# Pre-Analysis & Start-Up — Lesson 2

### Pre-Analysis

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.

The equations can be written as:

#### Hand Calculations

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

Step 1: We then look at the theta-beta-M chart here to 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.

Step 2: We calculate the value of the free stream Mach number normal to the shock, so we can use normal shock relations to relate quantities upstream and downstream of the shock.

Step 3: Now we can relate the normal Mach numbers to each other through the normal shock relations:

We expect that the flow downstream of the shock will still be supersonic as the flow experiences only a weak oblique shock, evident from looking at the theta-beta-M chart. This also becomes clear in the hand calculations.

Alternative Procedure:

In order to calculate the expected results behind the shock, you can also use an oblique shock wave calculator (link grc.nasa.gov). At Mach 3 and an angle of 15 degrees, we find the following:

### Open Ansys Workbench

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 you 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.

### Set Up Project

To begin, we need to tell Workbench 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.