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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
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. Refine Mesh
Problem 1Problem 2
Problem Specification
Search Cornell
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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
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. 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.
Higher Resolution Image
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.
http://courses.cit.cornell.edu/fluent/airfoil/images/01farfield_boundary.jpghttps://confluence.cornell.edu/download/attachments/90742023/NACA4412.jpghttps://confluence.cornell.edu/download/attachments/90742023/NACA4412.dat?version=2&modificationDate=1240347543000 -
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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:
Higher Resolution Image
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.
Higher Resolution Image
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.
See and rate the complete Learning Module
Go to all FLUENT Learning Modules
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!
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:
Higher Resolution Image
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
Edges Arrow Direction First Length Interval Count
DE Left to Right 0.02c 60
The resultant mesh should be symmetric about CG as shown in the figure below.
Higher Resolution Image
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.
Higher Resolution Image
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:
Edges Arrow Direction First Length Interval Count
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.
Higher Resolution Image
Go to Step 3: Specify Boundary Types in GAMBIT
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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. 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
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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 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
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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!
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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. 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 picture for larger image)
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.
(click picture for larger image)
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
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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
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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.
Higher Resolution Image
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?"
Higher Resolution Image
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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.
Higher Resolution Image
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.
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Higher Resolution Image
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.
Higher Resolution Image
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
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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!
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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:
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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.
-
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.
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
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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. 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
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Problem Specification1. 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 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.
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