3.3.2. Frequency Domain Assessment

Quite unexpectedly, the improvements just commented do not have a translation in the frequency domain. In the case of the reflection coefficients, shown in Figure 16, the influence of the new description is apparent, but the new results do not provide any improvement in the reproduction of the experimental trend, showing even a certain degree of degradation in the quality of the results, with the abnormally high values achieved around 1300 Hz when the junction is excited at port 1.

**Figure 16.** Influence of the description of the junction on the reflection coefficients (frequency domain), MDT method. (**a**) Excitation at port 1; (**b**) excitation at port 3. Ports are denoted as in Figure 1.

The same comments apply to the transmission coefficients shown in Figure 17. The strange behavior around 1300 Hz is again present in those coefficients associated with the excitation at port 1, while when the junction is excited at port 3 no significant improvement can be detected.

The only possible explanation for the behavior observed, this is, something that produces minor but evident improvements in the time domain, but that induces a rather severe degradation in the quality of the results in the frequency domain, would be that some spurious high-frequency oscillations are being generated at the interface between the quasi-3D junction and the 1D elements of the adjacent ducts, due to the virtual merging of four volumes into a single one.

In order to clarify this point, the whole system was meshed as shown in Figure 14b for the junction, and the results are shown in Figure 18, only for the case in which the junction is excited at port 1. It is apparent that a dramatic improvement in the quality of the transmission coefficients is achieved, now showing a more realistic influence of the change in direction. In the case of the reflection coefficients the improvement is not so apparent, but the amplitude of the oscillations is smaller, what indicates that further refining of the mesh could lead to substantially improved results. However, that would be

impractical, since the computation time increases substantially when the whole system is meshed in this way.

**Figure 17.** Influence of the description of the junction on the reflection coefficients (frequency domain), MDT method. (**a**) excitation at port 1, transmission through port 2; (**b**) excitation at port 1, transmission through port 3; (**c**) excitation at port 3, transmission through port 1; (**d**) excitation at port 3, transmission through port 2. Ports are denoted as in Figure 1.

**Figure 18.** Influence of using a quasi-3D approach for the whole system on the reflection and transmission coefficients (frequency domain). MDT method, excitation at port 1. (**a**) reflection at port 1; (**b**) transmission through port 2; (**c**) transmission through port 3. Ports are denoted as in Figure 1.
