September, 18-27, 2006, Leiden, The Nederlands Influence of Gravity and Lift on Particle Velocity Statistics and Deposition Rates in 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. Marchioli §, M. Picciotto § and Alfredo Soldati * Workshop on Environmental Dispersion Processes Lorentz Center – University of Leiden

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 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 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

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  =u  h/=150 Bulk Reynolds number: Re b =u b h/=2100

Numerical Methodology (2) Lagrangian Particle Tracking Equation of motion for the (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) d p + / 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 Force Flow Configurations No Gravity (G 0 ) Downflow (G d ) Upflow (G u )

Part I. Influence of the Gravity Force Particle Mean Streamwise Velocity Downflow Upflow No Gravity

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)

Following Cousins & Hewitt (1968) Non-Dimensional Deposition Coeff. Part I. Influence of the Gravity Force Particle Deposition Rates: Definition of the Deposition Coefficient Mean bulk particle concentration Mass flux of particles at deposition surface

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

Part II. Influence of the Lift Force Methodology: Lift Force Model Dimensionless Parameter Lift Coefficient References Mc Laughlin, J. Fluid Mech., 224, (1991); Kurose and Komori, J. Fluid Mech., 384, (1999).

Part II. Influence of the Lift Force Particle Mean Streamwise Velocity (“small” St) DownflowNo GravityUpflow

Part II. Influence of the Lift Force Particle Mean Streamwise Velocity (“large” St) DownflowNo GravityUpflow With lift!

Part II. Influence of the Lift Force Particle Wall-Normal Velocity (“small” St) DownflowNo GravityUpflow

Part II. Influence of the Lift Force Particle Wall-Normal Velocity (“large” St) DownflowNo GravityUpflow With lift!

Part II. Influence of the Lift Force Wall-Normal Particle Number Density Distribution (“small” St) DownflowNo GravityUpflow

Part II. Influence of the Lift Force Wall-Normal Particle Number Density Distribution (“large” St) DownflowNo GravityUpflow 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 St Downflow St Upflow St

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