Skin friction Reduction by Introduction of Micro-bubbles into Turbulent Boundary Layer

The phenomenon of drag reduction by the injection of micro- bubbles into turbulent boundary layer has been investigated using an Eulerian-Eulerian two-fluid model. Two variants namely the Inhomogeneous and MUSIG (MUltiple SIze Group) based on Population balance models are investigated. The simulated results are compared against the experimental findings of Madavan et al (1). The model employed in the investigation comprises of a two- dimensional micro-bubble laden flow wherein the Reynolds averaged Navier-Stokes (RANS) transport equations were used to describe both the phases of the flow. A SST (Shear Stress Transport) turbulence model is used as the turbulent closure for the primary phase and a zero equation turbulence model is used for the micro-bubbles. INTRODUCTION Numerous experimental and numerical studies have been carried out to investigate the aura of micro-bubbles along the turbulent boundary layer. The mere subsistence of the micro-bubbles seems to reduce the skin friction along the boundary layer for single phase flows. The pursuits of drag reduction by the shear presence of micro-bubbles have wide range of applications for ships, ship tankers of more prominence and to increase the efficiency of fluids which succumbs to long distance transport through pipelines. Micro- bubbles have a greater role of reducing drag for submarines, wherein the wetted surface of the vessel is 100%. Two broad theories can be spelled out from the micro-bubble drag reduction. Firstly, the drag reduction is attributed towards the material properties of the carrier (water) and the dispersed phase (mostly air), called the density ratio effect, wherein the density ratio between the phases is fairly high, as a result causing an elevated mixture viscosity and a reduced turbulent momentum transfer due to the dispersed phase, there by causing a subsequent drop in wall shear stress and hence the skin-friction (2). The second theory proposes that micro-bubble drag reduction is caused by turbulence distortion along the single phase boundary layer and the relative change instilled by it onto to the dispersed phase have received a heightened importance in recent years both numerically and experimentally(3,4,5,6) In this paper, the role of the micro-bubble in drag reduction has been numerically investigated. For this endeavor, two different numerical models namely the Inhomogeneous two-fluid and the population balance models have been employed. Population balance models have been employed to take in account of the break-up and the coalescence prevalent at higher gas injection rates. The skin friction co-efficient ratios are compared against the experimental results of Madavan et al (1). Streamwise velocity modulation effected due to the presence of micro-bubbles have been investigated along the boundary layer, this helps to shed more light on the change effected along the various regions of the turbulent boundary layer in the presence of the micro bubbles. This has been done by validating our numerical model results against most of the well established results; this is carried out in methodical manner in such an order to ensure the validity of our study. GOVERNING EQUATIONS Inhomogeneous Two-Fluid model Mass conservation Numerical simulations presented in this paper are based on the two- fluid model Eulerian-Eulerian approach. The liquid phase is treated as the carrier phase while the gas phase (bubbles) is considered as dispersed phase (ANSYS, 2006). In isothermal flow condition, with no interfacial mass transfer, the continuity equation of the two- phases with reference to Ishii (7) and Drew and Lahey (8) can be written as: