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 Rn = 250, which for this problem lies in the laminar range (the transitional range lies between 1200 < Rn  < 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 200

The Reynolds number is defined here as: Re = 2νmax·Dρ / 3μ 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/m.s

According to the previous equation we obtain

Re = 250