{panel}
[Problem Specification|FLUENT - Flow over an Airfoil- Problem Specification]
[1. Create Geometry in GAMBIT|FLUENT - Flow over an Airfoil- Step 1]
[2. Mesh Geometry in GAMBIT|FLUENT - Flow over an Airfoil- Step 2]
[3. Specify Boundary Types in GAMBIT|FLUENT - Flow over an Airfoil- Step 3]
[4. Set Up Problem in FLUENT|FLUENT - Flow over an Airfoil- Step 4]
[5. Solve\!|FLUENT - Flow over an Airfoil- Step 5]
{color:#ff0000}{*}6. Analyze Results{*}{color}
[7. Refine Mesh|FLUENT - Flow over an Airfoil- Step 7]
[Problem 1|FLUENT - Flow over an Airfoil- Problem 1]
[Problem 2|FLUENT - Flow over an Airfoil- Problem 2]
{panel}
h2. Step 6: Analyze Results
h4. Plot Velocity Vectors
Let's see the velocity vectors along the airfoil.
*Display > Vectors*
Enter 4 next to {color:#660099}{*}{_}Scale{_}{*}{color}. Enter 3 next to {color:#660099}{*}{_}Skip{_}{*}{color}. Click {color:#660099}{*}{_}Display{_}{*}{color}.
\\ !velocity magnitude_sm.jpg!
{newwindow: Higher Resolution Image}https://confluence.cornell.edu/download/attachments/90744040/velocity%20magnitude.jpg{newwindow}
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As can be seen, the velocity of the upper surface is faster than the velocity on the lower surface.
{tip:title=White Background on Graphics Window} To get white background go to:
*Main Menu > File > Hardcopy*
Make sure that {color:#660099}{*}{_}Reverse Foreground/Background{_}{*}{color} is checked and select {color:#660099}{*}{_}Color{_}{*}{color} in {color:#660099}{*}{_}Coloring{_}{*}{color} section. Click {color:#660099}{*}{_}Preview{_}{*}{color}. Click {color:#660099}{*}{_}No{_}{*}{color} when prompted "_Reset graphics window?_"
{tip}
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\\ !velocity magnitude leading edge_sm.jpg!
{newwindow: Higher Resolution Image} https://confluence.cornell.edu/download/attachments/90744040/velocity%20magnitude%20leading%20edge.jpg{newwindow}
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On the leading edge, we see a stagnation point where the velocity of the flow is nearly zero. The fluid accelerates on the upper surface as can be seen from the change in colors of the vectors.
\\ !velocity magnitude trailing edge_sm.jpg!
{newwindow: Higher Resolution Image}https://confluence.cornell.edu/download/attachments/90744040/velocity%20magnitude%20trailing%20edge.jpg{newwindow}
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On the trailing edge, the flow on the upper surface decelerates and converge with the flow on the lower surface.
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{info:title=}Do note that the time for fluid to travel top and bottom surface of the airfoil is not necessarily the same, as common misconception
{info}
h4. Plot Pressure Coefficient
*Pressure Coefficient* is a dimensionless parameter defined by the equation
{latex}
\large
$$
{C_p} = {{(p-p_{ref})} \over q_{ref}}
$$
{latex}
where _p_ is the static pressure,
_P{_}{_}{~}ref{~}_ is the reference pressure, and
_q{_}{_}{~}ref{~}_ is the reference dynamic pressure defined by
{latex}
\large
$$
q_{ref} = {1 \over 2}\rho_{ref}{v_{ref}}^2
$$
{latex}
The reference pressure, density, and velocity are defined in the *Reference Values* panel in [Step 5|FLUENT - Flow over an Airfoil- Step 5]. Please refer to FLUENT's help for more information. Go to {color:#660099}{*}{_}Help > User's Guide Index{_}{*}{color} for help.
*Plot > XY Plot...*
Change the {color:#660099}{*}{_}Y Axis Function{_}{*}{color} to {color:#660099}{*}{_}Pressure{_}{*}{color}{color:#660099}...{color}, followed by {color:#660099}{*}{_}Pressure Coefficient{_}{*}{color}. Then, select {color:#660099}{*}{_}airfoil{_}{*}{color} under {color:#660099}{*}{_}Surfaces{_}{*}{color}.
!pressure coefficient menu.jpg!
Click {color:#660099}{*}{_}Plot{_}{*}{color}.\\ !pressure coefficient plot_sm.jpg!\\
{newwindow:Higher Resolution Image}https://confluence.cornell.edu/download/attachments/90744040/pressure%20coefficient%20plot.jpg{newwindow}
The negative part of the plot is upper surface of the airfoil as the pressure is lower than the reference pressure.
h4. Plot Pressure Contours
Plot static pressure contours.
*Display > Contours...*
Select {color:#660099}{*}{_}Pressure..._{*}{color} and Static Pressure from under {color:#660099}{*}{_}Contours Of{_}{*}{color}. Click {color:#660099}{*}{_}Display{_}{*}{color}. Check also the {color:#660099}{*}{_}Filled{_}{*}{color} and {color:#660099}{*}{_}Draw Grid{_}{*}{color} under {color:#660099}{*}{_}Options{_}{*}{color} menu.
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[!step6_contoursm.jpg!|^step6_contour.jpg]
(Click picture for larger image)
From the figure, we see that in one grid, there is no more than 3 different pressure contours which suggests that our mesh is fine enough.
How can we compare the pressure contour with velocity vector plot? We see that the pressure on the upper surface is negative while the velocity on the upper surface is higher than the reference velocity. Whenever there is high velocity vectors, we have low pressures and vise versa. The phenomenon that we see comply with the Bernoulli equation.
h4. Comparisons
With our simulation data, we can now compare the Fluent with experimental data. The summary of result is shown in the table.
| \\ | CL | Cd |
| FLUENT | 0.647 \\ | 0.00249 \\ |
| Experiment | 0.6 \\ | 0.007 |
| Theory | \- | 0 |
{info:title= }The experimental data is taken from *Theory of Wing Sections* By Ira Herbert Abbott, Albert Edward Von Doenhoff pg. 493
{newwindow: Google scholar link}http://books.google.com/books?id=DPZYUGNyuboC&printsec=frontcover&dq=Theory+of+Wing+Sections&ei=u6a6SZLfBJ6cMtj-iOcL#PPA489,M1{newwindow}
{info}
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Go to [Step 7: Refine Mesh|FLUENT - Flow over an Airfoil- Step 7]
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