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In the hand calculations we will be applying the conservation of energy, mass and momentum equations for a 1D inviscid compressible flow. This differs from the way that FLUENT solves the problem as FLUENT instead uses the 2D inviscid compressible flow equations.

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Flow with M = 3 comes straight on in the x-direction towards the wedge. We know the wedge angle theta from our geometry of the wedge to be 15 degrees. See the figure below:

Image Added

Step 1: We then look at the Theta-Beta-M chart here we can find what the shock angle is corresponding to our conditions. The line M = 3 with wedge angle theta at 15 degrees corresponds to a shock angle beta of about 32 degrees. 

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\Large
\begin{equation}\nonumber
M_{2N}^2 = M_{1N}^2(\frac{(\gamma -1)M_{1N}+2}{2\gamma M_{1N}-(\gamma -1)})
\end{equation}
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\begin{equation}\nonumber
M_2 =\frac{M_{2N}}{sin(\beta-\theta)}
\end{equation}
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\begin{equation}\nonumber
\frac{p2p_2}{p1p_1} = \frac{2\gamma M_{1N}^2 - (\gamma - 1)}{\gamma + 1}
\end{equation}
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\begin{equation}\nonumber
\frac{T_2}{T_1} = \frac{(2\gamma M_{1N}^2 - (\gamma - 1))((\gamma -1)M_{1N}^2 +2)}{(\gamma +1)^2 M_{1N}^2}
\end{equation}
\\

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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:

Screen Management

This tutorial is designed such that the user can have both ANSYS Workbench and the tutorial open. As shown below, this online tutorial should fill approximately 1/3 of the screen, while ANSYS Workbench fills the remaining 2/3 of the screen.

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

Right-click the top box of the project schematic and go to Rename, and name the project Supersonic Flow Over a Wedge. You are ready to create the geometry for the simulation.

Go to Step 2: Geometry

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