FLOWLAB SOLUTION
9.110 Use the clarky template in FlowLab to investigate changes in the pressure
distribution on an airfoil as a function of the angle of attack, α. Assume the flow to be
incompressible and inviscid with a free stream Mach number of Ma = 0.15. Run
simulations for angles of attack of α = 0, 5, and 10. Plot values of the pressure
coefficient, Cp = p/(ρU 2/2), for the upper and lower surfaces for all three cases. Discuss
the changes in the pressure on the upper and lower surfaces of the airfoil as  increases.
Problem Setup
For this problem, the default geometry from FlowLab was used:
An approximate flight altitude of 10,000 ft. was used for the ambient conditions. The
Mach number was set according to the problem statement and the angle of attack was
varied.
The flow was set to inviscid for this problem.
For all simulation results presented below, the medium mesh resolution was used in
FlowLab. An example of this mesh is shown in the following figure.
A close-up of the grid around the airfoil is shown in the following figure.
Answer
For a medium grid and 0º angle of attack, the convergence history is shown below.
The students are required to plot the pressure coefficient values of the upper and lower
surfaces for all three angles of attack. The Reports section of FlowLab has the option to
plot the pressure coefficient under the XY Plots button. For  = 0º the pressure
coefficient distribution is shown below. This figure shows the high pressure region at the
stagnation point and the rapidly decreasing pressure as the air accelerates over the upper
surface.
To aid in comparison, the pressure coefficient data for various angle of attack values was
exported to ascii files through the File button on the XYPlot window. This data was then
imported into a spreadsheet application and plotted. The results are shown in the figure
below.
Students should offer discussion on the differences in the pressure distributions for the
various angles of attack. Possible topics include: reason for positive and negative
pressure coefficients, differences in maximum negative pressure coefficients (suction
peak), shifting of the maximum positive pressure coefficient values, relative magnitude
changes at a given chord location, integrated pressure as it relates to lift, etc.
1.5
1
0.5
Cp
0
0 aoa
5 aoa
10 aoa
-0.5
-1
-1.5
-2
-2.5
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Chord Location (m)
Additional Material
The streamlines are plotted for the flow past the airfoil at 0º angle of attack as shown
below.
The velocity contours are shown in the following two figures for  = 0º and 10º,
respectively. The plots show how the high velocity regions change as the angle of attack
is increased. Though the contour plots do not have a corresponding legend attached, the
maximum velocity around the airfoil is higher for the  = 10º case. The higher velocity
corresponds to the larger suction pressure values shown on the pressure plot.