Mechanisms of Particle Dispersion in a Turbulent, Square Duct Flow

1
Mechanisms of Particle Dispersion in a Turbulent,
Square Duct Flow
SPEME Faculty Of Engineering

• Jun YAO
• School of Process, Environmental and Materials
  Engineering, University of Leeds

KNOO Annual Meeting 2008, University of
Manchester, July 17-18
2
Work Introduction and Objectives

• Nuclear waste stored as solid-liquid sludge
• Waste processing and transportation in pipes,
  ducts, channels
• Particles dispersion, deposition, re-suspension
• Particle beds resulting in blockages to pipes and
  equipment
• An understanding of how these flows behave
  during transportation is of clear benefit to more
  cost effective process design, continued
  operation and accelerated clean-up

3
Methodology - LES

• Method The model for the SGS stress used in the
  present work Germano et al. (1991) Piomelli
  and Liu (1995) di Mare and Jones (2003).
• Speciality
• Represent the SGS stresses as the product of a
  SGS viscosity and the resolved part of the strain
  tensor
• Allow different values of the Smagorinsky
  constant at different filter levels.
• Test-filtering was performed in all space
  directions, with no averaging of the computed
  model parameter field.
• Computation
• Use the computer program BOFFIN (1991).
• Implement an implicit finite-volume
  incompressible flow solver using a co-located
  variable storage arrangement.
• Fourth-order pressure smoothing, based on the
  method proposed by Rhie and Chow (1983), is
  applied to prevent spurious oscillations in the
  pressure field.
• Time advancement is performed via an implicit
  Gear method for all transport terms and the
  overall procedure is second-order accurate in
  both space and time. The time step is chosen by
  requiring that the maximum Courant number lies
  between 0.1 and 0.3, with this requirement
  enforced for reasons of accuracy (1994).

Germano, M. et al. 1991, Phys. Fluids A 3 1760-
Piomelli, U. and Liu, J., 1995, Phys. Fluids
7, 839- di Mare, L., and Jones, W. P., 2003,
Int J Heat Fluid Fl 24, 606-615 Jones, W. P.,
1991, BOFFIN, Dept.Mech.Eng., Imperial College of
Science, Technology and Medicine. Rhie, C. M.
and Chow, W. L., 1983, AIAA J 21, 1525-1532.
Choi, H. and Moin, P., 1994, J Comput Phys 113,
1-.
4
Methodology Lagrangian Particle Tracking

• Prediction of the solid phase used a Lagrangian
  particle tracking approach (Fan et al. 2002 Yao
  et al, 2003) in which the particles are followed
  along their trajectories through the flow field.
• where Vp is the particle velocity, ?p particle
  density, dp particle diameter, ? fluid density, ?
  flow vorticity and g gravity. CD is the Stokes
  coefficient for drag, with
  , where Rep is the particle
  Reynolds number,
• To simplify the analysis, the following
  assumptions were made
• the multi-phase flow is dilute and the
  interactions between particles are neglected
• all particles are rigid spheres with the same
  diameter and density
• particle-wall collisions are elastic
• within the model a particle is assumed to
  interact with a turbulent eddy over a certain
  period of time, which is the lesser of the eddy
  lifetime and the transition time.
• A fourth-order Runge-Kutta scheme with adaptive
  step length was used to solve the equation of
  motion, given initial particle locations and
  velocity.

Fan, J. R. et al. 2002, AIChE J 48, 1401-1412
Yao, J. et al. 2003, Prog Nat Sci 13, 379-384.
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Working Parameter

• Fluid phase
• Fluid density (kg/m3) 1000
• Reynold number (Reb)
• 250000
• Grids 66,66,131
• Particle phase
• Particle diameter (µm)
• 5, 10, 50, 100, 500, 1000
• Material density (kg/m3) 2500
• Periodical conditions were applied for both phases

Schematic of the duct geometry and the
coordinate system
6
Mean Flow Field - Primary Flow Development
Comparison of predictions with data for
streamwise mean velocity along lower wall
bisector for (left) 2z/h 8, 16, 24, 40 and 84
(bottom to top), and (right) x/h 0.01, 0.02,
0.03, 0.05, 0.1, 0.2, 0.3 and 0.5 (bottom to
top).
Gessner, F. B. and Emery, A. F. 1981, J Fluid
Engin.103, 445-455 Gessner, F. B. et al. 1979,
Turbulent Shear Flows I, Springer-Verlag, New
York, 119-136
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Flow Field - Secondary Flow
An instantaneous flow field at the zLz/2 plane
is plotted in the Figure. This illustrates that
the instantaneous flow field can be significantly
different from and stronger than the averaged
field. It presents an example of typical
turbulence structures in this flow which are
responsible for the interactions between
ejections from both walls.
Velocity vectors showing secondary flow and
contours of streamwise mean velocity across duct
for Reb 250000. It predicts the existence of
secondary flows in the corners of the duct, which
constitute eight vortices of very weak streamwise
vorticity in the duct cross section, symmetric
about the duct diagonals.
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Particle Transportation
500µm
5 µm
Fairweather M and Yao J. 2008, AIChE J
9
Particle Dispersion Statistics transverse
direction
5 µm
10µm
50 µm
x
100µm
500µm
1000µm
Instantaneous distribution of particle at
transverse direction (t 13,954).
up
Fairweather M and Yao J. 2008, AIChE J
10
Particle Dispersion Statistics spanwise
direction
1000µm
500µm
100µm
vp
1000µm
500µm
100µm
Instantaneous distribution of particle at
spanwise direction top t 13,954 below t
200,000.
y
Fairweather M and Yao J. 2008, AIChE J
11
Particle Accumulation
Accumulation of 1000 µm particles at the corners
of the duct floor (t 37,211).
Fairweather M and Yao J. 2008, AIChE J
12
Particle Dispersion in the Wall Region
5µm
10µm
50µm
100µm
Particle distribution in the wall region on a
horizontal plane at x lt 30 from the duct floor.
Contours are of the streamwise fluctuating
velocity w (dark for w lt 0, light for w gt 0).
500µm
1000µm
Fairweather M and Yao J. 2008, AIChE J
13
Particle resuspension transverse direction
- -
Re10320 5, 10, 50, 100, 500 µm ? ?
? ? - ? -
Re36000 5, 10, 50, 100, 500 µm ? ?
? ? - ? -
Re83000 5, 10, 50, 100, 500 µm ? ?
? ? - ? -
Re250000 5, 10, 50, 100, 500 µm
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Mechanism
Mean relative slip velocity between particle and
fluid (Re250000, t 297,686).


Comparison of effect of main forces (gravity,
buoyancy and drag) on particles (Re250000, t
297,686).
Fairweather M and Yao J. 2008, AIChE J
15
Conclusions

• The secondary flow dominates small particle
  behaviour, causing such particles to be well
  distributed throughout the flow. The gravity
  effect is found to have little effect on their
  behaviour.
• Gravity promotes the deposition of large
  particles on the duct floor. For the largest
  particles, the secondary flows contribute to
  particle concentration in corners on the duct
  floor.
• Close to the floor of the duct, the particle
  number density distribution increases with
  particle size, with a high concentration of large
  particles associated with flow velocities lower
  than the mean, whilst small particles distribute
  evenly throughout the flow.

.
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Acknowledgement

• Professor Michael Fairweather
• Professor Simon Biggs
• Dr. Jim Young
• This work was carried out as part of the TSEC
  programme KNOO and as such we are grateful to the
  EPSRC for funding under grant EP/C549465/1.
• Thanks a lot for your attention and welcome
  questions

17
Particle Transportation
500µm
5 µm
Fairweather M and Yao J. 2008, AIChE J