FLUENT - Flat Plate Boundary Layer - Exercises

Exercises

Simulate the laminar boundary layer over a flat plate using FLUENT for a Reynolds number where

Change the value of the coefficient of viscosity µ from the tutorial example to get ReL =105 , keeping all other parameters the same. Use the same mesh as in the tutorial. You have the option of skipping the geometry and meshing steps in the tutorial by downloading the mesh at the top of the geometry step.

1. (a) While developing boundary-layer theory, Prandtl made the following key arguments about the boundary-layer flow to simplify the Navier-Stokes equations:

i. u ≫ v
ii. Steamwise velocity gradients ≪ Transverse velocity gradients; for instance,
∂u
∂u
≪
∂x
∂y
Since we are solving the Navier-Stokes equations, we can use the FLUENT solution to check the validity of the above two essential features of boundary layers. Consider the solution at x = 0.5 and x = 0.7 and make plots of appropriate profiles to check the validity of these two features. Make one figure to illustrate each feature. Choose the upper limit of your abscissa (vertical axis) such that you can clearly see the variation within the boundary layer (the flow outside the boundary layer is not very interesting in this case).

(b) For the FLUENT solution, plot the u-velocity profiles (y vs. u) at x=0.5, 0.7, and 0.9 in the same figure. Briefly comment on the change in the velocity profile with x.

(c) Prandtl's student Blasius deduced that the velocity profiles in a flat plate boundary layer obey the similarity principle i.e. if rescaled accordingly, they should collapse to a single curve. Re-plot the profiles from part (b) in terms of the Blasius variables (η vs. u/U ) in a different figure. Also plot the corresponding valuesfrom the Blasius solution in this figure.
How well does the FLUENT solution obey the similarity principle?