ANSYS AIM Tutorial Compressible Flow in a Nozzle

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1 ANSYS AIM Tutorial Compressible Flow in a Nozzle Author(s): Sebastian Vecchi Created using ANSYS AIM 18.1 Problem Specification Pre-Analysis & Start Up Pre-Analysis Start-Up Geometry Import Geometry Mesh Set Mesh Size Generate Mesh Physics Set-Up Boundary Conditions / Forces Solution/Results Verification

2 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.

3 Pre-Analysis & Start Up Pre-Analysis 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. π 2 A = 4 D A A * (1) = A e A th (2) A A * A e = 962mm 2 A th = 78.54mm 2 = 962mm2 = mm 2 The resulting Mach number at the end of the nozzle is found to be 4.15, which confirms that the exit flow is supersonic. Start-Up A few words on the formatting on the following instructions: 1) Notes that require you to perform an action are colored in blue 2) General information is colored in black, but does not require any action 3) Words that are bolded are labels for items found in ANSYS AIM 4) Most important notes are colored in red Now that we have the pre-calculations, we are ready begin simulating in ANSYS AIM. Open ANSYS AIM by going to Start > All Apps > ANSYS 18.1 > ANSYS AIM Once you are at the starting page of AIM, select the Fluid Flow template as shown below.

4 You will be prompted by the Fluid Flow template to either Define new geometry, Import geometry file, or Connect to active CAD session. Select Import geometry file and press Next.

5 Geometry Import Geometry Select and open the geometry file, which can be downloaded from here. Once successfully imported, enable the Compressible flow (ideal gas) option and press Finish.

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7 Mesh Set Mesh Controls Select the Mesh task in the Workflow. Under Boundary Layer Settings, change Collision avoidance to Layer compression. Under Global Sizing, change the Size function method to Proximity. This will produce continuous boundary layers and refine the mesh in the narrow section of the nozzle. AIM will prompt you to fix the boundary layer before generating the mesh. Click on Boundary Layer under Mesh Controls. Select every face except for the circular inlet and outlet faces. An easy way to do this is drag a square around the shape and then deselect the inlet and outlet using CTRL + click.

8 We will also change the mesh to use hexahedrons, to more accurately capture the effects in the critical nozzle region and aid convergence of the calculations. Click on Mesh Controls, then Element Shape 1. Change the Shape to Hexahedrons.

9 Generate Mesh Return to the Mesh panel and click Generate Mesh. AIM will detect that you are ready to generate the mesh and highlight the buttons in blue. Below, an example of the mesh is shown.

10 Physics Set-Up Boundary Conditions / Forces Select the Physics task in the Workflow. First, the inlet must be defined in the Fluid Flow Conditions. In the Add drop down menu by Fluid Flow Conditions, select Inlet. Then, using the Face selection tool, define an inlet at the small end of the nozzle. Change Flow specification to Pressure, input 3 [bar] as the Gauge total pressure, and 300 [K] as the Total temperature. Once the inlet is defined, the outlet is next. In the same Add menu, define an Outlet at the big end of the duct. Change the Regime to Supersonic.

11 Next, a Wall condition must be added to all surfaces that are not already defined. Wall can be found in the same Add menu as the previous conditions. AIM will automatically select the wall faces once the option is selected; AIM selects every face that doesn't already have a constraint on it. Change the Flow specification to Free slip.

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13 Solution/Results Press the Results button in the Workflow to extract information from the simulation. In order to find information that can be readily used, first press Evaluate Results. Once the evaluation is complete, AIM will automatically output a vector in the Results section under Objects. The vectors show air velocity, but may be hard to see. Select the Velocity vector to edit the settings with which the vectors are defined. Change the Symbol distribution to Based on mesh and At every Nth item to 5. Under Appearance, change Symbol sizing to 3. Press Evaluate to update the vectors. Press the Play button in the model window to see how these velocity vectors develop over time. To find the total pressure on the walls of the nozzle, select Contour from the Results Add dropdown menu. Select all of the outside faces of the flow volume (except the inlet and outlet) as the Location and change the Variable to Pressure.

14 The Mach number distribution inside the flow field can be displayed by adding a plane that evenly cuts through the nozzle. In the top right corner of the model window, click the Add plane button. By default, the plane is oriented to bisect the nozzle. Right click on the plane and select Add > Results > Contour, then change the Variable to Mach Number. Press Evaluate to see the contour.

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16 Verification The Mach number contour confirms that the behavior 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 pre-analysis. The maximum value from the simulation is shown in the Summary section of the Mach Number results panel. Table (1) compares the pre-analysis value to the value from the simulation. The percent difference confirms that the simulation result is very accurate, within 5% of the hand calculation. Pre-Analysis Value Simulation Value Percent Difference %