FLOW OVER AN AIRFOIL

Problem Specification

In this tutorial, we will show you how to simulate a NACA 0012 Airfoil at a 6 degree angle

of attack placed in a wind tunnel. Using FLUENT, we will create a simulation of this

experiment. Afterwards, we will compare values from the simulation and data collected

from experiment.

Pre-Analysis & Start-Up

Boundary Conditions

One of the simple things we can think about before we set up the simulation is begin

planning the boundary conditions of the set up. One of the popular meshes for simulating

a airfoil in a stream is a C-Mesh, and that is what we will be using. At the inlet of the

system, we will define the velocity as entering at a 6 degree angle of attack (as per the

problem statement), and at a total magnitude of 1. We will also define the gauge pressure

at the inlet to be 0. As for the outlet, the only thing we can assume is that the gauge

pressure is 0. As for the airfoil itself, we will treat it like a wall. Together, these boundary

conditions form the picture below:

Open ANSYS Workbench

Now that we have the pre-calculations, we are ready to do a simulation in ANSYS

Workbench! Open ANSYS Workbench by going to Start > ANSYS > Workbench. This will

open the start up screen seen as seen below

To begin, we need to tell ANSYS what kind of simulation we are doing. If you look to the

left of the start up window, you will see the Toolbox Window. Take a look through the

different selections. We will be using FLUENT to complete the simulation. Load theFluid

Flow (FLUENT) box by dragging and dropping it into the Project Schematic.

Once you have loaded FLUENT into the project schematic, you are ready to create the

geometry for the simulation.

Geometry

Download the Airfoil Coordinates

In this step, we will import the coordinates of the airfoil and create the geometry we will

use for the simulation. Begin by downloading this file and saving it somewhere

convenient. This file contains the points of a NACA 0012 airfoil.

Launch Design Modeler

Before we launch the design modeler, we need to specify the problem as a 2D problem.

Right click and select Properties. In the Properties of

Schematic A2: Geometry Window, select Analysis Type > 2D . Now, double

click to launch the Design Modeler. When prompted,

select Meters as the unit of measurement.

Airfoil

First, we will create the geometry of the airfoil. In the menu bar, go to Concept > 3D

Curve. In the Details View window, click Coordinates File and select the ellipsis to

browse to a file. Browse to and select the geometry file you downloaded earlier. Once you

have selected the desired geometry file, click to create the curve. Click to

get a better look at the curve.

Next, we need to create a surface from the curve we just generated. Go to Concepts >

Surfaces from Edges. Click anywhere on the curve you just created, and select Edges >

Apply in the Details View Window. Click to create the surface.

Create C-Mesh Domain

Now that the airfoil has been generated, we need to create the meshable surface we will

use once we begin to specify boundary conditions. We will begin by creating a coordinate

system at the tail of the airfoil - this will help us create the geometry for the C-mesh

domain. Click to create a new coordinate system. In the Details View window,

select Type > From Coordinates . For FD11, Point X, enter 1.

Click to generate the new coordinate system. In the Tree Outline Window,

select the new coordinate system you created (defaulted to Plane 4), then click to

create a new sketch. This will create a sketching plane on the XY plane with the tail of the

airfoil as the origin. At the bottom of the Tree Outline Window, click the Sketching tab to

bring up the sketching window.

The first action we will take is create the arc of the C-Mesh domain.

Click . The first click selects the center of the arc, and the next two clicks

determine the end points of the arc. We want the center of the arc to be at the tail of the

airfoil. Click on the origin of the sketch, making sure the P symbol is showing

For the end points of the arc, first select a point on the vertical axis above the origin (a C

symbol will show), then select a point on the vertical axis below the origin. You should end

up with the following:

To create the right side of the C-Mesh donain, click . Click the

following points to create the rectangle in this order - where the arc meets the positive

vertical axis, where the arc meets the negative vertical axis, then anywhere in the right

half plane. The final result should look like this:

Now, we need to get rid of necessary lines created by the rectangle. Select Modify in

the Sketching Toolboxes window, then select . Click the lines of the rectangle

the are collinear with the positive and negative vertical axises. Now, select the

Dimensions toolbox to dimension the C-Mesh domain. Click , followed by

the arc to dimension the arc. Assign the arc a value of 12.5. Next, select .

Click the vertical axis and the vertical portion of the rectangle in the right half plane. Also

assign the horizontal dimension a value of 12.5.

Next, we need to create a surface from this sketch. To accomplish this, go to Concept >

Surface From Sketches. Click anywehere on the sketch, and select Base Objects >

Apply in the Details View Window. Also, select Operation > Add Frozen . Once you

have the correct settings, click . The final step of creating the C-Mesh is

creating a surface between the boundary and the airfoil. To do this, go to Create >

Boolean. In the Details View window, select Operation > Subtract. Next,

select Target Bodies > Not selected , select the large C-Mesh domain surface, then

click Apply. Repeat the same process to select the airfoil as the Tool Body. When you

have selected the bodies, click

Selecting the Airfoil Body Because the C-Mesh domain and the airfoil overlap, once you click in the vicinity of the airfoil ANSYS will select the C-Mesh domain but give you the option of selecting multiple layers

Select the layer that corresponds to the airfoil and the airfoil will be highlighted.

Create Quadrants

In the final step of creating the geometry, we will break up the new surface into 4

quadrants; this will be useful for when we want to mesh the geometry. To begin,

select Plane 4 in the Tree Outline Window, and click . Open the sketching menu,

and select . Draw a line on the vertical axis that intersects the entire C mesh.

Trim away the lines that are beyond the C-Mesh, and you should be left with this:

Next, go to Concepts > Lines from Sketchs. Select the line you just drew and click Base

Objects > Apply, followed by . Now that you have created a vertical line,

create a new sketch and repeat the process for a horizontal line that is collinear to

horizontal axis and bisects the geometry.

Now, we need to project the lines we just created onto the surface. Go to Tools >

Projection. Select Edges press Ctrl and select on the vertical line we drew (you'll have to

select both parts of it), then press Apply. Next, select Target and select the C-Mesh

surface, then click Apply.

Once you click , you'll notice that the geometry is now composed of two

surfaces split by the line we selected. Repeat this process to create 2 more projections:

one projection the line left of the origin onto the left surface, and one projecting the right

line on the right surface. When you're finished, the geometry should be split into 4 parts.

The geometry is finished. Save the project and close the design modeler, as we are now

we are ready to create the mesh for the simulation

Mesh

Mapped Face Meshing

First, we will apply a mapped face meshing control to the geometry. In

the Outline window, click on Mesh to bring up the Meshing Toolbar. In the Meshing

Toolbar, select Mesh Control > Mapped Face Meshing. Making sure the face selection

filter is selected , select all four faces by holding down the right mouse button and

dragging the mouse of all of the quadrants of the geometry. When all of the faces are

highlighted green, in the Details view Window select Geometry > Apply. Next, select

Edge Sizing

Next, we will apply edge sizing controls to all of the edges of the mesh. To begin, go

to Mesh Control > Sizing. Next, click the edge selection filter . Select the following 4

edges buy holding Ctrl and using the left mouse button:

Once the edges are selected, in the Details View Window select Geometry > Apply .

Next, select Type > Number of Divisions . Change the Number of Divisions to 50.

Select Behavior > Hard . We also want the mesh to have a bias, so select the first bias

type: Bais > ----- - -, and give the edge sizing a Bias Factor of 150. The Edge sizing

should now look like this:

Notice that the element sizes get smaller towards the airfoil. This will give us a better

resolution around the airfoil where the flow gets more complicated. Create a new edge

sizing with the same parameters, but choose the 4 remaining straight edges (see figure

below). The number of divisions will still be 50, but now will be selecting a different

biasing type by selecting the second Bias option: Bias > - - -----. Again, set the Bias

Factor to 150

Finally, create a third edge sizing, and select the rounded edges as the geometry. Again,

select Type > Number of Divisions , and change Number of Divisions to 100.

Select Behavior > Hard . This time, we will not bias the edges.

Now, select Mesh > Generate to generate the mesh. It should look like this.

Edge Bias It is important to make sure that the edge divisions to this point are biased towards the center of the mesh : otherwise you may run into some problems later. If your mesh does not match the pictures in the tutorial, make sure to change the parameters of the mesh to make sure that they do: this might mean choosing different edges for the different biasing types than those outlined in this tutorial.

Named Selections

Now will assign names to some of the edges to make creating boundary conditions for the

mesh easier. Let's recall the boundary conditions we planned in the Pre-Analysis Step:

The edges highlighted blue are the inlet, the edges highlighted red are the outlet, and the

airfoil is highlighted white in the middle. Now we are ready to name the sections. In

the Outline window, select geometry - this will make seeing the edges a little easier.

Again make sure the edge selection tool is selected. Now, select the two vertical

edges on the far right side of the mesh. Right click, and select Create Named

Selections. Name the edges outlet. Next, select the edges that correspond to the inlet of

the flow as defined by the picture above. Again, right click and select Create Named

Selections and this time name the selection inlet. Finally, select the two edges making up

the airfoil, and name the selection airfoil.

Setup(Physics)

Launch the Solver

In this step, we will open fluent and define the boundary conditions of the problem. If you

haven't already, close the meshing window to return to the Project Outline window.

Now, click . This will load the mesh into FLUENT. Now, double clickSetup.

The Fluent Launcher Window should open. Check the box marked Double Precision.

To make the solver run a little quicker, under Processing Options we will

select Parallel and change the Number of Processes to 2. This will allow users with a

double core processor to utilize both.

Select the Solver

Click OK to launch Fluent. The first thing we will do once Fluent launches is define the

solver we are going to use. Select Problem Setup > General . Under Solver,

select Density-Based.

Models and Materials

Next, we will define the model we are going to use. We do this by going Problem Setup

> Models > Viscous-Laminar. Then press Edit... This will open the Viscous

Model Menu Window. Select Inviscid and press OK. Now, we will specify characteristics

of the fluid. Because we specified the fluid as inviscid, we will only have to define the

density of the fluid. To make matters even simpler, we are only looking for non-

dimensionalized values like pressure coefficient, so we will define the density of our fluid

to be 1 kg/m^3. To define the density, click Problem Setup > Materials > (double

click) Air. This will launch the Create/Edit Materials window.

Under Properties, ensure that density is set to Constant and enter 1 kg/m^3 as the

density. Click Change/Create to set the density.

Boundary Conditions

Inlet

Now that the fluid has been described, we are ready to set the boundary conditions of the

simulation. Bring up the boundary conditions menu by selecting Problem Setup >

Boundary Conditions . In the Boundary Conditions window, look underZones. First,

let's set the boundary conditions for the inlet. Select Inlet to see the details of the

boundary condition. The boundary condition type should have defaulted to velocity-

inlet: if it didn't, select it. Now, click Edit to bring up the Velocity-InletWindow. We

need to specify the magnitude and direction of the velocity. Select Velocity

Specification Method > Components . Remember, we want the flow to enter the inlet

at an angle of 6 degrees since the angle of attack of the airfoil is 6 degrees; thus, the x

velocity will be , and the y velocity will be . Specify X-Velocity as 0.9945

m/s and Y-Velocity as 0.1045 m/s. When you have finished specifying the velocity as

entering the inlet at 6 degrees (the same thing as having an angle of attack of 6 degrees),

press OK

Outlet

In the Boundary Conditions window, look under Zones. Select Outlet to see the details

of the boundary condition. The boundary condition type should have defaulted

to pressure-outlet: if it didn't, select it. Click Edit, and ensure that the Gauge

Pressure is defaulted to 0. If it is, you may close this window.

Airfoil

In the Boundary Conditions window, look under Zones and select airfoil. Select Type

> Wall if it hasn't been defaulted.

Reference Values

The final thing to do before we move on to solution is to acknowledge the reference

values. Go to Problem Setup > Reference Values . In the Reference Values Window,

select Compute From > Inlet . Check the reference values that appear to make sure they

are as we have already set them.

Solution

Methods

First, go to Solution > Solution Methods . Everything in this section should have

defaulted to what we want, but let's make sure that under Flow the selection is Second

Order Upwind. If this is the selection, we may move on.

Monitors

Now we are ready to begin solving the simulation. Before we hit solve though, we need to

set up some parameters for how Fluent will solve the simulation.

Let's begin by going to Solution > Monitors . In the Monitors Window, look

under Residuals, Statistic, and Force Monitors. Select Residuals - Print,Plot and

press Edit. In the Residual Monitors Window, we want to change all of theAbsolute

Criteria to 1e-6. This will give us some further trust in our solution.

Initial Guess

Now, we need to initialize the solution. Go to Solution > Solution Initialization . In

the Solution Initialization Window, select Compute From > Inlet . Ensure the values

that appear are the same values we inputted in Step 5. If the are, initialize the solution by

clicking Initialize.

Solve

Once the solution has been initialized, we are ready to solve the simulation. Go

to Solution > Run Calculation . Change Number of Iterations to 3000, then double

click Calculate. Sit back and twiddle your thumbs until Fluent spits out a converged

solution.

Results

Velocity

First, we will look at the velocity vectors of the solution to see if the make intuitive sense.

To plot the velocity vectors, go to Results > Graphics and Animations . In

the Graphics and Animations Window, select Vectors and click Set Up.... This will

bring up the Vectors Menu.

Make sure the settings of the menu match the figure above: namely Vectors of >

Velocity, Color by > Velocity , and set the second box as Velocity Magnitude . To see

the velocity vectors, press Display.

Pressure Contours

To view the pressure contours over the entire mesh, go to Results > Graphics and

Animations again, and in the Graphics and Animations Window, select Contours.

Click Set Up... to bring up the Contours Menu. Check the box next to Filled.

Under Contours Of , ensure that the two boxes that are selected

are Pressure... and Static Pressure .

Once these parameters are set, press Display to see the pressure contours.

Streamlines

To view the streamlines, keep the Contours window open, and change the Contours

Of box to Velocity, and the box below to Stream Function . Change Levels to 100.

Also, uncheck the box marked Auto Range, and set Min(kg/s) to 13.11,

and Max(kg/s) to 14.16

To view the streamlines, press Display

Pressure Coefficient

Next, we will plot the pressure coefficient along the surface of the airfoil. Click on Results

> Plots to open up the Plots Window. Under Plots, select XY Plot, and click Set Up....

In the window that pops up, change the settings Y-Axis Function > Pressure , and

change the second box to Pressure Coefficient . Ensure X-Axis Function > Direction

Vector. Under Surfaces, select airfoil. See the figure below for help.

When all the settings are correct, press Plot to plot the data to the command window. To

save the data to a text file, check the box next to Write to File. You'll notice that

the Plot button has been replaced by a button marked Write..., click it. Change the file

type to All Files and save the file name as Pressure_Coefficient.txt

Coefficients of Lift and Drag

To find the Coefficients of Lift and Drag, click Results > Reports to bring up

the Reports Window. In the Reports Window, select Forces and click Set Up.... This

will bring up the Force Reports menu

We need to set the parameters so drag across the airfoil (keep in mind, which is at an

angle) will be displayed. In the Force Reports window change the Direction

Vector such that X > .9945 and Y > .1045. Click Print to print the drag coefficient to

the command window. To print the lift coefficient, in the Force Reports window change

the Direction Vector such that X > -.1045 and Y > .9945. Again, press Print.

Verification and Validation

Verification

One of the ways we can verify our data is by refining the mesh. Open up the mesh, and

increase the Number of Divisions for Edge Sizing and Edge Sizing 2 to 100.

Click Mesh in the Outline window, and in the Details window, expand statistics. The

number of elements should now be 40000.

Exit out of the mesher. First, right click Setup and select Reset. Then

click in the project schematic. Open up the solver, and solve the

simulation using the same solver and boundary conditions (you'll have to input them

again), but this time change the number of iterations to 5000. Again, calculate the force

coefficients and graph the pressure coefficient.

Validation

To validate our data, we will take a compare the data from actual experiment.

Unrefined Mesh Refined Mesh Experimental Data

Lift Coeffient 0.6315 0.6670 0.6630

Drag Coefficient 0.0122 0.0063 0.0090

Below is a graph displaying the comparing Coefficient of Pressure along the airfoil for the

experimental data and the CFD simulation. The data is from Gregory & O'Reilly, NASA

R&M 3726, Jan 1970.

As we can see from the table and the graph, the CFD matches the data fairly well. There

are inaccuracies from factors like our assumption that the flow was inviscid, but we still

managed to extract some meaningful information from the simulation

Exercises

Consider the low-speed airflow over the NACA 0012 airfoil at low angles of attack. The

Reynolds number based on the chord is Rec = 2.88 10^6. This flow can reasonably be

modeled as incompressible and inviscid.

1. Incompressible, Inviscid Model

Explain why the incompressible, inviscid model for this ow should yield lift coefficient

values that match well with experiment but will yield a drag coefficient that is always zero.

2. Boundary Value Problem

What is the boundary value problem (BVP) you need to solve to obtain the velocity and

pressure distributions for this ow at an angle of attack of 10 degrees? Indicate governing

equations, domain and boundary conditions (u = 0 at a certain boundary etc.). For each of

the boundary conditions, indicate also the corresponding boundary type that you need to

select in FLUENT.

3. Coefficient of Pressure

Run a simulation for the NACA 0012 airfoil at angles of attack at 0 degrees and 10 degrees

for two cases: a mesh with 15000 elements and a mesh with 40000 elements. Plot the

pressure coefficient obtained from FLUENT on the same plot as data obtained from

experiment The experimental data is from Gregory & OReilly, NASA R&M 3726, Jan 1970

and is provided here Follow the aeronautical convention of flipping the vertical axis so

that negative Cp values are above and positive Cp values are below. This can be done in

MATLAB using set (gca, YDir, reverse);

4. Lift and Drag Coefficient

Obtain the lift and drag coefficients from the FLUENT results on the two meshes. Compare

these with experimental or expected values (present this comparison as a table). The

experimental values for 0 degree angle of attack are: Cl = 0.025; Cd = 0.0069, and the

experimental values for 10 degree angle of attack are: Cl = 1.2219; Cd = 0.0138.

Conclusions

Comment on the comparison with experiment for the two angles of attack. Also,comment

on the effect of mesh refinement. How does the pressure distribution over the airfoil

change on increasing the angle of attack?