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  • FLUENT - Flow over an Airfoil- Step 7

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Problem Specification
1. Create Geometry in GAMBIT
2. Mesh Geometry in GAMBIT
3. Specify Boundary Types in GAMBIT
4. Set Up Problem in FLUENT
5. Solve!
6. Analyze Results
7. Validate the Results
Problem 1
Problem 2

Step 7: Validate the Results

Report Force


Info
titleForce Conventions

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

Image Added

Drag due to pressure:

Latex

\large
$$
{(Drag)_{pressure}} = {\oint \-P \hat{n}.\hat{e_d}dS}
$$

Drag due to viscous effect:

Latex

\large
$$
{(Drag)_{viscous}} = {\oint \tau_w \hat{t}.\hat{e_d}dS}
$$

where

ed 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:

Latex

\large
$$
{(Lift)_{pressure}} = {\oint \-P \hat{n}.\hat{e_l}dS}
$$

Lift due to viscous effect:

Latex

\large
$$
{(Lift)_{viscous}} = {\oint \tau_w \hat{t}.\hat{e_l}dS}
$$

where

el 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

Let's look at the forces on the airfoil. 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
 

This is an inviscid model, we are expecting a drag coefficient of zero, and yet there is a small drag coefficient that present. We should investigate more into this.

Cd =  (Cd)pressure + (Cd)skin friction

...

Info
title

In reality, (Cd)skin friction has biggest contribution to drag but ignored because of the inviscid model that we specify. (Cd)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:

...

Info
title

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 (Cl)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.

...

Following table shows comparison of modeling result with experimental data.


CL

Cd

FLUENT

0.647

0.00249

Experiment

0.6

0.007

% Dif

7.8%

64%

CL l

Cd

FLUENT Fine Mesh

0.649

0.00137

Experiment

0.6

0.007

Theory

-

0

...