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

- Conference: AIChE Annual Meeting
- Year: 2013
- Proceeding: 2013 AIChE Annual Meeting
- Group: Engineering Sciences and Fundamentals
- Session:
- Time:
Wednesday, November 6, 2013 - 8:45am-9:00am

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