Exp: 03 - Simulation of Supersonic Flow Over A Wing of Convex Cross Section
Exp: 03 - Simulation of Supersonic Flow Over A Wing of Convex Cross Section
Exp: 03 - Simulation of Supersonic Flow Over A Wing of Convex Cross Section
Problem Specification
Consider a 15 angle wedge at zero angle of attack. The incoming flow conditions are: M1=3,
p1=1 atm, T1=300 K. Use FLUENT to obtain the flowfield over the wedge. Compare the pressure
coefficient on the wedge surface with the corresponding analytical result for an oblique shock.
Start GAMBIT
Create a new directory called wedge and start GAMBIT from that directory by typing gambit -id
wedge at the command prompt.
Under Main Menu, select Solver > FLUENT 5/6 since the mesh to be created is to be used in
FLUENT 6.0.
Create Vertices
A 0 0 0
B 0 1.259 0
C 0.5 1.259 0
D 1.5 1.259 0
E 1.5 0.268 0
F 0.5 0 0
Using bottom up approach, we start by creating vertices of the geometry using the coordinate
given.
Operation Toolpad > Geometry Command Button > Vertex Command Button >
Create Vertex
Create the vertices by entering the coordinates under Global and the label under Label:
Click the FIT TO WINDOW button to scale the display so that you can see all the vertices. The
resulting image should look like this:
Create Edges
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 for Label.
Click Apply. GAMBIT will create the edge. You will see a message saying something like
"Created edge: AB'' in the Transcript window.
Similarly, create the edges BC, CD, DE, EF, FA and CF. Click on the to select the vertices
from the list and move them to the picked list. You can also hold the shift button and mouse
click the vertices for selection.The resulting image should look like this.
Create Faces
The edges we have created can be joined together to form faces. We will need to define two
faces.
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.
We will call two faces face1 and face2. To create the face1, select the edges AB, BC, CF, and
FA. Enter face1 for the label and click Apply. GAMBIT will tell you that it has "Created face:
face1'' in the transcript window.
Similarly, create the face face2 by selecting CD, DE, EF and CF.
We are now ready to mesh the geometry.
We will mesh each of the 2 faces separately to get our final mesh. Before we mesh a face, we
need to define the point of distribution for each of the edges that form the face.
We will use the default setting for meshing of the edge.
Operation Toolpad > Mesh Command Button > Edge Command Button ** *> Mesh
Edges*
Select the edge AB. The edge will change color and an arrow will appear on the edge. This
indicates that you are ready to mesh this edge. Select interval size under Spacing. Enter 0.04
for interval size.
Next we will mesh the edge BC. Select the edge BC and enter 0.04 for interval size.
Do the same for edge CD and CF.
Now that the appropriate edge meshes have been specified, mesh the face face1:
Operation Toolpad > Mesh Command Button > Face Command Button > Mesh
Faces
Select the face1. The face will change color. You can use the defaults of Quad (i.e.
quadrilaterals) and Map. Click Apply.
The meshed face should look as follows:
Note that for each mesh face, we only define 2 mesh edges. Gambit will automatically define
the other two mesh edge for face mesh creation. Manual mesh of all edges can be done if more
control of the mesh is required. Please refer to the index of the GAMBIT User Guide and look
under Edge>Meshing for explanation on other type of meshing parameters.
We'll create groups of edges and then create boundary entities from these groups.
First, we will group AB, BC, CD and DE together.
Operation Toolpad > Geometry Command Button > Group Command Button > Create
Group
Select Edges and enter farfield for Label, which is the name of the group. Select the edges AB,
BC, CD and DE.
Note that GAMBIT adds the edge to the list as it is selected in the GUI.
Click Apply.
In the transcript window, you will see the message "Created group: farfield".
Similarly, create the other two groups. You should have created a total of three groups:
Group Name Edges in Group
farfield AB,BC,CD,DE
wedge EF
symmetry EF
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
Under Entity, select Groups.
Click on the wedge surface. Next to Name:, enter wedge. Leave the Type as WALL.
Click Apply.
In the Transcript Window, you will see a message saying "Created Boundary entity: wedge".
Similarly, create boundary entities corresponding to farfield and symmetry groups. Set Type the
to Pressure Farfield andsymmetry in each case.
Export Mesh
Launch FLUENT
Start > All Programs > ANSYS 12.0 > Fluid Dynamics > FLUENT
Select 2D under the Dimension list and Double Precision under the Options list, and click Run.
In the double-precision solver, each floating point number is represented using 64 bits in
contrast to the single-precision solver which uses 32 bits. The extra bits increase not only the
precision but also the range of magnitudes that can be represented. The downside of using
double precision is that it requires more memory.
Import File
Analyze Grid
First, we check the grid to make sure that there are no errors.
Problem Setup > General > Check
Any errors in the grid would be reported at this time. Check the output and make sure that there
are no errors reported.
Mesh > Info > Size
How many cells and nodes does the grid have?
General > Mesh > Display...
You can look at specific parts of the grid by choosing the items you wish to view
under Surfaces (click to select and click again to deselect a specific boundary).
Click Display again when you have selected your boundaries. Note what the surfaces farfield,
wedge, etc. correspond to by selecting and plotting them in turn.
Define Properties
Click OK. This means the solver will neglect the viscous terms in the governing equations.
Models > Energy
Double click on Energy - Off
In compressible flow, the energy equation is coupled to the continuity and momentum
equations. So we need to solve the energy equation for our problem.
To turn on the energy equation, check the box next to Energy Equation and click OK.
Problem Setup > Materials
Make sure air is selected under Fluid. Double click air, set Density to ideal-gas and make
sure Cp is constant and equal to 1006.43 j/kg-k. Also make sure the Molecular Weight is
constant and equal to 28.966 kg/kgmol. Selecting the ideal gasoption means that FLUENT will
use the ideal-gas equation of state to relate density to the static pressure and temperature.
Click Change/Create.
Define > Operating Conditions
To understand what the Operating Pressure is, read through the short-and-sweet section
8.14.2 in the user's guide. We see that for all flows, FLUENT uses the gauge pressure internally
in order to minimize round-off errors. Any time an absolute pressure is needed, as in the ideal
gas law, it is generated by adding the operating pressureto the gauge pressure:
absolute pressure = gauge pressure + operating pressure
Round-off errors occur when pressure changes p in the flow are much smaller than the
pressure values p. One then gets small differences of large numbers. For our supersonic flow,
we'll get significant variation in the absolute pressure so that pressure changes p are
comparable to pressure levels p. So we can work in terms of absolute pressure without being
hassled by pesky round-off errors. To have FLUENT work in terms of the absolute pressure, set
the Operating Pressure to 0.
Thus, in our case, there is no difference between the gauge and absolute pressures. Click OK.
Define > Boundary Conditions
Set the boundary condition for the pressure_farfield surface (aka zone) to the boundary
type pressure-far-field by clicking on the drop-down list. Select Yesin the pop-up window
asking if it's "OK to change pressure_farfield's type from wall to pressure-far-field?".
Set the Gauge Pressure to 101325. Set the Mach Number to 3. Under X-Component of Flow
Direction, enter a value of 1 (i.e. the farfield flow is in the X direction).
Next, click on the Thermal Tab. Change the temperature to 300K.
Click OK. The pressure-far-field boundary type effectively imposes that there is no upstream
propagation of disturbances if the flow at the boundary is supersonic. See section 7.9 of the
FLUENT help for more details about this boundary type.
Similarly, change the boundary condition for the symmetry surface to the symmetry boundary
type. No user input is required for the symmetry boundary type. At any boundary set to
the symmetry type, FLUENT internally sets
normal velocity = 0
normal gradients of all variables = 0
Step 5: Solve!
Solve > Controls or Solutions > Solution Controls
Click on the Equations button and select Flow, then click OK. Also, set the Courant
Number to 0.1.
Solve > Methods or Solutions > Solution Methods
We'll use a second-order discretization scheme. Under Spatial Discretization,
set Flow to Second Order Upwind.
We can see the flow turning through an oblique shock wave as expected. Behind the shock, the
flow is parallel to the wedge and the Mach number is 2.2. Save this figure to a file.