Comparing Results Using Spectral Analyses

To compare the Lighthill Wave solution with the Perturbed Convective Wave solution, you perform spectral analyses at the microphone and the pressure transducer. Using pre-defined Point Time Fourier Transforms, you transform the time signals (Lighthill pressure, acoustic pressure, and pressure perturbation) to the frequency domain. You display the results using monitor plots.

To compare the results:
  1. Import the Lighthill Wave results:
    1. Right-click the Tools > Tables node and select New Table > File Table.
    2. In the Open dialog, multi-select the previously exported files MicrophoneLighthillPressure.csv and PressureTransducerLighthillPressure.csv, then click Open.
  2. Set up the Point Time Fourier Transforms for the recorded time signals:
    1. Expand the Tools > Data Set Functions node and review the pre-defined Point Time Fourier Transforms.


    2. Right-click the G(p) Microphone > Tabular node and select New derived data from table.
    3. Rename the Tabular > Tabular node to Microphone: Lighthill Pressure.
    4. Select the Microphone: Lighthill Pressure node and set the following properties:
      Property Setting
      Update Active
      Input Data 1 MicrophoneLighthillPressure
      X Column 1 Time
      Y Column 1 Microphone: Lighthill Pressure Monitor: Microphone: Lighthill Pressure Monitor
    5. Right-click the G(p) Microphone > Monitor node and select New derived data from monitor.
    6. Rename the Monitor > Monitor node to Microphone: Acoustic Pressure.
    7. Select the Microphone: Acoustic Pressure node and set the following properties:
      Property Setting
      Update Active
      Input Data 1 Microphone: Acoustic Pressure Monitor
    8. Repeat Steps 2e - g to add the time signal from the monitor Microphone: Pressure Perturbation Monitor and rename the node to Microphone: Pressure Perturbation.
    9. Repeat the procedure described in Steps 2b - h to add the time signals recorded at the pressure transducer to G(p) Pressure Transducer.
  3. Add the derived data to monitor plots:
    1. Right-click the Plots node and select New Plot > Monitor Plot.
    2. Rename the plot to Microphone: Spectral Analysis.
    3. Right-click the Microphone: Spectral Analysis > Data Series node and select Add Data.
    4. In the Add Data Providers to Plot dialog, expand the Derived Data node and select the following objects:
      • Microphone: Lighthill Pressure
      • Microphone: Acoustic Pressure
      • Microphone: Pressure Perturbation
    5. Click OK.
    6. Select the Microphone: Spectral Analysis > Axes > Bottom Axes node and set Maximum to the desired frequency of 2500 Hz. This is the frequency the mesh was capable to resolve.
    7. Repeat Steps 3a - f to create a plot called Pressure Transducer: Spectral Analysis using the derived data at the pressure transducer.
  4. Save the simulation.
The following plots display the spectral analyses at the microphone and at the pressure transducer, respectively:




At the microphone, for frequencies > 500 Hz, the pressure perturbation and the acoustic pressure as computed by the Perturbed Convective Wave model show similar results. This indicates that the hydrodynamic pressure at the microphone is negligible in this frequency range. Here, the acoustic pressure also correlates with the Lighthill pressure, which indicates that the Lighthill Wave model is capable of predicting the acoustic pressure at the microphone. Only at low frequencies (< 500 Hz), different values indicate that the received pressure fluctuations are of hydrodynamic nature.

At the pressure transducer, where turbulent fluctuations are dominant, the Lighthill pressure differs significantly from the acoustic pressure. In this region, the Lighthill pressure is not capable of providing information on the noise.

Conclusion: For noise predictions in regions where the hydrodynamic pressure is negligible, the computationally less expensive Lighthill Wave model provides reasonable results. However, in regions where turbulent fluctuations are dominant, only the Perturbed Convective Wave model, which directly solves for the acoustic pressure, can provide insight into the sound field.