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FLUENT - Flow over an AirfoilAdded by [email protected] (Update Your Profile) , last edited by Steve Weidner on Nov 19, 2008 18:48

Problem Specification

Step 1: Create Geometry in GAMBIT

Start GAMBIT

Import Edge

Create Farfield Boundary

Create Faces

Step 2: Mesh Geometry in GAMBIT

Mesh Faces

Split Edges

Step 3: Specify Boundary Types in GAMBIT

Group Edges

Define Boundary Types

Save Your Work

Export Mesh

Step 4: Set Up P roblem in FLUENT

Launch FLUENT

Import File

Analyze Grid

Define Properties

Step 5: Solve!

Step 6: Analyze Results

Plot Velocity Vectors

Plot Pressure Coefficient

Plot Pressure Contours

Comparisons

Step 7: Refine Mesh

Problem 1

Problem 2

Author: Rajesh Bhaskaran, Cornell University


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. Refine Mesh

Problem 1Problem 2


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Consider air flowing over NACA 4412 airfoil. The freestream velocity is 50 m/s and the angle of attack is 2. Assume standard

sea-level values for the freestream properties:

Pressure = 101,325 Pa

Density = 1.2250 kg/m3Temperature = 288.16 K

Kinematic viscosity v= 1.4607e-5 m2/s

We will determine the lift and drag coefficients under these conditions using FLUENT.

Go to Step 1: Create Geometry in GAMBIT

See and rate the complete Learning Module

Go to all FLUENT Learning Modules






5. Solve!

6. Analyze Results

7. Refine Mesh

Problem 1

Problem 2

Step 1: Create Geometry in GAMBIT

If you wish to skip the steps for grid creation, you can download the mesh file here (right-clickand select Save As...) and

go to Step 4.

Higher Resolution Image

This tutorial leads you through the steps for generating a mesh in GAMBIT for an airfoil geometry. This mesh can then be read

into FLUENT for fluid flow simulation.

In an external flow such as that over an airfoil, we have to define a farfield boundary and mesh the region between the airfoil

geometry and the farfield boundary. It is a good idea to place the farfield boundary well away from the airfoil since we'll use the

ambient conditions to define the boundary conditions at the farfield. The farther we are from the airfoil, the less effect it has on

the flow and so more accurate is the farfield boundary condition.

The farfield boundary we'll use is the line ABCDEFA in the figure above. cis the chord length.
https://confluence.cornell.edu/download/attachments/90742023/01farfield_boundary.jpg?version=1https://confluence.cornell.edu/download/attachments/90742023/01farfield_boundary.jpg?version=1&modificationDate=1232474947000https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+4https://confluence.cornell.edu/download/attachments/90742023/airfoil.msh?version=2&modificationDate=1240412956000https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Problem+2https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Problem+1https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+7https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+6https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+5https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+4https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+3https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+2https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Problem+Specificationhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+Learning+Moduleshttps://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoilhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+1


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Start GAMBIT

Create a new directory called airfoiland start GAMBITfrom that directory by typing gambit -id airfoil at the command

prompt.

UnderMain Menu, select Solver > FLUENT 5/6 since the mesh to be created is to be used in FLUENT 6.0.

Import Edge

To specify the airfoil geometry, we'll import a file containing a list of vertices along the surface and have GAMBIT join these

vertices to create two edges, corresponding to the upper and lower surfaces of the airfoil. We'll then split these edges into 4

distinct edges to help us control the mesh size at the surface.

The file containing the vertices for the airfoil can be downloaded here: naca4412.dat (right click and select Save As...)

Let's take a look at the naca4412.dat file:

255 2

0 0 0

-0.00019628 0.001241474 0

-0.000247836 0.001759397 0

-0.000275577 0.002158277 0

-0.000290986 0.002495536 0

-0.000298515 0.002793415 0

-0.000300443 0.00306332 0

The first line of the file represents the number of points on each edge (255) and the number of edges (2). The first 255 set of

vertices are connected to form the edge corresponding to the upper surface; the next 255 are connected to form the edge for

the lower surface.

The chord length, cfor the geometry in naca4412.datfile is 1, so x varies between 0 and 1. If you are using a different airfoil

geometry specification file, note the range ofxvalues in the file and determine the chord lengthc. You will need this later on.

Main Menu > File > Import > ICEM Input ...

ForFile Name, browse and select the naca4412.datfile. Select both Vertices andEdges underGeometry to

Create: since these are the geometric entities we need to create. Deselect Face. ClickAccept.


We have more points around the nose area because of the high curvature around the nose.

Create Farfield Boundary

Next, we will create the following farfield boundary. This picture of the

farfield nomenclature

will be handy.

We will create the farfield boundary by creating vertices and joining them appropriately to form edges.
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Create the following vertices by entering the coordinates underGlobaland the label underLabel:

Label x y z

A c 12.5c 0

B 21c 12.5c 0

C 21c 0 0

D 21c -12.5c 0

E c -12.5c 0

F -11.5 0 0

G c 0 0

Click the FIT TO WINDOWbutton to scale the display so that you can see all the vertices. The resulting image should look

like this:


Now we can create the edges using the vertices created.

Operation Toolpad > Geometry Command Button > Edge Command Button > Create Edge

Create the edge AB by selecting the vertex A followed by vertex B. Enter AB forLabel. ClickApply. GAMBIT will create the

edge. You will see a message saying something like "Created edge: AB'' in the Transcriptwindow.

Similarly, create the edges BC, CD, DE, EG, GA and CG. Note that you might have to zoom in on the airfoil to select vertex G

correctly or click on the to select the vertices from the list and move them to the picked list. The rest of the tutorial will use

this method for vertices selection.

Next we'll create the ci rcular arc AF. Right-click on the Create Edge button and selectArc.

In the Create Real Circular Arcmenu, the box next to Centerwill be yellow. That means that the vertex you select will be

taken as the center of the arc. Select vertex G and clickApply. Now the box next to End Points will be highlighted in yellow.
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This means that you can now select the two vertices that form the end points of the arc. Select vertex A and then vertex F. Enter

AF underLabel. ClickApply.

If you did this right, the arc AF will be created. If you look in the transcript window, you'll see a message saying that an edge

has been created.

Similarly, create an edge corresponding to arc EF.


Create Faces

The edges we have created can be joined together to form faces. We will need to define three faces as shown in the image

above. Two rectangular faces, rect1 and rect2 lie to the right of the airfoil. The third face, circ1 consists of the area outside of

the airfoil but inside of the semi-circular boundary.

Operation Toolpad > Geometry Command Button > Face Command Button > Form Face

This brings up the Create Face From Wireframe menu. Recall that we had selected vertices in order to create edges.

Similarly, we will select edges in order to form a face.

To create the face rect1, select the edges AB, BC, CG, and GA. Enter rect1for the label and clickApply. GAMBIT will tell you

that it has "Created face: rect1'' in the transcript window.

Similarly, create the face rect2 by selecting ED, DC, CG and GE.

To create the last face we will need to make two separate faces, one for the outer boundary and one for the airfoil and then

subtract the airfoil from the boundary . Create semi-circular face circ1 by selecting GA, AF, FE and EG and enter circ1 for the

label. Create the face for the airfoil by selecting corresponding edges. Subtract the airfoil from circ1.

Operation Toolpad > Geometry Command Button > Face Command Button

right click on the Boolean Operations Button and select Subtract

The Face boxwill be highlighted yellow. Shift click to select circ1, the outer semi-circular boundary. Then select the lower box

labeled Subtract Faces which will allow you to select faces to subtract from our outer boundary. Select the airfoil face and

click apply.

Go to Step 2: Mesh Geometry in GAMBIT.








5. Solve!
https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+5https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+4https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+3https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+1https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Problem+Specificationhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+Learning+Moduleshttps://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoilhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+2https://confluence.cornell.edu/download/attachments/90742023/01farfield_edgesfull.JPG?version=2https://confluence.cornell.edu/download/attachments/90742023/01farfield_edgesfull.JPG?version=2&modificationDate=1232475725000


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6. Analyze Results

7. Refine Mesh

Problem 1

Problem 2

Step 2: Mesh Geometry in GAMBIT

Mesh Faces

We'll mesh each of the 3 faces separately to get our final mesh. Before we mesh a face, we need to define the point

distribution for each of the edges that form the face i.e. we first have to mesh the edges. We'll select the mesh stretching

parameters and number of divisions for each edge based on three criteria:

1. We'd like to cluster points near the airfoil since this is where the flow is modified the most; the mesh resolution as we approach

the farfield boundaries can become progressively coarser since the flow gradients approach zero.

2. Close to the surface, we need the most resolution near the leading and trailing edges since these are critical areas w ith the

steepest gradients.

3. We want transitions in mesh s ize to be smooth; large, discontinuous changes in the mesh size s ignificantly decrease the numerical

accuracy.

The edge mesh parameters we'll use for controlling the stretching are successive ratio, first length and last length. Each

edge has a direction as indicated by the arrow in the graphics window. The successive ratioRis the ratio of the length of

any two successive divisions in the arrow direction as shown below. Go to the index of the GAMBIT User Guide and look under

Edge>Meshingfor this figure and accompanying explanation. This help page also explains what the firstand last lengths

are; make sure you understand what they are.

Operation Toolpad > Mesh Command Button > Edge Command Button > Mesh Edges

Select the edge GA. The edge will change color and an arrow and several circles will appear on the edge. This indicates that

you are ready to mesh this edge. Make sure the arrow is pointing upwards. You can reverse the direction of the edge by

clicking on the Reverse button in the Mesh Edges menu. Enter a ratio of 1.15. This means that each successive mesh

division will be 1.15 times bigger in the direction of the arrow. Select Interval Count underSpacing. Enter 45 forIntervalCount. ClickApply. GAMBIT will create 45 intervals on this edge with a successive ratio of 1.15.

For edges AB and CG, we'll set the First Length (i.e. the length of the division at the start of the edge) rather than the

Successive Ratio. Repeat the same steps for edges BC, AB and CG with the following specifications:

Edges Arrow Direction Successive Ratio Interval Count

GA and BC Upwards 1.15 45

Edges Arrow Direction First Length Interval Count

AB and CG Left to Right 0.02c 60

Note that later we'll select the length at the trailing edge to be 0.02cso that the mesh length is continuous between IG and CG,

and HG and CG.

Now that the appropriate edge meshes have been specified, mesh the face rect1:

> > >
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Select the face rect1. The face will change color. You can use the defaults ofQuad(i.e. quadrilaterals) and Map. Click

Apply.

The meshed face should look as follows:


Next mesh face rect2 in a similar fashion. The following table shows the parameters to use for the different edges:

Edges Arrow Direction Successive Ratio Interval Count

EG and CD Downwards 1.15 45


DE Left to Right 0.02c 60

The resultant mesh should be symmetric about CG as shown in the figure below.


Split Edges

Next, we will split the top and bottom edges of the airfoil into two edges so that we have better control of the mesh pointdistribution. Figure of the splitting edges is shown below.

We need to do this because a non-uniform grid spacing will be used forx0.3c. To

split the top edge into HI and IG, select

Operation Toolpad > Geometry Command Button> Edge Command Button> Split/Merge Edge

Make sure Point is selected next to Split With in the Split Edge window.

Select the top edge of the airfoil by Shift-clicking on it.

We'll use the point atx=0.3con the upper surface to split this edge into HI and IG. To do this, enter 0.3 for x: under Global. If

yourcis not equal to one, enter the value of 0.3*cinstead of just 0.3.For instance, ifc=4, enter 1.2. From here on, whenever

you're asked to enter (some factor)*c, calculate the appropriate value for yourcand enter it.
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Click Apply. You will see a message saying "Edge edge.1 was split, and edge edge.3 created'' in the Transcriptwindow.

Repeat this procedure for the lower surface to split it into HJ and JG. Use the point atx=0.3c on the lower surface to split this

edge.


Finally, let's mesh the face consisting of circ1 and the airfoil surface. For edges HI and HJ on the front part of the airfoil surface,

use the following parameters to create edge meshes:

Edges Arrow Direction Last Length Interval Count

HI From H to I 0.02c 40

HJ From H to J 0.02c 40

For edges IG and JG, we'll set the divisions to be uniform and equal to 0.02c. Use Interval Size rather than Interval Count

and create the edge meshes:

Edges Arrow Direction Successive Ratio Interval Size

IG and JG Left to Right 1 0.02c

For edge AF, the number of divisions needs to be equal to the number of divisions on the line opposite to it, in this case, the

upper surface of the airfoil(this is a subtle point; chew over it). To determine the number of divisions that GAMBIT has created

on edge IG, select

Operation Toolpad > Mesh Command Button > Edge Command Button >Summarize Edge Mesh

Select edge IG and then Elements underComponentand clickApply. This will give the total number of nodes (i.e. points)

and elements (i.e. divisions) on the edge in the Transcriptwindow. The number of divisions on edge IG is 35. (If you are using

a di fferent geometry, this number will be different; I'll refer to it as NIG). So the Interval Countfor edge AF is NHI+NIG=

40+35= 75.

Similarly, determine the number of divisions on edge JG. This comes out as 35 for the current geometry. So the Interval

Countfor edge EF is 75.

Create the mesh for edges AF and EF with the following parameters:


AF From A to F 0.02c 40+NIG

EF From E to F 0.02c 40+NJG

Mesh the face. The resultant mesh is shown below.


Go to Step 3: Specify Boundary Types in GAMBIT
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5. Solve!

6. Analyze Results

7. Refine Mesh

Problem 1

Problem 2

Step 3: Specify Boundary Types in GAMBIT

We'll label the boundary AFE as farfield1 , ABDE as farfield2and the airfoil surface as airfoil. Recall that these will be thenames that show up under boundary zones when the mesh is read into FLUENT.

Group Edges

We'll create groups of edges and then create boundary entities from these groups.

First, we will group AF and EF together.

Operation Toolpad > Geometry Command Button > Group Command Button > Create Group

Select Edges and enter farfield1 forLabel, which is the name of the group. Select the edges AF and EF.

Note that GAMBIT adds the edge to the list as it is selected in the GUI.

ClickApply.

In the transcript window, you will see the message "Created group: farfield1 group".

Similarly, create the other two farfield groups. You should have created a total of three groups:

Group Name Edges in Group
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farfield1 AF,EF

farfield2 AB,DE

farfield3 BC,CD

airfoil HI,IG,HJ,JG (name might vary)

Define Boundary Types

Now that we have grouped each of the edges into the desired groups, we can assign appropriate boundary types to these

groups.

Operation Toolpad > Zones Command Button > Specify Boundary Types

UnderEntity, select Groups.

Select any edge belonging to the airfoil surface and that will select the airfoil group. Next to Name:, enter airfoil. Leave the

Type as WALL.

ClickApply.

In the Transcript Window, you will see a message saying "Created Boundary entity: airfoil".

Similarly, create boundary entities corresponding to farfield1 , farfield2and farfield3 groups. Set Type to Velocity-Inlet

forfarfield1 and farfield2. Set Type to Pressure-Outletforfarfield3.

Save Your Work

Main Menu > File > Save


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Main Menu > File > Export > Mesh...

Save the file as airfoil.msh.

Make sure that the Export 2d Mesh option is selected.

Check to make sure that the file is created.

Go to Step 4: Set Up Problem in FLUENT








5. Solve!

6. Analyze Results7. Refine Mesh

Problem 1

Problem 2

Step 4: Set Up Problem in FLUENT

Launch FLUENT

Start > Programs > Fluent Inc > FLUENT 6.3.26

Select 2ddp from the list of options and click Ru n.

Import File

Main Menu > File > Read > Case...

Navigate to your working directory and select the airfoil.msh file. Click OK.

The following should appear in the FLUENT window:

Check that the displayed information is consistent with our expectations of the airfoil grid.

Analyze Grid

Grid > Info > Size
https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Problem+2https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Problem+1https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+7https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+6https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+5https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+3https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+2https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+1https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Problem+Specificationhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+Learning+Moduleshttps://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoilhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+4


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How many cells and nodes does the grid have?

Display > Grid

Note what the surfaces farfield1, farfield2, etc. correspond to by selecting and plotting them in turn.

Zoom into the airfoil.

Where are the nodes clustered? Why?

Define Properties

Define > Models > Solver...

Under the Solverbox, select Pressure Based.

Click OK.

Define > Models > Viscous

Select InviscidunderModel.

Click OK.

Define > Models > Energy

The speed of sound under SSL conditions is 340 m/s so that our freestream Mach number is around 0.15. This is low enough

that we'll assume that the flow is incompressible. So the energy equation can be turned off.


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Make sure there is no check in the box next to Energy Equation and click OK.

Define > Materials

Make sure airis selected underFluid Materials. Set Densityto constantand equal to 1.225 kg/m3.

Click Change/Create.

Define > Operating Conditions

We'll work in terms of gauge pressures in this example. So set Operating Pressure to the ambient value of 101,325 Pa.

Click OK.

Define > Boundary Conditions

Set farfield1 and farfield2to the velocity-inletboundary type.

For each, click Set.... Then, choose Components underVelocity Specification Methodand set the x- and y-components to that for the freestream. For instance, the x-component is 50*cos(1.2)=49.99. (Note that 1.2 is used as our

angle of attack instead of 2 to adjust for the error caused by assuming the airfoil to be 2D instead of 3D.)


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Click OK.

Set farfield3 topressure-outle tboundary type, click Set... and set the Gauge Pressure at this boundary to 0. Click

OK.

Go to Step 5: Solve!








5. Solve!

6. Analyze Results

7. Refine Mesh

Problem 1

Problem 2

Step 5: Solve!

Solve > Control > Solution

Take a look at the options available.

UnderDiscretization , set Pressure to PRESTO!and Momentum to Second-Order Upwind.

(click picture for larger image)

Click OK.

Solve > Initialize > Initialize...

As you may recall from the previous tutorials, this is where we set the initial guess values (the base case) for the iterative

solution. Once again, we'll set these values to be equal to those at the inlet (to review why we did this look back to the tutorial

about CFG programs) . Select farfield1 underCompute From.
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Click Init.

Solve > Monitors > Residual...

Now we will set the residual values (the criteria for a good enough solution). Once again, we'll set this value to 1e-06.


Click OK.

Solve > Monitors > Force...

UnderCoefficient, choose Lift. UnderOptions, select Printand Plot. Then, Choose airfoilunderWall Zones.

Lastly, set the Force Vectorcomponents for the lift. The lift is the force perpendicular to the direction of the freestream. So to

get the lift coefficient, setXto -sin(1.2)=-020942 and Yto cos(1.2)=0.9998.


ClickApplyfor these changes to take effect.
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Similarly, set the Force Monitoroptions for the Dragforce. The drag is defined as the force component in the direction of

the freestream. So underForce Vector, setXto cos(1.2)=0.9998 and Yto sin(1.2)=0.020942 Turn on only Print for it.

Report > Reference Values

Now, set the reference values to set the base cases for our iteration. Select farfield1 underCompute From.

Click OK.

Note that the reference pressure is zero, indica ting that we are measuring gage pressure.

Main Menu > File > Write > Case...

Save the case file before you start the iterations.

Solve > Iterate

Make note of your findings, make sure you include data such as;

What does the convergence plot look like?

How many iterations does it take to converge?

How does the Lift coefficient compared with the experimental data?

Main Menu > File > Write > Case & Data...

Save case and data after you have obtained a converged solution.

Go to Step 6: Analyze Results








5. Solve!

6. Analyze Results
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7. Refine Mesh

Problem 1

Problem 2

Step 6: Analyze Results

Lift Coefficient

The solution converged after about 480 iterations.

476 1.0131e-06 4.3049e-09 1.5504e-09 6.4674e-01 2.4911e-03 0:00:48 524

! 477 solution is converged

477 9.9334e-07 4.2226e-09 1.5039e-09 6.4674e-01 2.4910e-03 0:00:38 523

From FLUENT main window, we see that the lift coefficient is 0.647. This compare fairly well with the literature result of 0.6

fromAbbott et al.

Plot Velocity Vectors

Let's see the velocity vectors along the airfoil.

Display > Vectors

Enter 4 next to Scale. Enter 3 next to Skip. Click Display.


As can be seen, the velocity of the upper surface is faster than the velocity on the lower surface.

White Background on Graphics Window

To get white background go to:

Main Menu > File > Hardcopy

Make sure that Reverse Foreground/Backgroundis checked and select Colorin Coloringsection.

Click Preview. Click No when prompted "Reset graphics window?"

https://confluence.cornell.edu/download/attachments/90744040/velocity%20magnitude%20leading%20edge.jpghttps://confluence.cornell.edu/download/attachments/90744040/velocity%20magnitude.jpghttps://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+7#FLUENT-FlowoveranAirfoil-Step7-refhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Problem+2https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Problem+1https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+7


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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.


On the trailing edge, the flow on the upper surface decelerates and converge with the flow on the lower surface.

Do note that the time for fluid to travel top and bottom surface of the airfoil is not necessarily the same, as

common misconception

Plot Pressure Coefficient

Pressure Coefficient is a dimensionless parameter defined by the equation

wherep is the static pressure,

Pref is the reference pressure, and

qref is the reference dynamic pressure defined by

The reference pressure, density, and velocity are defined in the Reference Values panel in Step 5. Please refer to FLUENT's

help for more information. Go to Help > User's Guide Indexfor help.

Plot > XY Plot...

Change the Y Axis Fu nction to Pressure ..., followed by Pressure Coefficient. Then, select airfoilunderSurfaces.

Click Plot.
https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+5https://confluence.cornell.edu/download/attachments/90744040/velocity%20magnitude%20trailing%20edge.jpg


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The lower curve is the upper surface of the airfoil and have a negative pressure coefficient as the pressure is lower than the

reference pressure.

Plot Pressure Contours

Plot static pressure contours.

Display > Contours...

Select Pressure... and Pressure C oefficientfrom underContours Of. Check the Filledand Draw Gridunder

Options menu. Set Levels to 50.

Click Display.


From the contour of pressure coefficient, we see that there is a region of high pressure at the leading edge (stagnation point)and region of low pressure on the upper surface of airfoil. This is of what we expected from analysis of velocity vector plot.

From Bernoulli equation, we know that whenever there is high velocity, we have low pressure and vise versa.

Go to Step 7: Refine Mesh








5. Solve!
https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+6https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+5https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+4https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+3https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+2https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+1https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Problem+Specificationhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+Learning+Moduleshttps://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoilhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+7https://confluence.cornell.edu/download/attachments/90744040/presssure%20coefficient%20contour%20plot.jpghttps://confluence.cornell.edu/download/attachments/90744040/pressure%20coefficient%20plot.jpg


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6. Analyze Results

7. Validate the Results

Problem 1

Problem 2

Step 7: Validate the Results

Force 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

Drag due to pressure:

Drag due to viscous effect:

where

edis the unit vector parallel to the flow direction.

n is unit vector perpendicular to the surface of airfoil.

tis 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:
https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Problem+2https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Problem+1https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+6


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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.

tis 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 . UnderForce Vector, enter0.9998 next toX. Enter0.02094 next to Y. Select airfoilunderWall

Zones. Click Print.

Here's is what we see in the main menu:

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

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

where

(Cd)pressure is due to pressure force.

(Cd)skin friction is due to viscous force.


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Indeed, we see that the (Cd)skin friction is zero because of the inviscid model.

In reali ty, (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 . UnderForce Vector, enter-0.02094 next toX. Enter0.9998 next to Y. Select airfoilunderWall

Zones. Click Print.

Here's is what we see in the main menu:

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.

Cl = (Cl)pressure + (Cl)skin friction

where

(Cl)pressure is due to pressure force.

(Cl)skin friction is due to viscous force.

Since our model is inviscid, (Cl)skin friction is zero. We see that the lift coefficient compare well with the experimental value of

0.6.

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

Cl 0.647 0.649 0.3%

Cd 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 Cd 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.


23/24



.

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.

Cl Cd

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

The experimental data is taken from Theory of Wing Sections By Ira Herbert Abbott, Albert Edward Von Doenhoff pg. 488

Google scholar link

Go to Problem 1








5. Solve!

6. Analyze Results

7. Refine Mesh

Problem 1

Problem 2

Problem 1

Consider the incompressible, inviscidairfoil calculation in FLUENTpresented in class. Recall that the angle of attack, ,

was 5.

Repeat the calculation for the airfoil for = 0 and = 10. Save your calculation for each angle of attack as a different case

file.

(a) Graph the pressure coefficient (Cp) distribution along the airfoil surface at = 5 and = 10 in the manner discussed in
https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Problem+2https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+7https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+6https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+5https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+4https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+3https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+2https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Step+1https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Problem+Specificationhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+Learning+Moduleshttps://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoilhttps://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Flow+over+an+Airfoil-+Problem+1http://books.google.com/books?id=DPZYUGNyuboC&printsec=frontcover&dq=Theory+of+Wing+Sections&ei=u6a6SZLfBJ6cMtj-iOcL#PPA489,M1


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. ., p - .

What change do you see in the Cp distribution on the upper and lower surfaces as you increase the angle of attack?

Which part of the airfoil surface contributes most to the increase in lift with increasing ?

Hint: The area under the Cp vs. x curve is approximately equal to Cl.

(b) Make a table ofCland Cdvalues obtained for = 0, 5, and 10. Plot Clvs. for the three values of . Make a linear least-

squares fit of this data and obtain the slope. Compare your result to that obtained from inviscid, thinairfoil theory:

,

where is in degrees.

Go to Problem 2



Problem Specification1. Create Geometry in GAMBIT




5. Solve!

6. Analyze Results

7. Refine Mesh

Problem 1

Problem 2

Problem 2

Repeat the incompressible calculation at = 5 including viscous effects. Since the Reynolds number is high, we expect

the flow to be turbulent. Use the k-turbulence model with the enhanced wall treatment option. At the farfield boundaries, set

turbulence intensity=1% and turbulent length scale=0.01.

(a) Graph the pressure coefficient (Cp) distribution along the airfoil surface for this calculation and the inviscid calculation done

in the previous problem at = 5. Comment on any differences you observe.

(b) Compare the Cland Cdvalues obtained with the corresponding values from the inviscid calculation. Discuss briefly the

similarities and differences between the two results.

Back to Problem Specification



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