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28.10.4 Using the FFT Utility

The FLUENT FFT utility is available through the Fourier Transform panel (Figure  28.10.1).

Plot $\rightarrow$ FFT...

Figure 28.10.1: The Fourier Transform Panel
figure



Loading Data for Spectral Analysis


FFT analysis requires an input signal data file consisting of time-sequence data. To load an input signal data file into the Fourier Transform panel, click the Load Input File... button. This displays a File Selection dialog box (see Section  here) where you can browse through your file directories and locate your data file containing your time-sequence data. To remove a file from the Files list, select it and then click the Free File Data button.

If you computed acoustic signals "on the fly'', you have the option of processing signal data from a file or processing receiver data stored in memory. To analyze signal data from an existing input file, select Process File Data under Process Options and proceed as described above. To analyze receiver data stored in memory, select Process Receiver under Process Options and select the appropriate receiver in the Receiver list.

Click Plot FFT to display the spectral analysis data.



Customizing the Input


With the input signal data file loaded into the Fourier Transform panel, you may want to customize the input signal data set. You can customize the input signal by clicking the Plot/Modify Input Signal button. This displays the Plot/Modify Input Signal panel (Figure  28.10.2).

Figure 28.10.2: The Plot/Modify Input Signal Panel
figure

The Plot/Modify Input Signal panel allows you to analyze a portion of the input signal, view input Signal Statistics ( Min, Max, Mean, and Variance), and set title and label information for the input signal data file.

Customizing the Input Signal Data Set

By default, the entire data set is analyzed. To analyze a portion of the input signal, turn on the Clip to Range option and specify the data range by entering Min and Max values under X-Axis Range. To have the $y$ axis quantities reduced by the Mean value of the relevant signal property, turn on the Subtract Mean Value option.

The Set Defaults button will reset the original values for the Min and Max fields under X-Axis Range and turn off the Clip to Range option.

Viewing Data Statistics

To aid in the signal analysis, whether for the entire input signal or for a certain range of data, the Signal Statistics portion of the Plot/Modify Input Signal panel displays signal information such as minimum, maximum, and average signal values, as well as signal variance.

Customizing Titles and Labels

You can create a new title or edit the original title for the input signal plot by entering a text string in the Signal Plot Title text box. Likewise, you can create a new axis label or edit the original axis label by entering a text string into either the Y-Axis Label text box or the X-Axis Label text box.

Applying the Changes in the Input Signal Data

To apply any changes you have made in the Plot/Modify Input Signal panel and view a plot of the input signal, click the Apply/Plot button.



Customizing the Output


In most practical applications with CFD data, you may want to find out how much power or energy is contained in a certain frequency range, but do not want to distinguish positive and negative frequency. In recognition of this, all the outputs from the FFT module in FLUENT pertain to one-sided spectra for the range of positive frequency.

The Fourier Transform (Figure  28.10.1) and Plot/Modify Input Signal (Figure  28.10.2) panels allow you to set several different functions for the $x$ and $y$ axes, apply different FFT windowing techniques, and set various output options.

Specifying a Function for the $y$ Axis

You can choose the $y$-axis function using the Y Axis Function drop-down list. Available options for the $y$-axis functions are as follows:

Power Spectral Density   is the distribution of signal power in the frequency domain. It has units of the signal magnitude squared (e.g., Pa $^2$) and is defined as
$\displaystyle E(f_n)$ $\textstyle =$ $\displaystyle \vert\hat{\phi}_0\vert^2$  
$\displaystyle E(f_n)$ $\textstyle =$ $\displaystyle 2 \, \vert\hat{\phi}_n\vert^2 \hspace{0.5in}n = 1,2,...,N/2$ (28.10-9)

Magnitude   (or amplitude) is the square root of the power spectral density.


$\displaystyle A(f_n) \equiv \sqrt{E(f_n)} \hspace{0.5in}n = 0,1,2,...,N/2$     (28.10-10)

Sound Pressure Level (dB)   is the decibel level. For either general or acoustic data, when the sampled data is pressure (e.g., static pressure or sound pressure), you can compute the power in decibel units using


$\displaystyle L_{\rm sp}(f_n) = 10 \log \left(\frac{p'^2(f_n)}{p_{\rm ref}^2} \right) \hspace{0.5in} ({\rm dB})$     (28.10-11)

where $p'^2(f_n)$ is the power spectral density of the pressure fluctuation and $p_{\rm ref}$ is the reference acoustic pressure. See Section  21.3.1 for details about specifying this parameter.

Sound Amplitude (dB)   is exactly one-half of the sound pressure level in Equation  28.10-11. This quantity is also applicable for acoustics analysis.


 A_{\rm sp}(f_n) = 10 \log \sqrt{\frac{p'^2 (f_n)}{p_{\rm ref}^2}} \hspace{0.5in} ({\rm dB}) (28.10-12)

A-Weighted, Sound Pressure Level (dB A)   is the calculated sound pressure level weighted by the A-scale function to more closely approximate the frequency response of the human ear. A-Weighting is applied for loudness levels below 55 phons (55 dB at 1 kHz) and is the most commonly used weighting function. See Figure  28.10.3 for a graphical representation.

B-Weighted, Sound Pressure Level (dB B)   is the calculated sound pressure level weighted by the B-scale function. B-Weighting is applied to loudness levels between 55 and 85 phons, though it is rarely used.

C-Weighted, Sound Pressure Level (dB C)   is the calculated sound pressure level weighted by the C-scale function. C-Weighting is applied for loudness levels above 85 phons and is commonly used for high-intensity sound such as traffic studies.

Figure 28.10.3: A-, B-, and C-Weighting Functions
figure

Further graphical customizations for the $y$ axis are available by clicking the Axes... button. For more information, see Section  28.8.8.

Specifying a Function for the $x$ Axis

There are three options for the $x$-axis function you can choose from. They are all related to the discrete frequencies at which the Fourier coefficients are computed. You can apply specific analytic functions for the $x$-axis using the X Axis Function drop-down list.

Available options for the $x$-axis functions are:

Frequency (Hz)   is defined as:


$\displaystyle f_n = \frac{1}{N \Delta t} \; n \hspace{0.5in}n = 0,1,2,...,N/2$     (28.10-13)

where $N$ is the number of data points used in the FFT.

Strouhal Number   is the nondimensionalized version of the frequency defined in Equation  28.10-13:


$\displaystyle {\rm St}_n \equiv \frac{f_n \, L_{\rm ref}}{U_{\rm ref}}$     (28.10-14)

where $L_{\rm ref}$ and $U_{\rm ref}$ are the reference length and velocity scales specified in the Reference Values panel.

Fourier Mode   is the index in Equations  28.10-7 and/or 28.10-8, which represents the $n$th or $k$th term in the Fourier transform of the signal.

Octave Band (Hz)   is a range of discrete frequency bands for different octaves within the threshold of hearing. The range of each octave band is double to that of the previous band (see Table  28.10.1).

1/3-Octave Band (Hz)   is a range of discrete frequency bands within the threshold of hearing. Here, the range of each band is one-third of an octave, meaning that there are three times as many bands for the same frequency range.


Table 28.10.1: Octave Band Frequencies and Weightings
Lower
Freq. (Hz)
Center Freq. (Hz) Upper Freq. (Hz) dB A dB B dB C
11 16 22 -56.7 -28.5 -8.5
22 31.5 45 -39.4 -17.1 -3.0
45 63 90 -26.2 -9.3 -0.8
90 125 180 -16.1 -4.2 -0.2
180 250 355 -8.6 -1.3 0.0
355 500 710 -3.2 -0.3 0.0
710 1000 1400 0.0 0.0 0.0
1400 2000 2800 1.2 -0.1 -0.2
2800 4000 5600 1.0 -0.7 -0.8
5600 8000 11200 -1.1 -2.9 -3.0
11200 16000 22400 -6.6 -8.4 -8.5

Further graphical customizations for the $x$-axis are available by clicking the Axes... button. For more information, see Section  28.8.8.

Specifying Output Options

You can write out the FFT data directly to a file by choosing the Write FFT to File option under Options in the Fourier Transform panel. Once the Write FFT to File option is selected, click the Write FFT button to display a file selection dialog box where you can choose a file and/or a location to hold the FFT data.

Further customizations for how the FFT data is displayed are available by clicking the Curves... button. For more information, see Section  28.8.9.

Specifying a Windowing Technique

You can use the various windowing techniques described in Section  28.10.2 by selecting any of the Window options in the Plot/Modify Input Signal panel. By default, None is selected so that no windowing technique is applied.

Specifying Labels and Titles

You can assign a title for your FFT plot using the Plot Title text field. You can also assign $y$-axis and $x$-axis labels for your FFT plot using the Y-Axis Label and X-Axis Label text fields, respectively. By default, FLUENT assigns the Y-Axis Label and the X-Axis Label to the particular selection of Y-Axis Function and X-Axis Function.


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