Influence of slip velocity in a two-phase bubbly jet

Abstract

The effect of the slip velocity in a bubbly jet ( $Re = 3000$ , initial void $\textrm {fraction} = 1.1\,\%$ ) is studied with various bubble slip ratios (0.07–2.1 times the inlet velocity, 0.01–0.31 m s $^{-1}$ in dimension). The governing equations, which are the conservation of mass, momentum and volume fraction, are solved by direct numerical simulations. A set of ordinary differential equations was derived by using a conventional one-dimensional integral framework on jets and by expressing the slip velocity using an exponential function. The one-dimensional analysis of bubbly jets successfully predicted the jet velocity radius, centreline velocity and the gas spread rate downstream of the bubbly jet. Second- and third-order statistics were also analysed to better understand the turbulent characteristics of the bubbly jet. A high slip ratio results in a rigid, narrower bubbly jet core region, where the turbulent kinetic energy is conserved along the centreline but does not diffuse towards the ambient region. The narrow, circular region around the core at high slip ratios decreased the turbulent kinetic energy. In the rigid bubbly jet core, turbulent diffusion of the gas phase is suppressed and has low correlations with the velocity fluctuations. Turbulence characteristics such as turbulence stress were compared with single-phase jet and plume results from existing literature. The magnitude of the turbulence characteristics at the lowest slip ratio is comparable with what is found in the literature, but there is a rapid transition from slip ratios of $0.14$ to $0.7$ . Furthermore, the turbulent kinetic energy budget was analysed for each case. The production term had the largest contribution, and its magnitude was almost five times the buoyancy production downstream. High slip ratio cases show a positive peak of pressure strain and turbulent diffusion along the centreline.