Acoustic Fluent

Tutorial: Modeling Flow-Induced (Aeroacoustic) Noise

Problems Using FLUENT

Introduction

This tutorial demonstrates how to model 2D turbulent flow across a circular cylinder usinglarge eddy simulation (LES) and compute flow-induced (aeroacoustic) noise using FLUENT’sacoustics model.

You will learn how to:

• Perform a 2D large eddy simulation.

• Set parameters for an aeroacoustic calculation.

• Save acoustic source data for an acoustic calculation.

• Calculate acoustic pressure signals.

• Postprocess aeroacoustic results.

Prerequisites

This tutorial assumes that you are familiar with the FLUENT interface and that you have agood understanding of basic setup and solution procedures. Some steps will not be shownexplicitly.

In this tutorial you will use the acoustics model. If you have not used this feature before,first read Chapter 21, Predicting Aerodynamically Generated Noise, of the FLUENT 6.2User’s Guide

c© Fluent Inc. May 11, 2005 1

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Modeling Flow-Induced (Aeroacoustic) Noise Problems Using FLUENT

Problem Description

The problem considers turbulent air flow over a 2D circular cylinder at a free stream ve-locity (U) of 69.2 m/s. The cylinder diameter (D) is 1.9 cm. The Reynolds number basedon the diameter is 90,000. The computational domain (Figure 1) extends 5D upstream and20D downstream of the cylinder.

U = 69.2 m/s D = 1.9 cm

Figure 1: Computational Domain

Preparation

1. Copy the file cylinder2d.msh to your working directory.

2. Start the 2D version of FLUENT.

Approximately 2.5 hours of CPU time is required to complete this tutorial. If you areinterested exclusively in learning how to set up the acoustics model, you can reduce thecomputing time requirements considerably by starting at Step 7 and using the provided caseand data files.

2 c© Fluent Inc. May 11, 2005


Step 1: Grid

1. Read the grid file cylinder2d.msh.

File −→ Read −→Case...

As FLUENT reads the grid file, it will report its progress in the console window.

Since the grid for this tutorial was created in meters, there is no need to rescale thegrid. Check that the domain extends in the x-direction from -0.095 m to 0.38 m.

2. Check the grid.

Grid −→Check

FLUENT will perform various checks on the mesh and will report the progress in theconsole window. Pay particular attention to the reported minimum volume. Makesure this is a positive number.

3. Reorder the grid.

Grid −→ Reorder −→Domain

To speed up the solution procedure, the mesh should be reordered, which will substan-tially reduce the bandwidth and make the code run faster.

FLUENT will report its progress in the console window:

>> Reordering domain using Reverse Cuthill-McKee method:zones, cells, faces, done.

Bandwidth reduction = 32634/253 = 128.99Done.


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4. Display the grid.

Display −→Grid...

(a) Display the grid with the default settings (Figure 2).

Use the middle mouse button to zoom in on the image so you can see the meshnear the cylinder (Figure 3).

Grid FLUENT 6.2 (2d, segregated, LES, unsteady)

Figure 2: Grid Display



Grid FLUENT 6.2 (2d, segregated, LES, unsteady)

Figure 3: The Grid Around the Cylinder

Quadrilateral cells are used for this LES simulation because they generate lessnumerical diffusion than triangular cells. The cell size should be small enough tocapture the relevant turbulence length scales, and to make the numerical diffusionsmaller than the subgrid-scale turbulence viscosity. The mesh for this tutorialhas been kept coarse in order to speed up the calculations. A high quality LESsimulation will require a finer mesh near the cylinder wall.


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Step 2: Models

1. Select the segregated solver with second-order implicit unsteady formulation.

Define −→ Models −→Solver...

(a) Retain the default selection of Segregated under Solver.

(b) Under Time, select Unsteady.

(c) Under Transient Controls, select Non-Iterative Time Advancement.

(d) Under Unsteady Formulation, select 2nd-Order Implicit.

(e) Under Gradient Option, select Node-Based.

(f) Click OK.


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2. Select the LES turbulence model.

The LES turbulence model is not available by default for 2D calculations. You canmake it available in the GUI by typing the following command in the FLUENT consolewindow:

(rpsetvar ’les-2d? #t)

Define −→ Models −→Viscous...

(a) Under Model, select Large Eddy Simulation.

(b) Retain the default option of Smagorinsky-Lilly under Subgrid-Scale Model.

(c) Retain the default value of 0.1 for the model constant Cs.

(d) Click OK.

You will see a Warning dialog box, stating that Bounded Central-Differencing isdefault for momentum with LES/DES. Click OK.

The LES turbulence model is recommended for aeroacoustic simulations because LESresolves all eddies with scales larger than the grid scale. Therefore, wide band aeroa-coustic noise can be predicted using LES simulations.


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Step 3: Materials

You will use the default material, air, which is the working fluid in this problem. Thedefault properties will be used for this simulation.

Define −→Materials...

1. Retain the default value of 1.225 for Density.

2. Retain the default value of 1.7894e-05 for Viscosity.

You can modify the fluid properties for air or copy another material from the database ifneeded. For details, refer the chapter Physical Poperties in the FLUENT User’s Guide.

Step 4: Operating Conditions

Define −→Operating Conditions...

1. Retain the default value of 101325 Pa for the Operating Pressure.

Step 5: Boundary Conditions

1. Retain the default conditions for the fluid.

Define −→Boundary Conditions...

(a) Under Zone, select fluid.

The Type will be reported as fluid.

(b) Click Set... to open the Fluid panel.

i. Retain the default selection of air as the fluid material in the Material Namedrop-down list.

ii. Click OK.

2. Set the boundary conditions at the inlet.

(a) Under Zone, select inlet.

The Type will be reported as velocity-inlet

(b) Click Set... to open the Velocity Inlet panel.

i. Set the Velocity Magnitude to 69.2 m/s.

ii. Retain the default No Perturbations in the Fluctuating Velocity Algorithmdrop-down list, and click OK..

This tutorial does not make use of FLUENT’s ability to impose inlet pertur-bations at velocity inlets when using LES. It is assumed that all unsteadinessis due to the presence of the cylinder in the flow.


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3. Set the boundary conditions at the outlet.

(a) Under Zone, select outlet.

The Type will be reported as pressure-outlet

(b) Click Set... to open the Pressure Outlet panel.

i. Confirm that the Gauge Pressure is set to 0.

ii. Retain the default option of Normal to Boundary in the Backflow DirectionSpecification Method drop-down list, and click OK.

The top and bottom boundaries are set to symmetry boundaries. No user input isrequired for this boundary type.

Step 6: Quasi-Stationary Flow Field Solution

Before extracting the source data for the acoustic analysis, a quasi-stationary flow needs tobe established. The quasi-stationary state will be judged by monitoring the lift and dragforces.

1. Set the solution controls.

Solve −→ Controls −→Solution...

(a) Retain the default PISO scheme for Pressure-Velocity Coupling.

(b) Under Discretization, select PRESTO! in the Pressure drop-down list.

PRESTO! is a more accurate scheme for interpolating face pressure values fromcell pressures.


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(c) Retain the default Bounded Central Differencing for Momentum.

For LES calculations on unstructured meshes, the Bounded Central Differencingscheme is recommended for Momentum.

(d) Set the Relaxation Factor for Pressure to 0.75.

(e) Retain the default Relaxation Factor for Momentum.

The pressure field is relaxed only during the initial transient phase. The Relax-ation Factor for Pressure will be increased to 1 at a later stage.

(f) Click OK.

2. Initialize the solution.

Solve −→ Initialize −→Initialize...

(a) Initialize the flow from the inlet conditions by selecting inlet in the Compute Fromdrop-down list.

(b) Click Init to initialize the solution and click Close.

3. Enable the plotting of residuals.

Solve −→ Monitors −→Residual...

(a) Select Plot under Options.

(b) Under Storage, enter 10000 Iterations.

(c) Under Plotting, enter 20 Iterations.

(d) Retain the default values for the other parameters and click OK.

4. Set the time step parameters.

Solve −→Iterate...

(a) Set the Time Step Size (s) to 5e-6.

The time step size required in LES calculations is governed by the time scaleof the smallest resolved eddies. That requires the local Courant-Friedrichs-Lewy(CFL) number to be of an order of 1. It is generally difficult to know the propertime step size at the beginning of a simulation. Therefore, an adjustment afterthe flow is established, is often necessary. For a given time step ∆t, the highestfrequency that the acoustic analysis can produce is f = 1

2∆t . For the time step sizeselected here, the maximum frequency is 100kHz. Typically in most aeroacousticcalculations, the maximum frequency obtained from the analysis is higher thanthe audible range of interest.


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(b) Click Apply.

5. Save the case and data files (cylinder2d t0.00.cas.gz and cylinder2d t0.00.dat.gz).

File −→ Write −→Case & Data...

Save the case and data files before the first iteration. This will save you time in theevent of user error or code divergence, where the case file would have to be set up allover again.

6. Run the case for a few time steps before activating the force monitors.


(a) Set the Number of Time Steps to 20.

(b) Click Iterate.

The residual history will be displayed as the calculation proceeds. When the non-iterative time advancement scheme is used, by default, two residuals are plotted pertime step .



7. Enable the monitoring of the lift and drag forces.

Setting the force monitors after some initial transient state limits the range of the dragcoefficient when starting from an impulse initial condition.

Solve −→ Monitors −→Force...

(a) In the Coefficient drop-down list, select Drag.

(b) In the Wall Zones list, select wall cylinder.

(c) Verify that the X and Y values under Force Vector are 1 and 0, respectively.

(d) Under Options, select Plot to enable plotting of the drag coefficient.

(e) Under Options, select Write to save the monitor history to a file, cd-history willbe the default file name.

If you do not select the Write option, the history information will be lost whenyou exit FLUENT.

(f) Click Apply.

(g) In the Coefficient drop-down list, select Lift.

(h) Under Force Vector, specify X and Y to be 0 and 1, respectively.

(i) Under Options, select Plot to enable plotting of the lift coefficient.

(j) Under Options, select Write to save the monitor history to a file. This time,cl-history will be the default file name.

(k) Close the panel.



8. Set the reference values to be used in the lift and drag coefficient calculation.

Report −→Reference Values...

(a) Set the values as shown in the table:

Parameter ValueArea 0.019

Velocity 69.2Length 0.019

(b) Retain the default values for the other parameters and click OK.

The reference area is calculated using the cylinder diameter, D, and the defaultdepth of 1 m for 2D problems. Adjust the reference area if a different depth(Depth) value is used.

For the actual force coefficient calculation, only the reference area, density andvelocity are needed. The reference length (Length) will be needed later for theStrouhal number calculation.


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9. Overwrite the previously saved initial conditions (cylinder2d t0.00.cas.gz andcylinder2d t0.00.dat.gz).


10. Advance the flow in time until a quasi-stationary state is reached.


(a) Set the Number of Time Steps to 4000.

(b) Click Iterate.

The 4000 time steps will advance the flow up to t=0.02 s. At that time the bulk flowwill have crossed the computational domain about three times.

The residual history, lift and drag force histories will be displayed as the calculationproceeds. The lift and drag histories should be similar to Figure 4 and Figure 5,respectively. Differences in the long-term flow evolution can occur due to operatingsystem dependent round-off errors. Once the lift and drag histories are sufficientlyoscillatory and periodic in nature, you are ready to set up the acoustics model andperform the acoustic calculations.

Lift Convergence (Time=2.0100e-02)FLUENT 6.2 (2d, segregated, LES, unsteady)

Time

Cl

0.0220.020.0180.0160.0140.0120.010.0080.0060.0040.0020

2.50e+00

2.00e+00

1.50e+00

1.00e+00

5.00e-01

0.00e+00

-5.00e-01

-1.00e+00

-1.50e+00

-2.00e+00

-2.50e+00

Figure 4: Lift Coefficient History

11. Verify that the selected time step size is reasonable for the given mesh and flowcondition.

Plot −→Histogram...


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Drag Convergence (Time=2.0100e-02)FLUENT 6.2 (2d, segregated, LES, unsteady)

Time

Cd

0.0220.020.0180.0160.0140.0120.010.0080.0060.0040.0020

2.25e+00

2.00e+00

1.75e+00

1.50e+00

1.25e+00

1.00e+00

7.50e-01

5.00e-01

2.50e-01

0.00e+00

Figure 5: Drag Coefficient History

(a) Under Histogram of, select Velocity....

(b) From the Velocity... category, select Cell Courant Number.

(c) Set the value for Divisions to 100.

(d) Click Plot and verify that the peak CFL value is less than 3.5. The histogram(Figure 6) shows that most cells have a Cell Courant Number of less than 1.




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Histogram of Cell Courant Number (Time=2.0100e-02)FLUENT 6.2 (2d, segregated, LES, unsteady)

Cell Courant Number

3.532.521.510.50

12

10

8

6

4

2

0

Figure 6: A Histogram Displaying the Range of the CFL Number

Step 7: Aeroacoustics Calculation

1. Define the acoustics model settings.

Define −→ Models −→Acoustics...

(a) Under Model, select Ffowcs-Williams & Hawkings.

(b) Under Options, select Export Acoustic Source Data.



(c) Click the Sources... button.

This will open the Acoustic Sources panel.

i. Under Source Zones, select wall cylinder.

All relevant acoustic source data (i.e. pressure in this case) will be extractedfrom the wall cylinder surface.

ii. In the text-entry box for Source Data Root Filename, enter cylinder2d.

This is the filename root of the index file which will be created. The indexfile contains information about the source data files that are created whenyou run the case. The index file is automatically created with a .index fileextension.

iii. Under Write Frequency, enter 2.

Depending on the physical time step size and the important time scales inthe flow, it is not necessary to write the acoustic source data at every timestep. In this tutorial, the source data is coarsened (in time) by a factor oftwo. Thus, the highest possible frequency the acoustic analysis can generateis reduced to f = 1

2(2∆t) =50 kHz.

iv. Set the No. of Time Steps Per File to 200.

The source data can be conveniently segmented into multiple source datafiles. This makes it easier to process partial sequences when calculating thereceiver signals. A value of 200 for No. of Time Steps Per File means thateach source data file covers a time span of 200 time steps. With a WriteFrequency of 2, there are 100 data sets written into each source data file.

v. Click Apply and Close.


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(d) Click OK to close the Acoustics Model panel.

2. Modify the solution controls.

Solve −→ Controls −→Solution...

(a) Increase the Relaxation Factor for Pressure to 1.

(b) Click OK.

3. Resume the calculation.


(a) Retain the Number of Time Steps at 4000.

(b) Click Iterate.

The additional 4000 time steps will advance the flow up to t=0.04 s.

At every second time step, a message will be displayed in the FLUENT console windowinforming you that data is written to a source data file (.asd file extension).



5. Set the acoustics model constants.

Define −→ Models −→Acoustics...

(a) Retain the Far-Field Density at 1.225 kg/m3.

The far-field density is the density of the fluid outside the computational domain,i.e. the density of the fluid near the receivers. In most calculations it is the sameas the density within the computational domain.

(b) Use the default value of 340 m/s for the Far-Field Sound Speed.

(c) Leave the Reference Acoustic Pressure at 2e-05 Pa.

The reference acoustic pressure is used to calculate decibel values during postpro-cessing.

(d) Set the Source Correlation Length to 0.095 m. That is equal to five cylinderdiameters.

The source correlation length is very important when performing aeroacoustic cal-culations in 2D. FLUENTassumes that the sound sources are perfectly correlatedover the specified correlation length, and zero outside. That is, FLUENTinternallybuilds a source volume with a depth equal to the specified correlation length andneglects sources outside. In your practical 2D application, you will have to esti-mate the source correlation length; your obtained sound pressure levels will de-pend on your input. That makes it difficult to rely on 2D calculations to obtainabsolute sound pressure levels. Therefore, you should use aeroacoustic 2D simu-lations primarily to observe trends. The source correlation length is not neededfor 3D calculations.

(e) Click OK to close the panel.


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6. Calculate the acoustic signals.

Solve −→Acoustic Signals...

(a) Click the Receivers... button.

This will open the Acoustic Receivers panel.

Note that you can open the Acoustic Receivers panel also from the Acoustics Modeland Acoustic Sources panels.

i. Increase the No. of Receivers to 2.

ii. For the receiver-1 coordinates, enter 0 m for X-Coord., -0.665 m (35D) forY-Coord., and 0 for Z-Coord.

iii. For the receiver-2 coordinates, enter 0 m for X-Coord., -2.432 m (128D) forY-Coord., and 0 for Z-Coord.



iv. Retain the defaults for Signal File Name (receiver-1.ard and receiver-2.ard).

v. Click OK to close the Acoustic Receivers panel.

(b) Under Active Source Zones, select wall cylinder.

All source zones which were selected in the Acoustic Sources panel are now avail-able under the Active Source Zones. In this tutorial, the sound sources are ex-tracted from only one zone. It is important to select the source zones consistentlyif redundant source zones were selected in the Acoustic Sources panel.

(c) Under Source Data files, select all files available.

Selecting a subset of the available source files is a convenient way to analyzeshorter sequences. It is important to select a contiguous set of source data files.

(d) Under Receivers, select the two available receivers.

As soon as the source zones, source data files, and receivers are selected, theCompute/Write function becomes available.

(e) Click Compute/Write.

The FLUENT console window will confirm that the source data files are beingread and that the receiver signals are computed and written into receiver files.

(f) Click Close to close the Acoustic Signals panel.

Step 8: Aeroacoustic Postprocessing

1. Display the acoustic pressure signals at the two receiver locations.

Plot −→File...

(a) Click Add... in the File XY Plot panel.

This will open the Select File panel where you can now select receiver-1.ardand receiver-2.ard from the Files list.



(b) Click OK to close the Select File panel.

(c) Click Plot to display the receiver signals (Figure 7). Modify the line and markerstyles as necessary, using the Curves panel.

You will notice a shift in time of approximately 5e-3 s for the signal at the secondreceiver. Receiver-2 is farther away from the source surface and the sound willtherefore arrive later. Also notice that the signal at receiver-2 is weaker due tothe increased distance and geometrical attenuation.



Pressure at receiver-1 (0 -0.665 0) (Time=4.0100e-02)FLUENT 6.2 (2d, segregated, LES, unsteady)

Time

PressureAcoustic

0.050.0450.040.0350.030.0250.02

3.00e+01

2.00e+01

1.00e+01

0.00e+00

-1.00e+01

-2.00e+01

-3.00e+01

-4.00e+01

Pressure at receiver-2 (0 -2.432 0)Pressure at receiver-1 (0 -0.665 0)

Acoustic Pressure

Figure 7: Acoustic Pressure Signals

2. Perform a spectral analysis of the receiver signals.

Plot −→FFT...



(a) Under Process Options, select Process Receiver. This will activate the Receiverlist.

If the Ffowcs Williams and Hawkings (FW-H) acoustics model is used and thereceiver signals have been calculated, then the signals are directly available forpostprocessing. As an alternative, the receiver data can be loaded manually fromfiles by using the Process File Data option under Process Options.

(b) Select receiver-1 from the Receiver list.

(c) Select Sound Pressure Level (dB) from the Y Axis Function drop-down list.

(d) Select Frequency (Hz) from the X Axis Function drop-down list.

(e) Click Plot FFT to plot the sound pressure spectrum for receiver-1 (Figure 8).

The overall sound pressure level (OASPL) is printed to the FLUENT consolewindow:

>> Overall Sound Pressure Levelin dB (reference pressure = 2.000000e-05) = 1.156790e+02

Note that the maximum frequency plotted is f = 12(2∆t) = 50 kHz, as expected.

Spectral Analysis of Pressure at receiver-1 (Time=4.0100e-02)FLUENT 6.2 (2d, segregated, LES, unsteady)

Frequency (Hz)

(dB)Level

PressureSound

6e+045e+044e+043e+042e+041e+040

1.10e+02

1.00e+02

9.00e+01

8.00e+01

7.00e+01

6.00e+01

5.00e+01

4.00e+01

3.00e+01

PressureSpectral Analysis of Pressure at receiver-1

Figure 8: Spectral Analysis of Pressure Signal for receiver-1


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(f) Click Axes....This will open the Axes - Fourier Transform panel.

i. Deselect Auto Range for the X Axis.

ii. Manually set the Maximum for Range to 5000.

iii. Click Apply and Close the panel.

(g) Replot the sound pressure spectrum for receiver-1. The spectrum peaks at about900 Hz (Figure 9).

Note that the spectral resolution is only about 50 Hz, since the receiver signal wascalculated for a short period only (approximately 0.02 s). For a sampled signal oflength T , the spectral resolution is 1

T . You may increase the spectral resolutionby running the simulation longer in time before recalculating the receiver signals.

(h) Select the Strouhal Number from the X Axis Function drop-down list.

i. Reset the Maximum for the x-axis Range to 1, in the Axes - Fourier Transformpanel.

(i) Replot the sound pressure spectrum as a function of the Strouhal Number. Thespectrum peaks at a Strouhal Number of about 0.25 (Figure 10).

If the Strouhal number calculation does not seem correct, verify that the correctvalues are specified in the Reference Values panel.

(j) Repeat the spectral analysis for receiver-2 by selecting receiver-2 from the Receiverlist. You should expect an OASPL of about 104 dB for receiver-2.

3. Plot the power spectral density of the lift force history to see that the observed peaksin the receiver spectra match the dominant frequency in the lift force history.

(a) Under Process Options, select Process File Data.

(b) Click Load Input File... and select the lift monitor file (cl-history).

(c) Select Power Spectral Density from the Y Axis Function drop-down list.




Frequency (Hz)

(dB)Level

PressureSound

5e+034.5e+034e+033.5e+033e+032.5e+032e+031.5e+031e+035000

1.10e+02

1.05e+02

1.00e+02

9.50e+01

9.00e+01

8.50e+01

8.00e+01

7.50e+01

7.00e+01


Figure 9: Spectral Analysis of Pressure Signal for receiver-1 at a Reduced Frequency Range


Strouhal Number

(dB)Level

PressureSound

10.90.80.70.60.50.40.30.20.10

1.10e+02

1.05e+02

1.00e+02

9.50e+01

9.00e+01

8.50e+01

8.00e+01

7.50e+01

7.00e+01


Figure 10: Spectral Analysis of Pressure Signal for receiver-1 as a Function of StrouhalNumbers



(d) Under X Axis Function, select Strouhal Number.

(e) Verify that the Maximum for the x-axis Range in the Axes - Fourier Transformpanel is 1.

(f) Click Plot/Modify Input Signal... to open the Plot/Modify Input Signal panel. Thispanel lets you modify and plot the signal before the Fourier Transform is applied.

i. Select Clip to Range and set the Min value for X Axis Range to 0.02.

Without clipping the temporal range, the complete lift monitor history wouldbe analyzed including the initial transient state leading up to the quasi-stationary state.

ii. Click Apply/Plot and Close to return to the Fourier Transform panel.

Since the x-axis range was manually set for the spectral plot, you will not seethe proper range when plotting the modified signal. You will need to temporarilyreset the range if you want to plot the input signal.

(g) Click Plot FFT to plot the power spectral density for the lift monitor history(Figure 11). The spectrum peaks at a Strouhal number of about 0.25.

As indicated in Step 7, 2D aeroacoustic predictions depend strongly on the selectedsource correlation length. As a consequence, the results can be fine-tuned to be inbetter agreement with experimental data.

4. You can repeat the calculation of the acoustic signals for the additional source corre-lation lengths of 2.5D and 10D, using Step 7 as a starting point.

Table 1 compares the obtained OASPL values with experimental values reported byRevell et al. [1]. Reasonable agreement is found for correlation lengths 2.5D and 5D.



Spectral Analysis of Lift Convergence (Time=4.0100e-02)FLUENT 6.2 (2d, segregated, LES, unsteady)

Strouhal Number

DensitySpectral

Power

10.90.80.70.60.50.40.30.20.10

3.00e-01

2.50e-01

2.00e-01

1.50e-01

1.00e-01

5.00e-02

0.00e+00

Figure 11: Spectral Analysis of Lift Force History

Table 1: Dependence of the Predicted OASPL on the Specified Source Correlation Lengths(L = 2.5D, 5D, 10D)

2.5D 5D 10D Experimental Resultsreceiver-1 109.7 115.7 121.6 117receiver-2 98.4 104.4 110.4 100



Summary

This tutorial demonstrated the use of FLUENT’s acoustics model to calculate the far-fieldsound signals generated by the flow over a 2D cylinder. You have learned how to set up therelevant parameters, save the acoustic source data, calculate, and postprocess the acousticpressure signals.

The main computational efforts are spent calculating the time dependent turbulent flow.It is therefore advisable to export the sound sources during the flow calculation. Thisallows you to recalculate the acoustic signals for different receivers or model parameterswith minimal computational costs.

The tutorial demonstrated the use of the Ffowcs Williams and Hawkings acoustics tool ona 2D case. You have seen that it is difficult to obtain absolute SPL predictions in 2D due tothe need to estimate the correlation length of the turbulent flow structures in the spanwisedirection. This difficulty does not exist when solving 3D acoustics problems.

References

1. Revell, J.D., Prydz, R.A., and Hays, A.P., “Experimental Study of Airframe Noise vs.Drag Relationship for Circular Cylinders,” Lockheed Report 28074, Feb. 1977. FinalReport for NASA Contract NAS1-14403.


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