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[Problem Specification|FLUENT - Supersonic Flow Over a Wedge - Problem Specification]\\
[1. Pre-Analysis & Set-Up|FLUENT - Supersonic Flow Over a Wedge- Step 1]\\
[2. Geometry|FLUENT - Supersonic Flow Over a Wedge- Step 2]\\
[3. Mesh|FLUENT - Supersonic Flow Over a Wedge- Step 3]\\
[4. Setup (Physics)|FLUENT - Supersonic Flow Over a Wedge- Step 4 (FLUENT 6.3.26)]\\
[5. Solutions|FLUENT - Supersonic Flow Over a Wedge- Step 5 (FLUENT 6.3.26)]\\ {color:#ff0000}{*}6. Results{*}{color}\\
[7. Verification & Validation|FLUENT - Supersonic Flow Over a Wedge- Step 7]
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{info:title=Useful Information}
[Click Here|SIMULATION:FLUENT - Supersonic Flow Over a Wedge - Step 4 *New] for the FLUENT 6.3.26 version.
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h2. *Step 6: Analyze Results*
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*Plot Velocity Vectors*
Let's plot the velocity vectors obtained from the FLUENT solution.
*Display > Graphics and Animations{*}or{*}Results > Graphics and Animations*
Select {color:#660099}{*}{_}Vectors{_}{*}{color}, click on the {color:#660099}{*}{_}Set up{_}{*}{color} button. Under {color:#660099}{*}{_}Color by{_}{*}{color}, select {color:#660099}{*}{_}Mach Number{_}{*}{color} in place of {color:#660099}{*}{_}Velocity Magnitud{_}{*}{color}{color:#990066}{*}{_}e{_}{*}{color}since the former is of greater interest in compressible flow. The colors of the velocity vectors will indicate the Mach number. Use the default settings by clicking {color:#660099}{*}{_}Display{_}{*}{color}.
This draws an arrow at the center of each cell. The direction of the arrow indicates the velocity direction and the magnitude is proportional to the velocity magnitude (not Mach number, despite the previous setting). The color indicates the corresponding Mach number value. The arrows show up a little more clearly if we reduce their lengths. Change Scale to 0.2. Click {color:#660099}{*}{_}Display{_}{*}{color}.
!Step6-image1.png|thumbnail,width=221,height=261!
Zoom in a little using the middle mouse button to peer more closely at the velocity vectors.
!step6-image2.png|thumbnail!
{color:blue} {color}
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:
*Main Menu > File > Hardcopy*
Select {color:#660099}{*}{_}JPEG{_}{*}{color} and {color:#660099}{*}{_}Color{_}{*}{color}. Uncheck {color:#660099}{*}{_}Landscape Orientation{_}{*}{color}. Save the file as wedge_vv.jpg in your working directory. Check this iimage by opening this file in an image viewer.
!step6-image4.png|thumbnail,width=220,height=111!
Let's investigate how many mesh cells it takes for the flow to turn. To turn on the mesh do the following:
*Display > Graphics and Animations{*}or{*}Results > Graphics and Animations*
Select {color:#660099}{*}{_}Vectors{_}{*}{color}, click on the {color:#660099}{*}{_}Set up{_}{*}{color} button. Under options select the {color:#660099}{*}{_}Display Mesh{_}{*}{color} checkbox and a new window will pop up. Under Surfaces select {color:#660099}{*}{_}default-interior,_{*}{color}click {color:#660099}{*}{_}Display{_}{*}{color}and close it.
!step6-image5.png|thumbnail,width=216,height=183!
The mesh will substitute the arrows and to display both the mesh and the arrows go back to the Vector Set up window click {color:#660099}{*}{_}Display{_}{*}{color} again and now the mesh and arrows will appear on the same picture.
We see that it takes 2-3 mesh cells for the flow to turn. According to inviscid theory, the shock is a discontinuity and the flow should turn instantly. In the FLUENT results, the shock is "smeared" over 2-3 cells. In the discrete equations that FLUENT solves, there are terms that act like viscosity. This introduced viscosity contributes to the smearing. A more thorough explanation would have to go into the details of the numerical solution procedure.
*Plot Mach Number Contours*
Let's take a look at the Mach number variation in the flowfield.
*Display > Graphics and Animations{*}or{*}Results > Graphics and Animations*
Select {color:#660099}{*}{_}Contours{_}{*}{color}, click on the {color:#660099}{*}{_}Set up{_}{*}{color} button. Under {color:#660099}{*}{_}Contours of{_}{*}{color}, choose {color:#660099}{*}{_}Velocity.._{*}{color} and {color:#660099}{*}{_}Mach Number{_}{*}{color}. Select the {color:#660099}{*}{_}Filled{_}{*}{color} option. Increase the number of contour levels plotted: set {color:#660099}{*}{_}Levels{_}{*}{color}to 100.
!step6-image7.png|thumbnail!
Click {color:#660099}{*}{_}Display{_}{*}{color}.
We see that the Mach number behind the shockwave is uniform and equal to 2.2. Compare this to the corresponding analytical result.
*Plot Pressure Coefficient Contours*
Let's set the reference values necessary to calculate the pressure coefficient.
*Report > Reference Values*
Select {color:#660099}{*}{_}pressure-farfield{_}{*}{color} under {color:#660099}{*}{_}Compute From{_}{*}{color}.
!step6-image9.png|thumbnail,width=159,height=240!
The above reference values of density, velocity and pressure will be used to calculate the pressure coefficient from the pressure.
*Display > Graphics and Animations{*}or{*}Results > Graphics and Animations*
Select {color:#660099}{*}{_}Contours{_}{*}{color}, click on the {color:#660099}{*}{_}Set up{_}{*}{color} button. Select {color:#660099}{*}{_}Pressure..._{*}{color} and Static Pressure from under{color:#660099}{*}{_}Contours Of{_}{*}{color}. Then select {color:#660099}{*}{_}Pressure Coeffient{_}{*}{color}.
The pressure coefficient after the shockwave is 0.293, very close to the theoretical value of 0.289. The pressure increases after the shockwave as we would expect.
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Now we will plot the pressure coefficient along the wedge. Go to:
*Results (left-hand side of the screen) > Plots*
Select {color:#660099}{*}{_}XY Plot{_}{*}{color} and then click on the {color:#660099}{*}{_}Set up{_}{*}{color} button. In the pop-up window specify the {color:#660099}{*}{_}Y Axis Function{_}{*}{color} to{_}pressure_ and _pressure coefficient_. Select the{_}wedge_ from the available surfaces and click {color:#660099}{*}{_}Plot._{*}{color}Your specifications should look like the picture below.
!step6-image11.png!
The picture above, though descriptive might not give you the details you are looking for. You can save the data used in this plot to a file by checking the {color:#660099}{*}{_}Write to File{_}{*}{color} checkbox under {color:#660099}{*}{_}Options._{*}{color} Then click the {color:#660099}{*}{_}Write..._{*}{color} button, give the file a name and click {color:#660099}{*}{_}Function{_}{*}{color}.
To measure the Shock Angle we can add a new line to the plot. Click on {color:#660099}{*}{_}New Surface{_}{*}{color} and select the {color:#660099}{*}{_}Line/Rake{_}{*}{color}option. Set the first point to (0,0.35) and the second one to (1.5,0.35) name the line y=0.35 and click on {color:#660099}{*}{_}Create{_}{*}{color}.
!step6-image12.png!
The new line will be added to the available surfaces. From these select {color:#660099}{*}{_}Symmetry, Wedge and y=0.35{_}{*}{color}. You will notice that there is no {color:#660099}{*}{_}Plot{_}{*}{color} button, this happened because the {color:#660099}{*}{_}Write to file{_}{*}{color} checkbox under options is still checked. Uncheck it and then click on {color:#660099}{*}{_}Plot{_}{*}{color}. You will now be able to see the lines on the plot.
Nest, we will plot the Total Pressure. To achieve this on the Solution XY Plot pop-up window select {color:#660099}{*}{_}Total Pressure{_}{*}{color} under {color:#660099}{*}{_}Y Axis Function{_}{*}{color} and click {color:#660099}{*}{_}Plot{_}{*}{color}.
Finally, we will find out what the drag coefficient for this scenario is. Close the pop-up window if it's still open and go to
*Problem Setup > Reference Values*
Make sure that the parameter for Area is 1. Then go to
*Results > Reports > Forces > Set up... > Print*
The drag coefficient should be the value listed in the last column of the values in the output window.
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