Investigation of the effect of small bubbles on energy dissipation in a vertical Couette–Taylor system

Abstract

The effect of small bubbles on reduction of energy dissipation has been numerically investigated in a vertical Couette-Taylor system. Flow is in the annular space between two concentric cylinders as the internal cylinder is rotating while the outer cylinder is stationary. Main fluid between cylinders is silicone, while air bubbles are constantly injected into the main flow at the bottom of cylinders' gap. The air bubbles rise through the flow when they are injected into the silicone flow. The flow is fully turbulence and Taylor vortices have appeared in the annulus gap. The rotational Reynolds number (Re x) varies from 700 to 3000. The fully two-phase turbulent flow has been studied using a discrete phase model and Euler-Lagrange approach. Air bubbles distribution or bubbles pattern through the main flow, which is acquired using numerical method, shows a good agreement to those acquired via experimental data in all Reynolds numbers. To investigate the changes of skin friction drag, the rate of energy dissipation in the system is calculated. The effect of injected air with constant flow rate on the total energy dissipation rate and the drag coefficient is also investigated. The results confirmed reduction of energy dissipation and about 25% of drag reduction when small bubbles were injected in the system. This reduction was the effect of the bubbles on the density of fluid and transformed momentum. Moreover, the acquired numerical results were in good agreement with those found in the previous experimental works, in which maximum Re x is up to 3000. Keywords Bubbly flow Á Taylor coquette system Á Energy loss List of symbols F D Drag force Fr Froude number G Gravity (m/s 2) I Turbulence intensity M Mach number Q Volume rate (m 3 /s) Re Reynolds number R Radius Ta Taylor number U The average velocity U Velocity(m/s) u 0 Velocity in Reynolds stress (m/s) m w The kinematic viscosity of the pure water Y Dissipation term We Weber number Subscripts B Bubble D Drag K Power gain factor i X direction j Y direction k Z direction T Temperature Greek symbols a Volume fraction (closure coefficient in the dissipation rate equation) b* Closure coefficient in the turbulent-kenetic energy equation d Radial gap