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This example is taken from Cornell University’s ANSYS AIM Learning Modules

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Contents

1. Learning Goals
2. Problem Specification
3. Geometry
4. Mesh
5. Physics Setup
6. Results
7. Validation

Learning Goals

In this tutorial, you will learn to:

• To determine the total pressure on the walls of the nozzle.
• To show the Mach number distribution along the cross-section of flow field using Ansys AIM.

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Problem Specification

Compute the converging-diverging nozzle flow using AIM and plot the pressure and velocity (Mach number) graphs. The pressure at the inlet is 3 bar at 300 K.

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Geometry

The geometry of the Nozzle can be downloaded from here .

The following video shows how to navigate through Discovery AIM to import the geometry.

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Mesh

In this example, we will be using Automatic Physics-Aware Meshing. Automatic physics-aware meshing helps automate and simplify your problem setup. With automatic physics-aware meshing, the computational mesh is generated automatically based on the solution fidelity setting and the physics inputs.

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Physics Setup

This video shows how to set up the Boundary Conditions for solving Compressible flow through the nozzle.

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Results

This video explains how to determine the distribution of velocity vector through the nozzle volume and determine the pressure on the walls of the nozzle. It also explains how to determine the Mach number and produce a contour of it along the cross-sectional plane.

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Hand Calculations

In quasi-one-dimensional flow for this converging-diverging nozzle, we expect that the Mach number at the inlet will be subsonic and accelerating until, at the minimum nozzle area (the throat), the flow becomes sonic with M = 1. Since the nozzle starts to diverge, the fluid will continue accelerating until the exit, where it continues as supersonic. The Mach number at the end of the nozzle can be calculated in the equations below. The diameters of the end and throat area were converted to Area using formula (1) and compared using formula (2) to find the Mach number using isentropic flow tables.

The resulting Mach number at the end of the nozzle is found to be 4.15, which confirms that the exit flow is supersonic.

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Simulation Result

The Mach number contour confirms that the behaviour at the outflow is supersonic.  To sufficiently validate the results from the simulation, the maximum Mach number must be compared to the value from the hand calculations.  The maximum value from the simulation is shown in the ‘Summary’ section of the Mach Number results panel n Discovery AIM. The table below compares the calculated value to the value from the simulation. The percentage difference confirms that the simulation result is very accurate, within 5% of the hand calculation.

Pre-Analysis Value	Simulation Value	Percent Difference
4.15	4.11	0.96%