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UNDER CONSTRUCTION
{panel}
Author: Daniel Kantor and Andrew Einstein, Cornell University

{color:#ff0000}{*}Problem Specification{*}{color}
[1. Create Geometry in GAMBIT|FLUENT - Turbulent Flow Past a Sphere - Step 1]
[2. Mesh Geometry in GAMBIT|FLUENT - Turbulent Flow Past a Sphere - Step 2]
[3. Specify Boundary Types in GAMBIT|FLUENT - Turbulent Flow Past a Sphere - Step 3]
[4. Set Up Problem in FLUENT|FLUENT - Turbulent Flow Past a Sphere - Step 4]
[5. Solve\!|FLUENT - Turbulent Flow Past a Sphere - Step 5]
[6. Analyze Results|FLUENT - Turbulent Flow Past a Sphere - Step 6]
[7. Refine Mesh|FLUENT - Turbulent Flow Past a Sphere - Step 7]
[Problem 1|FLUENT - Turbulent Flow Past a Sphere - Problem 1]
{panel}

h2. Step 6: Analyze Results

For all of our analysis we will be looking at the {color:#660099}{*}{_}Sphere{_}{*}{color} surface under {color:#660099}{*}{_}Surfaces{_}{*}{color}, unless otherwise noted.

h4. Plot Velocity Vectors

Let's plot the velocity vectors obtained from the FLUENT solution.

*Display > Vectors*

Set the {color:#660099}{*}{_}Scale{_}{*}{color} to 141 and {color:#660099}{*}{_}Skip{_}{*}{color} to 40. Click {color:#660099}{*}{_}Display{_}{*}{color}.

\\  [!step6_velocity_vectorsm!Vectors.jpg!|^step6_velocity_vector.jpg]

\**\**\**\**From this figure, we see that there is a region of low velocity and recirculation at the back of cylinder.*\*************\*|thumbnail!
 
 *If we look closely at the sphere we can start to see where the separation occurs.*

{info:title=Zoom in the cylinder using the middle mouse button.}
{info}
Now, let's take a look at the Contour of PressureVelocity Coefficientmagnitude variation around the cylindersphere.

*Display > Contours*

Under {color:#660099}{*}{_}Contours of{_}{*}{color}, choose {color:#660099}{*}{_}PressureVelocity..._{*}{color} and {color:#660099}{*}{_}PressureVelocity CoefficientMagnitude{_}{*}{color}. Select the {color:#660099}{*}{_}Filled{_}{*}{color} option. Increase the number of contour levels plotted: set {color:#660099}{*}{_}Levels{_}{*}{color} to {{100}}.

!step6_Cphowto !Contours.jpg|width=32,height=32!
thumbnail!
Click {color:#660099}{*}{_}Display{_}{*}{color}.
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[!step6_Cp_contoursm !VelocityMag.jpg!|^step6_Cp_contour.jpg]

\****\**\**\**Because|thumbnail!
*We see the cylinderflow is symmetry mostly what we would expect in shape, we see that the pressure coefficient profile is symmetry between the top and bottom of cylinder.*\*******\*
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this case.*

Now, let's take a look at the Contour of Turbulent Intensity around the sphere. This will give us a picture of the turbulence that is occurring around the sphere. \\

*Display > Contours*

Under {color:#660099}{*}{_}Contours of{_}{*}{color}, choose {color:#660099}{*}{_}Turbulence..._{*}{color} and {color:#660099}{*}{_}Turbulent Intensity{_}{*}{color}. Select the {color:#660099}{*}{_}Filled{_}{*}{color} option. Increase the number of contour levels plotted: set {color:#660099}{*}{_}Levels{_}{*}{color} to {{100}}.

 Click {color:#660099}{*}{_}Display{_}{*}{color}.\\ !TurbulentInt.jpg|thumbnail!\\ \\

h4. Plot Stream Function

Now, let's take a look at the Stream Function.

*Display > Contours*

Under {color:#660099}{*}{_}Contours of{_}{*}{color}, choose {color:#660099}{*}{_}Velocity.._{*}{color} and {color:#660099}{*}{_}Stream Function{_}{*}{color}. Deselect the {color:#660099}{*}{_}Filled{_}{*}{color} option. Click {color:#660099}{*}{_}Display{_}{*}{color}.
\\

[!step6_streamlinesm.jpg!|^step6_streamline.jpg]

\***\**\**\**\**Enclosed streamlines at the back of cylinder clearly shows the recirculation region.*\***********\*

h4. Plot Vorticity Magnitude

Let's take a look at the Pressure Coefficient variation around the Sphere. Vorticity is a measure of the rate of rotation in a fluid.

*Display > Contours*

Under {color:#660099}{*}{_}Contours of{_}{*}{color}, choose {color:#660099}{*}{_}Velocity.._{*}{color} and {color:#660099}{*}{_}Vorticity Magnitude{_}{*}{color}. Deselect the {color:#660099}{*}{_}Filled{_}{*}{color} option. Click {color:#660099}{*}{_}Display{_}{*}{color}.

[!step6_vorticitysm.jpg!|^step6_vorticity.jpg]

h4. Pressure Coefficient

 
Pressure coefficient is a dimensionless parameter defined by the equation !step6_cp_equation.gif|width=32,height=32! where _p_ is the static pressure, _p_ ~ref~ is the reference pressure, and _q_ ~ref~ is the reference dynamic pressure defined by
{latex}\large $$ q_{ref} = {1 \over 2}{\rho_{ref}v_{ref}^2}$${latex}
The reference pressure, density, and velocity are defined in the *Reference Values* panel in Step 5.

Let's plot pressure coefficient vs x-direction along the cylinder.

*Plot > XY Plot...*

Change the {color:#660099}{*}{_}Y Axis Function{_}{*}{color} to {color:#660099}{*}{_}Pressure{_}{*}{color}{color:#660099}...{color}, followed by {color:#660099}{*}{_}Pressure Coefficient{_}{*}{color}. Then, select {color:#660099}{*}{_}Sphere{_}{*}{color} under {color:#660099}{*}{_}Surfaces{_}{*}{color}.

\\  !Step6_CpPanel.png|width=32,height=32!

Click {color:#660099}{*}{_}Plot{_}{*}{color}.

\\  [!step6_Cpplotsm.jpg!|^step6_Cpplot.jpg]

We see that there is a lot of scatter in our data, so we will be creating a line along the sphere to try and get a better picture of the pressure coefficient. To accomplish this we will create a surface of Z-axis position zero, and plot the line _y^2+(x-12)^2_, which is the equation of a ring around the sphere in the x-y plane.
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*Surface > Iso-Surface*
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Under {color:#660099}{*}{_}Surface of Constant{_}{*}{color} choose {color:#660099}{*}{_}Grid..._{*}{color} and {color:#660099}{*}{_}Z-Coordinate{_}{*}{color}. Under {color:#660099}{*}{_}Iso-Values{_}{*}{color} input _0_. This will create a plane in our flow in which the Z coordinate is zero everywhere. 

 (INSERT PIC)
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Call this _Zero_Plane_ and click {color:#660099}{*}{_}Create{_}{*}{color}.
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*Define > Custom Field Functions*

 Here we input our formula _y^2+(x-12)^2_ under {color:#660099}{*}{_}Definition{_}{*}{color}. To do use the {color:#660099}{*}{_}Field Functions{_}{*}{color} section and choose {color:#660099}{*}{_}Grid..._{*}{color} and choose {color:#660099}{*}{_}X-Coordinate{_}{*}{color} and {color:#660099}{*}{_}Y-Coordinate{_}{*}{color} for the "x" and "y" in the above formula.
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(INSERT PIC)
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Call this _Ring_ and click {color:#660099}{*}{_}Define{_}{*}{color}.
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*Surface > Iso-Surface*
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Now under {color:#660099}{*}{_}Surface of Constant{_}{*}{color} choose {color:#660099}{*}{_}Custom Field Functions{_}{*}{color} and choose our function {color:#660099}{*}{_}Ring{_}{*}{color}. Keep the default {color:#660099}{*}{_}Iso-Values{_}{*}{color} to _0_. Then, within {color:#660099}{*}{_}From Surfaces{_}{*}{color} select {color:#660099}{*}{_}Zero_Plane{_}{*}{color}.

(INSERT PIC)
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Call this _CpLine_ and click {color:#660099}{*}{_}Create{_}{*}{color}.
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We have now created the necessary line around the sphere to view the data better. Follow the same steps as before to plot the Pressure Coefficient, except that under {color:#660099}{*}{_}Surfaces{_}{*}{color} choose {color:#660099}{*}{_}CpLine{_}{*}{color}.
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We now see that the data is has less scatter (this effect, however, is far more significant on a more refined mesh). 
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(INSERT PIC)
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\*\**AFTER EXPLANATION OF PLOTTING*\*\*

Comparison

With our simulation data, we can now compare the Fluent with experimental data.  Click HERE to download the experimental data. The two sets of data for Pressure Coefficients are shown here:
(INSERT PICTURE).

The two sets of data for drag coefficient are shown here:
| Experimental | 0.1 |
| Simulation | 0.4 |
*[*Go to Step 7: Refine Mesh*|FLUENT - Turbulent Flow Past a Sphere - Step 7]*

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