Fluid DynamicsCAx Tutorial: Flow over an airfoilGuided Tutorial
#7
Deryl O. Snyder C. Greg JensenBrigham Young University Provo, UT
84602
Special thanks to: PACE, Fluent, UGS Solutions, Altair
Engineering; and to the following students who assisted in the
creation of the Fluid Dynamics tutorials: Leslie Tanner, Cole
Yarrington, Curtis Rands, Curtis Memory, and Stephen McQuay.
Flow over an airfoil2D FlowIn this tutorial, Gambit will be used
to create and mesh the geometry for the problem. Fluent will be
used to solve for the flow field within the domain and calculate
the inviscid lift coefficient and surface velocity profile for a
NACA 632-015 airfoil. This 2D tutorial will provide more experience
with 2D inviscid flows, as well as introduce an ICEM input method
in Gambit. An explanation of how to report lift and drag
coefficients on an object will also be given.
The methods expressed in these tutorials represent just one
approach to modeling, defining and solving 2D problems. Our goal is
the education of students in the use of CAx tools for modeling,
defining and solving fluids application problems. Other techniques
and methods will be used and introduced in subsequent
tutorials.
The normalized squared velocity for an airfoil at 0 and 1.85
degrees angle of attack is shown below. Compare the graph obtained
using CFD, and calculate the coefficient of lift cL at 1.85 degrees
angle of attack.
3
Flow over an airfoilCreating GeometryBegin the problem by
creating geometry in Gambit.
Begin by importing the data points for the airfoil, and creating
the top and bottom edges.
File > Import > ICEM Input
Locate the file NACA.63.015.dat Under Geometry to Create select
vertices and edges, and deselect faces. The points will be loaded,
and an edge will be placed through the vertices. Select Accept.
4
Flow over an airfoilCreating GeometryNow create verticies that
will be used to define the outer flow domain. The seven are shown
in the table below. Operation > Geometry > Vertex > Create
Real Vertex Name each point by typing the letter next to Label.
Label A B C D E F G X 1 1 -14 25 25 25 1 Y 15 -15 0 15 0 -15 0 Z 0
0 0 0 0 0 0
5
Flow over an airfoilCreating GeometryCreate edges for meshing.
Operation > Geometry > Edge > Create Straight Edge Create
edges using the following vertices, and label them according to
their vertices. GE, BF, AD, AG, BG, DE, EF
Create two arcs, CA and CB.
Operation > Geometry > Edge > Create Real Circular
Arc
For the Center of the arc, select vertex G. Select vertices C
and A as the end-points. Select Apply. Repeat this procedure to
create arc CB.
6
Flow over an airfoilCreating GeometryMake three faces that will
be meshed later. Operation > Geometry > Face > Create Face
From Wireframe Create a semicircular face from the arc edges and
the two center vertical edges. Create a face from the airfoil
edges. Subtract the airfoil face from the semicircular face without
retaining either original face. Select the following edges, and
select Apply to create the final two faces. AD, AG, GE, DE BG, GE,
EF, BF If problems are encountered in creating the geometry, the
geometry can be loaded from the file Airfoil_Geometry.dbs.
7
Flow over an airfoilMeshing GeometryFirst mesh the edges.
Operation > Mesh > Edge > Mesh Edges
Select the upper edge of the airfoil. Make sure the arrow is
pointing from left to right. Use the following parameters Type:
Last Length Length: 0.02 Interval Count: 120 Select Apply. Repeat
this procedure, using the same values for the lower edge of the
airfoil.
8
Flow over an airfoilMeshing GeometryMesh the horizontal edges.
Use the following values for edges AD, GE, and BF, making sure that
the arrow on each edge points left to right. Type: First Length
Length: 0.02 Interval Count: 50 Use these values for edges AG, and
DE, with the arrow going from bottom to top. Type: Successive Ratio
Ratio: 1.1 Interval Count: 50 Use the previous values to mesh edges
BG and EF, with the arrow going from top to bottom. Finally, mesh
the two arcs CA, and CB. With the arrow pointing right to left, use
the following values: Type: First Length Length: 0.02 Interval
Count: 120 Mesh the faces. Operation > Mesh > Face > Mesh
Faces Select the three faces, and select Apply. If problems are
encountered in meshing the geometry, the meshed geometry can be
loaded from the file Airfoil_Meshed.dbs.
9
Flow over an airfoilBoundary ConditionsThe next task is to
specify the boundary conditions. The Fluent solver should be
specified by default. If not, change it now. Solver > Fluent 5/6
Boundary condition specification will be facilitated by grouping
certain edges together. Operation > Geometry > Group >
Create Groups Select Edges from the pull down menu. Select edges CA
and CB, and name the group arc. Select Apply. Select edges AD and
BF and name the group level. Select Apply. Select edges DE and EF
and name the group out. Select Apply. Select the airfoil edges and
name it airfoil. Select Apply.
10
Flow over an airfoilBoundary ConditionsNow specify the specific
boundary conditions. Operation > Zones > Specify Boundary
Types From the Entity pull down menu, select groups. Specify the
boundaries as follows: Group: Arc Type: Velocity_Inlet Name: Arc
Select Apply after each group. Group: Level Type : Velocity_Inlet
Name: Level Group: Airfoil Type: Wall Name: Airfoil Group: Out
Type: Pressure Outlet Name: Out If problems are encountered in
specifying boundary conditions, the mesh with boundary conditions
specified can be loaded from the file Airfoil_Complete.dbs.
11
Flow over an airfoilExporting the MeshExport the mesh File >
Export > Mesh (It is a 2-D Mesh).
Export the mesh as Airfoil.msh and save the Gambit file. Exit
out of Gambit.
12
Flow over an airfoilDefining the ProblemOpen the 2D version of
Fluent. Import the mesh created in Gambit. File > Read > Case
Locate Airfoil.msh and select OK. Check the grid for errors. Grid
> Check Define the solver parameters. Define > Models >
Solver... The default 2D segregated solver will work just fine for
this problem. Select OK. Now Define the viscous model for the
problem. Define > Models > Viscous. Select Inviscid and OK.
Confirm that the default material is air. Define >
Materials...
13
Flow over an airfoilDefining the ProblemDefine the boundary
conditions that were specified in Gambit. Define > Boundary
Conditions...
Default values for airfoil, default-interior, fluid, and out are
sufficient. Select arc from the Zone menu. It is a Velocity_Inlet
Type Select Set... Select Components from the Velocity
Specification Method pull down menu. Specify the X and Y velocity
components according to 1.85 degrees angle of attack, using a
freestream velocity of 40 m/s. X: 39.97915 from (40*cos(1.85)) Y:
1.291319 from (40*sin(1.85)) Select OK. Repeat the procedure for
the level zone.Note: For 0 degrees angle of attack, simply change
the X velocity component to 40, and the Y component to 0.
14
Flow over an airfoilSolving the ProblemSpecify the solution
control parameters. Solve > Controls > Solution... Make the
following changes to the default entries. Discretization Pressure:
Presto! Momentum: Second Order Upwind Leave all other entries at
their default values as shown to the right. Select OK.
15
Flow over an airfoilSolving the ProblemNow initialize the
solution. Solve > Initialize > Initialize... Under Compute
From select arc. Select Init then Close. To view a real-time plot
of the residuals Solve > Monitors > Residual. Select Plot
under the Options menu. Under Plotting select 1 under Window.
Uncheck the three Check Convergence boxes. We will allow the
iterations to continue, and the residuals should level off and
approach a minimum value, indicating that the solution is
converged. Select OK.
16
Flow over an airfoilSolving the ProblemHave Fluent report the
values of the lift and drag coefficients during iteration. Solve
> Monitors > Force... With Drag selected under Coefficient
Select Print under Options. Under Force Vector enter in the
components of the drag force, namely X = .99947877 from (cos(1.85))
Y = .03228298 from (sin(1.85)) Select airfoil under Wall Zones.
Select Apply. Select Lift under Coefficient. Select Print under
Options. Under Force Vector enter in the components of the lift
force. X = -.03228298 from (-sin(1.85)) Y = .99947877 from
(cos(1.85)) Select airfoil under Wall Zones. Select Apply. Report
> Reference Values... In order to properly calculate the lift
and drag coefficients, fluent needs correct reference values. Next
to Velocity, enter 40. During iterations, the drag and lift
coefficients will print out to the command window.
17
Flow over an airfoilSolving the ProblemNow iterate to find a
solution Solve > Iterate... Under Number of Iterations enter
500. Select Iterate.
18
Flow over an airfoilAnalyzing the ResultsThe image which
accompanies the problem statement shows that the lift coefficient,
cL for the airfoil at an angle of attack of 1.85 degrees is 0.22
(found experimentally). A quick inspection of the coefficient in
the main Fluent window shows that our numerical data is in good
agreement. The experimental data also shows a plot of
non-dimensional velocity squared vs. nondimensional airfoil
location. To compare the computational results with the
experimental results, a custom field function must be defined.
Define > Custom Field Functions... Start by selecting the open
parenthesis, (, from the calculator pad. Under Field Functions
select Velocity, and then Velocity Magnitude. You must click on the
Select button for it to appear in the function. Select the divide
button ( / ). Select the numbers 4 then 0 (for U = 40 m/s). Select
the close parenthesis, ), select y^x, then select 2 (for squared).
Name the function ratio, and select Define.
19
Flow over an airfoilAnalyzing the ResultsTo view a plot of
(u/U)^2 vs. airfoil location Plot > XY Plot... Under Y Axis
Function, select Custom Field Functions, and then ratio. Leave X
Axis Function as Direction Vector. Select airfoil under Surfaces.
Select Plot.
The plot should resemble the one shown to the right.
If problems are encountered in setting up or analyzing this
problem in Fluent, the solved problem can be read in as a Case
& Data... from the file Airfoil_1.85_degrees.cas.
20
Flow over an airfoilSolving the ProblemFinally, define the
problem again for 0 degrees angle of attack. Changes need to be
made in the following areas before iterating again. Define >
Boundary Conditions. For the Level zone and the Arc zone, define
the components of velocity to be X = 40, Y = 0. Solve > Monitors
> Force... For the drag coefficient, set the X and Y components
of the force to X = 1, Y = 0. Select Apply. For the lift
coefficient, set the X and Y components of the force to X = 0, Y =
1. Select Apply. Again, during iterations drag and lift coefficient
values will be printed to the command window. Check that the lift
coefficient for the level case (0-degree angle of attack) is
zero.
21
Flow over an airfoilAnalyzing the Results
1.8
Shown to the right is a comparison of the empirical data with
the computational solution. The graphs are qualitatively very
similar, and have quantitative values that are very similar as
well. Refining the grid by about double will bring the two sets of
data into excellent agreement.(u/U)^2
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 0.0 0.2 0.4 0.6
Fluent Emperical
0.8
1.0
x/c
1.6 1.4 Fluent Emperical
Also shown to to the right is another comparison of the same
airfoil, but at 0 degrees angle of attack. Again, the discrepancy
is due to a solution that is not grid-independent. Try refining the
grid by about double and repeating the solution.
1.2 1
(u/U)^2
0.8 0.6 0.4 0.2 0
0
0.2
0.4
0.6
0.8
1
x/c
22