(440b) Simulations of Solid-Liquid Scalar Transfer in Turbulent Flow

We numerically study scalar transfer
from a single solid sphere into a surrounding fluid phase that undergoes
turbulent flow. The conditions are such that the diameter of the sphere is an
order of magnitude larger than the Kolmogorov length scale so that the sphere
experiences an inhomogeneous and strongly time varying flow.

In the simulations, the turbulence as
well as the sphere are fully resolved. This is achieved by means of the
lattice-Boltzmann method. Its uniform, cubic lattice has a spacing close to the
Kolmogorov length scale. The no-slip condition on the surface of the
translating and rotating sphere is imposed by an immersed boundary method.
Turbulence in the fully periodic, three-dimensional domain has been created
through linear forcing.

In addition to the flow dynamics, we
solve a convection-diffusion equation for the passive scalar c with c=1
at the solid surface and initially c=0 in the rest of the domain. Since
we deal with liquid systems, the Schmidt number is high and we anticipate issues
with the spatial resolution of the scalar concentration field, at least close
to the sphere. To mitigate these we solve the scalar transport equation on two
connected grids: an inner spherical grid that moves with the sphere, and an
outer cubic grid that is the same as the grid on which the flow is solved (see
Figure 1). For solving the scalar transport equation a finite volume method
with a TVD scheme has been used.

This dual-grid approach has first been
benchmarked for the case of a sphere suspended in simple shear. Reference data
for this case are available due to Yang et al (2011). This benchmark provides
us with notions as to the spatial resolutions required as a function of Schmidt
and Peclet numbers.

First results with the sphere immersed
in turbulent flow (illustrated in Figure 2) show the erratic structure of the
mass transfer process close to the sphere with strong inhomogeneities due to
the turbulent flow. Further analysis of the results gives credit to mass
transfer models based on surface renewal with time scales of the order of 50
Kolmogorov times.

Chao Yang, Jingsheng Zhang, Donald L.
Koch, Xiaolong Yin. Mass/heat transfer from a neutrally buoyant sphere in
simple shear flow at finite Reynolds and Peclet numbers. AIChE J. 57, p1419,
2011.

Figure 1                                                      

Figure 2