Channel flow for low Reynolds number (power law)

The aim of this study is to demonstrate the influence of the power law model for the stress tensor with nonlinear viscosity nu(u),

nu(u) = nu (|D(u)|)**(-alpha),

on the resulting profile of the velocity (with norm |D(u)| of the deformation tensor). As could be expected for the performed parameters, an increase of the parameter `alpha' in the exponent leads to a more and more flat profile, while for `alpha=0' (Newtonian!) the flow shows the typical parabolic profile. We also made calculations for values `alpha' less than 0 (for `alpha=-1') which leads to even "steeper" profiles. All calculations have been performed with prescribed pressure drops only, without imposing any Dirichlet boundary conditions at the left and right edges, to let the resulting flow be "free" as possible. All flows reach their steady state due to the "small" Reynolds number.

• Distribution of temperature/concentration via Boussinesq model

  Visualization via tracing of concentration, starting from the left side. Each row corresponds to two different color maps (all between 0.4 MB and 1.0 MB). The first column is for `alpha=-1', then followed by alpha=0' (Newtonian!), by `alpha=0.5' (third) and by `alpha=1' (fourth).

  -1.0 0.0 0.5 1.0

  -1.0 0.0 0.5 1.0

  
  
  
• Pressure

  Visualization via shaded pressure plots. All configurations lead to the same linear pressure, due to the prescribed pressure drops. The following gif-picture shows a typical steady-state snapshot, here for 'alpha=1'.

  
  
  

• Streamfunction

  Visualization via shaded streamline plots (only gif's!). All configurations lead to similar results. The "small" changes correspond to the subsequent velocity profiles.

  -1.0 0.0 0.5 1.0

  
  
  
• Velocity

  Visualization of the typical velocity profile (only gif's!). All configurations lead to the typical parabolic or to more flat or to more steep profiles.

  alpha=-1.0

  alpha= 0.0

  alpha= 0.5

  alpha= 1.0