Particles turbulence interactions in boundary layers Challenging Turbulent Lagrangian Dynamics Particles turbulence interactions in boundary layers M. Picciotto, C. Marchioli and Alfredo Soldati* Centro Interdipartimentale di Fluidodinamica e Idraulica & Dipartimento di Energetica e Macchine, Università di Udine Department of Fluid Mechanics, International Center for Mechanical Sciences, Udine 1-4 Settembre, 2005, Castel Gandolfo, Roma (Italy)

Motivation: Sedimentation, Deposition Example 1 Motivation: Sedimentation, Deposition Example 1. LES of Droplets over Waves Air Flow 2m/s, droplets 40 mm Droplets follow LARGE scale structures and small turulence scales; Reentrainment and deposition mechanisms observed

Motivation: Jet Dispersion, Reaction Engineering Example 2. LES of Particles in a diffuser Air Flow 8m/s, particles 20 mm Green isosurface: vorticity Blue isosurface: Q < u > h Re = = 16000 n m 50 20, 10, d =

Premise: Phenomenon known as Turbophoresis Observation: Due to inertia  local particle accumulation in low vorticity, high strain regions (Caporaloni et al., 1975 JAtmosSci Reeks, 1983, JAeroSci, Wang & Maxey, 1993, JFM, Rouson & Eaton, 2001, JFM, ... ); Consequences: 1. Particles do not sample the vortical flow field homogeneously; 2. The flow field (statistics) perceived by inertial particles may be different from the fluid flow field. 3. Directed (non-random) particles motions leading to preferential Macro-Scale concentration are generated. 4. Current models are not fit for accurate design! Objects: 1. Understanding relationships between flow scales dynamics and particles to control instantaneous concentration field. 2. Examine the influence of Force models. 3. Examine the influence of 1-way, 2-way coupling. 4. Derive Subgrid models for Design Optimization

Current Work Computational Methodology: DNS and Lagrangiang Tracking Time-dependent 3D turbulent flow field with Direct Numerical Simulation (Pseudo-Spectral for Channel Flow; FD for Pipe-Flow); Accurate to smallest significant scales 2. Lagrangian Tracking (O[105] particles/bubbles); Particles Subject to Drag (and gravity) One-Way coupling/two-way coupling Particle momentum time derivative (Inertia) Sum of external forces acting on the particle

(Cfr. Exp. by Young & Hanratty, AIChEJ, 1993) Wall Segregation in Pipe flow 1. Microscale phenomena induce Macroscale Effects concentration (Cfr. Exp. by Young & Hanratty, AIChEJ, 1993) Particle Relaxation Time tp = dp2 rp/18 m tp+ = 2.8

Wall Segregation in Channel flow 2 Wall Segregation in Channel flow 2. Microscale phenomena induce Macroscale Effects Observation – In Channel flow (like in pipe flow) particles accumulate at the wall at different rates depending on their inertia (forces:drag and inertia) Number Concentration tp+ tp+ = 25 tp+ = 5 tp+ = 1 tp+ = 0.2 Accumulation at the wall is turbulence induced and non uniform. Phenomenon will persist from a qualitative viewpoint until gravity will dominate (large particles)

tp+ = 25 Front View Top View Red: Vel > Blue: Vel < Turbulent Boundary Layer: From microscale phenomena to Macroscale Effects Front View Look Closer: Particle in the Channel, once at the wall, segregate into low-speed regions tp+ = 25 Top View Red: Vel > Blue: Vel < Mean U

Observation – Particle Transfer and segregation is controlled by streamwise vortical structures Red: high Streamwise vel. Purple Particles: To the wall Blue: low Streamwise vel. Blue Particles: off the wall

\rowcolor{panelbackground} $\tau_p^+(= St)$ & $d_p^+$ & $\rho_p^+$ & $v_{sett}^+$ & $n_p$ & $\Phi_V$ & $\Phi_M$ & Coupling & $\Delta T_p^+$ \\\dash \rowcolor{panelbackground} 0.2 & 0.068 & 769.23 & $18.84 \cdot 10^{-3}$ & $10^5$ & $3.05 \cdot 10^{-8}$ & $2.35 \cdot 10^{-5}$ & 1w~~~ & 1080 \\ 1 & 0.153 & 769.23 & $9.42 \cdot 10^{-2}$ & $10^5$ & $3.52 \cdot 10^{-7}$ & $2.71 \cdot 10^{-4}$ & 1w/2w & 1080 \\ 5 & 0.342 & 769.23 & $4.71 \cdot 10^{-1}$ & $10^5$ & $3.93 \cdot 10^{-6}$ & $3.02 \cdot 10^{-3}$ & 1w/2w & 1080 \\ 25 & 0.765 & 769.23 & 2.355 & $10^5$ & $4.40 \cdot 10^{-5}$ & $3.38 \cdot 10^{-2}$ & 1w/2w & 1080 \\ Local high concentration. Limitations of the 1-way coupling model (Fm=<10-3; FV=<10-3) Questions: i) Where do particles go? ii) Can we control/modify their distribution? iii) how much are these behavior influenced by forces/couplings/collisions? Database for the following particles with i) 1w/2w; ii) lift/no lift; iii) Gravity (upward, downard, horizontal) tp + (= St) dp+ rp vsett + np FV FM 1.0 0.153 769.23 9.42 10-2 10-5 3.52 10-7 3.02 10-3 5.0 0.342 769.23 4.71 10-1 10-5 3.93 10-6 3.02 10-3 25 0.765 769.23 2.35 10-5 4.40 10-5 3.38 10-2 125 1.710 769.23 11.775 10^5 4.92 10-4 3.78 10-2

Velocity Gradient Tensor = Rate-of-Rotation + Rate-of-Strain First: Characterize Particles accumulation regions. Particle and Flow Topology.1. Velocity Gradient Tensor = Rate-of-Rotation + Rate-of-Strain Invariants

Q I, QII = Vortical Flow Regions Q III, QIV = Convergence Regions Particles and Flow Topology.2. Stable focus- stretching Unstable focus- compressing Stable node- saddle-saddle Unstable node- D > 0 D < 0 D = 0 Q II Q I Rotation Rate > Strain Rate Q I, QII = Vortical Flow Regions Q III Q IV Q III, QIV = Convergence Regions Part ll

Particles and Flow Topology.3. Wall region (z+ < 5) tp+ = 5 tp+ = 1 tp+ = 25 tp+ = 125 More than 70 % of particles in the convergence regions (III and IV)... Hard to see the regions in a 3D space...

Particles and Flow Topology.4. At the wall the velocity gradient tensor degenerates: only du’/dz and dv’/dz are non zero (z+=0). tp+ = 5 tp+ = 1 Mean Flow u, x v, y w, z du’/dz>0 du’/dz<0 dv’/dz<0 dv’/dz>0 tp+ = 25 tp+ = 125 Average Statistics

A possibility to control wall particle distribution is to control instantaneous wall shear stress. Behavior of the spanwise strain rate component along the line A-A STA: Short Term Accumulation LTA: Long Term Accumulation Instantaneous St=25 particle distribution in the viscous sublayer, z+5. The mean flow is directed top down.

is there an optimum for particle non-uniform distribution is there an optimum for particle non-uniform distribution? To characterize their non-uniformity... Regular distribution Random distribution Clustered Distribution D = (s-sp)/l, with l = average number of particle per cell s = standard deviation of the PDF

Kd = Deposition coefficient Particles are non-uniformly distributed and they have an optimum. Wall region (z+ < 5) The optimum is for St= 25, which scales with the time scale of the large-scale structures of the TBL. It is not surprising thus that also the deposition velocity has a maximum... Kd = Deposition coefficient

Influence of Two-Way Coupling (PSIC): The fluid Feels particle Momentum Exchange

Influence of 2-way coupling (at this low concentration) Particle concentration in the wall normal direction...little effect St = 1 St = 5 St = 25

Influence of gravity (St = 25 and 125) Gravity has an influence (of course)...quantitative

and Future Developments Conclusions and Future Developments Can we control wall particle distribution by wall manipulation? can we derive simpler models for engineering significant variables (deposition rates) for such non-uniform distribution? Can we derive subgrid models for higher Reynolds number, complex geometry simulations? Up to which local concentration values 1-way or 2-way coupling results are valid before energy transfer by collisions enter the picture?

Status of Experimental Data on Particle Wall Deposition.... Uncertainty -> Orders of magnitude... Encouraging...