September, 18-27, 2006, Leiden, The Nederlands

Influence of Gravity and Lift onInfluence of Gravity and Lift on

Particle Velocity Statistics and Deposition RatesParticle Velocity Statistics and Deposition Rates

in Turbulent Upward/Downward Channel Flowin Turbulent Upward/Downward Channel Flow

§§ Dipartimento di Energetica e Macchine, Università di Udine

*Centro Interdipartimentale di Fluidodinamica e Idraulica &

Department of Fluid Mechanics, International Center for Mechanical Sciences, Udine

C. MarchioliC. Marchioli§§, M. Picciotto, M. Picciotto§§ and Alfredo Soldati and Alfredo Soldati**

Workshop on Environmental Dispersion Processes

Lorentz Center – University of Leiden

MotivationWhy 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

http://cfd.cineca.it/cfd

Over than 1 Tbyte DNS fluid-dynamics raw data for different benchmark and test cases available on line at:

Free CFD database, kindly hosted by Cineca supercomputing center (Bologna, Italy).

CFD databaseWhat’s on?

1. CFD raw data repository (12 DB, 1.5 Tb) DNS test case: particle-ladenturbulent channel flow at lowReynolds number

2. CFD Preprocessed data repository (2 DB)

DNS database: influence ofgravity and lift on particlevelocity statistics anddeposition 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: Re=uh/=150

• Bulk Reynolds number: Reb=ubh/=2100

Numerical Methodology (2)Lagrangian Particle Tracking

Equation ofmotion forthe (heavy)particles

* Stokes Number: St=p/f Flow Time Scale: f=/u

*

Numerical Methodology (3)Lagrangian Particle Tracking

Non-Dimensional Kolmogorov Time Scale,

+,vs Wall-Normal Coordinate, z+

Kolmogorov scales:

length scale 1.6 < k+ < 3.6 (k,avg

+ =2)

time scale 2.5 < k+ < 13 (k,avg

+ =4)

dp+/k

+ ~ O(1) [In principle, it should be << 1!]St/k

+ ~ O(10)

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 non- dimensional 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 ForceFlow Configurations

No Gravity (G0) Downflow (Gd) Upflow (Gu)

Part I. Influence of the Gravity ForceParticle Mean Streamwise Velocity

Downflow

Upflow

No Gravity

Part I. Influence of the Gravity ForceParticle Wall-Normal Velocity

Downflow

Upflow

No Gravity

Part I. Influence of the Gravity ForceStreamwise RMS of Particle Velocity

Downflow

Upflow No Gravity

Part I. Influence of the Gravity ForceWall-Normal RMS of Particle Velocity

Part I. Influence of the Gravity ForceWall-Normal Particle Number Density Distribution (“small” St)

Part I. Influence of the Gravity ForceWall-Normal Particle Number Density Distribution (“large” St)

Part I. Influence of the Gravity ForceIntegral Particle Number Density in the Viscous Sublayer (z+<5)

Following Cousins & Hewitt (1968)

Non-DimensionalDeposition Coeff.

Part I. Influence of the Gravity ForceParticle Deposition Rates: Definition of the Deposition Coefficient

Mean bulk particleconcentration

Mass flux of particlesat deposition surface

Ref: Young and Leeming, J. Fluid Mech., 340, 129-159 (1997); Marchioli et al., Int. J. Multiphase Flow, in Press (2006).

Part I. Influence of the Gravity ForceParticle Deposition Rates

Part II. Influence of the Lift ForceMethodology: Lift Force Model

• Dimensionless Parameter

• Lift Coefficient

• 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 ForceParticle Mean Streamwise Velocity (“small” St)

DownflowNo Gravity Upflow

Part II. Influence of the Lift ForceParticle Mean Streamwise Velocity (“large” St)

DownflowNo Gravity Upflow

With lift!

With lift! With lift!

With lift!

With lift!

Part II. Influence of the Lift ForceParticle Wall-Normal Velocity (“small” St)

DownflowNo Gravity Upflow

Part II. Influence of the Lift ForceParticle Wall-Normal Velocity (“large” St)

DownflowNo Gravity 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 ForceWall-Normal Particle Number Density Distribution (“small” St)

DownflowNo Gravity Upflow

Part II. Influence of the Lift ForceWall-Normal Particle Number Density Distribution (“large” St)

DownflowNo Gravity 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 ForceCoupling between near-wall transfer mechanisms and lift force

Part II. Influence of the Lift ForceParticle Deposition Rates

No Gravity

St

Downflow

St

Upflow

St

C

Jkd

Conclusions andFuture 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