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Is the fluctuation pressure the same as the sound pressure?

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Old   August 29, 2017, 11:06
Default Is the fluctuation pressure the same as the sound pressure?
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I use an in-house CFD code to simulate the flow over Idealized Side Mirror. The reference paper is Caraeni2011. To compare with the reference paper, I obtain the pressure history at the monitor points. By subtracting the mean of the pressure history, the fluctuation pressure is obtained.

Sound Pressure Level is defined as follows,



Now, my question is: is the fluctuation pressure the same as the sound pressure? Can I directly use my fluctuation pressure to calculate the SPL?

I know SPL is a single value and it requires Root Mean Square of the pressure history. What I want to calculate is actually the spectra of SPL. Just like the following pic. The unit of frequency is dB, and I guess it's typo.



In order to get the spectra of SPL, I apply FFT on the fluctuation pressure history and then feed the absolute value of the FFT result as input into the SPL formula to get the spectra of SPL.




[Caraeni2011]: Caraeni, M., Aybay, O., & Holst, S. (2011). Tandem Cylinder and Idealized Side Mirror Far-Field Noise Predictions Using DES and An Efficient Implementation of FW-H Equation. In 17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference) (pp. 58). Reston, Virigina: American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2011-2843
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Old   August 29, 2017, 11:29
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I agree that in the picture, Hz and dB are wrong, Hz should be in the x-axis and dB in the y-axis.
I think you can take the FFT of the whole pressure signal (the means should be the C0 coefficents of the Fourier representation) and reporting the square of the Fourier coefficient.
The main problem I can see is the window to take for the FFT, it should work on a periodic temporal interval. How do you manage that?
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Old   August 29, 2017, 12:20
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Quote:
Originally Posted by FMDenaro View Post
I agree that in the picture, Hz and dB are wrong, Hz should be in the x-axis and dB in the y-axis.
I think you can take the FFT of the whole pressure signal (the means should be the C0 coefficents of the Fourier representation) and reporting the square of the Fourier coefficient.
The main problem I can see is the window to take for the FFT, it should work on a periodic temporal interval. How do you manage that?

The window function is hamming. I just multiply the original fluctuation pressure with the hamming function. The code I use is simple. The window function is just applied to the whole fluctuation pressure history. In fact, I also tried dividing the whole history into several segments and apply the hamming function on each one, calculate FFT, then average them. It's just averaging, no big difference.

Code:
p0=2E-5
f_sample=1.0/dt
var_fluc=var_arr-var_arr.mean()
var_fluc=var_fluc*hamming(var_fluc.size)
var_fluc_freq,var_fluc_fft=fft(var_fluc,f_sample)
spl=20*np.log10(np.abs(var_fluc_fft)/p0)

def fft(in_u, in_sample_freq):
    from numpy.fft import fft, fftfreq, fftshift
    #  from numpy import mean
    #  in_u = in_u - mean(in_u)
    dx = 1.0 / in_sample_freq
    nx = in_u.size
    out_freq = fftfreq(nx, dx)
    out_fft = fft(in_u)/nx
    out_freq = fftshift(out_freq)
    out_fft = fftshift(out_fft)
    return out_freq, out_fft
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Old   August 29, 2017, 12:30
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In principle, I would choice to segment the total interval in several periodic sub-interval, taking the FFT and doing the ensemble averaging of the Fourier coefficients. Of course, C0 (the mean pressure) will remain the same.

You should try to compare with a well documented case and check for your results
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Old   August 29, 2017, 12:37
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Quote:
Originally Posted by FMDenaro View Post
In principle, I would choice to segment the total interval in several periodic sub-interval, taking the FFT and doing the ensemble averaging of the Fourier coefficients. Of course, C0 (the mean pressure) will remain the same.

You should try to compare with a well documented case and check for your results

What do you mean by "periodic sub-interval"? The pressure history is like the following pic.



How do you make sure the sub-interval is periodic?

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Old   August 29, 2017, 12:39
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Another point is that is the fluctuation pressure the same as the sound pressure? Can I directly use the fluctuation pressure to get its FFT results and then calculate the spectra of SPL?
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Old   August 29, 2017, 12:54
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Quote:
Originally Posted by aerosjc View Post

What do you mean by "periodic sub-interval"? The pressure history is like the following pic.



How do you make sure the sub-interval is periodic?


I see a numerical transient that seems to end at around 0.2. Then, it seems to me that the interval is to short to take a meaningful ensemble averaging. I see about two time segment where a periodicity can be supposed. To have a meaningful statistics you should collect about 20 temporal segments.
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Old   August 29, 2017, 13:00
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Quote:
Originally Posted by FMDenaro View Post
I see a numerical transient that seems to end at around 0.2. Then, it seems to me that the interval is to short to take a meaningful ensemble averaging. I see about two time segment where a periodicity can be supposed. To have a meaningful statistics you should collect about 20 temporal segments.

Yes. I agree. The time length of this pic maybe insufficient for averaging.

Thank you for the discussing!
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