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===== V-funnel simulation =====
==== Test setup and Geometry ====

V-funnel problem simulates the emtying of SCC from V-shaped reservoir due to gravity force. The thickness of the specimen is rather small and the effect of the thickness would be negligible, so that the analysis is performed in 2D. This test can be conviniently used to evaluate the influence of different boundary conditions applied on slip walls. The geometry of the test setup is shown in Figure 1a. The basic parameter, compared to the experiments is the time between opening the gate and the moment, when it is posible to look through the gate.

|{{:tailorcrete:examples:v_funnel_geometry.png?300|}} | {{ :tailorcrete:examples:v_funnel_mesh_bc.png?300|}} |
|  Fig. 1.a: Geometry of the test  |  Fig. 1.b: Boundary conditions  |

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==== Computational Model ====
{{ :tailorcrete:v-funnel_geometry.png?500|}}
The setup of 2D computational model is illustrated in Fig. 1b. The problem is modeled as a two-phase flow problem, consisting of two inmissible fluids: one representing the self compacting concrete and the other representing air. The evolving interface between the two fluids is tracked using the Level Set Method, see reference [1] for details. The Figure 1.b also illustrates the applied boundary boundary conditions. At the beginning of the simulation, the problem domain is divided into two regions, one initially filled with SCC (modelled as non-Newtonian fluid using Bingham model) and another one on the top of SCC representing air (modelled as newtonian fuid). The following constitutive parameters for Bingham model of SCC were assumed in the simulation:
  *yield stress 60 [Pa] 
  *plastic viscosity 20 [Pa*s]
So called "Slip with friction" boundary condition was used on walls, when tangential component of the velocity is proportional to the tangential component of the stress tensor.

The next picture ilustrates the computational mesh. The lower part is refined in order to improve accuracy of predicted flow pattern near the neck. The mesh contains 2907 nodes and 5567 tringular elements with linear interpolation (same approximation used for both velocity and pressure field). Since such element is not satisfying LBB condition, PSPG stabilization is used for preventing oscilations in pressure field. SUPG stabilization improving accuracy in connection with non-linear convective term is also used. For further information, see [2].

The link below contains the complete input file for OOFEM code of the V-funnel simulation. Basically, it is a text file containing specifications of geometry (mesh), physics (constitutive model) and numerical solver.

The general input specification can be found here: [[tailorcrete:input_file_description|Input File Description]].

==== Results ====
On the video below, motion of concrete-air interface is shown. The characteristic "V-funnel time" (the time from opening the gate at the bottom to the moment when it is possible to look through the gate) is aproximately 2s.

{{video>http://www.oofem.org/wiki/lib/exe/fetch.php?media=tailorcrete:examples:v_funnel_tau60_mu20.avi|Animation of V-funnel emptying.}}

==== References ====

- BARTH, T.; SETHIAN, J.A. (2009), Numerical Schemes for the HamiltonJacobi and Level Set Equations on Triangulated Domains. Journal of computational physics, 145 1-40.
  - TEZDUYAR, T : Stabilized Finite Element Formulations for Incompressible Flow Computations, Advances in Applied Mechanics, Volume 28, 1991, Pages 1-44

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