Direct numerical simulations (DNS) of a three-dimensional spatially-developing mixing
layer (ML) laden with spherical gaseous bubbles are performed, with both one-way
and two-way coupling between the two phases. Forcing is used to initialize the
spanwise vortex roll-up and to create a pair of counter-rotating streamwise vortices,
rendering the carrier flow three-dimensional. The characteristics of the resulting ML
flow field are similar to those reported in numerous experimental and numerical studies.
The volume fraction (or concentration) of the bubble phase is considered small
enough to neglect bubble–bubble interactions. The no-slip fluid velocity condition
is assumed at the bubble surface, and the bubble Reynolds number is less than 1
throughout the simulation time. The two-fluid formulation (TF) is used to compute
the bubble-phase velocity and concentration and the two-way coupling source term
in the fluid momentum equation. A Lagrangian–Eulerian mapping (LEM) solver is
employed to solve the equations for the bubble velocity and concentration. LEM is
capable of resolving the gradients of concentration created by the bubble preferential
accumulation without numerical instabilities. Two different inflow profiles (Cref(z)) of
bubble-phase concentration are considered: a uniform profile and a tanh-profile. In
the latter case, the high-speed (upper) stream is devoid of bubbles, and the low-speed
(lower) stream is uniformly laden with bubbles at the inflow plane.
The DNS results show that in addition to the well-known preferential accumulation
of bubbles in the vortex centres, sheets of increased bubble concentration (C-sheets)
develop in the rollers created by the vortex pairing in the ML core, with two local
maxima of vorticity and an enhanced strain-rate field. The development of C-sheets
is governed by the stretching and contraction along the principal axes of the local
In the case of uniform Cref, the two-way coupling reduces the average ML vorticity
thickness and the entrainment of the irrotational fluid into the ML core, as compared
to the bubble-free case, upstream of the location of the first vortex pairing. However,
both ML vorticity thickness is increased and entrainment is enhanced by the bubbles
farther downstream, after the pairing. The fluid velocity fluctuations are reduced by
the bubbles throughout the ML, as compared to the one-way coupling case.
In the case of the tanh-profile of Cref, the velocity fluctuations and the ML vorticity
thickness are increased by the bubbles upstream the location of the first vortex pairing
owing to the ‘unstable’ inflow bubble stratification (Druzhinin & Elghobashi 1998).
On the other hand, the velocity fluctuations are reduced by the bubbles, and the ML
vorticity thickness oscillates with the streamwise distance farther downstream.