(45e) Modelling of the Boundary Layer in Turbulent Two-Phase-Flows

Particle deposition and separation is one
key issue in multiphase flow modelling. The goal of such simulations is for
example the result of desired or undesired separation processes. We denote painting
processes or precipitation processes in air purification as desired processes. In
contrast, the separation of particles during pneumatic conveying is an example
for undesired processes. From this point, it is essential to simulate the
particle motion accurate, especially the near wall region. The focus of this
presentation is held on the modelling of discrete particle tracks called Lagrangian
approach. The essential point is turbulence modelling and the influence on the
disperse phase. The presentation compares the results obtained by a conventional
code with results obtained by a code developed in our group. The two different
approaches to model the turbulent fluctuations within the boundary layer of the
fluid field will be compared with experimental results published by Agarwal [1].
The results will show the significant influence of the different models on the
resulting particle deposition. The last step will evaluate in which regimes the
accurate boundary layer modelling has a dominant influence. This will be done
by comparing the turbulent deposition with other influences like electrical
deposition.

The simulation of a separation process contains
the simulation of the continuous phase and the simulation of the disperse
phase. The model for the Lagrangian approach is based on Newton's equation of motion. In the present case, rigid
spherical particles are assumed. The diameter of those particles is in a range
between 1 and 20 micron. A gaseous fluid is assumed for the continuous phase.
Based on these assumptions the equation of motion comprises inertia, drag force
and Coulomb force if necessary. Other forces like Basset history or pressure
gradient can be neglected under the conditions mentioned above [2].
Essentially, the drag force is caused by the difference in actual particle and
actual fluid velocity. A sticky wall is assumed as boundary condition for the
particles. That means no bumping or reentrainment is considered. The influence
of Saffmann's lift force model published by McLaughlin [3] will be discussed.

In practical applications, the commonly
used approach to simulate the continuous phase is the k-e model. The solution of the fluid field is used as
input for the Lagrangian approach for the disperse phase discussed above. The fluid
flow is based on the Reynolds-Averaged-Navier-Stokes equations and results in time
averaged values for the fluid velocity and some statistical turbulence
quantities. The time averaged value within the boundary layer is calculated
with help of wall functions. The actual fluid velocity is the sum of the time
averaged value and the fluctuating part. However, essentially for the turbulent
deposition of particles is the fluctuating part which is calculated with help
of the turbulence quantities. Those quantities are modelled based on the values
of k and e [2]. The wall functions for the boundary
layer do not support turbulence quantities. This lack is commonly overcome by a
linear interpolation within the last element of the numerical mesh. This
interpolation results in over-estimated fluctuating velocity normal to the wall,
which intern results in too high deposition rates.

An extended model is implemented in a code
developed in our group. It is based on a model for the turbulence quantities,
which has been published by Kallio and Reeks [4]. The equation for the
fluctuating velocity is based on the dimensionless wall distance. A similar
approach has been published by Matida et al. [5]. Their model shows similar
results and has been derived from direct numerical simulation (DNS). Finally,
the code uses time averaged values simulated by a conventional solver (CFX 10
by Ansys) as well as statistical turbulence quantities k and e within the core flow. The extended model is only
used within boundary layer. This will show that the combination of adequate
wall functions for the boundary layer and turbulence models for the core flow
field allows the simulation of complex flows.

The results compare the deposition rate
with the experimental results from literature. The results are obtained for
moderate Reynolds numbers Re = 9000 and higher ones Re=50000. The
reason for the choice is the availability of experimental results. The simulations
represent a simple pipe flow of size 1m in length and 1.27cm in diameter. The
results will show the very good agreement of our model especially for smaller
particles.  In contrast, the conventional approach is not able to reflect the
behaviour of small particles at all.

After the verification with experimental
results, the model is used to show the limits of practical applications when
such a detailed model is necessary. The first step is to check the particle
sizes of such a limit. Of course, the lower limit is given by the assumption to
neglect the Brownian motion. The next steps will map the limits given by
Reynolds number that means fluid characteristic. The influence of electrical
enhanced deposition will be compared to the turbulent deposition. This is
necessary in many practical applications, when electrical effects are used.

The first time results will be presented
of particle deposition in this small particle size range, which is based on
standard turbulence models for the continuous phase. The presentation will show
the lack of accuracy in common implementations. But the presented implementation
introduces a way to overcome these problems for many applications as addressed.

[1] B. Y. H. Liu, J. K. Agarwal, J. Aerosol Sci., 1974, 5, 145.

[2] H.-J.
Schmid, L. Vogel, Powder Technology, 2003, 135-136, 118.

[3] J. B. McLaughlin,
Phys. Fluids A, 1989, 1 (7), 1211.

[4] M. W. Reeks, G. A. Kallio, Int. J. Multiphase Flow, 1989,
15 (3), 433.

[5] E. A. Matida, K. Nishino, K. Torii, Int. J. Heat
Fluid Flow, 2000, 21, 389.