The Complex Rheology Polymer Solver deals with flows of polymer melts and polymer suspensions, injection moulding processes as well as with powder injection moulding (CIM – ceramic injection moulding, MIM – metal injection moulding).

In case of viscoelastic flow problems two general classes of constitutive equations are available:

• generalized Newtonian fluids, i.e. models whose viscosity η=η(κ,T,p) can be written as a function of the local shear rate tensor κ and thermodynamic parameters like temperature T and pressure p.
• non-Newtonian fluids, i.e. the elastic stress part is modelled with the memory integral constitutive equations, like OldroydB, Doi-Edwards, etc.

Prediction of the shear viscosity and first normal stress difference

The figures beside show the predicted effective shear viscosity η and the first normal stress difference N1 is defined as η= Txy/κxy and N1=Txx-Tyy, respectively. The integral Doi-Edwards model was used in these simulations.

Injection moulding:

• free surface flow is approximated with VOF (volume of fluid) method.
• free surface can be coupled to all constitutive equations.

Powder injection moulding (NUSIM project):

• shear induced particle migration model is used to predict particle concentration in feedstock (binder + powder).
• binder is modelled via a generalized Newtonian fluid.

The Complex Rheology Fiber Solver is designed to deal with fibre suspension flows occurring e.g. in compression / injection moulding of fiber reinforced thermoplastics. Our models are designed to capture the influence of fiber orientation on the rheology of the polymer melt. Calculation of the fiber orientation and flow fields is considered physically realistic as a fully coupled problem. It is thus applicable to situations where the simple Folgar Tucker model fails, but is nevertheless very often used. The Folgar Tucker model is contained in our models as the correct limit for low fiber concentrations (< 2 %vol). In addition models for fiber flexibility are available.
To capture the coupling of flow and fiber orientation, constitutive relations expressing the stress in suspension in terms of fiber orientation and shear rate tensor have been developed.

The following models are available:

• Folgar-Tucker model describing short fibre suspensions in dilute and semi-dilute regimes.
• Extension of Folgar-Tucker model incorporating the excluded volume effect for concentrated suspension regime.
• Model describing the C-shaped bending of fibres in presence of curvature of suspension velocity field

Prediction of rigid fibre orientation in a mould

The figure beside shows results based on a Folgar Tucker model. It shows the visualization of second order moment of fibre orientation distribution (ellipsoids) and the average angle between fibre orientation and Y-direction (color).

Semiflexible fibre orientation model

The figure on the left hand side is a Three-beads model for semi-flexible fibres. Orientation ellipsoids visualize a generalized second order moment field. Vectors visualize fibre bending — the colours visualize the degree of bending while the direction is an averaged direction of the curvature vector.

The Complex Rheology Grain Solver is developed to deal with the flows of granular materials (for example sand). To deal with industrial problems two competing goals have to be met:

• The whole range of the complex three dimensional dynamic behaviour of granular flow has to be reproduced as realistic as possible
• The computation time must be short enough for the use in an industrial environment.

Both requirements are best fulfilled by using a special nonlinear hydrodynamic model, which has been developed at the ITWM. Our hybrid model combines the characteristics of rapid granular flow with ansatzes from soil mechanics for dense slow flows. It reproduces known results from granular dynamics as e.g. dilatancy, existence of shear bands and solid like behaviour.

Silo Flows:

A basic effect of silo flow is the distinction of core and mass flow depending on the steepness of the silo cone, the wall stress and the internal friction of the granular material. For flat silos, so called core flow occurs where the grains flow towards the centre of the silo and only in the centre a flow towards the outlet occurs.

For steep silos, the grains flow downwards at every point in the silo, no inverse core in the centre is observable and mass flow occurs. Not only this can be reproduced in our simulations, but also the full velocity field including the size of the stagnant zone and the pressure distribution in the silo is predicted.

Coreshooting:

Sand cores are widely used in the casting industry for casting complicated machine parts. They are produced by shooting a pressurized sand air mixture with high velocity in a core box, which has to be filled as homogeneously as possible. To obtain a homogeneously filled form, vents have to be drilled at appropriate positions in the core box to avoid blocking of the sand flow e.g. due to compressed air pockets. Simulation of the whole core shooting process will help to find the optimal positions for the vents depending on the geometry of the core box and the properties of the sand. The sand dynamic is coupled to the compressible Navier-Stokes equation for air.
Figures show the sand flow prediction in the meander geometry (VIGI project). The first plot shows the experimental results (performed by the Institute für Gießereitechnik in Duesseldorf) and the second plot shows the simulation results.

Pile Formation:

We are able to simulate a sandpile with predictable slopes, which is shown in the figures beside.

• Left figure: angle of repose approximately 25 degree.
• Right figure: angle of repose approximately 15 degree.

"Sand Flow with Obstacles":

The simulation shows the behaviour of a simple non cohesive granular material in double step geometry.