glycerin is too much higher than air and viscous fingering strongly depends upon the viscosity differences of fluids pairs so that the air-glycerin system is taken. In this work, an immiscible fluid–fluid displacement flow process occurs and a low viscous fluid air displaces another high viscous fluid glycerin in the rectangular Hele-Shaw cell then due to unstable displacement of glycerin by air a single finger shape instability appears at the air-glycerin interface. This phenomenon is called viscous fingering. The viscous fingering has got importance in many natural and industrial applications such as geologic carbon dioxide sequestration, oil recovery, water infiltration into the soil, mixing of fluids at low Reynolds numbers in microfluidic devices, and many more. This numerical simulation is based on the transient solver. Volume of fluid (VOF) model has been accounted for tracking of the air- glycerin interface. The Geo-reconstruct scheme has been selected for precise interface tracking. The PISO (Pressure Implicit with Splitting of Operators) scheme has been adopted because it has improved the calculation efficiency. The objectives of this paper are to track the growth of a single finger at the air-glycerin interface and calculate the displacement efficiency by image processing. We found that air displaces only 74.15% of glycerin from the entire cell. We have also shown the distribution of pressure and velocity in the entire cell domain.