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Tutorial: Modeling Aeroacoustics for a Helmholtz ResonatorUsing the Direct Method (CAA)

Introduction

The purpose of this tutorial is to provide guidelines and recommendations for the basicsetup and solution procedure for a typical aeroacoustic application using computationalaeroacoustic (CAA) method.

In this tutorial you will learn how to:

Model a Helmholtz resonator.

Use the transient k-epsilon model and the large eddy simulation (LES) model foraeroacoustic application.

Set up, run, and perform postprocessing in FLUENT.

Prerequisites

This tutorial assumes that you are familiar with the user interface, basic setup and solutionprocedures in FLUENT. This tutorial does not cover mechanics of using acoustics model, butfocuses on setting up the problem for Helmholtz-Resonator and solving it. It also assumesthat you have basic understanding of aeroacoustic physics.

If you have not used FLUENT before, it would be helpful to first review FLUENT 6.3 UsersGuide and FLUENT 6.3 Tutorial Guide.

Problem Description

A Helmholtz resonator consists of a cavity in a rigid structure that communicates through anarrow neck or slit to the outside air. The frequency of resonance is determined by the massof air in the neck resonating in conjunction with the compliance of the air in the cavity.

The physics behind the Helmholtz resonator is similar to wind noise applications like sunroof buffeting.

We assume that out of the two cavities that are present, smaller one is the resonator. Themotion of the fluid takes place because of the inlet velocity of 27.78 m/s (100 km/h). Theflow separates into a highly unsteady motion from the opening to the small cavity. Thisunsteady motion leads to a pressure fluctuations. Two monitor points (Point-1 and Point-2)act as microphone points to record the generated sound. The acoustic signal is calculatedwithin FLUENT. The flow exits the domain through the pressure outlet.

c Fluent Inc. March 12, 2008 1
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Modeling Aeroacoustics for a Helmholtz Resonator Using the Direct Method (CAA)

Preparation

1. Copy the files steady.cas.gz, steady.dat.gz, execute-by-name.scm, stptmstp4.scm,ti-to-scm-jos.scm and stptmstp.txt into your working directory.

2. Start the 2D double precision (2ddp) version of FLUENT.

Setup and Solution

Step 1: Grid

1. Read the initial case and data files for steady-state (steady.cas.gz and steady.dat.gz).

File Read Case & Data...

Ignore the warning that is displayed in the FLUENT console while reading these files.

2. Keep default scale for the grid.

Grid Scale...

3. Display the grid and observe the locations of the two monitor points, Point-1 andPoint-2 (Figure 1).

Figure 1: Graphics Display of the Grid

4. Display and observe the contours of static pressure (Figure 2) and velocity magnitude(Figure 3) for the initial steady-state solution.

Display Contours..

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Figure 2: Contours of Static Pressure (Steady State)

Figure 3: Contours of Velocity Magnitude (Steady State)


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Step 2: Models

1. Select unsteady solver.

Define Models Solver...

(a) Select Unsteady in the Time list.

(b) Select 2nd-order-implicit in the Unsteady formulation list.

(c) Retain the default settings for other parameters.

(d) Click OK to close the Solver panel.

2. Define the viscous model.

Define Models Viscous...

(a) Select Non-Equilibrium Wall Functions in the Near-Wall Treatment list.

(b) Retain the default settigns for other parameters.

(c) Click OK to close the Viscous Model panel.

Near-Wall Treatment predicts good separation and re-attachment points.

Step 3: Materials

Define Materials...

1. Select ideal-gas from the Density drop-down list.

2. Retain the default values for other parameters.

3. Click Change/Create and close the Materials panel.

Ideal gas law is good in predicting the small changes in the pressure.

Step 4: Solution

1. Monitor the static pressure on point-1 and point-2.

Solve Monitors Surface...

(a) Enter 2 for the Surface Monitors.

(b) Enable Plot and Print options for monitor-1 and monitor-2.

(c) Select Time Step from the When list.

(d) Click Define... for monitor-1 to open Define Surface Monitor panel.


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i. Select Vertex Average from the Report Type drop-down list.

ii. Select Flow Time from the X Axis drop-down list.

iii. Enter 1 for Plot Window.

iv. Select point-1 from the Surfaces selection list.

(e) Similarly, specify the surface monitor parameters for point-2.

2. Start the calculations using the following settings.

Solve Iterate...

(a) Enter 3e-04 s for Time Step Size.

The expected time step size for this problem is of the size of about 1/10th of thetime period. The time period depends on the frequency (f ) which is calculatedusing the following equation:

f =c

2

S

V[L + 2.Dh2

]

where,

c = Speed of sound

S = Area of the orifice of the resonator

V = Volume of the resonatorL = Length of the connection between the resonator and the free flow area

Dh = Hydraulic diameter of the orifice

For this geometry, the estimated frequency is about120 Hz.

(b) Enter 250 for the Number of Time Steps.

(c) Enter 50 for Max Iterations per Time Step.

(d) Click Apply.


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(e) Read the scheme file (stptmstp4.scm).

File Read Scheme...

This file activates a alternative convergence criteria. For acoustic simulationswith CAA it is obligatory that the pressure is completely converged at the reciever

position. FLUENT compares the monitor quantities within the last n-defined it-erations to judge if the deviation is smaller than a y-defined deviation.

(f) Specify the number of previous iterations from which monitor values of eachquantity used are saved and compared to the current (latest) value (include theparanthesis):

(set! stptmstp-n 5)

(g) Specify the relative (the smaller of two values in any comparison) differenceby which any of the older monitor values (for a selected monitor qauntity) maydiffer from the newest value:

(set! stptmstp-maxrelchng 1.e-02)

(h) Define the execute commands.

Solve Execute Commands

i. Enter (stptmstp-resetvalues) for the first command and select Time Stepfrom the drop-down list.

ii. Enter (stptmstp-chckcnvrg "/report/surface-integrals vertex-avg point-1() pressure") and select Iteration from the drop-down list.

iii. Click OK.(i) Click Iterate to start the calculations.

The iterations will take a long time to complete. You can skip this simulation af-ter few time steps and read the files (transient.cas.gz andtransient.dat.gz)provided with this tutorial. These files contain the data for the flow time of 0.22seconds. As seen in Figures 4 and 5, no pressure fluctuations are present at thisstage. The oscillations of the static pressure at both monitor points has reacheda constant value.

The RANS-simulation is a good starting point for Large Eddy Simulation. Ifyou choose to use the steady solution as initial condition for LES, use the TUI

command /solve/initialize/init-instantaneous-vel provides to get a more realisticinstantaneous velocity field. The usage of LES for acoustic simulations is obliga-tory. The next two pictures compare the static pressure obtained with RANS andLarge Eddy Simulation for a complete simulation until 0.525 seconds. Obviously,the k-epsilon model underpredicts the strong pressure oscillation after reachinga dynamically steady state (> 0.3 s) due to its dissipative character. Under-predicted pressure oscillations lead to underpredicted sound pressure level whichmeans the acoustic noise is more gentle.


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Figure 4: Convergence History of Static Pressure on Point-1 (Transient)



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Step 5: Enable Large Eddy Simulation

1. Enter the following TUI command in the FLUENT console:

(rpsetvar les-2d? #t)

2. Enable large eddy simulation effects.

The k-epsilon model cannot resolve very small pressure fluctuations for aeroacousticdue to its dissipative character. Use Large Eddy Simulation to overcome this problem.

Define Models Viscous...

(a) Enable Large Eddy Simulation (LES) in the Model list.

(b) Enable WALE in the Subgrid-Scale Model list.

(c) Click OK to close the Viscous Model panel.

An Information panel will appear, warning about bounded central-deferencing be-

ing default for momentum with LES/DES.


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(d) Click OK to close the Information panel.

3. Retain default discretization schemes and under-relaxation factors.

Solve Controls Solution...

4. Enable writing of two surface monitors and specify file names as monitor-les-1.out andmonitor-les-2.out for monitor plots of point-1 and point-2 respectively.

Solve Monitors Surface...

To account for stochastic components of the flow, FLUENT provides two algorithms.These algorithms model the fluctuating velocity at velocity inlets. With the spec-tral synthesizer the fluctuating velocity components are computed by synthesizing adivergence-free velocity-vector field from the summation of Fourier harmonics.

5. Enable the spectral synthesizer.

Define Boundary Conditions...

(a) Select inlet in the Zone list and click Set....

i. Select Spectral Synthesizer from the Fluctuating Velocity Algorithm drop-downlist.

ii. Retain the default values for other parameters.

iii. Click OK to close the Velocity Inlet panel.

(b) Close the Boundary Conditions panel.


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Typically it takes a long time to get a dynamically steady state. Additionally, thesimulated (and recorded for FFT) flow time depends on the minimum frequency in thefollowing relationship:

flowtime =

10

minimumfrequency (1)

The standard transient scheme (iterative time advancement) requires a considerableamount of computaional effort due to a large number of outer iterations performed foreach time-step. To accelerate the simulation, the NITA (non-iterative time advance-ment) scheme is an alternative.

6. Set the solver parameters.

Define Models Solver...

(a) Enable Non-Iterative Time Advancement in the Transient Controls list.

(b) Click OK to close the Solver panel.7. Set the solution parameters.

Solve Controls Solution...

(a) Select Fractional Step from the Pressure-Velocity Coupling drop-down list.

(b) Click OK to close the Solution Controls panel.

8. Disable both the execute commands.

Solve Execute Commands...

9. Continue the simulation with the same time step size for 1500 time steps to get a

dynamically steady solution.

10. Write the case and data files (unsteady-final.cas.gz and unsteady-final.dat.gz).

File Write Case & Data...


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Step 6: Postprocessing

1. Display the contours of static pressure to visualize the eddies near the orifice.

2. Enable the acoustics model.

Define Models Acoustics...

(a) Enable Ffowcs-Williams & Hawkings from the Model selection list.

(b) Retain the default value of 2e-05 Pa for Reference Acoustic Pressure.

To specify a value for the acoustic reference pressure, it is necessary to activate

the acoustic model before starting postprocessing.(c) Retain default settings for other parameters.

(d) Click OK to accept the settings.

A Warning dialog box appears. This is an informative panel and will not affectthe postprocessing results.

(e) Click OK to acknowledge the information and close the Warning panel.

3. Plot the sound pressure level (SPL).

Plot FFT...


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(a) Click Load Input File... button.

(b) Select monitor plot file for Point-1 (monitor-les-1.out).

(c) Click Plot/Modify Input Signal....

i. Select Clip to Range, in the Options list.

ii. Enter 0.3 for Min and 0.5 for Max in the X Axis Range group box.


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iii. Select Hanning in the Window drop-down list.

Hanning shows good performance in frequency resolution. It cuts the timerecord more smoothly, eliminating discontinuities that occur when data iscut off.

iv. Click Apply/Plot and close the Plot/Modify Input Signal panel.

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

(e) Select Frequency (Hz) in the X Axis Function drop-down list.

(f) Click Plot FFT to visualize the frequency distribution at Point-1.

(g) Select Write FFT to File in the Options list.

Note: Plot FFT button will change to Write FFT.

(h) Click Write FFT and specify the name of the FFT file in the resulting Select Filepanel.

(i) Similarly write the FFT file for monitor plot for point-2 (Figure 9).


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Figure 8: Spectral Analysis of Convergence History of Static Pressure on Point-1



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In Figures 8 and 9, the sound pressure level (SPL) peak occurs at 125 Hz which isclose to the analytical estimation. Considering that this tutorial uses a slightly largetime step and a 2D geometry, the result is fine.

4. Compare the frequency spectra at point-1 and point-2.

Plot File...

(a) Click Add... and select two FFT files (point-1-fft.xy and point-2-fft.xy)that you have saved in the previous step.

(b) Click Plot to visualize both spectra in the same window (Figure 10).

Note that the peak for Point-1 is a little higher than forPoint-2. This is due to the dissipativebehaviour of the sound in the domain. The bigger the distance between the reciever pointand the noise source, the bigger is the dissipation of sound. This is the reason, why we useCAA method only for near field calculations.

Figure 10: Comparison of Frequency Spectra at Point-1 and Point-2

A second issue is the dissipation of sound due to the influence of the grid size. This appliesespecially for which the wave lengths are very short. Thus, a too coarse mesh is not capableof resolving high frequencies correctly. In the present example, the mesh is rather coarsein the far-field. Thus, the discrepancy between both spectra is more evident in the highfrequency range.

This behaviour can be seen in Figure 11.

For high frequencies, the monitor for Point-1 generates much fewer noise than monitor forPoint-2 due to coarse grid resolution.


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Figure 11: Spectral Analysis of Convergence history of Static Pressure

The deviation of sound pressure level between the first two maximum peaks (50 Hz and 132Hz) is quite small. The postprocessing function magnitude in fourier transform panel issimilar to the root mean square value (RMS) of the static pressure at these frequencies.We can use the RMS value to derive the amplitude of the pressure fluctuation which is

responsible for the SPL-peak. The resolution of frequency spectra is limited by the temporaldiscretization. With the temporal discretization, the maximum frequency is

fmax =1

2t(2)

This frequency is defined as Nyquist frequency. It is the maximum educible frequency. Toresolve up to fmax the maximum allowable time step size is

fmax =1

2 fmax(3)


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An instability of the fluid motion coupled with an acoustic resonance of the cavity (helmholtzresonator) produces large pressure fluctuations (at 132 Hz). Compared to this dominanthelmholtz resonance the pressure fluctuation at 50 Hz is quite small.


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Summary

Aeroacoustic simulation of Helmholtz resonator has been performed using k-epsilon modeland Large Eddy Simulation model. The advantage of using LES model has been demon-strated. You also learned how the sound dissipation occurs in the domain by monitoring

sound pressure level at two different points in the domain. The importance of using CAAmethod has also been explained.

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