Olesen, John Forbes

Poulsen, Peter Noe

Skocek, Jan

Stang, Henrik

Svec, Oldrich

To correctly predict the casting process of a ﬁber reinforced self compacting concrete on a structural level is a challenging task since the distribution and orientation of ﬁbers inﬂuence the global ﬂow pattern and vice versa. In this contribution, a modeling approach capable to represent accurately the most important phenomena is introduced. A conventional Lattice Boltzmann method has been chosen as a ﬂuid dynamics solver of the non-Newtonian ﬂuid. A Mass Tracking Algorithm has been implemented to correctly represent a free surface and a modiﬁed Immersed Boundary Method (IBM) with direct forcing is used to explicitly represent individual ﬁbers in the ﬂuid. A novel variable time sub-stepping algorithm for dynamics of immersed rigid particles ensuring stability of simulations has been developed which, together with the IBM, provides an efﬁcient, yet accurate way to simulate ﬂow of suspensions. In the following, the developed model is used to simulate ﬂow of the ﬁber reinforced self compacting concrete. Fibers are modeled as slender rigid cylinders using the previously developed correction for particles of a sub-grid size. A lubrication force correction term and collisions with Coulomb friction between ﬁbers and between ﬁbers and boundary conditions are introduced. Several simulation scenarios are presented and compared to experimental data to validate the proposed approach. Further an extension of the model to the structural scale is discussed and demonstrated on an example modeling the ﬁnal dispersion and orientation of ﬁbers during a real casting process

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Downloaded from orbit.dtu.dk on: Dec 18, 2017Fully coupled Lattice Boltzmann simulation of ber reinforced self compacting concreteowSvec, Oldrich; Skocek, Jan; Stang, Henrik; Olesen, John Forbes; Poulsen, Peter NoePublication date:2011Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Svec, O., Skocek, J., Stang, H., Olesen, J. F., & Poulsen, P. N. (2011). Fully coupled Lattice Boltzmannsimulation of ber reinforced self compacting concrete ow. Abstract from Computer Methods in Mechanics,Warsaw, Poland, .CMM-2011 – Computer Methods in Mechanics 9–12 May 2011, Warsaw, PolandFully coupled Lattice Boltzmann simulation of fiber reinforced self compacting concrete flowOldrˇich Švec1a, Jan Skocˇek1b, Henrik Stang1, John Forbes Olesen1, Peter Noe Poulsen11Department of Civil Engineering, Technical University of DenmarkBrovej, Building 118, Kgs. Lyngby, DenmarkE-mails: aolsv@byg.dtu.dk, bjas@byg.dtu.dkAbstractTo correctly predict the casting process of a fiber reinforced self compacting concrete on a structural level is a challenging task sincethe distribution and orientation of fibers influence the global flow pattern and vice versa. In this contribution, a modeling approachcapable to represent accurately the most important phenomena is introduced. A conventional Lattice Boltzmann method has beenchosen as a fluid dynamics solver of the non-Newtonian fluid. A Mass Tracking Algorithm has been implemented to correctly representa free surface and a modified Immersed Boundary Method (IBM) with direct forcing is used to explicitly represent individual fibers inthe fluid. A novel variable time sub-stepping algorithm for dynamics of immersed rigid particles ensuring stability of simulations hasbeen developed which, together with the IBM, provides an efficient, yet accurate way to simulate flow of suspensions.In the following, the developed model is used to simulate flow of the fiber reinforced self compacting concrete. Fibers are modeledas slender rigid cylinders using the previously developed correction for particles of a sub-grid size. A lubrication force correction termand collisions with Coulomb friction between fibers and between fibers and boundary conditions are introduced. Several simulationscenarios are presented and compared to experimental data to validate the proposed approach. Further an extension of the model tothe structural scale is discussed and demonstrated on an example modeling the final dispersion and orientation of fibers during a realcasting process.Keywords: fluid mechanics, concrete, multiscale problem, numerical analysis, structural mechanics1. IntroductionSelf compacting concrete (SCC) is a promising material inthe civil engineering industry. One of the benefits of the SCC is afast and simplified casting followed by decreased labor costs. TheSCC as any other type of concrete has a significantly lower ten-sile and shear strength in comparison to the compression strengthand, therefore, needs to be reinforced. Fiber reinforced concreteis an alternative to traditional stirrups reinforcement leading tolowered labor costs. To be able to access mechanical propertiesof the fiber reinforced concrete, knowledge of the final spreadand orientation of fibers is necessary. Computational fluid dy-namics (CFD) comes to play at this stage since the final spreadand fiber orientation are dependent on the flow patterns in thefresh material. Formulation of a possible CFD model that isable to solve multi-phase and multi-component non-Newtonianflow with complex boundary conditions and fiber suspension andpreferably in reasonable time constitutes a very challenging task.A proposed model is presented in Section 2 whereas a possi-ble application of the model is shown in Section 3. Section 2.1deals with a fluid dynamics solver of the model, Section 2.2presents a simple free surface method and Sections 2.3, 2.4, 2.5and 2.6 are devoted to solid particles representation, movementof the particles and interaction of the particles respectively.2. Model2.1. Fluid Dynamics SolverA Lattice Boltzmann Method (LBM) [6] is used as a fluid dy-namics solver of the non-Newtonian flow. Traditional CFD toolsformulate the problem in a form of macroscopic quantities suchas pressure and velocity fields. The LBM on the other hand, withits roots in a kinetic theory of gases and cellular automata, treatsthe fluid as mesoscopic particle distributions where the micro-scopic particles can be seen as e.g. molecules. The LBM pro-vides rules for mutual collisions and propagation of the particledistributions as well as for the computation of the macroscopicquantities.Contrary to other methods, the LBM is very simple toimplement and reason about. The lid-driven cavity problem,for example, fits into approx. 50 lines of Matlab code (seewww.lbmethod.org). Due to the simplicity of the code and lo-cality of the LBM, the code is relatively easily parallelized.2.2. Free SurfaceA free surface has been implemented in the form of a MassTracking Algorithm (MTA) [3]. In the framework of the MTA,fluid, gas and interface phases are present. The LBM computa-tions are conducted in the fluid and interface phases only. Inter-face cells separate fluid phase and gas phase and are thereforeresponsible for mass conservation. Interface cells are moreoverthe only place where the MTA comes into play in the form of lo-cal mass tracking and reconstruction of missing information fromthe gas phase.Although the method theoretically conserves the mass ex-actly, small oscillations due to numerical errors are observed inthe range of 10 3 % which after several thousand iterations canlead to a complete loss of the mass. Correction of the total massis therefore suggested.The MTA is despite of the correction a very simple and fastalgorithm which contrary to other methods theoretically con-Support from the Innovation Consortium: "Sustainable Concrete Structures with Steel Fibres - The SFRC Consortium" funded by the Danish Agency for Science Technologyand Innovation is acknowledged.CMM-2011 – Computer Methods in Mechanics 9–12 May 2011, Warsaw, Polandserves mass precisely.2.3. Immersed Particles RepresentationThe Immersed Boundary Method with direct forcing(IBM) [2] is used to explicitly represent rigid or deformablesolid particles immersed in the fluid in the form of a force field.A traditional approach of modeling particles in the field of theLBM would be to use a Standard Bounce Back rule (SBB) [1].Shape and boundary movement of the particles are stepwise in theframework of SBB which restricts the minimum discretized sizeof the particles to approx. 5 lattice units to obtain reasonable re-sults. Using the IBM, particle shapes are represented in a diffuseform using a Dirac delta function leading to satisfactory resultsfor particles down to approx. 2 lattice units. In the framework ofIBM, the movement of particle boundaries is smooth.The limiting dimension of particles with high aspect ratiosuch as fibers, i.e. the diameter, is restricted to a minimum sizeof approx. 2 lattice units. The discretized length of the parti-cles therefore reaches a range of 100 lattice units which makesit impossible to simulate the casting process on a structural levelin a reasonable amount of time and with a reasonable computa-tional power. A correction term has been proposed to overcomethe approx. 2 lattice units restriction.2.4. Correction TermThe problematics has been studied in [5] and, as a conclusion,a correction term of the direct forcing, Fcor = CFIBM , has beenproposed by fitting for the case of fibers to overcome the limit of2 lattice units asC = 1:8d 1:2; d < 1:5 (1)1; d > 1:5; (2)where d stands for the diameter of fibers. The correction termallows to reduce the minimum dimension of the particle down to0.3 lattice units without any significant loss in accuracy. Fiberdiameter of 0.3 lattice units instead of 2 lattice units results inapprox. 1000 times shorter computational time.2.5. Variable Sub-Step TimeMovement of the immersed particles is driven by the New-ton’s second law discretized with the explicit forward Eulermethod. When the acceleration varies significantly during onelattice time step, the method might become unstable. A variablesub-stepping has been proposed by [4] to address the problem.The limiting time step is computed analytically by restricting amaximum change in the forces exerted on the particle by the sur-rounding fluid.Particles move and interact with each other and with theboundary conditions on the sub-step level whereas the fluid re-mains frozen during the sub-stepping procedure.2.6. Interaction ForcesDue to discretization, the LBM is not capable to properlycatch the flow and especially the pressure field between two solidparticles when the distance between them falls bellow 1 latticeunits. For sub-grid particles, the problem is even more pro-nounced. Lubrication forces correction [7] between fibers andbetween fibers and boundary conditions were therefore added tothe model.A simple collision model with Coulomb friction based on aforce impulse is introduced in the model as well.3. ApplicationSeveral simulations and an experimental work is presented tovalidate the proposed set of tools. As an example, a 3D fiber re-inforced SCC slump test has been simulated and different timesnaps are shown in the Figure 1.Figure 1: Sections of a 3D slump test at different time snaps.Dark region represents high viscosity4. ConclusionThe Lattice Boltzmann method together with other ingredi-ents such as the corrected Immersed Boundary Method, variabletime sub-stepping or the Mass Tracking Algorithm has been pre-sented in this contribution. The developed model has been used tosimulate a non-Newtonian liquid together with particle inclusionswith a focus on steel fiber reinforced self compacting concrete.The presented model is based on well established methodsand provides an efficient tool that can be applied to a range ofengineering problems on different length scales yielding resultsmatching favorably theoretical and experimental results.References[1] C. K. Aidun and Y. Lu. Lattice Boltzmann simulation of solidparticles suspended in fluid. Journal of Statistical Physics,81(1-2):49–61, Oct. 1995.[2] Z. Feng and E. Michaelides. Proteus: a direct forcing methodin the simulations of particulate flows. Journal of Computa-tional Physics, 202(1):20–51, Jan. 2005.[3] C. Körner, M. Thies, T. Hofmann, N. Thürey, and U. Rüde.Lattice Boltzmann Model for Free Surface Flow for Model-ing Foaming. Journal of Statistical Physics, 121(1-2):179–196, Oct. 2005.[4] J. Skocˇek, O. Švec, J. Spangenberg, H. Stang, M. R. Geiker,N. Roussel, and J. Hattel. Modeling of flow of flow of parti-cles in non-Newtonian fluid using lattice Boltzmann method.In Proceedings of ICCC, 2011.[5] O. Švec, J. Skocˇek, H. Stang, J. F. Olesen, and P. N. Poulsen.Flow simulation of fiber reinforced self compacting concreteusing Lattice Boltzmann method. In Proceedings of ICCC,2011.[6] D. A. Wolf-Gladrow. Lattice-Gas Cellular Automata andLattice Boltzmann Models: An Introduction (Lecture Notesin Mathematics). Springer, 2000.[7] Y. Yamane, Y. Kaneda, and M. Dio. Numerical simula-tion of semi-dilute suspensions of rodlike particles in shearflow. Journal of Non-Newtonian Fluid Mechanics, 54:405–421, Aug. 1994.

Fully coupled Lattice Boltzmann simulation of ﬁber reinforced self compacting concrete ﬂow

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Fully coupled Lattice Boltzmann simulation of ﬁber reinforced self compacting concrete ﬂow

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