Example 3: Backward-Facing Step

This example is a two-dimensional study of a fluid flow within a channel with a backwards-facing step.

The flow pattern will again be calculated using the incompressible Navier-Stokes equations for a Reynolds number of Re = 250, which for this problem lies in the laminar range (the transitional range lies between 1200 < Re < 6600).

The geometry consists basically of a box, representing the channel, with a step on the channel bottom.

Backward-facing step

Viscous, non-turbulent case

Reynolds number of 250

The Reynolds number is defined here as: Re = 2νmax D r / 3m with the characteristic length of the problem, D being the height of the inlet channel.

 

The factor 2/3 derives from the assumption of a parabolic velocity profile in the inlet section with vmax being the maximum velocity value attained in this section.

The Reynolds number derives from the choice of the following parameters:

D = 1.5 m

νmax = 0.5 m/s

r= 1000 kg/m3

m= 2 kg/ms

According to the previous equation we obtain

Re = 250