(302f) Computational Fluid Dynamics Modelling of Single and Two-Phase Heat and Mass Transfer in Micro- and Milli-Scale Flows

Computational Fluid Dynamics modelling of
single and two-phase heat and mass transfer in micro- and milli-scale flows

Simon Kuhn

Department of Chemical Engineering, University
College London, UK

The investigation and characterization of heat and mass transfer
phenomena in single and two-phase flow is important in understanding transport
mechanisms influencing chemical reactions in micro- and milli-scale devices,
where no (or only little) turbulent actions promote mixing and interfacial
transport processes. This detailed analysis is accomplished by
a rational approach, identifying the physical mechanisms of heat and
interfacial mass transfer on various length-scales using non-invasive,
laser-optical measurement techniques^1-3, and to use these
experimental results to validate and develop predictive multiphase flow models
for computational fluid dynamics (CFD).

For this presentation we will focus on the
CFD modelling aspect of the work, where we use the open-source software
OpenFOAM^¨ to predict single and two-phase flow heat and
interfacial mass transfer on the micro-scale (i.e. 400 μm microchannels) and on the milli-scale. Our model geometry for the
milli-scale is the Corning Advanced Flow Reactor (AFR) depicted in Fig. 1,
which consists of several rows of heart-shaped cells in series.

The aim of these simulations is to
understand interfacial transport processes in more detail, and to use this
knowledge to design optimized milli-scale multiphase flow reactors. The
developed models and obtained results will therefore directly impact the efforts
in process intensification and sustainable advanced manufacturing.

The numerical
work is conducted using the volume-of-fluid (VOF) approach to simulate two-phase
flows, which uses an indicator function α to describe the volumetric phase fraction in each
computational cell. Since the phase interface definition is highly coupled to
the mesh resolution extra terms are needed to account for numerical diffusion,
and to provide a sharp interface definition. In the current version of the standard
OpenFOAM^¨
solver interFoam an interface compression approach is used, and in
initial simulations we validated this implementation for the test case of
bubble generation in a microfluidic T-junction against experimental results. It
was found that the standard implementation is too diffusive, thus we introduced
changes in the interface compression scheme to increase the interface sharpness,
which then matched the experimental results and proved also successful on the
milli-scale (see Fig. 2).

The standard interFoam
solver does not include scalar transport processes, thus we implemented the energy
equation in the VOF solver (the indices denote the gas (G) and liquid (L) phase
respectively, and can be transformed to liquid-liquid systems as well):

                                                                                                     (1)

where μ denotes the dynamic
viscosity of the fluid, and Pr is the Prandtl number defined as Pr= μc_P/λ
, with the thermal conductivity λ, and the heat capacity c_p.
This equation can be readily adapted for the VOF approach by calculating the
fluid properties (ρ, μ, c_p, and λ) using the
phase fraction α.

The implementation of species concentration
in the VOF framework uses the same approach, i.e. we define the concentration c
and the diffusion coefficient D as

c= αc_G+(1- α)c_L;      and
    D= αD_G+(1- α)D_L
.                                                                    (2)

The boundary condition at the
interface between the gas and liquid phase is satisfied by Henry's law

c_G=Hc_L                                                                                                                                                                         (3)

with the Henry
coefficient H describing the equilibrium solubility of the species in
the liquid phase. However, as the VOF approach only solves a single species
equation this needs to be taken into account as an explicit source term in the
scalar transport equation, which then reads in the VOF framework

_.                                             (4)

Figure 3 depicts the predicted temperature field in single
and two-phase flow in a microfluidic T-junction. The fluids are brought in
contact at even temperature and then heat up as they flow downstream in the
microchannel. For the single phase case a parabolic temperature field is
observed, which is expected for laminar convective heat transfer. The
temperature field of the gas-liquid flow case reveals the influence of the
bubble generation process in the entrance region of the microchannel on heat
transfer. Initially the gas phase is still in contact with the wall and heats
up faster than the liquid phase. After detachment of the gas bubble it is
isolated from the wall by the thin liquid film surrounding it, which is
expressed in the slight temperature difference between the gas and liquid
phases further downstream.

Figure 4 depicts the comparison of temperature fields for
the Corning AFR. In single phase flow the individual heart design leads to
considerable temperature gradients within a single cell. Elevated temperatures
are observed in regions of low fluid velocity, these zones are characterized by
a recirculating fluid motion, which develops between the U-shaped structure and
the downstream post. These regions of warmer fluid are bypassed by fluid of
lower temperature, thus this particular design leads to limited cross-mixing in
single phase flow. These recirculation zones are not able to establish in
two-phase flow due to the bubble dynamics (constant break-up and merging), and
as a consequence the developing temperature field is much smoother and the heat
transfer performance is increased, as seen by the higher average temperature in
the final heart compared to single phase flow.

We will report in detail on the implemented VOF method, and
the obtained heat and mass transfer data are validated against available
experimental results and are further interpreted to characterize the transport
processes on the micro- and milli-scale.

References:

[1] Kuhn, S.; Jensen, K.F. (2012) A pH sensitive Laser-Induced
Fluorescence technique to monitor mass transfer in multiphase flows in
microfluidic devices. Ind. Eng. Chem. Res. 51:8999-9006.

[2] Kuhn, S.; Woitalka, A.; Jensen, K.F. (2012) Mass Transfer in gas-liquid
and liquid-liquid multiphase flows. Proceedings of the 3rd European Conference
on Microfluidics.

[3] Nieves-Remacha, M.J.; Kulkarni, A.A.; Jensen, K.F. (2012) Hydrodynamics
of Liquid-Liquid Dispersion in an Advanced-Flow Reactor. Ind. Eng. Chem.
Res. 51:16251–16262.