Simulation and verification of forces on particles in ultrasound agitated gases

Transcription

1 Simulation and verification of forces on particles in ultrasound agitated gases Claas Knoop, Udo Fritsching PiKo Workshop Dialogue: Experiment -Model Siegen 2012 Partikeln im Kontakt DFG SPP

2 characterization of resonant ultrasound-fields background and application of ultrasound in disperse systems - particles in us-fields - agglomerates in us-fields simulation of sound induced forces outline 2

3 project embedded in DFG-priority program PiKo Particles in Contact understand and describe particle contact d<100µm breakage/dispersion project-aim: investigation of dynamicparticle-particle-interactions in ultrasound agitated particle-systems motivation 3

4 Computational Fluid Dynamics (CFD): coupling representation of gaseous phase stress on particle/agglomerate Discrete Element Method (DEM): formation/deagglomerationof agglomerates in US particle contact mechanics (d prim <100µm) coupling coupling experimental investigations: static/dynamic agglomerate-strength agglomerate(-collective) behavior in ultrasonic fields etc. project introduction 4

5 SiO 2 -particles 2./4. step: scanning + image analysis Malvern G3 (x) 1. step: particle deposition glass-substrate T;φ =const. SiO 2 -particles (x) glass-substrate 3. step: ultrasound treatment numerical calculation of the sound field (x) 6

6 ρ* = n part; us treated n part;0

7 standing wave field - schematic 5

8 spatial discretization: λ/ x 100 time discretization: T/ t = 250 time t / µs position x / mm particle velocity ux / m/s acoustic pressure p / kpa pressure field field-parameters: f = 20 khz λ = 25.7 mm velocity field time t / µs position x / mm pressure-and velocity-field of resonant standing wave

9 f=20khz; Y=2 µm; u 0 =0,25 m/s pressure field of resonant standing wave 8

10 linear: f=20khz; Y=2 µm; u 0 =0,25 m/s; t=2 µs acoustic pressure p / kpa acoustic pressure p / kpa position x / mm non-linear: f=20khz; Y=80 µm; u 0 =10 m/s; t=2 µs particle velocity u x / m/s particle velocity u x / m/s position x / mm position x / mm position x / mm acoustic pressure/sound velocity curves from linear to non-linear 9

11 piezo-electric pressure sensor x max. acoustic pressure vs. elongation 10

12 d p =1mm λ/d p =25.7 (particles enlarged for visualization) acoustic pressure p / kpa 1mm particle velocity u x / m/s position x / mm position x / mm particle in acoustic standing wave field 11

13 F x (t 2 ) acoustic drag force F x / mn F x (t 1 ) λ/d p =25.7 t 2 = t / 2 T dimensionless time t* / - acoustic drag force on particle 12

14 Y = 20 µm Y = 60 µm acoustic drag force depending on particle position 13

15 F x : acoustic drag force F x : acoustic radiation force acoustic radiation force: simulation vs. analytic correlations 14

16 mesh castellated snapped x min =17.2 µm geometry n cells x refinement steps: n R =7 x x D=250 µm d prim =80 µm n prim =13 x refinement steps: n R =8 x x min =8.6 µm n cells numerical setup: agglomerate in resonant standing wave 17

17 f=20khz; Y=20 µm; u 0 =2,5 m/s; t=2 µs D p D ag agglomerate D p = D ag acoustic drag force: particle vs. agglomerate 18

18 y (4) x 3 7 magnitude of acoustic drag force on primary particles 19

19 y (4) x 3 7 x-component of acoustic drag force on primary particles 20

20 2D/3D-representation of ultrasound fields in gases derivation of sound induced forces on particles/agglomerates differentiation between dynamic und static forces validation of acoustic radiation force by analytic equations calculation of mechanical stresses on particulate structures in ultrasound fields by CFD summary 21

21 Backup

22 y (4) x 3 7 y-component of acoustic drag force on primary particles

23 z 9 (8) (4) 7 (12) x z-component of acoustic drag force on primary particles

24 soundfield: 2D-mesh: atmosphere - wavetransmissivebc f = 20 khz λ = 25.7 mm reflector inlet sonotrode inlet: u x = u 0 sin(2πf t) symmetry-axis spatial discretization: particle Geschw.-amplitude velocity u x / / m/s m/s 1,5 1,4 1,3 1,2 1,1 1 0, ,8 1,0E+03 1,0E+04 1,0E+05 1,0E+06 time discretization: f 2 f simulation Simulation 2f f Schall sound C u t = x <1 number Zellanzahl of cells / - n / - λ/ x 100 Nyquist-criterion Courant-number T/ t = 250 numerical setup: resonant standing wave field 7

25 sound field: calculation based on continuum assumption Navier-Stokes-equation (compressible): mass balance: ρ = ( ρ v) t ρ v =0 momentum balance: = ( ρ vv) τ p + ρ g t energy balance: t 1 2 ρ v 2 + ρu = 1 2 ρv 2 + ρu v q& ( pv) ( [ τ v]) + ρ( v g) solving compressible N-S-equations non-linear effects in sound field considered Finite-Volume-discretization(OpenFOAM rhopisofoam) gravitation neglected numerical calculation of the sound field 6