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

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 *.

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

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  1. Workshop on Environmental Dispersion Processes Lorentz Center – University of Leiden Influence of Gravity and Lift onParticle Velocity Statistics and Deposition Ratesin 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

  2. 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 Free CFD database, kindly hosted by Cineca supercomputing center (Bologna, Italy). Over than 1 Tbyte DNS fluid-dynamics raw data for different benchmark and test cases available on line at: http://cfd.cineca.it/cfd

  3. CFD databaseWhat’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

  4. 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

  5. Numerical Methodology (2)Lagrangian Particle Tracking Equation of motion for the (heavy) particles * * Stokes Number: St=tp/tf Flow Time Scale: tf=n/ut2

  6. 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!]

  7. 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

  8. Part I. Influence of the Gravity ForceFlow Configurations No Gravity (G0) Downflow (Gd) Upflow (Gu)

  9. Part I. Influence of the Gravity ForceParticle Mean Streamwise Velocity Downflow No Gravity Upflow

  10. Part I. Influence of the Gravity ForceParticle Wall-Normal Velocity Downflow Upflow No Gravity

  11. Downflow Upflow No Gravity Part I. Influence of the Gravity ForceStreamwise RMS of Particle Velocity

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

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

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

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

  16. Part I. Influence of the Gravity ForceParticle 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.

  17. Part I. Influence of the Gravity ForceParticle Deposition Rates Ref: Young and Leeming, J. Fluid Mech., 340, 129-159 (1997); Marchioli et al., Int. J. Multiphase Flow, in Press (2006).

  18. Part II. Influence of the Lift ForceMethodology: 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).

  19. Part II. Influence of the Lift ForceParticle Mean Streamwise Velocity (“small” St) No Gravity Downflow Upflow

  20. Part II. Influence of the Lift ForceParticle Mean Streamwise Velocity (“large” St) No Gravity Downflow Upflow With lift! With lift! With lift! With lift! With lift!

  21. Part II. Influence of the Lift ForceParticle Wall-Normal Velocity (“small” St) No Gravity Downflow Upflow

  22. Part II. Influence of the Lift ForceParticle 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!

  23. Part II. Influence of the Lift ForceWall-Normal Particle Number Density Distribution (“small” St) No Gravity Downflow Upflow

  24. Part II. Influence of the Lift ForceWall-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!

  25. Part II. Influence of the Lift ForceCoupling between near-wall transfer mechanisms and lift force

  26. Part II. Influence of the Lift ForceParticle Deposition Rates No Gravity Downflow St St Upflow St

  27. 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

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