Flow past a wedge

Governing equations and problem set up

Numerical solution

Plots of the results at different angles

Here I save some old results, which I must do after a run. (You need to do these yourself, they will not just run !!).  Just make up a name for the result that you wish to save and then equate this to "zz" as I show below.  Your newly chosen name will store all of the useful results of the calculation.

For example, for -πi/5.05 I did

[Graphics:../Images/boundary_layer_gr_112.gif]

For -πi/8 I did

[Graphics:../Images/boundary_layer_gr_113.gif]

For 0

[Graphics:../Images/boundary_layer_gr_114.gif]

π//2

[Graphics:../Images/boundary_layer_gr_115.gif]

π/1.3

[Graphics:../Images/boundary_layer_gr_116.gif]

Here I plot some of them together.  The middle one is the flow plate.  The two to the left of it are for a converging flow (more stress, thinner layer), the two to the right are for diverging flow (thicker layer, less stress).

[Graphics:../Images/boundary_layer_gr_117.gif]

[Graphics:../Images/boundary_layer_gr_118.gif]

[Graphics:../Images/boundary_layer_gr_119.gif]

[Graphics:../Images/boundary_layer_gr_120.gif]

The important result is that in a converging region, m>0, the stress increases and the layer thins.  In a diverging region, m<0, the stress decreases, to 0, and the layer thickens.   This tells us the qualitative behavior for flow past any shape body.  Further it provides insight into boundary layer separation which occurs when the tangential velocity gradient at the wall equals zero indicating that a backflow will start to occur.


Converted by Mathematica      November 27, 2000