1. A Survey of Turbulence in Pipe Flows with
Suspensions, Slurries, and Fluidized Beds
with Applications to
Tubular Metal-Air Fuel Cells
Denis Vasilescu
Illinois Institute of Technology
May 5th
2011

2. ● Suspensions are mixtures of a base fluid with
very fine particles, indistinguishable to the naked
eye, and low volume fractions. The laminar flow
profile is not significantly affected.
● Slurries are like suspensions, but the particles
may be coarser and/or have a higher volume
fraction. Slurry flows blunt the velocity profile
and can be non-Newtonian.
● Fluidized beds are like slurries, but the particles
do not inhabit the entire flow domain, rather they
collect at the bottom and slide along the wall.
Very complicated.
What am I talking about?

3. ● Grains, concrete mix, shale oil, and chemical
powders are transported via pipes and ducts
throughout product life. Minimizing hydraulic
losses can lead to substantial energy savings
● Unwanted particles in a flow can damage pipes
through various erosion mechanisms.
Maintenance and repair can be reduced by
mitigating particle erosion.
● For electric vehicles, metal-air fuel cells with tube
geometries may be able to use turbulence in
order to enhance power density, and thus car
performance, increasing competitiveness
Why does this matter?

4. ● Laminar Flow
-Particle Attrition
● Transition to Turbulence
-Matas Experiment
-Effect of Size and Volume Fraction
-Interpretation
● Turbulent Flow
- Kolmogorov scale dependencies
- Eskin numerical experiment for dissipation
- Mixing length as verification
Outline of Topics

5. Some typical concerns and their principle physics:
● Hydraulic loss
- Deposition: porous media or moving beds
● Wall erosion
- Fracture mechanics: surface free energy
● Particle attrition & chemical reaction rate
- Molecular diffusion: shrinking core model
- Convection: corrosion-erosion model
- Solid dynamics: Particle and wall collisions
Laminar Flow

6. Some typical concerns and their principle physics:
● Hydraulic loss
- Deposition: porous media or moving beds
● Wall erosion
- Fracture mechanics: surface free energy
● Particle attrition & chemical reaction rate
- Molecular diffusion: shrinking core model
- Convection: corrosion-erosion model
- Solid dynamics: Particle and wall collisions
Laminar Flow

7. ● The onset of intermittent turbulent behavior is
demarcated by a critical Reynolds number, which
is ~2,100 for pure pipe flows.
● The effect of particles on the transition is not as
well studied as their effect on fully turbulent
flows. Principle contributions from Matas et al @
IUSTI France and Vlasak et al @ ASCR
Transition

8. ● [Matas 2003] experimental set up:
Transition
● Identify onset
of transition
from pressure
fluctuations
● Measure
critical
Reynolds
number based
on flow rate

9. ● Measured p' using electronic manometers:
Transition
● Determine when
p' spectra gains
energy in nonzero
frequencies
● Critical Re taken
as midpoint
between laminar
Re and 'strongly
intermittent' Re

10. ● Same method in [Vlasak 2004]
Transition

11. ● Critical Re as function of size and vol. fraction:
Transition
● Smallest two
diameters
collapse on
same curve
● Largest two
diameters only
collapse for
very high
volume
fractions

12. ● Critical Re as function of size and vol. fraction:
Transition
● Smallest two
diameters
monotonically
increase,
delaying
transition
● Largest two
diameters dip for
very small
concentrations,
hastening
transition

13. ● Intuitive reasoning for delaying onset of
turbulence: particles increase the effective
viscosity of the fluid
μeffective
= μ (1 – φ / φm
)-1.82
where φm
is the maximum spherical packing factor,
0.68.
● Is this effective viscosity hypothesis true?
Scale the curve by viscosities to find out
Transition

14. ■ Critical Re plot scaled by μ /μeffective
Transition
● Smallest two
diameters now
return critical Re
back to ~2,100
● Largest two
diameters still
hasten transition,
effective viscosity
does not tell the
whole story

15. ● High volume fraction behavior expected;
asymptotically, the pipe becomes clogged with
particles, becoming a porous media flow which
increases friction forces.
● Low volume fraction behavior for particles of
large enough size may be tripping the transition
by providing just the right amplitude and wave
number disturbance.
● What differentiates small versus big diameter
behavior either related to D/d ratio or to d/lkol
Transition

16. ● The unifying idea in turbulence is the
Kolmogorov energy cascade. For particle flows,
the key to understanding their impact is to
understand what scales they interact with.
● As was seen in [Matas 2003], slurry behavior
changed when particle sizes approached the
order of Kolmogorov length scale. Was this a
coincidence or no?
● It was also seen that volume fraction changed the
effective viscosity of the slurry; the Kolmogorov
length scale is based on the effective viscosity
Turbulent Flow

17. ● [Eskin 2004] investigated the matter. First they
used an alternative model for effective viscosity:
νeffective
= νliquid
(ρliquid
/ρslurry
)(1+2.5 φ + 10 φ2
+ 0.0019 e20φ
)
● This model was then substituted into
lkol
= 4
√νeffective
3
/ε
● Note that [Eskin 2004] believed the effective
viscosity model to be applicable for all slurry
concentrations based on a Bagnold number
estimate.
Turbulent Flow

18. ■ Analytical Kolmogorov scale according to
volume fraction (sand, ε = 1)
Turbulent Flow
● Kol. length scale
increases with
volume fraction, and
exponentially for
high values.
● This is independent
of size, thus one can
envision situations
where the particles
are significantly
smaller than the Kol.
length scale

19. ● [Eskin 2004] uses [Schook and Roco 1991] model for one-
dimensional steady-state turbulent slurry flow:
where τvisc
= μslurry
du/dr and τturb
= d/dr [αslurry
u2
]
● Although this model has an analytic solution, [Eskin 2004]
solves it numerically to get other quantities and relations,
with the promise that the largest disagreement between
this numeric model's results and experiments cited in
[Schook and Roco 1991] was 15% among the pressure
gradients.
Turbulent Flow

20. ■ Energy Dissipation Contribution due to
Turbulence According to Slurry Volume Fraction
Turbulent Flow
● Increased
concentration reduces
turbulence's
contribution to energy
dissipation
● It was seen earlier that
increased volume
fraction enlarges the
Kol. length scale;
smallest eddies
transfer energy as
kinetic motion to
particles rather than as
heat!

21. ■ Mixing Length (Prandtl hypothesis for
Newtonian fluid) versus radial distance
Turbulent Flow
● Not shown: mixing
length was found to
be independent of
volume fraction
● Independence from
vol. fraction and
distribution of mixing
lengths validate that
the model is
capturing the
physics and the
previous graph can
be more or less
accepted

22. ● Particle concentration delays the onset of
transition in general, but for large sizes may
hasten it by tripping the flow with Goldilocks
perturbations
● When particles are at or below the Kolmogorov
length scale, they cannot produce meaningful
perturbations and only influence the effective
viscosity
● When particles are at or below the Kolmogorov
length scale, the smallest eddies no longer
occupy the space between particles and dissipate
heat, but the particles are swept in their motions
and transfer the dissipation into kinetic motion
Summary

23. Conclusion
Questions?

24. ● Matas, J.P. et al. “Influence of Particles on the
Transition to Turbulence in Pipe Flow”
Philosophical Transactions from the Royal
Society 361. 2003. pp 911-919.
● Vlasak, P. et al. “Laminar and Tyrbulent
Transition of Fine-Grained Slurries” Particulate
Science and technology 22: 189-200. 2004.
● Eskin, D. et al. “On a Turbulence Model for Slurry
Flow in Pipelines” Chemical Engineering Science
59 (2004) pp 557-565.
References