Abstracts - KTH Mechanics

62
On the translational and rotational motion of ellipsoidal
particles in a turbulent channel flow
P. H. M. Mortensen ∗ ,H.I.Andersson ∗ , J. J. J. Gillissen †
and B. J. Boersma †
The translational and rotational motion of ellipsoidal particles suspended in a turbulent
channel flow is being studied. The continuous fluid phase is solved by means
of direct numerical simulation and a Lagrangian description of the dispersed particle
phase is used to track the particle paths. In the particle translational equation of
motion, the force acting on the particles is the steady Stokes drag. The rotational
motion of the particles is achieved by solving the three Euler equations expressed
in a coordinate system fixed to and rotating with the particles’ mass center. The
axes of this system are along the ellipsoids’ principal directions of inertia. The complete
orientation of the particles is described by the three independent Euler angles,
but due to singularities for certain orientations, four dependent Euler parameters or
quaternions are used for the orientational description 1 2 .
In the present case, the behavior of small ellipsoidal particles with an aspect ratio of
10 and non-dimensional momentum response time τ + p
=0.18 is investigated. It is well
accepted that particles tend to accumulate in the viscous sublayer due to the action
of near-wall coherent structures 3 . Figure 1(a) verifies this trend for small-inertia ellipsoidal
particles where it is observed a peak in the instantaneous probability density
function of particle position close to the wall. Figure 1(b) shows the mean orientation
of the ellipsoids, i.e., the absolute values of the mean direction cosines of the particles’
semi-major axis to the fixed wall-normal axis. It is observed that the particles tend
to orient more towards the wall in the center of the channel. Close to the wall, the
particles are more aligned with the wall.
The effect of varying the momentum response time, and also the inclusion of the
hydrodynamic Saffman lift force, will be also be addressed in the presentation. The
outcome of these effects will be compared and analyzed.
∗ NTNU Energy and Process Engineering, 7491 Trondheim, Norway.
† TU Delft J.M. Burgers centre, 2628 Delft, The Netherlands
1 Goldstein, Classical Mechanics,2nd Ed., Addison-Wesley, Reading, Ma (1980).
2 Fan and Ahmadi, J. Aerosol Sci. 31, 1205 (1999).
3 Marchioli and Soldati, J. Fluid Mech. 468, 283 (2002).
PDF(z/h)
3
2
1
0.4
(a) (b)
0.3
0
0 0.1 0.2 0.3 0.4 0.5
z/h
mean z−orientation
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5
z/h
Figure 1: (a) Probability density function of particle position. (b) Mean direction
cosine of particle semi-major axis to channel wall-normal axis.