Particles in turbulence: the need for a multi-scale approach

Transcription

1 Particles in turbulence: the need for a multi-scale approach Jos Derksen Multi-Scale Physics Department Delft University of Technology The Netherlands jos@klft.tn.tudelft.nl

2 Motivation Outline solid particles in turbulent flows: relevance to crystallization two scales of modeling Small-scale simulations numerical issues particle-turbulence interaction collisions Euler/Lagrange modeling in stirred tanks impact of modeling assumptions (the quest for just-suspended) concentration profiles, slip velocities... collisions (particle-particle & particle-impeller) How to connect the scales?

3 Turbulent flow and crystalliation Highly turbulent, agitated slurry flow Re to 20 vol% solids Macro crystalliser 1-10 m flow < 10 m Micro crystals µm turbulence µm Collisions attrition agglomeration secondary nucleation

4 A two-scale approach Our goal prediction of collision frequencies and collision intensities in crystallizers LES of an entire tank containing point particles no resolution of the solidliquid interface DNS of the particulate flow periodic flow domain isotropic turbulence Comparison of the two approaches at the different scales (still to do)

5 DNS versus Euler/Lagrange An alternative: point particles with d p < Unfeasible in a stirred tank: DNS with full resolution of the liquid/solid interface Particle dynamics: forces from single-particle correlations (drag, lift,...) collisions simple two-way coupling limits the applicability to low φ V

6 Direct Numerical Simulation Turbulence: Fluctuating bodyforce Particles: lattice-boltzmann simulation fully resolved particles Particle interactions: Short-range interaction Particle collisions Results: Particle turbulence interaction Collision statistics few hundred particles in a periodic box

7 Forcing turbulence 10-2 single-phase k -5/3 E(k) 10-4 F(k) Re k

8 Settings for solid-liquid simulations Particle size in grid units: 8 Kolmogorov scale in grid units: 1.2 Vol % ρ p / ρ f Np

9 Particle-turbulence interaction k d =2π /d p 10 vol% 5vol% 2vol% k/kd 0vol%

10 Flow field cross section Velocity magnitude u/umax

11 Energy dissipation rate Flow field cross section ln(ε/p)

12 Short range interactions Multiple collisions primary collision secondary collisions t contact t release 0.01 PDF of time between contacts e-06 1e δt/t e

13 primary collisions: Short range interactions (2) exponential behavior of the PDF (Poisson-process) effect of number density effect of solids density pdf pdf vol % high 1e-06 1e e vol % low δt/t e δt/t e

14 Back to the stirred tank A starting point: Agitated liquid-solid flow just-suspended experiments: Zwietering (1958); Baldi et al. (1978) N js Issues: solid-liquid heat and mass transfer attrition (role of collisions) power consumption scale-up... d = s 0. 2 p µ ( g ρ) 0. 1 L ρl D m T T with s 15 for = = 3 C D (Rushton turbine in baffled tank) φ collisions and/or 2way coupling

15 Large-eddy simulation Rushton turbine in baffled tank T T = = 3 C D 2 ND Re = ν Smagorinsky SGS model (c S =0.1) Lattice-Boltzmann discretization v tip Re=10 5 average flow midway between baffles single realization midway between baffles

16 Discrete (solid) phase dynamics Equations of motion for the solid (spherical) particles dx p = v added mass p forces: gravity, drag, lift, stress gradients dt dvp 0 ( mp + ma ) = F C p D = +. Rep dt Rep dω particle rotation: Magnus force p I = Tp rotational slip velocities dt Particle-particle collisions: at most one collision per particle per time step (order M 2 process) Particle-impeller and particle wall collisions: fully elastic 687 ( ) missed collisions

17 Impressions

18 Single realizations d p =0.3 mm d p =0.47 mm same tank-averaged particle number concentration

19 Two physical cases Case 1 T=0.23 m (10 liter vessel) working fluid: water Re=10 5 N=16.5 rev/s glass spheres d p =0.3 mm; ρ p /ρ liq =2.5 φ V =0.95% N js =13 rev/s Case 2 T=0.23 m (10 liter vessel) working fluid: water Re= N=25 rev/s glass spheres d p =0.47 mm; ρ p /ρ liq =2.5 φ V =3.6% N js =17 rev/s

20 The quest for (just) suspended Case 1 (d p =0.3 mm; φ V =0.95%) vertical concentration profiles at 2r/T=0.45 closest packing of spheres: c cp /c av =78 ratio drag and lift force F F lift drag 0. 1 d 2 p ν ω e.g. if ω=10n: F lift 0.5F drag 3 z/d (1) gravity, drag, added mass (2) see (1) & lift forces, stress-gradient forces c/c av 3 z/d (3) see (1) & (2) & particle-particle collisions (4) see (1) & (2) & (3) & two-way coupling c/c av

21 phase-averaged concentration midway between baffles Solids concentrations c/c av d p =0.3 mm, φ V =0.95% d p =0.47 mm, φ V =3.6%

22 Solids concentration (2) 15 o d p =0.47 mm, φ V =3.6% 30 o 45 o 55 o c/c av

23 One- and two-way coupling 2z/W 1 phase-averaged turbulent kinetic energy in the impeller outstream 0-1 2r/D=1.2 1way 2way, 0.95% 2way, 3.6% 2r/D= k/v tip 2 1 way trailing vortex system 30 o 45 o 1 way 2 way, 3.6% 1 way 2 way, 3.6% 2 way, 3.6% k/v tip ω/2πn

24 Particle-particle collisions refer collision rates to Von Smulochowski: d p =0.3 mm, φ V =0.95% r coll,sm 4 = γ d 3 3 p M 2 γ = ε ν d p =0.47 mm, φ V =3.6% collision intensities d p =0.3 mm, φ V =0.95% 0 o proper collisions missed collisions proper collisions missed collisions 55 o d p =0.47 mm, φ V =3.6% 0 o r coll /r coll,sm 1 9 r coll /r coll,sm v rel2 /v tip 2 55 o

25 d p =0.3 mm, φ V =0.95% Particle-impeller collisions front surface of impeller blade collision frequency collision intensity probability density function (pdf) of particle-impeller collision velocities pdf (a.u.) d p =0.47 mm, φ V =3.6% d p =0.47 mm d p =0.3 mm r/r 0 r 0 =6c av V blade N/A blade v / rel v tip v rel / v tip

26 Slip velocities Re p = d p v p ν u Re s = d 2 p 1 ω p 2 ω ν d p =0.3 mm, φ V =0.95% d p =0.47 mm, φ V =3.6% Re p Re s Re p Re s

27 How to connect simulations at various scales?