Adaptive time stepping for explicit euler implementation of spherical and non-spherical particle speed up

G Boiger, M Mataln, W Brandstätter

Abstract


Numerical implementation schemes of drag force effects on Lagrangianparticles can lead to instabilities or inefficiencies if static particle timestepping is used. Despite well known disadvantages, the programmingstructure of the underlying, C++ based, Lagrangian particle solver led to thechoice of an explicit EULER, temporal discretization scheme. To optimizethe functionality of the EULER scheme, this paper proposes a method ofadaptive time stepping, which adjusts the particle sub time step to the needof the individual particle. A user definable adjustment between numericalstability and calculation efficiency is sought and a simple time stepping ruleis presented. Furthermore a method to quantify numerical instability isdevised and the importance of the characteristic particle relaxation time asnumerical parameter is underlined. All derivations are being conducted for(non-)spherical particles and finally for a generalized drag forceimplementation. Important differences in spherical and non-sphericalparticle behaviour are pointed out.

Full Text:

PDF

References


M.Mataln, G.Boiger, W.Brandstätter, B.Gschaider, (2008). Simulation of Particle Filtration Processes in Deformable Media, Part 1: Fluid-Structure Interaction, ICE Stroemungsforschung GmbH., Montanuniversitaet Leoben. Int.Journal of Multiphysics, Vol.2,( No.2), July 2008 , pp. 179-189(11);
Link

G.Boiger, M.Mataln, W.Brandstätter, B.Gschaider, (2008). Simulation of Particle Filtration Processes in Deformable Media, Part 2: Large Particle Modelling, ICE Stroemungsforschung GmbH., Montanuniversitaet Leoben. Int.Journal of Multiphysics, Vol.2,(No.2), July 2008 , pp. 191-206(16)8;
Link

M.Mataln, W.Brandstätter, (2004). A Unified Approach to Model Fluid-Structure Interactions. Montanuniversitaet Leoben, Austria. Society of Petroleum Engineering, seminar notes, 2004.


W.Brandstätter, (2005). Flow and Combustion Modelling. Montanuniversitaet Leoben, Austria. Lecture notes February 2005-July 2005.

C.Crowe, M.Sommerfeld, Y.Tsuji, (1998). Multiphase Flows with Droplets and Particles, Boca Raton, FL: CRC Press 1998; ISBN-10: 0849394694/0-8493-9469-4.

R.P. King. Introduction to Particle Fluid Flow, Butterworth-Heinemann; (2002).

S.Lain, D.Bröder, M.Sommerfeld, (1999). Experimental and numerical studies of the hydrodynamics in a bubble column. Chemical Engineering Science, 54, 4913.
CrossRef

S.Lain, M.F.Göz, (2000). Instabilities in numerical simulations of dispersed two-phase flow. Mechanical Research Communication, 27, 475.
CrossRef

S.Lain, M.F.Göz, (2001). Numerical instabilities in bubble tracking in two-phase flow. International Journal of Bifurcation and Chaos, 11(4), 1169.
CrossRef

S. Lain, M.F. Göz, (2004). Study of the numerical instabilities in Lagrangian tracking of bubbles and particles in two-phase flow. Computers and Chemical Engineering 28 (2004) 2727-2733.
CrossRef

S.Lain, M.F.Göz, M.Sommerfeld, (2006). Instabilities in LaGrangian Tracking of Bubbles and Particles in Two-Phase Flow numerical. Wiley InterScience, 52: 469-477.


A.Haider, O.Levenspiel, (1988). Drag Coefficient and Terminal Velocity of Spherical and Non Spherical Particles. Powder Technology, 58 (1989), 63-70.
CrossRef

A.Hölzer, M.Sommerfeld, (2007). New, simple correlation formula for the drag coefficient of Non - Spherical Particles. Martin-Luther-Universität, Halle-Wittenberg, Germany. Powder Technology, Vol.184(3) (2007), 361-365.
CrossRef

S.V.Apte, K.Mahesh, T.Lundgren, (2003). A Eulerian-Lagrangian model to simulate two-phase/particulate flows, Center for Turbulence Research, Annual Research Briefs, (2003).

W.J.Kowalski, W.P.Bahnfleth, T.S.Whittam, (1999). Filtration of Airborne Microorganisms: Modelling and Prediction. Pennsylvania State University, 1999. ASHRAE Transactions 105(2), 4-17. http://www.engr.psu.edu/ae/iec/abe/publications. http://www.engr.psu.edu/ae/iec/abe/publications

C.L.Cox, E.W.Jenkins, P.J.Mucha, (2005). Modelling of Debris Deposition in an Extrusion Filter Medium. Clemenson University, Clemenson, SC. Proceedings of the 21st Annual Meeting of the Polymer Processing Society, Leipzig, Germany, June 19-23, 2005.

W. Bohl, W.Elmendorf, (2005). Technische Strömungslehre, Vogel Fachbuch, Kamprath Reihe Aufl.:13.2005. ISBN-10: 3834330299.

http://www.opencfd.co.uk/openfoam/ http://www.opencfd.co.uk/openfoam/

http://www.cfd-online.com/Wiki/CFD-Wiki:Introduction http://www.cfd-online.com/Wiki/CFD-Wiki:Introduction

G.Boiger, M.Mataln, W.Brandstätter, (2009). Simulation of Particle Filtration Processes in Deformable Media, Part 3.1: Basic concepts and particle-fluid force implementation of a non-spherical dirt particle solver, ICE Stroemungsforschung GmbH., Montanuniversitaet Leoben. Article in review since Jan 2009. Int.Journal of Multiphysics;


G.Boiger, M.Mataln, W.Brandstätter, (2009). Simulation of Particle Filtration Processes in Deformable Media, Part 3.2: Interaction modelling and solver verification of a non-spherical dirt particle solver, ICE Stroemungsforschung GmbH., Montanuniversitaet Leoben. Article in review since Jan 2009. Int.Journal of Multiphysics;





DOI: http://dx.doi.org/10.1260/175095409788922301

Copyright (c) 2016 The International Journal of Multiphysics