(182g) HPC Modeling and Simulation of Mass Transport in Wavy Falling Liquid Films

Corresponding
author. E-mail address: hengyi@mail.sysu.edu.cn (Yi Heng)

It is known that the wavy falling
film exhibits better heat and mass transfer performance. However, the
underlying kinetic phenomena are still not fully understood. In recent years, different
modeling and simulation studies for local hydrodynamics and mass transport of falling
film have received great attention in both academia and industry. A typical way
for calculating the fluid dynamics in a falling film is to solve the
Navier-Stokes equations (NSE) in the liquid and gas phases simultaneously and use
volume-of-fluid (VOF) method to capture the gas-liquid interface. To the best
of our knowledge, only a few direct numerical simulation (DNS) results related
to the modeling of two-phase falling films are available in the literature. Xu
et al. [1] used a hydrodynamic
parameter  to characterize
the scalar transport across the interface and gave an empirical relation. Albert
et al. [2] employed a two-scalar
approach to simulate the absorption of oxygen into wavy film and identified the
enhancement mechanism of mass transfer related to local Sherwood number and hydrodynamic
phenomena. Hu et al. [3] found out that the
concentration of CO₂ absorbed in the film is closely related to the
vorticity and defined a correlation coefficient to characterize the
relationship between them. Besides the VOF method, other methods such as the Arbitrary-Lagrangian-Eulerian
approach [4] or level set method [5, 6] can also be used to simulate
the mass transport if fluid dynamics is apriori known.

However, DNS approaches usually
require significant computational effort that is in general not applicable in
practice. An alternative way, which can reduce computational effort, is to
apply a simplified single-phase model, i.e., by solving the NSE only in the
liquid phase with a free boundary at the two-phase interface. Sisoev
et al. [7] used a simplified Navier-Stokes
model derived by Shkadov to study the gas absorption into a wavy falling film. Bandi
et al. [8] utilized a reduced
model, i.e., the long-wave expansion developed by Balakotaiah et al. [9, 10], to simulate the
absorption of wavy falling film and validated the results with 2-D experimental
data obtained by the PLIL measurement method. Wylock and Scheid [11] reduced the 2-D
governing equations into a 1-D second-order weighted integral boundary layer
(WIBL) model and obtained similar hydrodynamic with the 2-D model when Reynolds
number is less than 100.

In this work, instead of using the
simplified model to reduce computational effort, the DNS of the falling film is
investigated by means of high performance computing (HPC) techniques on the
supercomputer. The long-term goal is to establish an efficient computing
platform that can solve large-scale forward and inverse problems arising in
falling film on an industrial scale (decimeters to meters) at high calculation precision. As a first step, a
series of 2-D simulations for a laminar, Newtonian and incompressible water
film flowing down a vertical flat plane are investigated in this work. Ansys
Fluent 18.0 is adopted to solve the NSE with the VOF method [12] employed to capture the
gas-liquid interface and the continuum surface force (CSF) model [13] to account for the
surface tension. To simulate the oxygen transport in the film, the user-defined
scalar (UDS) function is used to calculate the convection-diffusion equation.
The inlet water velocity is assumed as a well-accepted parabolic Nusselt velocity
profile with a sinusoidal perturbation to generate wavy film. The rest of the
computation domain is assumed to be filled with air. The oxygen concentration
at the gas-liquid interface is assumed to be equal to the equilibrium
concentration, i.e. 0.28 mol/m³ according to Henrys law [8]. Homogeneous Neumann conditions are applied at the
remaining boundaries.

A grid independence analysis is
carried out at different grid levels. The grid size of 0.02*0.04 mm²,
in the height and flow direction, respectively, is an appropriate choice to balance
the computational effort and solution accuracy (cf. the red line in Figure 1).
A time step size of 3*10^-5 s is applied to ensure the numerical
stability.

Figure
1  A representative
example of simulated instantaneous film thickness at t=0.3 s using three different
levels of grids

Furthermore, based on the proposed
computational model, scalability tests on the supercomputing platform (24 cores
per node) are carried out (cf. Figure 2). Without loss of generality, the
results for Re=41 with a simulation time of 0.1s are presented.

Figure 2  (left)
Strong scalability test (right) Weak scalability test

In the strong scalability analysis,
a fixed-size problem of 1.4*960 mm² is computed by using a series of
increasing number of cores/nodes. Figure 2(left) shows that for a problem of
such size the speed-up ratio can be increased up to 2 nodes (48 cores). As more
nodes are used the communication overhead across the nodes becomes the choke
point and limits the possibility of further speed-up. In the weak scalability analysis,
the problem size is set to be proportional to the CPU cores, i.e. the
computational domain of 1.4*60 mm² for 3 cores, 1.4*120 mm²
for 6 cores, 1.4*240 mm² for 12 cores, 1.4*480 mm² for 24
cores (1 node), 1.4*960 mm² for 48 cores (2 nodes), and 1.4*1920 mm²
grid for 96 cores (4 nodes). Figure 2(right) shows that the speed-up ratio can
be increased by using the multi-node parallel computing if the problem size is sufficiently
large. In this case, the influence of communication overhead can be diluted.

Based on the proposed HPC
computational strategy, a series of simulations for a range of Re numbers are performed.
The waves are induced by a perturbation of frequency f=12 in a computational
domain of 0.25 m. The simulated velocity and concentration distributions in
quasi-steady state for 4 representative Re numbers are shown in Figure 3 and
Figure 4, respectively. The perturbation in the inlet generates solitary waves
followed by several capillary waves periodically. Similar to the patterns of
high concentrations locally found in other literature [8,9,10], it is also observed
that the velocity magnitude in the wave crest is higher than other zones, which
results in intensified convection mass transfer and high concentration in the
solitary wave.

Figure 3  Instantaneous
velocity distributions at t=1s for different Re(tenfold scaling of the Y axis
is used for better view)

Figure 4  Instantaneous
concentration distributions at t=1s for different Re(tenfold scaling of the Y
axis is used for better view)

In summary, a 2-D wavy laminar
falling film model was proposed for the simulation of the oxygen absorption into
water. Through parallel computing by the supercomputing platform, it has high
potential to solve large-scale forward problems at a practically reasonable cost.
Moreover, the separability of the problem allows to perform batch processing at
different operating conditions. In the future work, it is expected to prepare big
data generated by large-scale simulations on falling film by using the proposed
HPC computational strategy, so as to meet the future industrial requirements. Future
work will also include the development of optimal experiment design techniques for
the mass transport in falling films by solving arising large-scale inverse
problems. The forward modeling approach with high efficiency and precision proposed
in this work is considered as an important step toward this long-term modeling
goal.

References

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