Keywords: fresh concrete flow, non-Newtonian flow, interface-capturing.

Modeling the flow of freshly mixed concrete is very important for the construction industry because concrete is usually put into place in its plastic form. In the construction field, subjective terms like workability, flowability, and cohesion are used, sometimes interchangeably, to describe the behavior and flow properties of fresh concrete. These factors depend on flow (rheological) properties of concrete, that have direct influence on the strength and durability of concrete. Concrete that is not properly cast or consolidated may have defects, such as air voids, honeycombs, and aggregate segregation. The modeling of fresh concrete flow can significantly contribute to durability and strength of structure and it is necessary for design optimization of casting procedure. This contribution represents a first step toward this goal - it addresses the numerical aspects of fresh concrete flow modeling.

The fresh concrete is considered as a fluid. This assumption is valid, when a certain degree of flow can be achieved and when the concrete is homogeneous. This is usually satisfied, because concrete is put in place in its plastic form in the majority of industrial applications. It is widely recognized, that concentrated suspensions, such as concrete, typically behave as non-Newtonian fluids. The constitutive equations that have a physical basis should include at least two parameters, one being the yield stress. The Bigham model is considered, with the yield stress and plastic viscosity as parameters.

As the characteristic flow velocity will be very small compared to the speed of sound in the fresh concrete, the fluid will be treated as incompressible. In a case of incompressible flow, the mass and momentum conservation equations, together with the incompressibility condition and constitutive equation form a complete system.

The numerical solution is based on the finite element method and the interface-capturing method to track the position of a free surface. The solution algorithm is based on the stabilized FEM formulation to prevent potential numerical instabilities. The stabilization techniques include streamline-upwind / Petrov-Galerkin (SUPG) and pressure-stabilizing / Petrov-Galerkin (PSPG) formulations. These stabilization techniques were introduced by Tezduyar and Hughes [1,2].

The interface-capturing method is based on the Volume-of-Fluid (VOF) approach, that introduces another unknown: the fluid volume fraction in each grid cell. In principle, if we know the amount of fluid in each cell it is possible to locate surfaces, as well as determine surface slopes and surface curvatures. Surfaces are easy to locate because they lie in cells partially filled with fluid or between cells full of fluid and cells that have no fluid. To compute the time evolution of surfaces, a technique is required to move volume fractions through a grid in such a way that the step-function nature of the distribution is retained. A straightforward numerical approximation cannot be used to model this equation because numerical diffusion and dispersion errors destroy the sharp, step-function, nature of the VOF distribution. An important advantage of the VOF method is the fact that it is based on a volume tracking concept, and this means that it is robust enough to handle the breakup and coalescence of fluid masses. The surface tracking algorithm used in this work is based on the paper by Shahbazi et al [4]) and consists of three parts:

1. The Lagrangian part, in which original mesh is projected along trajectories.
2. The reconstruction part. In this step the volume materials are reconstructed on the updated grid, assuming that volume fractions remain constant during the Lagrangian phase. This includes the calculation of interface segment normals, line constants, and material volume truncation at each Lagrangian cell.
3. The remapping part, consisting in deposition of the Lagrangian truncated material volumes to the target (original) grid. This phase is performed by a series of polygon intersection procedures.

This contribution represents a first step toward modeling of fresh concrete flow - it addresses the numerical aspects of fresh concrete flow modeling. The fresh concrete is considered as a non-Newtonian fluid. The Bigham model is used as constitutive model, with the yield stress and plastic viscosity as parameters. To track the position of free surface, an interface-capturing approach is presented. This approach is based on Volume-of-Fluid approach. The advantage of the above approach is the fact that it is based on a volume tracking concept and can implicitly handle the breakup and coalescence of fluid masses.

1

A.N. Brooks, T.J.R. Hughes, "Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows with Particular Emphasis on the Incompressible Naview-Stokes Equations", Computer Methods in App. Mechanics and Engng., 32, 199-259, 1982. doi:10.1016/0045-7825(82)90071-8

2

T.E. Tezduyar, "Stabilized Finite Element Formulations for Incompressible Flow Computations", Advances in Applied Mechanics, 28, 1-44,1992. doi:10.1016/S0065-2156(08)70153-4

3

T.E. Tezduyar, S. Stahe, "Stabilization Parameters in SUPG and PSPG Formulations", Journal of Comput and Appl Mechanics, 4(1), 71-88, 2003.

4

K. Shahbazi, M. Paraschivoiu, and J. Mostaghimi, "Second order accurate volume tracking based on remapping for triangular meshes", Journal of Comput. Physics, 188, 100-122, 2003. doi:10.1016/S0021-9991(03)00156-6

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