Download Lift - Lorentz Center

Workshop on Environmental Dispersion Processes
Lorentz Center – University of Leiden
Influence of Gravity and Lift on
Particle Velocity Statistics and Deposition Rates
in Turbulent Upward/Downward Channel Flow
C. Marchioli§, M. Picciotto§ and Alfredo Soldati*
§ Dipartimento di Energetica e Macchine, Università di Udine
*Centro Interdipartimentale di Fluidodinamica e Idraulica &
Department of Fluid Mechanics, International Center for Mechanical Sciences, Udine
September, 18-27, 2006, Leiden, The Nederlands
Motivation
Why the need for a DNS database?
• Lack of complete and homogeneous source of data on particle
velocity statistics and on particle deposition rates (->)
• Validation and testing of theoretical deposition models
Free CFD database, kindly hosted
by Cineca supercomputing center
(Bologna, Italy).
Over than 1 Tbyte DNS fluiddynamics raw data for different
benchmark and test cases
available on line at:
http://cfd.cineca.it/cfd
CFD database
What’s on?
1. CFD raw data repository (12 DB, 1.5 Tb)
DNS test case: particle-laden
turbulent channel flow at low
Reynolds number
2. CFD Preprocessed data
repository (2 DB)
DNS database: influence of
gravity and lift on particle
velocity statistics and
deposition rates
http://cfd.cineca.it/cfd
Numerical Methodology (1)
Flow Field Calculation
•
•
•
•
Time-dependent 3D turbulent gas flow field with pseudo-spectral DNS
128x128x129 Fourier-Fourier modes (1D FFT) + Chebyschev coefficients
Shear Reynolds number: Ret=uth/n=150
Bulk Reynolds number: Reb=ubh/n=2100
Numerical Methodology (2)
Lagrangian Particle Tracking
Equation of
motion for
the (heavy)
particles
*
* Stokes Number: St=tp/tf
Flow Time Scale: tf=n/ut2
Numerical Methodology (3)
Lagrangian Particle Tracking
Kolmogorov scales:
length scale 1.6 < hk+ < 3.6 (hk,avg+ =2)
time scale
2.5 < tk+ < 13 (tk,avg+ =4)
Non-Dimensional Kolmogorov
Time Scale, th+,
vs Wall-Normal Coordinate, z+
St/tk+ ~ O(10)
dp+/hk+ ~ O(1) [In principle, it should be << 1!]
Numerical Methodology (4)
Lagrangian Particle Tracking
Further Relevant Simulation Details:
• Point-particle approach: local flow distortion is assumed negligible (Stokes
flow around the particle)
• One-way coupling: dilute flow condition is assumed (NB: the averaged mass
fraction for the largest particles is O(0.1), however two-way
coupling effects do not affect significantly particle statistics
for the current simulation parameters).
• Particle-wall collisions: fully elastic (particle position and velocity at impact
and time of impact are recorded for post-processing!)
• Fluid velocity interpolation: 6th-order Lagrangian polynomials
• Total tracking time: ΔT+= 1192 in wall time units i.e. ~ 9.5 times the nondimensional response time of the largest particles (St=125).
• Time span during which statistics have been collected: Δt+= 450 (from
t+=742 to t+=1192) i.e. 3.6 times the response time
of the largest particles (St=125)
• Statistically-developing condition for particle concentration
Part I. Influence of the Gravity Force
Flow Configurations
No Gravity (G0)
Downflow (Gd)
Upflow (Gu)
Part I. Influence of the Gravity Force
Particle Mean Streamwise Velocity
Downflow
No Gravity
Upflow
Part I. Influence of the Gravity Force
Particle Wall-Normal Velocity
Downflow
Upflow
No Gravity
Part I. Influence of the Gravity Force
Streamwise RMS of Particle Velocity
Downflow
Upflow
No Gravity
Part I. Influence of the Gravity Force
Wall-Normal RMS of Particle Velocity
Part I. Influence of the Gravity Force
Wall-Normal Particle Number Density Distribution (“small” St)
Part I. Influence of the Gravity Force
Wall-Normal Particle Number Density Distribution (“large” St)
Part I. Influence of the Gravity Force
Integral Particle Number Density in the Viscous Sublayer (z+<5)
Part I. Influence of the Gravity Force
Particle Deposition Rates: Definition of the Deposition Coefficient
Following Cousins & Hewitt (1968)
Mass flux of particles
at deposition surface
Mean bulk particle
concentration
Non-Dimensional
Deposition Coeff.
Part I. Influence of the Gravity Force
Particle Deposition Rates
Ref: Young and Leeming, J. Fluid Mech., 340, 129-159 (1997);
Marchioli et al., Int. J. Multiphase Flow, in Press (2006).
Part II. Influence of the Lift Force
Methodology: Lift Force Model
• Lift Coefficient
• Dimensionless Parameter
• References
Mc Laughlin, J. Fluid Mech., 224, 261-274 (1991);
Kurose and Komori, J. Fluid Mech., 384, 183-206 (1999).
Part II. Influence of the Lift Force
Particle Mean Streamwise Velocity (“small” St)
No Gravity
Downflow
Upflow
Part II. Influence of the Lift Force
Particle Mean Streamwise Velocity (“large” St)
No Gravity
Downflow
Upflow
With lift!
With lift!
With lift!
With lift!
With lift!
Part II. Influence of the Lift Force
Particle Wall-Normal Velocity (“small” St)
No Gravity
Downflow
Upflow
Part II. Influence of the Lift Force
Particle Wall-Normal Velocity (“large” St)
No Gravity
Downflow
Upflow
With lift!
With lift!
With lift!
With lift!
With lift!
With lift!
With lift!
With lift!
With lift!
Part II. Influence of the Lift Force
Wall-Normal Particle Number Density Distribution (“small” St)
No Gravity
Downflow
Upflow
Part II. Influence of the Lift Force
Wall-Normal Particle Number Density Distribution (“large” St)
No Gravity
Downflow
Upflow
With lift!
With lift!
With lift!
With lift!
With lift!
With lift!
With lift!
With lift!
With lift!
Part II. Influence of the Lift Force
Coupling between near-wall transfer mechanisms and lift force
Part II. Influence of the Lift Force
Particle Deposition Rates
No Gravity
Downflow
St
St
Upflow
St

J
k d   
C
Conclusions and
Future Developments
• We have quantified the effects of gravity and lift on particle
velocity statistics and deposition rates in channel flow.
• Gravity modifies particle statistics via the crossing-trajectory
effect, which decreases velocity correlations along the particle
trajectories as the particle Stokes number increases (St = 25
being the threshold value to discriminate between “small” and
“large” particles).
• Lift affects weakly the particles with St>25, whereas particles
with St < 25 will either increase or decrease their deposition
rate depending on the orientation of gravity with respect to the
mean flow.
• Gravity and lift seem to modify the particle statistics mostly
quantitatively: particle distribution is primarily a result of the
dynamic interaction between particles and near-wall turbulence.
• Improve the lift force model
• Include collisions