Martin-Lther-Universität Halle-Wittenberg 13 th Int. onf. Mltihase low in Indstrial Plants, MIP014 Setember 17-19, 014, Sestri-Levante, Italy MODELLING AND OMPUTATION O IRREGULAR NON- SPHERIAL PARTILES TRANSPORT IN ONINED TURBULENT LOW Santiago Laín b, Martin Sommerfeld a,b, Brian Qintero b and Zeeshan Qadir a a Martin-Lther-Universität Halle-Wittenberg, Zentrm für Ingenierwissenschaften,, 06099 Halle (Saale), Germany. www-mvt.iw.ni-halle.de b Universidad Atonoma de Occidente (UAO), lid Mechanics Research Gro, ali, olombia.
1. Motivation Martin-Lther-Universität Halle-Wittenberg Otline. Aerodynamic coefficients correlations 3. Wall collision arameters correlations 4. Nmerical aroach Motion eqations Stochastic modelling aroach Elementary rocess Drolast articles volme eqivalent mean diameter 40μm 5. omarison with exeriments 6. Smmary and onclsions Qartz sand volme eqivalent mean diameter 185µm
Martin-Lther-Universität Halle-Wittenberg Nmerical redictions of disersed article-laden flows sally assme sherical articles, bt in ractice articles are often non-sherical. Modelling the behavior of non-sherical articles is essential for a reliable nmerical calclation of (confined) article-laden rocesses. Lagrangian treatment of non-sherical articles Reglarly shaed non-sherical articles: Additionally solve for the article orientation and torqe Reqires information on the resistance coefficients in deendence of article orientation (e.g. Hölzer and Sommerfeld 009) Irreglar non-sherical articles: Statistical generation of the forces acting on the articles Reqires information on the PD`s of the resistance coefficients for random orientation of the articles in the flow (LBM) Re = 90 c D 1.5 Re Pa =90 1.4 1.3 1. 1.1 1.0 0 10 0 30 40 50 60 70 80 90 [degree] Additionally, the wall collision rocess is treated in a stochastic manner, based on statistical measrements of the restittion and friction coefficients.
Martin-Lther-Universität Halle-Wittenberg Resistance oefficients Determination by Lattice Boltzmann Method O U T L E T Symmetry Symmetry I N L E T P D D A U 0 P L L A U 0 0 P P T D A U T Drag Lift Pitching Torqe d l T (D VES,hll = 100 m, = 0.87) Simlations for 4 different articles = 0.87; for each Re nmber the article was randomly rotated to 71 ositions; derivation of PD`s of the coefficients omtational Domain
mean resistance coefficients [ - ] rms resistance coefficients [ - ] Martin-Lther-Universität Halle-Wittenberg orrelations Resistance oefficients D D 10 L M 1 L M 1 0.1 0.1 1 10 100 Re [ - ] x 4 Re B 1 ARe 1 Re 00 1 D / Re 1 10 100 Re [ - ] Parameter A B D D 0.56050 0.75899 0.64044 7.45770 s D -0.99615-0.005536 0.1343 0.111044 L -0.96964-0.031363 0.374803 51.7880 s L -0.966977-0.00794 0.114544 3.1660 T -0.973699-0.011175 0.116584 3.05970 s T -0.98897-0.004679 0.058604 3.158780
Martin-Lther-Universität Halle-Wittenberg Wall collision irreglar non-sherical articles (imaging exeriments) Side view To view
Normal Restittion oefficient [ - ] riction oefficient [ - ] 1.0 Martin-Lther-Universität Halle-Wittenberg Wall collision coefficients (exeriments) 1.4 0.8 0.6 1. 1.0 0.8 measrements S&H 1999 model assmtion 0.4 0. measrements mean model assmtion 0.0 0 10 0 30 40 50 60 70 80 90 Imact Angle [Degree] 0.6 0.4 0. 0.0 0 10 0 30 40 50 Imact Angle [Degree] 1 0.0 5 A e ( ) ( ) 1 B n 0.5 5 A = 0.5048, B = 3.8069, = 0.3916 s ( ) 0.07
Martin-Lther-Universität Halle-Wittenberg Nmerical Method: Eler Lagrange aroach lid Phase: Reynolds-averaged Navier-Stokes eqations in connection with the Reynolds Stress trblence model. General form of the 3D conservation eqations:
Martin-Lther-Universität Halle-Wittenberg Nmerical Method: Eler Lagrange aroach Particle Phase: simltaneos, time-deendent tracking of a large nmber of articles i i dt dx Li Di i i g m dt d m 1 i i T dt d I D D c m D ) ( 4 3 n D L L ˆ 4 1 ˆ' 8 1 3 n D T T P t ˆ 0 ˆ ˆ n t res res t ˆ' 0 ˆ' ' ˆ n t L D res
onts [ - ] Martin-Lther-Universität Halle-Wittenberg Stochastic oefficients Determination irst aroach: Gassian random rocess 80 Instantaneos flow coefficients, D, L, T 70 60 50 Re = 100 x (Re, t) x (Re ) s x (Re ) N(0,1) 40 30 0 10 Instantaneos restittion coefficient, e n : 0 0.8 1.0 1. 1.4 1.6 1.8 D [ - ] e n (, t) e ( ) s ( ) N(0,1) Instantaneos friction coefficient, : N (0, 1): standard gassian random rocess n (, t) ( ) s ( ) N(0,1) e n
Martin-Lther-Universität Halle-Wittenberg Particle-rogh wall collision momentm eqations + olomb s law of friction with modified coefficients = 1.0 Elementary rocesses 1 1 Inter-article collisions (Sommerfeld, 001) Based on the fictitios collision artner concet soltion of the imlse eqations olomb`s law of friction obliqe inelastic collision (Hard Shere Model) 1 L rel collision cylinder 1 Aroximation: inter-article collisions of isometric articles with high rotation rates are treated as sherical articles
Martin-Lther-Universität Halle-Wittenberg hannel flow laden with non-sherical articles (Kssin, 004) hannel length: 6000 mm hannel heigth: 35 mm Mean conveying velocity: 0 m/s Measring location: 5800 mm Qartz articles Eqivalent mean D = 185 m = 650 kg/m 3 Measred shericity = 0.8 Mass loading: 0.1
Normalised height [ - ] Martin-Lther-Universität Halle-Wittenberg hannel low Reslts (1) 1.0 0.8 0.6 0.4 0. Ex. articles Nm. L&S 007 Nm. non-sherical no coll. Nm. non-sherical coll. Nm. sherical coll. 0.0 0. 0.4 0.6 0.8 1.0 1. 1.4 1.6 Normalised Particle Nmber lx [ - ] There is not a large difference in the nmber flx rofiles for the varios cases.
Normalised height [ - ] Martin-Lther-Universität Halle-Wittenberg hannel low Reslts () 1.0 0.8 0.6 0.4 0. Ex. lid Ex. Particles Nm. lid Nm. L&S 007 Nm. non-sherical no coll. Nm. non-sherical coll. Nm. sherical coll. 0.0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Normalised Mean Velocity [ - ] or non-sherical articles comared to sherical ones the mean velocity near the bottom is lower.
Normalised Height [ - ] Martin-Lther-Universität Halle-Wittenberg hannel low Reslts (3) 1.0 0.8 0.6 0.4 0. Ex. lid Ex. Particles Nm. lid Nm. L&S 007 Nm. non-sherical no coll. Nm. non-sherical coll. Nm. sherical coll. 0.0 0.04 0.06 0.08 0.10 0.1 0.14 Normalised Streamwise rms [ - ] The stream-wise article velocity flctation is remarkably higher comared to sherical articles.
Normalised Height [ - ] Martin-Lther-Universität Halle-Wittenberg 1.0 hannel low Reslts (4) 0.8 0.6 0.4 0. Ex. lid Ex. Particles Nm. lid Nm. L&S 007 Nm. non-sherical no coll. Nm. non-sherical coll. Nm. sherical coll. 0.0 0.01 0.0 0.03 0.04 0.05 0.06 Normalised Vertical rms [ - ] The vertical article velocity flctation is remarkably lower than for sherical articles.
Martin-Lther-Universität Halle-Wittenberg Smmary and conclsions Stochastic models for flid dynamic resistance coefficients of nonsherical isometric articles have been constrcted from PD`s obtained with DNS-LBM simlations (Qadir & Sommerfeld, 013) Stochastic models for article-wall collision arameters (PD`s of normal restittion and friction coefficients) for non-sherical isometric articles have been constrcted from imaging exeriments (Saeed, 013) Pnematic conveying of qartz non-sherical isometric articles has been considered for validating the stochastic models. omarison with measrements of Kssin (004) Reasonable agreement fond for article mean and flctating velocities as well as for article nmber flx imroving revios reslts of Laín & Sommerfeld (007) Rotational and shear lift forces coefficients derived from DNS- LBM are exected to imrove the resent reslts
Martin-Lther-Universität Halle-Wittenberg Acknowledgement The financial sort of the resent stdies by the Detsche orschngs Gemeinschaft nder contract SO04/39-1 and Universidad Atónoma de Occidente throgh the joint roject Transort von nicht-shärischen Partikeln in trblenten Innenströmngen is grateflly acknowledged. Also, the sort of DAAD & olciencias throgh the German- olombian exchange mobility rogram is grateflly acknowledged.