Numerical simulations of turbulent thermal, bubble and hybrid plumes

• Turbulence resolving, large eddy simulations of multi-phase, deep-water plumes are conducted.
• An efficient, computable model accounting for primary effects of a dispersed gas phase is derived.
• The turbulence enhancement in two-phase plumes is quantified and explained.

To understand the near-field dynamics of blowout plumes such as the one produced by the 2010 Deepwater Horizon oil spill in the Gulf of Mexico, the effects of gas bubbles on turbulent mixing and entrainment are studied via turbulence resolving simulations. We compare the evolution of three plumes where extremely large buoyancy anomalies are produced either thermally (single phase), solely by an imposed gas phase volume fraction, or by a combination of both buoyancy forcings. The plumes, with identical volume, momentum and buoyancy fluxes at the inlet, are released into an environment stratified with a constant temperature gradient. To clarify the first-order effects of dynamically active, dispersed bubbles, we employ a simple model which neglects the momentum of the gas phase while retaining bubble induced buoyancy in the seawater momentum equation. The gas phase is then distinguished by a single, measurable parameter, the slip velocity relative to that of the liquid phase. We find that bubbles, parameterized simply by a constant slip velocity, without any explicit assumptions of direct bubble induced turbulent production, significantly increase turbulent mixing in the plume in agreement with previous experimental results. Examination of mean momenta and turbulent kinetic energy budgets shows that the increased turbulence is due to direct modification of the mean profiles of both the momentum and the active scalar fields by the slipping gas phase. The narrowing of the active scalar field in the two-phase flow results in larger direct buoyancy production of turbulent energy at all vertical levels. The turbulence production is, however, primarily mechanical. At modest values of z/D, where the slip velocity is only a small fraction of the liquid phase velocity, slip stretches the mean vertical velocity field producing larger radial gradients and increased conversion of mean to turbulent energy. This first order effect, acting on the mean vertical velocity component and not directly on the turbulence, implies that even relatively small gas volume fractions significantly enhance turbulent mixing with respect to a single phase plume.