# Mec208: Tutorial 6 – Cfd Compressible Flow

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MEC208: Tutorial 6 – CFD Compressible flow

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Learning Outcomes:

• Practice operating the Ansys software and workbench interfaces (Instructions for ANSYS 18.2)
• Create geometries from a coordinates file
• Implement a mapped mesh with defined sizing
• Use a density-based solver, suitable for compressible flow.
• Change fluid properties to use an ideal gas, required if the fluids required to compress.
• Utilize a standard initialisation scheme
• Extract relevant data to compare with theoretical calculations.

Contents

0. Theory        2

1. Workbench        2

2. Geometry        3

3. Mesh        5

4. Solver (FLUENT) Setup        6

5. Solver (FLUENT) Solution        9

6. Results        9

7. Stretch Goals        11

Appendix 1 – Creating a geometry coordinates file.        12

• You will simulate the flow of air in a convergent divergent nozzle using Ansys FLUENT, and extract Mach number data.
• A 2D, axisymmetric, inviscid flow will be assumed to reduce computational time.

## 0. Theory

A convergent divergent (CD) or de Laval nozzle is one in which the area changes along its length, at first contracting to a minimum (called the throat) and then expanding out. These types of nozzles are very useful because when dealing with compressible flows (i.e. Mach number, M > 0.3) reducing the cross-sectional area to increase flow velocity is only valid in subsonic (M < 1) regime. Once the flow is supersonic (M > 1) then the cross-sectional area needs to increase to increase the velocity.

In this tutorial you will simulate the flow through a CD nozzle whose cross-sectional area changes according to the following equation:

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Figure 1: Schematic of a convergent-divergent nozzle

The stagnation pressure, P0 at the inlet is 101325 Pa (1 atm) and the stagnation temperature, T0 is 300K. The static pressure at the outlet Poutlet is 3738.9 Pa. For this case consider the nozzle to be choked i.e. the flow at the throat is sonic (M=1). From the Little Book of Thermofluids we can determine that the pressure ratio P0/Pinlet = 1.02019 so that the static pressure at the inlet is 99348 Pa

Given that the Reynolds number for a high-speed flow like this one is quite large, then the viscous forces will be confined to a small region close to the wall. Hence, it is reasonable to assume the fluid to be inviscid.

## 1. Workbench

The Ansys Workbench interface serves as a bookkeeping interface which will keep track of the individual components needed to setup and run the simulation i.e. the geometry, the mesh, the solver and postprocessor. Given that the case being run in this tutorial is a simple one, we will use a fluid flow analysis system rather than a linked set of component systems to run this analysis.

1. Launch Workbench by typing “workbench” on the search bar next to the windows start button. At this point save the project to a relevant location that you have write access.
2. Drag an instance of Fluid Flow (Fluent) from the Analysis Systems Toolbox to the Project Schematic Window. (A dashed green box should appear in the top left corner of the window, drag the fluid flow system here).
3. Right click on the Geometry component (row 2) and select Properties. The same can be achieved by going to the View menu and enabling Properties and then selecting the Geometry component.
4. Change the Analysis Type from 3D to 2D
5. Again, right click on the Geometry component (row 2) and click on New DesignModeler Geometry…

Refer to figure 2 for the locations of each step on the Project Schematic Window.

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Figure 2: Workbench project window

## 2. Geometry

In this section you will create the geometry of the nozzle by importing a set of coordinates from a file. Since the geometry has rotational symmetry, we can create a geometry only for the top half of the pie in 2D and then apply an axisymmetric condition in the solver. For this tutorial the coordinate file, NozzleWallCoords.txt, has been provided. For reference, there are detailed instructions on how these coordinate files need to be formatted for proper importing into DesignModeler in Appendix 1.

1. Ensure that you have downloaded the file NozzleWallCoords.txt and saved it in the same location you saved the entire project.
2. Go to the Units menu at the top of the window and select Meter
3. Go to the Concept menu and select 3D Curve
4. On the Details View change Definition to From Coordinates File
5. For Coordinates File browse to where you saved the NozzleWallCoords.txt file and click Open.
6. Click Generate.
7. Click Zoom to fit.  [pic 5]

You should now have four line bodies imported into DesignModeler as shown in figure 3.

1. Create a new surface by selecting the Concept menu and then Surfaces From Edges.
2. Select all four edges and then in the Details View for Edges click Apply. There are two ways to select the edges:
1. Hold down the “Ctrl” key and mouse click on each edge individually.
2. Change the Select Mode to Box Select and dragging the left mouse over all four edges.
1. Click Generate
2. In order to only carry the surface (not the lines) over to the Mesher, right click each Line Body (under 5 parts, 5 bodies) and select Suppress Body.

Your geometry should now be as shown in figure 4. If so, save your work, close down DesignModeler and return to workbench for the next stage of the process: Meshing.

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Figure 3: DesignModeler with the geometry imported

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Figure 4: DesignModeler with the surface generated and the line edges suppressed

## 3. Mesh

Back in the Project Schematic Window in Workbench the Geometry component (row 2) should now have a green tick next to it.

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