**5. Research on TCFs**

#### **5.1. Frequency spectra analysis**

The frequency spectra in **Figure 11** (left and right) report the comparison between the two setups C1 (black) and C3 (red). **Figure 11** (left) shows that the highest amplitudes may be identified at the blade passing frequency of the HP rotor and its first harmonic. The red graph is shifted by 100 Hz for a better visibility.

**Figure 11.** Frequency spectra of the time‐signal reconstructed by the HP trigger for the setup without splitters (red) and with splitters (black). Right: Frequency spectra of the microphone array for the sum of the BPF of the two rotors after rotor synchronic averaging; without splitters (red) and with splitters (black).

An opposite trend is observed at the *BPFLP* + *BPFHP*, where the amplitude is 10 dB lower than the one of the HP rotor alone. The amplitude at the frequency 2*BPFHP* − *BPFLP* is almost the same as the logarithmic sum of the two rotors. Nearly 20 dB difference in the sound pressure level is observed between the amplitudes of the HP and the LP rotor. At *BPFLP* the pattern of the peaks of the two different setups is like the one at *BPFLP* + *BPFHP*.

## **5.2. Azimuthal mode analysis BPF**

An overview of the propagating modes is given in **Table 9** for the different blade passing frequencies. The modes are asymmetric, because the theoretical prediction taken into account for a swirl model [20].


**Table 9.** Range for the propagating modes dependent on the BPF.

#### **5.3. HP rotor noise**

For explanation of the complex pattern of the sound field due to the vane/blade interactions, the modes predicted by Tyler and Sofrin at the *BPFHP* are listed for the baseline setup (also given in Lengani et al. [21]): HP stator‐HP rotor interaction creates modes *m*=36 + *k∆*24=..−36; −12; 12;36. HP rotor‐LP stator interaction results in modes *m*=36 + *k∆*16=..−28; −12;4;20;36. The interaction of HP stator‐HP rotor‐LP stator creates modes *m*=36 + *k*1*∆*24 + *k*2*∆*16=..−44; −36; −28; −20; −12; −4; 4;12;20;28. These modes may be identified in **Figure 12** on the left side for the baseline configuration C1. The picture shows the sound pressure level (SPL) for the *BPFHP* in dB, for the different azimuthal mode orders m. In **Figure 12** propagating modes are marked with black bars. It is clear that the propagating mode ranges from mode ‐44 to +36. Mode orders *m*< −44 and *m*> + 36 are cut off; however, a low amplitude is visible; hence they are not fully decayed within the duct. Furthermore, all modes with high amplitudes can be predicted according to Eq. (7) as linear combination of HP vane‐ HP blade‐LP stator, and they are scattered by 8 (see also **Table 9**). Hence, noise emanated from the HP rotor has to be attributed to its interaction with the up‐and downstream vanes. For the splitter setup the prediction of modes for the HP‐rotor‐LP stator interaction as well as for the HP stator‐HP rotor‐LP stator interaction can be done with different vane numbers. The LP vane count may be considered equal to 48 because of the 32 additional splitters. However the geometry of the splitters is not the same as the one of the struts and the splitter leading edge is far downstream in the strut passage, but for a first estimation it can be assumed that the interaction is similar. Therefore, the theory of Tyler and Sofrin is not fully satisfied but can be applied. For the interaction of HP stator‐HP rotor‐LP vanes the following modes may be predicted in the ideal case of assumed 48 identical LP vanes: *m*=36 + *k*1*∆*24 + *k*2*∆*48=..−36; −12;12;36; Without this assumption and further considering that

LP vanes and splitters as separate vane rows (HP stator‐HP rotor‐LP vane‐splitter interaction) the modes can again be obtained from this simple linear combination:

$$\text{1. } 36 + k\_{\text{1}} \cdot 24 + k\_{\text{2}} \cdot 32 + k\_{\text{3}} \cdot 16 = \dots - 44; \\ -36; \\ -28; \\ -20; \\ -12; \\ -4; \\ 4; \\ 12; \\ 20; \\ 28; \\ 36$$

The modes propagating in the case of the splitter setup are shown on the right side of **Figure 12**. The modes, which change significantly between the two setups, are labelled in the picture. Particularly, the power levels of modes *m*= −44 and *m*= −28 are significantly reduced by almost 20 dB for the configuration with splitters. Also the amplitude of mode *m*= + 28 is 10 dB lower. It should be noticed that these modes are not predicted assuming the ideal LP vane number of 48. It seems that the presence of splitter vanes changes the acoustic transmis‐ sion of sound waves through the LP vanes for modes which are instead propagating for the baseline case. Further, modes from HP stator‐HP rotor interaction are partially scattered at the leading edges of the 16 LP vanes and partially scattered further downstream in the LP vane passage at the 32 splitter leading edges. The modes mean value in the setup with the splitters is 5 dB lower than the one in the baseline setup.

**Figure 12.** Azimuthal mode analysis of the flow with the HP trigger; without splitters (left) and with splitters (right).

#### **5.4. LP rotor noise**

**5.2. Azimuthal mode analysis BPF**

22 Recent Progress in Some Aircraft Technologies

**Frequency Range of the modes**

*BPFHP* -44 : 8 : 36 2*BPFHP* -96 : 8 : 80 *BPFLP* -32 : 8 : 24 2*BPFLP* -64 : 8 : 48 *BPFLP* + *BPFHP* -84 : 8 : 68

**Table 9.** Range for the propagating modes dependent on the BPF.

for a swirl model [20].

**5.3. HP rotor noise**

An overview of the propagating modes is given in **Table 9** for the different blade passing frequencies. The modes are asymmetric, because the theoretical prediction taken into account

For explanation of the complex pattern of the sound field due to the vane/blade interactions, the modes predicted by Tyler and Sofrin at the *BPFHP* are listed for the baseline setup (also given in Lengani et al. [21]): HP stator‐HP rotor interaction creates modes *m*=36 + *k∆*24=..−36; −12; 12;36. HP rotor‐LP stator interaction results in modes *m*=36 + *k∆*16=..−28; −12;4;20;36. The interaction of HP stator‐HP rotor‐LP stator creates modes *m*=36 + *k*1*∆*24 + *k*2*∆*16=..−44; −36; −28; −20; −12; −4; 4;12;20;28. These modes may be identified in **Figure 12** on the left side for the baseline configuration C1. The picture shows the sound pressure level (SPL) for the *BPFHP* in dB, for the different azimuthal mode orders m. In **Figure 12** propagating modes are marked with black bars. It is clear that the propagating mode ranges from mode ‐44 to +36. Mode orders *m*< −44 and *m*> + 36 are cut off; however, a low amplitude is visible; hence they are not fully decayed within the duct. Furthermore, all modes with high amplitudes can be predicted according to Eq. (7) as linear combination of HP vane‐ HP blade‐LP stator, and they are scattered by 8 (see also **Table 9**). Hence, noise emanated from the HP rotor has to be attributed to its interaction with the up‐and downstream vanes. For the splitter setup the prediction of modes for the HP‐rotor‐LP stator interaction as well as for the HP stator‐HP rotor‐LP stator interaction can be done with different vane numbers. The LP vane count may be considered equal to 48 because of the 32 additional splitters. However the geometry of the splitters is not the same as the one of the struts and the splitter leading edge is far downstream in the strut passage, but for a first estimation it can be assumed that the interaction is similar. Therefore, the theory of Tyler and Sofrin is not fully satisfied but can be applied. For the interaction of HP stator‐HP rotor‐LP vanes the following modes may be predicted in the ideal case of assumed 48 identical LP vanes: *m*=36 + *k*1*∆*24 + *k*2*∆*48=..−36; −12;12;36; Without this assumption and further considering that

**Figure 13** depicts the sound power levels of the modal decomposition for the *BPFLP*. This figure shows the baseline configuration on the left side and the splitter configuration on the right side. The interaction of the LP vane and the LP blade generates the following modes: *m*= −72 + *k∆*16=..−72; −56; −40; −24; −8;8;24. These modes can be clearly identified in the left side of **Figure 13**, and are additionally indicated in black. The highest sound pressure level is observed for mode *m*= −24. In‐between −24<*m*<24 other modes are blackened (e.g. *m*= −16, 0, + 16) that can be predicted when the linear combination of LP vane and blade additionally considers the interaction with the HP vane (−72 + *k*1*∆*16 + *k*2*∆*24). However, the interaction between the HP vane and LP blade is weak (e.g. there is a difference of more than 20 dB between mode *m*= −24 and *m*= −16). Modes ‐72, ‐56, and ‐40 are still visible in the figure. These modes are generated by the LP rotor itself and by the LP stator‐LP rotor interaction. However, those modes are cut off and therefore have a lower amplitude than the cuton modes. The cutoff modes will decay further downstream of the duct. In the case of the splitter setup (right side of **Figure 13**), again a different LP vane count may be considered. Ideally, the LP vane‐LP rotor interaction would consist of the modes: *m*= −72 + *k∆*48=..−72; −24;24. Mode *m*= −24 has still the highest amplitude; however it is now in the same order of magnitude of the amplitude of mode *m*= −8. In the assumed ideal case of the splitter setup, mode *m*= −8 should not be there. However, as observed by Spataro et al. [22, 23] the unsteady effects induced by strut and splitter vane wakes differ considerably downstream of the LP rotor. The modes generated due to the interaction of the 48 LP vanes with the LP blades may be predicted when the modes are scattered at the 16 struts (e.g. mode *m*= −8 is obtained adding the 16 vanes to mode ‐24). In the case of the splitter setup, the mode *m*= −8 is more than 20 dB higher than in the baseline case. Also the sound pressure level of the modes generated due to the interaction HP vanes‐LP vanes‐LP‐rotor is altered. It seems that the splitter design shifts the important modes to lower orders (e.g. mode ‐8 which was hardly identifiable for the baseline setup). As can be seen in the mean spectrum (**Figure 11** (right)), the modes mean value is almost 3 dB lower for the baseline configuration.

**Figure 13.** Azimuthal mode analysis of the flow with the LP trigger; without splitters (left) and with splitters (right).

Also for the splitter setup the modes *m*= −72, −56 are cut off as previously discussed for the baseline design. Mode *m*= −40 is significantly reduced by more than 20 dB in the splitter configuration. The high sound pressure level at the *BPFLP* may be due to the effect of "shifting" modes towards lower orders and not necessarily to an enhanced unsteady interaction. Unsteady measurements by means of a fast response aerodynamic pressure probe down‐ stream of the LP rotor reported in Spataro et al. [23] revealed that the unsteady pressure fluctuations, evaluated for the LP rotor phase, are of comparable order of magnitude for both setups.

In **Figure 14** the sound power levels of the modal decomposition is shown for the sum of the blade passing frequencies of the two rotors (*BPFLP* + *BPFHP*) for the baseline setup (left) and the setup with splitters (right). The modes mean value is almost the same for both setups. However, there are some predominant modes clearly visible. Its amplitudes changing up to 23 dB and results from stator/rotor/stator/rotor interaction. Although mode *m*= −28 has one of the highest sound power levels for the baseline setup, its amplitude is significantly reduced for the splitter design. But in the case of the splitters, other modes like *m*= −20 and *m*= −4 appear, with amplitudes that are 20 dB and 14 dB, respectively, higher than in the baseline setup. Therefore the sound pressure level of both setups is almost the same for that specific frequency (sum of the blade passing frequencies of the two rotors). The largest reduction of the modes mean amplitude for the splitter setup is associated to the HP rotor. There is a 5 dB lower amplitude at the *BPFHP* compared to the baseline design. At 2*BPFHP* the results and trends of the azimuthal mode analysis are similar. A sound pressure level reduction of 4 dB was achieved with the splitter design. In contrast, the sound pressure level at *BPFLP* and 2*BPFLP* is 3 dB lower for the setup without splitters, and at the *BPFLP* + *BPFHP* it is nearly the same in both cases.

20 dB between mode *m*= −24 and *m*= −16). Modes ‐72, ‐56, and ‐40 are still visible in the figure. These modes are generated by the LP rotor itself and by the LP stator‐LP rotor interaction. However, those modes are cut off and therefore have a lower amplitude than the cuton modes. The cutoff modes will decay further downstream of the duct. In the case of the splitter setup (right side of **Figure 13**), again a different LP vane count may be considered. Ideally, the LP vane‐LP rotor interaction would consist of the modes: *m*= −72 + *k∆*48=..−72; −24;24. Mode *m*= −24 has still the highest amplitude; however it is now in the same order of magnitude of the amplitude of mode *m*= −8. In the assumed ideal case of the splitter setup, mode *m*= −8 should not be there. However, as observed by Spataro et al. [22, 23] the unsteady effects induced by strut and splitter vane wakes differ considerably downstream of the LP rotor. The modes generated due to the interaction of the 48 LP vanes with the LP blades may be predicted when the modes are scattered at the 16 struts (e.g. mode *m*= −8 is obtained adding the 16 vanes to mode ‐24). In the case of the splitter setup, the mode *m*= −8 is more than 20 dB higher than in the baseline case. Also the sound pressure level of the modes generated due to the interaction HP vanes‐LP vanes‐LP‐rotor is altered. It seems that the splitter design shifts the important modes to lower orders (e.g. mode ‐8 which was hardly identifiable for the baseline setup). As can be seen in the mean spectrum (**Figure 11** (right)), the modes mean value is almost 3 dB

**Figure 13.** Azimuthal mode analysis of the flow with the LP trigger; without splitters (left) and with splitters (right).

Also for the splitter setup the modes *m*= −72, −56 are cut off as previously discussed for the baseline design. Mode *m*= −40 is significantly reduced by more than 20 dB in the splitter configuration. The high sound pressure level at the *BPFLP* may be due to the effect of "shifting" modes towards lower orders and not necessarily to an enhanced unsteady interaction. Unsteady measurements by means of a fast response aerodynamic pressure probe down‐ stream of the LP rotor reported in Spataro et al. [23] revealed that the unsteady pressure fluctuations, evaluated for the LP rotor phase, are of comparable order of magnitude for both

In **Figure 14** the sound power levels of the modal decomposition is shown for the sum of the blade passing frequencies of the two rotors (*BPFLP* + *BPFHP*) for the baseline setup (left) and the setup with splitters (right). The modes mean value is almost the same for both setups.

lower for the baseline configuration.

24 Recent Progress in Some Aircraft Technologies

setups.

**Figure 14.** Azimuthal mode analysis of the flow with the two triggers; without splitters (left) and with splitters (right).

**Figure 15.** Section of the HP an LP stage showing the different clocking positions.

The comparison of the baseline setup C1 and the shortened setup C2 showed an increase of the sound pressure level between 5 and 9 dB dependent on the operating point. Especially the interaction modes between the struts and the LP rotor increase due to the 10% shortening of the duct length.

As a next step the influence of airfoil clocking on the acoustics was investigated. The results of this investigation of noise generation and propagation for different clocking positions (CP) of the HP vanes and the struts are presented. A meridional section presenting the six vane‐ vane positions can be found in **Figure 15**.

**Figure 16.** Radial mode analysis with reference to the HP trigger.

The sound power levels for *BPFHP* both in positive (gray bars in **Figure 16**) and in negative (white bars in **Figure 16**) flow direction were calculated and plotted for all the radial modes over the azimuthal modes at the abscissa. Furthermore an overall sound power level was determined by logarithmic addition for both directions of propagation. Further, **Figure 16** shows the sound power level in decibel (dB) over the propagatable azimuthal modes m summed over the radial mode order n in the up‐ and downstream direction for all clocking positions (CP1–CP6).

Several interaction modes are clearly visible in the figures. The amplitudes of these significant modes are 20 dB larger than those of the non‐interaction modes. In particular, the modes *m*= −20 and *m*= −12 are dominant for all clocking positions except CP4 here the mode *m*= −4 is higher than *m*= −12. Clocking position CP4 is that relative stator‐stator position, where the sum of the most significant modes has its minimum. For the following discussion only the six dominating modes with the highest sound power levels are considered. With this analysis of certain modes the origin of a higher or a lower overall sound power level dependent on the clocking position can be determined. The most significant modes, which can be derived from different stator/rotor/stator interactions that can be predicted with Eq. (6) or Eq. (7), are selected and compared for all the different clocking positions. These interaction modes have the most influence on the overall sound power level, because if the difference between two incoherent sound signals is larger than 10 dB, the acoustic source with the smaller level has no noticeable influence on the sum of the power levels. The following significant azimuthal interaction modes (HP stator, HP rotor, and TMTF) were predicted: *m*=36 + *k*1*∆*24 + *k*2*∆*16=..−20; −12; −4; 4;12;20; …. Mode *m*= −20 has the highest amplitude. This mode rises over the first three clocking positions (see **Figure 17**) reaching its maximum at clocking position 3, which is close to the optimum aerodynamic clocking position.

**Figure 17.** Six most dominant modes at seven different clocking positions.

interaction modes between the struts and the LP rotor increase due to the 10% shortening of

As a next step the influence of airfoil clocking on the acoustics was investigated. The results of this investigation of noise generation and propagation for different clocking positions (CP) of the HP vanes and the struts are presented. A meridional section presenting the six vane‐

The sound power levels for *BPFHP* both in positive (gray bars in **Figure 16**) and in negative (white bars in **Figure 16**) flow direction were calculated and plotted for all the radial modes over the azimuthal modes at the abscissa. Furthermore an overall sound power level was determined by logarithmic addition for both directions of propagation. Further, **Figure 16** shows the sound power level in decibel (dB) over the propagatable azimuthal modes m summed over the radial mode order n in the up‐ and downstream direction for all clocking

the duct length.

vane positions can be found in **Figure 15**.

26 Recent Progress in Some Aircraft Technologies

**Figure 16.** Radial mode analysis with reference to the HP trigger.

positions (CP1–CP6).

Defining the optimum aerodynamic clocking position was performed by means of pre‐test CFD calculations. In that way, most of the wakes of the HP stator impinge on the leading edges of the TMTF struts [24]. It is important that mode *m*= −20 can only be predicted by the interactions of HP stator, HP rotor and the TMTF. It is assumed that this particular mode originates from an effect where the TMTF plays a significant role. That means that the wakes of the HP stator impinge on the leading edges of the struts and the flow through the strut passage remains more or less undisturbed. However, the flow downstream the turning mid turbine frame shows larger differences of flow quantities between the wake and the main passage flow. By changing the relative vane‐vane position (=clocking also known as stator indexing) to the fourth clocking position the amplitude of *m*= −20 is reduced. For the next two clocking positions 5 and 6 the sound power level remains almost the same. The high sound power level of mode *m*= −20 is due to the vane/rotor/strut interaction. However, this mode is neither predicted by the HP stator‐HP rotor interaction nor by the HP rotor/TMTF interaction. The unsteady interaction of the HP‐stage is scattered by the downstream turning struts in the flow path. Mode *m*= −20 is generated by the scattering of the HP‐stage interaction at the TMTF. **Figure 17** shows that the sound power levels of mode *m*= −12 decrease from clocking position 1 to 4 and increase again from clocking position 4 to 6. The minimum sound power level can be seen at clocking position 4. The mode *m*= −12 is either generated by the HP stator‐HP rotor interaction or by the HP rotor‐TMTF interaction. In case of mode *m*= −12 the strongest influence of the different clocking positions can be determined. This particular mode is reduced by 4 dB when changing the relative vane‐vane position from CP1 to CP4. For the modes *m*= + 12 and *m*= + 20 a similar trend to mode *m*= −12 can be observed. These modes also show significant changes of the sound power levels of up to 3 dB due to different relative positions of the HP vanes and the TMTF struts. Both modes reach their minimum sound power level at clocking position 5, whereas the level of the amplitudes is decreasing from 1 to 4. The mode *m*= + 12 is generated by the interaction of the HP vanes and the HP blades but also by scattering of the HP stage interaction modes at the TMTF. The mode *m*= + 20 is always generated in conjunction with the TMTF‐vanes, either with the HP rotor or with the HP stage. While the amplitude of mode *m*= −4 seems to be almost constant for all clocking positions, mode *m*= + 4 changes from CP2 to CP6 by 4 dB, whereas at the last clocking position the amplitude of m=+4 has its lowest value. Both modes are the result of the interaction of the HP‐stage and the TMTF. Summing up the sound power levels (depicted in **Figure 17**) reveals that there is a minimum sound power at clocking position CP4. A difference in sound power level of app. 2 dB between the acousti‐ cally best (CP4) and worst (CP2) clocking position is observed.

## **6. Conclusions**

Three different turbine exit casings with different turbine exit guide vane (TEGV) designs have been compared to a state‐of‐the‐art (reference) TEGV design. The possible reduction of sound power levels when applying the different designs and a rough estimation of the aerodynamic losses have been presented. When comparing the overall reduction of PWL (only considering the main airfoil interaction modes) it was revealed that the acoustically optimised inverse cutoff TEC has the largest reduction of sound power level of 14 dB. The aerodynamically optimised H‐TEC even increases the overall sound power level by about 2 dB. The leaned TEC also decreases the PWL by about 11 dB, but is still as twice as loud as the inverse cutoff TEC. However, for the operating point approach the aerodynamic losses are increased for all TEC designs. The losses measured at the aero design point are lower for the aerodynamically optimised H‐TEC and the inverse cutoff TEC than for the reference TEC. Both, the H‐TEC and the inverse cutoff TEC provide a much more uniform yaw angle distribution downstream of the trailing edge. These results give confidence that it is possible to design an aerodynamically and acoustically optimised TEC. Further, the effect of a change in stage design onto a TEGV with a compound lean was investigated and presented in this chapter. It was shown that while keeping the shaft power constant, the noise emissions downstream of the TEGV can be reduced by 0.7 dB for the given geometry and operating point. This decrease in sound power level is not caused by a decrease in interactions, but rather by acoustic modes not attributable to these interactions. The overall sound power level of the modes is increased by 0.3 dB. When having the same rotational speed for the high loaded stage and the datum stage, the main interaction modes are identical. In addition to that main modes, several additional modes are found, that have been leading to an overall increase in sound power level. The TEGV inlet flow show only minor differences between the two stage designs. The main change occurs in the tip region. The main flow features of the TEGV exit flow remain identical. But it was observed that the shape of the wake changes due to the changes in the rotor tip leakage flow upstream of the TEGV. This increases the total pressure loss of the TEGV by approximately 16%.

Because of the possible significant reduction of the generated noise at the turbine exit casing noise from more upstream engine components such as the turbine centre frame can become a problem. Therefore, the noise generation between high pressure turbine, turbine centre frame, and low pressure turbine was investigated. Three different setups have been compared to each other. A baseline case C1 is designed with turning struts. A second design C2 reduces the axial length of the turbine centre frame. The third design C3 is characterized by the presence of two non‐lifting splitters embedded into the strut passage. In the frequency spectra, the peak at the *BPFHP* is 3 dB lower for the splitter setup. In the azimuthal mode analysis the difference is even higher. The sound power level decreased 5 dB at the *BPFHP* for the setup with the splitters. Additionally, both the frequency spectra and the azimuthal mode analysis have shown that the noise generated by the LP rotor is slightly higher for the setup with the splitters. The splitter design is suppressing some modes, while others are scattered or are even more pronounced than in the baseline configuration. The splitters reduce the overall noise propagation by 5 dB acting as a cutoff filter for the HP stage rotor. The comparison of the baseline setup C1 and the shortened setup C2 showed an increase of the sound pressure level between 5 and 9 dB dependent on the operating point. Additionally, an experimental investigation in order to explore the potential of different vane‐vane clocking positions on the noise generation and propagation was conducted. The six most significant modes have been analyzed regarding their sound power levels for the six clocking positions. The modes varied in their absolute values for the sound power and also their trend over the clocking positions changed. An optimum clocking position for acoustics was found, but it does not to coincide with the optimum aerodynamic clocking position. The difference of the overall sound power level for the six most relevant modes between the optimum acoustic clocking position (CP4) and the aerodynamic one (CP3) is about 2 dB.
