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Exercises

Simulate the laminar boundary layer over a flat plate using FLUENT for a Reynolds
number Reynoldsnumber ReL =105 where
ρU L
ReL =
.
µ

A tutorial that shows how to solve this problem using FLUENT is available at https://con^{Image Removed}fluence.cornell.edu/x/9YxoBQ. The Reynolds number in the tutorial problem is
104 . Change the value of the coefficient 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. Students enrolled in the Tuesday section should
use the mesh they generated for the section HW.

1. (a) While developing boundary-layer theory, Prandtl made the following key argu-
ments 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 solu-
tion 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 bound-
ary boundary layer obey the similarity principle i.e. if rescaled accordingly, they should col-
lapse 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 different figure. Also plot the corresponding values
from valuesfrom the Blasius solution in this figure (you should have this from Homework 6).
How well does the FLUENT solution obey the similarity principle?