Flow simulation in a single blade partially filled mixer

Flow simulation in a single blade partially filled mixer 

The governing equations used in this case are identical to Equations (4.1) and (4.4) describing the creeping flow of an incompressible generalized Newtonian fluid. In the air-filled sections if the pressure exceeds a given threshold the equations should be switched to the following set describing a compressible flow 

The shear-dependent viscosity of the compound is found using the temperature-dependent form of the Carrean equation, described in Chapter 1, given as 

Temperature variations are found by the solution of the energy equation. I he finite element scheme used in this example is based on the implicit 0 time-stepping/continuous penalty scheme described in detail in Chapter 4, Section 5. 

As described in Chapter 3, Section 5.1 the application of the VOF scheme in an Eulerian framework depends on the solution of the continuity equation for the free boundary (Equation (3.69)) with the model equations. The developed algorithm for the solution of the described model equations and updating of the free surface boundaries is as follows  

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