Exercises

Consider the low-speed airflow over the NACA 0012 airfoil at low angles of attack. The
Reynolds number based on the chord is Rec = 2.88 × 106 . This flow can reasonably be
modeled as incompressible and inviscid.

1. Explain why the incompressible, inviscid model for this flow should yield lift coefficient
values that match well with experiment but will yield a drag coefficient that is always
zero.

2. What is the boundary value problem (BVP) you need to solve to obtain the velocity
and pressure distributions for this flow at an angle of attack of 10◦ ? Indicate governing
equations, domain and boundary conditions (u = 0 at a certain boundary etc.). For
each of the boundary conditions, indicate also the corresponding boundary type that
you need to select in FLUENT.

3. Set up this BVP in FLUENT and solve it numerically to obtain the velocity and
pressure distributions at an angle of attack of 10◦

(a) Plot the pressure coefficient Cp obtained from FLUENT in the
same figure. Add the corresponding experimentally measured pressure values as
symbols. The experimental data is from Gregory & O'Reilly, NASA R&M 3726,
Jan 1970 and provided in the same zip file as the meshes. Follow the aeronautical
convention of flipping the vertical axis so that negative Cp values are above and
positive Cp values are below. This can be done in MATLAB using
set(gca, 'YDir', 'reverse');
Add a suitable legend to distinguish between the curves.

(b) Obtain the lift and drag coefficients from the FLUENT results on the two meshes.
Compare these with experimental or expected values (present this comparison as
a table). The experimental values for 10◦ angle of attack are:
Cl = 1.2219; Cd = 0.0138.

(c) Repeat 3a and 3b for 0◦ angle of attack but only on the unrefined mesh. The
experimental values for 0◦ angle of attack are:
Cl = 0.663; Cd = 0.0090.

(d) Comment on the comparison with experiment for the two angles of attack. Also,
comment on the effect of mesh refinement. How does the pressure distribution
over the airfoil change on increasing the angle of attack?
Compare your results visually with that obtained by Prof. Caughey with his code.
His results are provided in a pdf file within the zip file.

Spring 2011