Fluent - Compressible Flow in a Nozzle - Simulation - Confluence

Fluent - Compressible Flow in a Nozzle - Simulation - Confluence

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Fluent - Compressible Flow in a NozzleAdded by [email protected] (Update Your Profile) , last edited by Javier Gutierrez Gallardo on Mar 08, 2010

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Problem Specification

Step 1: Pre-Analysis & Start-up

Start GAMBIT

Create Axis Edge

Create Wall Edge

Create Inlet and Outlet Edges

Create Face

Save Your Work

Step 2: Geometry

Mesh Edges

Mesh Face

Save Your Work

Step 3: Mesh

Specify Boundary Types

Save and Export

Step 4: Setup (Physics)

Launch FLUENT

Import File

Check and Display Grid

Define Solver Properties

Step 5: Solution

Set Initial Guess

Set Convergence Criteria

Iterate Until Convergence

FLUENT - Compressible Flow in a Nozzle- Step 6

Step 6: Results

Velocity Vector

Pressure Contour Plot

Total Pressure Contour Plot

Temperature Contour Plot

Total Temperature Contour Plot

Mach Number Contour

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Pressure Plot

Mach Number Plot

Step 7: Verification & Validation

Problem 1

Problem 2

Problem Specification

Consider air flowing at high-speed through a convergent-divergent nozzle having a circular cross-sectionalarea, A, that varies with axial distance from the throat, x, according to the formula

A = 0.1 + x2; -0.5 < x < 0.5

where A is in square meters and x is in meters. The stagnation pressure po at the inlet is 101,325 Pa. The

stagnation temperature To at the inlet is 300 K. The static pressure p at the exit is 3,738.9 Pa. We will

calculate the Mach number, pressure and temperature distribution in the nozzle using FLUENT andcompare the solution to quasi-1D nozzle flow results. The Reynolds number for this high-speed flow islarge. So we expect viscous effects to be confined to a small region close to the wall. So it is reasonable tomodel the flow as inviscid.

Go to Step 1: Pre-Analysis & Start-up

See and rate the complete Learning Module

Author: Rajesh Bhaskaran, Cornell University

Problem Specification1. Pre-Analysis & Start-up2. Geometry3. Mesh4. Setup (Physics)5. Solution6. Results7. Verification & ValidationProblem 1Problem 2

https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Compressible+Flow+in+a+Nozzle-+Step+1




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Go to all FLUENT Learning Modules

Step 1: Pre-Analysis & Start-upSince the nozzle has a circular cross-section, it's reasonable to assume that the flow is axisymmetric. Sothe geometry to be created is two-dimensional.

Start GAMBIT

Create a new folder called nozzle and select this as the working directory. Add -id nozzle to the startupoptions.

Create Axis Edge

We'll create the bottom edge corresponding to the nozzle axis by creating vertices A and B shown in theproblem specification and joining them by a straight line.

Operation Toolpad > Geometry Command Button >Vertex Command Button >Create Vertex

Create the following two vertices:

Vertex 1: (-0.5,0,0)Vertex 2: (0.5,0,0)

Operation Toolpad > Geometry Command Button > Edge Command Button > Create Edge

Select vertex 1 by holding down the Shift button and clicking on it. Next, select vertex 2. Click Apply in theCreate Straight Edge window.

Author: Rajesh Bhaskaran & Yong Sheng Khoo, Cornell University


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https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Compressible+Flow+in+a+Nozzle-+Problem+Specification











Create Wall Edge

We'll next create the bottom edge corresponding to the nozzle wall. This edge is curved. Since

A = Î r2

where r( x ) is the radius of the cross-section at x and

A = 0.1 + x2

for the given nozzle geometry, we get

r( x ) = [(0.1 + x2)/Î ]0.5; -0.5 < x < 0.5

This is the equation of the curved wall. Life would have been easier if GAMBIT allowed for this equation tobe entered directly to create the curved edge. Instead, one has to create a file containing the coordinates ofa series of points along the curved line and read in the file. The more number of points used along thecurved edge, the smoother the resultant edge.

The file vert.dat contains the point definitions for the nozzle wall. Take a look at this file. The first line is

21 1

which says that there are 21 points along the edge and we are defining only 1 edge. This is followed by x,rand z coordinates for each point along the edge. The r -value for each x was generated from the aboveequation for r ( x ) . The z-coordinate is 0 for all points since we have a 2D geometry.

Right-click on vert.dat and select Save As... to download the file to your working directory.

Main Menu > File > Import > ICEM Input ...

Next to File Name:, enter the path to the vert.dat file that you downloaded or browse to it by clicking onthe Browse button.

Then, check the Vertices and Edges boxes under Geometry to Create as we want to create thevertices as well as the curved edge.

Click Accept .

http://courses.cit.cornell.edu/fluent/nozzle/vert.dat

http://courses.cit.cornell.edu/fluent/nozzle/vert.dat



This should create the curved edge. Here it is in relation to the vertices we created above:

Higher Resolution Image

Create Inlet and Outlet Edges

Create the vertical edge for the inlet:

Operation Toolpad > Geometry Command Button > Edge Command Button > Create Edge

Shift-click on vertex 1 and then the vertex above it to create the inlet edge.

Similarly, create the vertical edge for the outlet.


Create Face

Form a face out of the area enclosed by the four edges:

Operation Toolpad > Geometry Command Button >Face Command Button >Form Face

Recall that we have to shift-click on each of the edges enclosing the face and then click Apply to createthe face.

Save Your Work

https://confluence.cornell.edu/download/attachments/90740664/01curved_edge.JPG?version=1&modificationDate=1223480962000

https://confluence.cornell.edu/download/attachments/90740664/01curved_edge.JPG?version=1

https://confluence.cornell.edu/download/attachments/90740664/01curved_edge.JPG?version=1

https://confluence.cornell.edu/download/attachments/90740664/01edges.JPG?version=1&modificationDate=1223481554000

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Main Menu > File > Save

This will create the nozzle.dbs file in your working directory. Check that it has been created so that you willable to resume from here if necessary.

Go to Step 2: Geometry



Step 2: GeometryNow that we have the basic geometry of the nozzle created, we need to mesh it. We would like to create a50x20 grid for this geometry.

Mesh Edges

As in the previous tutorials, we will first start by meshing the edges.

Operation Toolpad > Mesh Command Button > Edge Command Button > Mesh Edges

Like the Laminar Pipe Flow Tutorial, we are going to use even spacing between each of the mesh points.We won't be using the Grading this time, so deselect the box next to Grading that says Apply .

Then, change Interval Count to 20 for the side edges and Interval Count to 50 for the top and bottomedges.





https://confluence.cornell.edu/display/SIMULATION/FLUENT+-+Laminar+Pipe+Flow+-+Problem+Specification













Mesh Face

Now that we have the edges meshed, we need to mesh the face.

Operation Toolpad > Mesh Command Button > Face Command Button > Mesh Faces As before, select the face and click the Apply button.


Save Your Work


Go to Step 3: Mesh




Problem Specification1. Pre-Analysis & Start-up

https://confluence.cornell.edu/download/attachments/90740823/01edge_meshfull.JPG?version=1&modificationDate=1232056455000

https://confluence.cornell.edu/download/attachments/90740823/01edge_meshfull.JPG?version=1

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https://confluence.cornell.edu/download/attachments/90740823/01face_meshfull.JPG?version=1&modificationDate=1232056442000

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Step 3: Mesh

Specify Boundary Types

Now that we have the mesh, we would like to specify the boundary conditions here in GAMBIT .

Operation Toolpad > Zones Command Button > Specify Boundary Types Command Button

This will bring up the Specify Boundary Types window on the Operation Panel. We will first specify thatthe left edge is the inlet. Under Entity :, pick Edges so that GAMBIT knows we want to pick an edge (faceis default).

Now select the left edge by Shift-clicking on it. The selected edge should appear in the yellow box nextto the Edges box you just worked with as well as the Label/Type list right under the Edges box.

Next to Name :, enter inlet.

For Type:, select WALL .

Click Apply . You should see the new entry appear under Name/Type box near the top of the window.

2. Geometry3. Mesh4. Setup (Physics)5. Solution6. Results7. Verification & ValidationProblem 1Problem 2










Repeat for the outlet, centerline, and wall edges.

You should have the following edges in the Name/Type list when finished:

Save and Export


Main Menu > File > Export > Mesh...

Type in nozzle.msh for the File Name:. Select Export 2d Mesh since this is a 2 dimensional mesh.Click Accept .



Check nozzle.msh has been created in your working directory.

Go to Step 4: Setup (Physics)



Step 4: Setup (Physics)

If you have skipped the previous mesh generation steps 1-3, you can download the mesh by right-clickingon this link. Save the file as nozzle.msh in your working directory. You can then proceed with the flowsolution steps below.

Launch FLUENT

Start > Programs > ANSYS 12.0 > Fluid Dynamics > FLUENT

Select 2D from the list of options and click OK.

Import File

Main Menu > File > Read > Case...

Navigate to your working directory and select the nozzle.msh file. Click OK.

The following should appear in the FLUENT window:



Useful InformationThese instructions are for FLUENT 12. Click here for instructions for FLUENT 6.3.26.



https://confluence.cornell.edu/download/attachments/90740910/nozzle.msh?version=1&modificationDate=1232115303000













Check that the displayed information is consistent with our expectations of the nozzle mesh.

Check and Display Mesh

First, we check the grid to make sure that there are no errors.

Under Problem Setup > General > Mesh > Check (button)

Any errors in the grid would be reported at this time. Check the output and make sure that there are noerrors reported.

Main Menu > Mesh > Info > Size

How many cells and nodes does the grid have?

The mesh is being displayed by default but the steps to accomplish this when the grid is not being displayedare the following:

Main Menu > Display > Mesh

Make sure all items under Surfaces is selected. Then click Display. The graphics window opens and themesh is displayed in it.

Some of the operations available in the graphics window are:

Translation: The mesh can be translated in any direction by holding down the Left Mouse Button andthen moving the mouse in the desired direction.



Zoom In: Hold down the Middle Mouse Button and drag a box from the Upper Left Hand Corner tothe Lower Right Hand Corner over the area you want to zoom in on.

Zoom Out: Hold down the Middle Mouse Button and drag a box anywhere from the Lower RightHand Corner to the Upper Left Hand Corner .

The mesh has 50 divisions in the axial direction and 20 divisions in the radial direction. The total number ofcells is 50x20=1000. Since we are assuming inviscid flow, we won't be resolving the viscous boundary layeradjacent to the wall. (The effect of the boundary layer is small in our case and can be neglected.) Thus, wedon't need to cluster nodes towards the wall. So the mesh has uniform spacing in the radial direction. Wealso use uniform spacing in the axial direction.

Look at specific parts of the mesh by choosing each boundary (centerline, inlet, etc) listed under Surfacesin the Mesh Display menu . Click to select and click again to deselect a specific boundary. Click Displayafter you have selected your boundaries.

Define Solver Properties

Define > Models > Solver...

We see that FLUENT offers two methods ("solvers") for solving the governing equations: Pressure-Basedand Density-Based. To figure out the basic difference between these two solvers, let's turn to thedocumentation.

Main Menu > Help > User's Guide Contents ...

This should bring up FLUENT 12.0 User's Guide in your web browser. If not, access the User's Guidefrom the Start menu: Start > Programs > ANSYS 12.0 > Help > FLUENT Help. This will bring up theFLUENT documentation in your browser. Click on the link to the user's guide.

Go to chapter 26 in the user's guide. It discusses the Pressure-Based and Density-Based solvers. Section26.1 introduces the two solvers:

" In ANSYS FLUENT, two solver technologies are available:

pressure-based

density-based

Both solvers can be used for a broad range of flows, but in some cases one formulation may perform better(i.e., yield a solution more quickly or resolve certain flow features better) than the other. The pressure-basedand density-based approaches differ in the way that the continuity, momentum, and (where appropriate)energy and species equations are solved, as described in this section in the separate +Theory Guide.+Thepressure-based solver traditionally has been used for incompressible and mildly compressible flows. Thedensity-based approach, on the other hand, was originally designed for high-speed compressible flows.Both approaches are now applicable to a broad range of flows (from incompressible to highly compressible),but the origins of the density-based formulation may give it an accuracy (i.e. shock resolution) advantage



over the pressure-based solver for high-speed compressible flows."

Since we are solving a high-speed compressible flow, let's pick the density-based solver.

In the Solver menu, select Density Based .

Under Space , choose Axisymmetric. This will solve the axisymmetric form of the governing equations.

Then we will setup the models for the problem:

Define > Models > Energy > Edit

The energy equation needs to be turned on since this is a compressible flow where the energy equation iscoupled to the continuity and momentum equations.

Make sure there is a check box next to Energy Equation and click OK.

Define > Models > Viscous - Laminar > Edit

Select Inviscid under Model .



Click OK.

This means the solver will neglect the viscous terms in the governing equations.

Define > Materials

Select air under Fluid materials and click the Create/Edit... button. Under Properties , choose IdealGas next to Density. You should see the window expand. This means FLUENT uses the ideal gasequation of state to relate density to the static pressure and temperature.

Click Change/Create. Close the window.

Define > Operating Conditions

We'll work in terms of absolute rather than gauge pressures in this example. So set Operating Pressurein the Pressure box to 0.



Click OK.

It is important that you set the operating pressure correctly in compressible flow calculations since FLUENTuses it to compute the absolute pressure used in the ideal gas law.

Define > Boundary Conditions

Set boundary conditions for the following surfaces: inlet, outlet, centerline, wall.

Select inlet under Zone and pick pressure-inlet under Type as its boundary condition. Automatically,the Pressure Inlet window should come up.

Set the total pressure (noted as Gauge Total Pressure in FLUENT) at the inlet to 101,325 Pa as



specified in the problem statement. For a subsonic inlet, Supersonic/Initial Gauge Pressure is theinitial guess value for the static pressure. This initial guess value can be calculated from the 1D analysissince we know the area ratio at the inlet. This value is 99,348 Pa. Note that this value will be updated by thecode. After you have entered the values check that under the Thermal tab, the Total Temperature is300K. Then click OK to close the window.

Using the same steps as above, pick pressure-outlet as the boundary condition for the outlet surface.Then, when the Pressure Outlet window comes up, set the pressure to 3738.9 as specified in the problemstatement. Click OK.

Set the centerline zone to axis boundary type. Accept any prompts that might appear and leave the nameas centerline if you'd like.

Make sure that wall zone is set to wall boundary type.

Go to Step 5: Solution







Step 5: Solution

Now we will set the solve settings for this problem and then solve using an iterative approximation process.

Under Solution > Solution Methods

We'll just use the defaults. Note that a second-order Upwind scheme will be used. Click OK.

Set Initial Guess

Main Menu > Solve > Initialization

As you may recall from the previous tutorials, this is where we set the initial guess values for the iterativesolution. We'll set these values to be the ones at the inlet, so under Compute From select inlet.This willautomatically set the initial values for all the cells. You can also type the values by hand and the results willbe equivalent.
















Click Initialize . This completes the initialization.

Set Convergence Criteria

FLUENT reports a residual for each governing equation being solved during the iterative process. Theresidual is a measure of how well the current solution satisfies the discrete form of each governing equation.We'll iterate the solution until the residual for each equation falls below 1e-6.

Main Menu > Solve > Monitors or Under Solution > Monitors select Residual > Edit

Change the residual under Convergence Criterion for continuity , x-velocity , y-velocity andenergy to 1e-6.

Also, under Options select Plot if is not selected yet. This will plot the residuals in the graphics window asthey are calculated.



Click OK.

Iterate Until Convergence

Main Menu > Solve > Run calculation or Under Solution > Run Calculation

In the Iterate Window that comes up, change the Number of Iterations to 500. Click Calculate .

The residuals are printed out as well as plotted in the graphics window for each iteration.

Save the case and data after you have obtained a converged solution by going to File > Write > Case &Data

Go to Step 6: Results



FLUENT - Compressible Flow in a Nozzle- Step 6


Problem Specification1. Pre-Analysis & Start-up2. Geometry3. Mesh4. Setup (Physics)5. Solution











Step 6: Results

Velocity Vector

Let's first look at the velocity vector in the nozzle.

Display > Graphics and Animations > Vectors > Set up...

Select Velocity under Vectors of and Velocity.. . under Color by. Set Scale to 0.4

Click Display. step6_2.png

We see that the flow is smoothly accelerating from subsonic to supersonic.

6. Results7. Verification & ValidationProblem 1Problem 2


To include the lower half of nozzle, do the following: Display > Views...Select centerline and click Apply

https://confluence.cornell.edu/download/attachments/118470184/step6_2.png?version=1&modificationDate=1268075137000







Pressure Contour Plot

Let's look at how pressure changes in the nozzle.

Display > Graphics and Animations > Contours > Set up

Select Pressure... and Static Pressure under Contours of . Use Levels of 30

Click Display.

White Background on Graphics WindowTo get white background go to:Main Menu > File > HardcopyMake sure that Reverse Foreground/Background is checked and select Color inColoring section.

Click Preview . Click No when prompted "Reset graphics window?"



Notice that the pressure decreases as it flows to the right.

Total Pressure Contour Plot

Let's look at the total pressure in the nozzle

Display > Graphics and Animations > Contours

Select Pressure... and Total Pressure under Contours of . Select Filled. Use Levels of 100.

Click Display.

https://confluence.cornell.edu/download/attachments/118470184/step6_4.png



Around the nozzle outlet, we see that there is a pressure loss because of the numerical dissipation.

Temperature Contour Plot

Let's investigate or verify the temperature properties in the nozzle.


Select Temperature... and Static Temperature under Contours of . Use Levels of 30.

Click Display.




As we can see, the temperature decreases from left to right in the nozzle, indicating a transfer of internalenergy to kinetic energy as the fluid speeds up.

Total Temperature Contour Plot

Now let's look at the total pressure in the nozzle


Select Temperature.. .and Total Temperature under Contours of . Select Filled. Use Levels of100.

Click Display.




Looking at the scale, we see that the total temperature is uniform 300 K throughout the nozzle. The contourabnormality at the outlet of the nozzle is due to the round off errors.

Mach Number Contour

Let's now look at the Mach number

Display > Contours

Select Velocity...under Contours of and select Mach Number . Set Levels to 30.

Click Display.




For 1D case, mach number is a function of x position. For 1D case, we are supposed to see vertical contourof mach numbers that are parallel to each other.

For 2D case, we are seeing curving contour of mach number. The deviation from vertical indicates the 2Deffect.

Do note that 1D approximation is fairly accurate around the centerline of nozzle.

Pressure Plot

Let's look at the pressure along the centerline and the wall.

Under Results > Plots > XY Plot > Set up

Make sure that under Y-Axis Function , you see Pressure...and Static Pressure . Under Surfaces ,




select centerline and wall . Click Plot . By default FLUENT displays the plots using graphics but we willmodify them to display lines which can be more helpful when analyzing the plot.

On the XY Plot window click on the Curves button. Change the Pattern to a line, Select a blank as aSymbol and change the Weight to any number greater than 2. To do this for multiple curves use thearrow buttons to navigate through the different curves displayed on the plot.

It is good to write the data into a file to have greater flexibility on how to present the result in the report. Atthe same XY Plot windows, select Write to File . Then click Write... Name the file "p.xy" in the directorythat you prefer. Open "p.xy" file with notepad or other word processing software. At the top, we see:

(title "Static Pressure")(labels "Position" "Static Pressure")

The first line tells us the properties we are comparing. In this case we are looking at Static Pressure. Thesecond line tells us about the labels for the x and y axes, respectively. There is a header at the beginning of each the data sets so that we can differentiate which data sets we arelooking at. In this case, we have "centerline" and "wall" data sets.

Following is an example of two data sets (centerline and wall).

((xy/key/label "centerline")

-0.5 97015.3

-0.48 96949.9




.

.

.

0.5 6012.92

)

((xy/key/label "wall")

-0.5 100853

-0.480911 100496

.

.

.

0.5 2874.7

)

Try copying the appropriate data sets to excel and plotting the results.

Mach Number Plot

Let's plot the variation of Mach number in the axial direction at the axis and wall. In addition, we will plot thecorresponding variation from 1D theory. You can download the file here: mach_1D.xy. This file is a text file.You can look at the format of this file by reading it into Wordpad.

Plot > XY Plot. Under the Y Axis Function , select Velocity... and Mach Number .

Also, since we are going to plot this number at both the wall and axis, select centerline and wall underSurfaces .

Then, load the mach_1D.xyby clicking on Load File....

ClickPlot .

CorrectionThe green line in the plot below SHOULD be in symbols. This will be corrected soon.

https://confluence.cornell.edu/download/attachments/118470184/mach_1D.xy?version=1&modificationDate=1268084392000



How does the FLUENT solution compare with the 1D solution?

Is the comparison better at the wall or at the axis? Can you explain this?

Save this plot as machplot.xy by checking Write to File and clicking Write... .

Go to Step 7: Verification & Validation



Step 7: Verification & ValidationSolve the nozzle flow for the same conditions as used in class on a 80x30 grid. Recall that the staticpressure p at the exit is 3,738.9 Pa. The grid for this calculation can be downloaded here.

(a) Plot the variation of Mach number at the axis and the wall as a function of the axial distance x. Also, plot






http://courses.cit.cornell.edu/fluent/nozzle/nozzle80x30.msh












the corresponding results obtained on the 50x20 grid used in class and from the quasi-1D assumption.Recall that the quasi-1D result for the Mach number variation was given to you in the M_1D.xy file. Note allfive curves should be plotted on the same graph so that you can compare them. You can make the plots inFLUENT, MATLAB or EXCEL.

(b) Plot the variation of static pressure at the axis and the wall as a function of the axial distance x. Also, plotthe corresponding results obtained on the 50x20 grid used in class and from the quasi-1D assumption.Calculate the static pressure variation for the quasi-1D case from the Mach number variation given inM_1D.xy.

(c) Plot the variation of static temperature at the axis and the wall as a function of the axial distance x. Also,plot the corresponding results obtained on the 50x20 grid used in class and from the quasi-1D assumption.Calculate the static temperature variation for the quasi-1D case from the Mach number variation given inM_1D.xy.

Comment very briefly on the grid dependence of your results and the comparison with the quasi-1D results.

Go to Problem 1



Problem 1Consider the nozzle flow problem solved using FLUENT in the tutorial. Recall that the nozzle has a circularcross-sectional area, A, that varies with axial distance from the throat, x, according to the formula:

A = 0.1 + x2

where A is in square meters and x is in meters. The stagnation pressure poand stagnation temperature To



http://courses.cit.cornell.edu/fluent/nozzle/mach_1D.xy

http://courses.cit.cornell.edu/fluent/nozzle/mach_1D.xy














at the inlet are 101,325 Pa and 300 K, respectively.

Using the quasi-1D flow assumption, determine the static pressure at the nozzle inlet and outlet for thefollowing conditions:

(a) Sonic flow at the throat, and supersonic, isentropic flow in the diverging section.(b) Sonic flow at the throat, and subsonic, isentropic flow in the diverging section.(c) Sonic flow at the throat and normal shock at the exit.

Go to Problem 2



Problem 2Change the exit pressure to 40,000 Pa while keeping all the other boundary conditions the same. What flowregime do you expect for this exit pressure based on the quasi-1D results in problem 1? Re-run theFLUENT calculation with this exit pressure on the 50x20 grid.

(a) Plot contours of the Mach number and static pressure for this case. Is the flow regime as predicted byquasi-1D theory? Explain briefly the possible causes for any similarities or disparities.

(b) Plot the static and stagnation pressures at the axis as a function of the axial distance. Also, plot thecorresponding values from the case where the exit pressure is 3,738.9 Pa. (These four curves should be onthe same graph.) Explain briefly the salient features of this plot.

(c) Plot the static and stagnation temperatures at the axis as a function of the axial distance. Again provide abrief explanation for the salient features.

Back to Problem Specification




















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