Step 7: Validate the Results
Info  

 
FLUENT report forces in term of pressure force and viscous force. For instance, we are interested in the drag on the airfoil, (Drag)_{total} = (Drag)_{pressure} + (Drag)_{viscous} Drag due to pressure:
Drag due to viscous effect:
where e_{d} is the unit vector parallel to the flow direction. n is unit vector perpendicular to the surface of airfoil. t is unit vector parallel to the surface of airfoil. Similarly, if we are interested in the lift on the airfoil, (Lift) = (Lift)_{pressure} + (Lift)_{viscous} Lift due to pressure:
Lift due to viscous effect:
where e_{l} is the unit vector perpendicular to the flow direction. n is unit vector perpendicular to the surface of airfoil. t is unit vector parallel to the surface of airfoil. 
Report Force
We will first investigate the Drag on the airfoil.
Main Menu > Report > Forces...
Select Forces. Under Force Vector, enter 0.9998
next to X. Enter 0.02094
next to Y. Select airfoil under Wall Zones. Click Print.
Here's is what we see in the main menu:
No Format 

Force vector: (0.99980003 0.02094 0) pressure viscous total pressure viscous total zone name force force force coefficient coefficient coefficient n n n        airfoil 3.8125084 0 3.8125084 0.0024897052 0 0.0024897052        net 3.8125084 0 3.8125084 0.0024897052 0 0.0024897052 
C_{d} = (C_{d})_{pressure} + (C_{d})_{skin friction}
where
(C_{d})_{pressure} is due to pressure force.
(C_{d})_{skin friction} is due to viscous force.
Indeed, we see that the (C_{d})_{skin friction} is zero because of the inviscid model.
Info  

 
In reality, (C_{d})_{skin friction} has biggest contribution to drag but ignored because of the inviscid model that we specify. (C_{d})_{pressure} should be zero, but it is not zero because of inaccuracies and numerical dissipation during the computation. 
Now, let's look at the lift coefficient.
Main Menu > Report > Forces...
Select Forces. Under Force Vector, enter 0.02094
next to X. Enter 0.9998
next to Y. Select airfoil under Wall Zones. Click Print.
Here's is what we see in the main menu:
No Format 

Force vector: (0.02094 0.99980003 0) pressure viscous total pressure viscous total zone name force force force coefficient coefficient coefficient n n n        airfoil 1008.3759 0 1008.3759 0.6585058 0 0.6585058        net 1008.3759 0 1008.3759 0.6585058 0 0.6585058 
Similarly, lift force is due to the contribution of pressure force and viscous force.
C_{l} = (C_{l})_{pressure} + (C_{l})_{skin friction}
where
(C_{l})_{pressure} is due to pressure force.
(C_{l})_{skin friction} is due to viscous force.
Since our model is inviscid, (C_{l})_{skin friction} is zero. We see that the lift coefficient compare well with the experimental value of 0.6.
Info  

 
Do note that the lift coefficient for inviscid model is higher than the experimental value. In reality, if we take into account the effect of viscosity, we will have (C_{l})_{skin friction} of negative value. The viscous effect will lower the overall lift coefficient. Since our inviscid model neglect the effect of viscosity, we have a slightly higher lift coefficient compared to the experimental data. 
Grid Convergence
A finer mesh with four times the original mesh density was created. The lift coefficient was found to be 0.649.
 Original Mesh  Fine Mesh  %Dif 

C_{l}  0.647  0.649  0.3% 
C_{d}  0.00249  0.00137  45% 
We see that the difference in drag coefficient is very large. We used inviscid case for our model, so we are expecting a C_{d} of zero. However, since the parameter of interest is the lift coefficient, and the value lift coefficient does not deviate much from original mesh to fine mesh, we concluded that the fine mesh is good enough.
Info  

 
The modeling result obtained is still off from the literature result. Further validation steps are needed before we can conclude about the accuracy of our model. Other parameter that will affect the validity of our result is the choice of viscous model. We used inviscid model which basically assumed that the flow inviscid and totally ignore the effect of boundary layer near the airfoil surface. We might want to try out turbulence model for this high Reynolds number flow. 
Summary
Following table shows comparison of modeling result with experimental data.
C_{l}  C_{d}  

FLUENT Fine Mesh  0.649  0.00137 
Experiment  0.6  0.007 
Theory    0 
Though further validation steps are still needed before we can come up with a model that will accurately represent the physical flow, this simple tutorial demonstrates the use of reasonable assumption and approximation in obtaining understanding of physical flow properties around an airfoil.
Reference
Anchor  


newwindow  

 
http://books.google.com/books?id=DPZYUGNyuboC&printsec=frontcover&dq=Theory+of+Wing+Sections&ei=u6a6SZLfBJ6cMtjiOcL#PPA489,M1 
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