Prediction of the acoustic shielding by aircraft empennage for contra-rotating open rotors

Computational fluid dynamics

The objective of the CFD is to compute the aeroacoustic sources of the propellers. The unsteady Reynolds-averaged Navier–Stokes simulation (URANS) is suitable for the calculation of the unsteady flow of propellers. In the present work, it is achieved with CIRA’s multi-block structured solver U-ZEN,^17,18 using the k-ω TNT turbulence model. ¹⁹ Front and rear propeller meshes rotate in opposite directions and the resulting non-conformal interface (sliding mesh) is updated at each time step. Figure 5 exhibits the coarse mesh (about 900,000 cells in the computation domain) initially used for the computation of the CROR with pylon. A finer mesh (about 7 million cells) was subsequently used for the CFD of the CROR and the outputs were used as input to the acoustic computations described in the following paragraph. These computations are part of a larger CFD study investigating the influence of rotational speed and incidence. In this latter study, an additional refinement generated a 66 million cells mesh for validation purpose. This very fine mesh has been computed on a slightly different case (2949 r/min, M = 0.1, incidence of 6°) and the aerodynamic results have been compared to the results produced by the two coarser meshes. It has been concluded that the 7 million cells mesh is convenient for this case and it has been inferred that the 7 million cells mesh is convenient too for the present case. In the present CFD simulation, 64 time steps per blade passing period are computed which corresponds to an angular time step of 0.46875°. The highest frequency studied in the current work is the fourth blade passing frequency, the resolution of higher frequencies being found to be too low, that is less than 16 time steps per period. OPEN IN VIEWER

Figure 6 shows the blade thrust coefficient of each propeller and its Fourier transform. The effect of the pylon wake on the thrust is obvious on the front blade with the sudden increase of thrust whereas it is minimal on the rear blade which is much more affected by the front propeller wake as the double maxima pattern, duplicated 2*B times, illustrates. These two maxima are related to the specificity of the blade geometry. In contrast, the potential effect of the rear propeller on the front propeller is very weak. These two observations are confirmed by the harmonic analysis. For the 2*B harmonic, the thrust coefficient levels are significantly increased on the rear blade whereas they hardly increase on the front blade. The high levels of the multiples of the 2*B harmonic suggest that the interaction tones noise could be significant as we will see in the paragraph dedicated to the CROR noise analysis. OPEN IN VIEWER

FW-H surface IM

In the present study, we consider the CROR in take-off conditions. The axial flow Mach number (see Table 2) and rotational tip Mach number are largely subsonic. Thus, it is assumed that the loading noise dominates the CROR noise whereas the quadrupole sources in the wake are not significant since they are generally associated with transonic phenomena. ²⁰ The noise sources are mostly characterized by dipoles on the blades. Therefore, the FW-H IM using the blade pressure fluctuations is adapted to compute the CROR noise emission. The noise computations are performed by solving the FW-H equation in the time domain with ONERA’s code KIM^21,22 and a Fast Fourier Transform (FFT) is applied to the acoustic signatures to provide the emitted pressure in the frequency domain.

Boundary element method

The last computational step is to solve a scattering problem where the aircraft is the obstacle and the CROR is the source. In the present case, the low flow speed (28 m/s) and the viscous effect of the fluid are neglected so that the scattering problem assumes an infinite space of an inviscid fluid at rest in which an acoustic source and a scattering surface lie. Rapid numerical methods (BEM) for solving the Helmholtz equation in the presence of arbitrary geometries (the scattering effect) are based on mathematical approximations of an interaction matrix, representative of a perturbed linear system applied to these surfaces. ONERA’s in-house BEMUSE code ²³ solves this system using either a Brakhage–Werner ²⁴ or Burton–Miller ²⁵ integral formulation. The Sommerfeld radiation condition applies at infinity and the scattering surface defines the boundary conditions which can be, for instance, Neumann, Dirichlet or Robin. These elements are coupled with an algebraic approach of the kernel approximation (inverse matrix) based on the adaptive cross approximation (ACA) method. The method implemented follows the work of Grasedyck ²⁶ on asymptotically smooth kernel operators, initially introduced by Bebendorf. ²⁷ It computes a low-rank approximation of appropriate matrix blocks, independent of the kernel operator. The size of the final matrix to be solved, within the above considerations, is largely diminished from an N² to an N*log(N) order.

Dominating harmonics of the contra-rotating propellers

The semi-analytical model of counter-rotating propellers noise proposed by Hanson, ²⁸ offers an insight into the parameters controlling the efficiency of the noise emitted in the general case of two contra-rotating propellers with B₁ and B₂ blade numbers and Ω₁ and Ω₂ rotational speeds. It can be applied to the distortion case of a pylon in front of a single propeller, that is B₁ = 1 and Ω₁ = 0, but we prefer stressing the particular case of the current propellers defined by an equal blade number, B, and rotational speed, Ω, and highlighting the resulting dominating harmonics. Generally speaking, the harmonic noise from a propeller – either the front one or the rear one in the following – is theoretically composed of an infinity of sound harmonics m, to which an infinity of load harmonics k contribute. But only a small number of pairs (m, k) are associated with an efficient contribution to the noise emission. From the noise formula proposed by Hanson, ²⁸ one can relate the acoustic pressure p emitted by a rotor at distance r from the centre of the CROR to be

p ∼ ∑ m = − ∞ ∞ ∑ k = − ∞ ∞ e i { ( m − 2 k ) B ( φ − φ ( 2 ) − π 2 ) + m B ( Ω r c 0 − Ω t ) } ∫ r o o t t i p J ( m − 2 k ) B ( m B z 0 M T sin θ 1 − M x cos θ ) A r A k d z 0

A_r takes into account the relative mach number, offset and sweep of the blade section

A_k takes into account the kth drag and lift harmonic coefficients, for example the loading sources

M_T and M_x are the blade tip rotational Mach number and axial Mach number, respectively

ϕ and θ are observer angles

The Bessel function term significantly controls the efficiency of the contribution of the harmonic (m, k). Bessel functions J_n(x) decay rapidly for |x| < |n|. As suggested by Hanson, ²⁸ we can define a low-efficiency criterion for the sound radiated at θ = 90° from the blade tip, that is z₀ = 1, which states

| mBM T | < | m - 2 k | B

This low-efficiency criterion underlines the corollary stating that the efficiency is high if m = 2 k. This corresponds to the Bessel function of order zero. Generally, the zero-order Bessel functions dominate the other orders whatever the directivity θ and radius z₀ are therefore one can expect that even harmonics dominate the CROR noise emission. In addition, J₀(x) is maximum for x = 0, for example θ = 0 or θ = π. In other words, acoustic output tends to be greatest along the axis of the CROR.

Computed noise directivity of the isolated CROR with pylon

We now move on to the FW-H acoustic calculation based on the blade pressure fluctuations extracted from the CFD of the isolated CROR with pylon. Figure 7 shows the computed directivity of the CROR noise. In the pylon plane, the 2*BPF and 4*BPF dominate with maxima located along the CROR axis. Correlating the previous analysis based on Hanson’s model, one can identify the first and second even sound harmonics corresponding to the interaction tones BPF1 + BPF2 and 2*BPF1 + 2*BPF2, respectively. In the following, we keep the frequency denomination n*BPF for the interaction tones. Along the mid-propeller plane, the 2*BPF dominates at almost all angles. The high levels of the BPF in both planes are related to the impact of the pylon wake on the front propeller. Globally, the noise directivity of the CROR is more complex and only two specific trends are noticeable for this case where B₁ = B₂: (i) noise is maximum towards the flow axis and (ii) the 2*BPF tone dominates. OPEN IN VIEWER

Comparison with WENEMOR windtunnel measurements

Several microphones arrays were used during the WENEMOR test campaign (see Bennett et al. ¹⁴ for more details). Two of them, depicted in Figure 8, have been selected for the comparison with the computations. Closer to the CROR is the moveable near-field array located at 1.5 D off the model centre. The near-field array consisted of five microphones in a near-vertical alignment that were moved through seven measurement planes from upstream to downstream of the blade planes. The seven measurement planes of the five microphone array are indicated in Figure 8 by squares. The central microphone of this five microphone array has been selected so that the near-field comparison is achieved with the measurements, acquired one after the other, along a linear side line corresponding to seven microphone positions. The second microphone array is linear, located in the far-field and equipped with 13 microphones covering angles from 30° to 145° with respect to the flow axis (spheres on Figure 8). OPEN IN VIEWER

Figure 9 compares the FW-H computation using CFD blade pressure fluctuations with the measurements in the near-field of the CROR. The predicted Sound Pressure Levels (SPLs) of the odd sound harmonics are the closest to the measured SPLs. The computed 4*BPF underestimates the measurement but shows a qualitative agreement with it. As for the 2*BPF, the measurement shows a sudden decrease in the front propeller plane which is not found in the computations. There is no trace of this decrease in far-field so that it is assumed to be specific to the near-field. From the author’s point of view, this is related to a destructive interference and the close position of the floor in the wind tunnel might be a key element in this interference. Figure 10 compares the numerical results with the measurements in far-field. Computations and measurements show a qualitative agreement for the four tones with similar relative SPL variation according to the microphone positions. A significant delta at all frequencies is found all along the array. The computations unevenly underestimate the noise levels and the order of the underestimation is up to 10 dB on many microphones. This underestimation is attributed to the free-field conditions of the computations compared to the closed section of the windtunnel, whose walls have unequal acoustic absorptivity. The sawtooth pattern of the experimental BPF SPLs between 60° and 120° along the linear array, similar to a standing wave pattern, suggests the assumption of interference due to reflections. More generally, it is assumed that multiple reflections occur during the measurements and increase the measured SPL of all harmonics. In the next section, we attempt to quantify the effect of these reflections. OPEN IN VIEWER

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Figure 10.

Far-field noise comparison on the linear array. BPF: blade passing frequency; SPL: sound pressure level.

Wind-tunnel installation effect

The calculation of the installation effect of the wind-tunnel facility on the acoustic measurements is achieved according to the methodology previously presented. Instead of considering an aircraft architecture, we consider the wind-tunnel geometry for the BEM calculation. The Burton–Miller formulation of BEM problem is used and includes boundary conditions of Robin type so that complex impedances at the wall can be provided. This formulation requires a closed volume for the diffraction object so that the section of the wind-tunnel is artificially closed outside, as illustrated in Figure 11. One can see by transparency the interior section of the wind-tunnel. The half-circular inlet and outlet have been extended to isolate the acoustic interaction inside the section from the exterior domain. Several lengths were tested before convergence of the results was achieved (not presented here). The characteristics of the two meshes used for the BEM calculation at BPF and 2*BPF, respectively are summarized in Table 3. From the BPF mesh to the 2*BPF mesh the ratio between the wavelength λ and the cell size d has been reduced in order to save memory resources. The drawback is a longer convergence time in the latter calculation. OPEN IN VIEWER

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Table 3.

Mesh characteristics of the BEM calculations according to the selected frequency.

Tone	Mesh nodes count	λ/d
BPF	235,000	9
2*BPF	417,000	6

BPF: blade passing frequency; BEM: boundary element method.

Ground map definition

The approach for the assessment of the noise shielding effectiveness is inspired by the flight test certification procedure for noise certification levels. ³⁰ The noisiest phase of flight for CROR is the take-off operation which is the one addressed by the present work. For this phase of flight, the procedure for the noise level certification focuses on the lateral points during the engine full power phase and the flyover centre line points during the engine power cutback. Although the present work deals with only one flight condition, the purpose of the created ground map is to be globally representative of the key areas measured during certification even if this static calculation does not take into account the Doppler Effect occurring during a flight test. Figure 15 describes the ground map used in the computations. This ground map is separated between the flyover centre area and the two sideline bands, centred on the lateral points around ± 10% of the classic 56° sideline angle. The map is a structured grid of squares whose size is defined so that the directivity shift between two ground microphones is less than 1.5°. The angle aperture at the aircraft centre between upstream and downstream is 143° so that a long enough virtual flyover is considered. As a result, the map is made of 90,751 microphones. OPEN IN VIEWER

Hereafter, the analysis of the ground map relies on (i) the maximum of the flyover band and sideline band, respectively, and (ii) the sound power level (PWL). This latter is based on the integration of the acoustic intensity on the map surface and it is defined as

PWL ( dB ) = 10 log ( W ac W ref ) with W ac = ∫ map I ac d S , W ref = 10 - 13 W

This sound power level is not the one generally defined for an acoustic source which requires a close surface but it is an integrated value representative of the acoustic radiation through the whole ground map. It has the advantage of providing a global level indicating the shielding benefit towards the ground or not. The consideration of the SPLs maxima is another way to assess the drawback of some configurations.

Contribution of two uninstalled CRORs

The tonal noise contribution of the aircraft model comes from its two CROR models. Since the current CROR noise directivity does not show any symmetry and depends on the pylon orientation (see Figure 7), the right and left open rotors have different contributions towards the ground. In the following, it is assumed that there is no coherence between their respective emitted acoustic pressure signal otherwise it would imply a perfect synchronisation of the open rotors between themselves and an exactly identical rotation speed for each open rotors, that is to say two unrealistic assumptions. As a first step, we will focus on the summed noise contribution from the two open rotors located and oriented according to their integration, that is pylon orientation, but without the scattering effect of the aircraft skin.

Figure 16(a) shows the ground map for the selected CROR tones for the PS-A open rotor locations (see Figure 1). The highest noise levels are concentrated under the sources and the even sound harmonics shows high levels around the flyover centre line in agreement with the directivity presented in Figure 7(b) dominated by the CROR axis direction. OPEN IN VIEWER

The slight extension of the open rotor along the pylon (PS-C configuration) does not induce any discrepancies in the ground map when the two open rotors are not installed (not showed), but the additional rotation of the pylon by 27° (PS-E configuration) induces slight modifications in the noise levels (Figure 16(b)). Table 4 gives the discrepancies between the PS-A and PS-E configurations in terms of SPL maxima and sound power levels. The shift of the open rotors from PS-A to PS-E locations globally induces a reduction of the maxima both in flyover and sideline and a small increase of the sound power levels.

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Table 4.

Comparison of SPL maxima and sound power level discrepancies on the ground map between PS-A and PS-E open rotors locations.

	Δ(PS-E - PS-A) in dB
	Flyover maxima	Sideline maxima	PWL
BPF	−1.5	−1.6	0.27
2*BPF	−0.1	−0.3	0.20
3*BPF	−0.3	−0.6	−0.06
4*BPF	−0.9	0.5	0.01

The details of the contributions from left and right open rotors are not shown here but it is noteworthy that the highest discrepancy between the contribution of each open rotor comes from the flyover centre band at 3*BPF where the right open rotor, in comparison with the left one, induces a maximum of 4.9 dB higher for the PS-A configuration and 6.7 dB higher for the PS-E configuration. This result suggests that either one open rotor or the other may be the major cause of the unpleasantness of an harmonic sound.

Acoustic shielding

The calculation of the open rotors installation effect with BEM applied to an aircraft geometry – characterized by its empennage shape – is run separately for each rotor – left and right – then the respective results are incoherently summed for the same reasons previously raised. The final results of all selected configurations lead to a significant amount of data to be analysed. Two parameters are carefully observed: (i) the modification of the open rotor location while keeping the T-tail empennage and (ii) the modification of the empennage geometry while keeping the PS-E open rotor location. The name of the configurations is referred to as OpenRotorLocation_EmpennageGeometry, that is PS-A_T-Tail for instance. In addition to the tail shapes presented in Figure 2, a configuration without empennage, that is without any vertical and horizontal control surfaces, namely PS-E_W-Tail, is computed. This test point examines the scattering from the fuselage only.

Table 5 offers a global estimate of the noise shielding effectiveness for all configurations. It shows the sound power level discrepancy between the selected configuration and the corresponding one for the pylon-installed isolated case, that is CRORs uninstalled as in Figure 16. For each tone, the maximum and minimum PWL discrepancy is underlined by bold and italic characters, respectively. This display highlights the benefit of the PS-E location with a low tail empennage (PS-E_L-Tail) in terms of noise shielding. In contrast, the worse configuration is the PS-A location with a T-tail empennage.

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Table 5.

Discrepancy in terms of sound power levels between the selected configurations and their uninstalled open rotor configurations.

in dB	PS-A_T-Tail	PS-C_T-Tail	PS-E_T-Tail	PS-E_L-Tail	PS-E_U-Tail	PS-E_W-Tail
BPF	1.4	0.6	0.4	−0.9	−0.7	0.2
2*BPF	0.3	−0.1	−1.0	−2.0	−1.4	−0.3
3*BPF	0.1	0.2	−0.5	−3.4	−3.2	−0.5
4*BPF	0.1	0.0	−0.1	−0.7	−0.7	−0.5

More generally, in terms of open rotor location, focusing on the T-tail configurations, the benefit of the PS-E location is confirmed and the effect of the PS-C location is not relevant. The most interesting result is surely the comparison of the empennage geometries with the same PS-E location. For that purpose, the PS-E_W-Tail configuration is a relevant reference since it gives the shielding effect of the whole aircraft geometry without the empennage. It is noticeable that this configuration has a shielding benefit of 0.3–0.5 dB (PWL) except for BPF (+0.2 dB on PWL). The absolute value of 0.5 dB can therefore be set as the threshold for a significant shielding effect of the empennage. The L-tail and U-tail are the only configurations with a globally significant shielding benefit even if it is particularly weak for the 4*BPF. This weak shielding is thought to be related to the significant contribution of the 4*BPF to the whole flyover centre line whereas one can guess that L-tail and U-tail imply shielding concentrated towards the area under the aircraft. This is confirmed by Figure 17 which compares the worse and best configurations in terms of acoustic shielding. It is quite obvious that the benefit at all frequencies is located at the centre of the plane, that is under the aircraft. OPEN IN VIEWER

Table 6 is a record of the flyover and sideline maxima of each tone for all configurations. It is expressed in terms of discrepancy with the respective flyover and sideline maxima found when the two open rotors are not installed, as in Table 5. This display underlines two global trends: the PS-E_L-Tail configuration induces the most mitigating maximum SPLs whereas the PS-A_T-Tail configuration concentrates the highest maximum SPLs. These two trends are in full agreement with the previous observation of the sound power levels and the focus on the maxima of Table 6 brings the same conclusions in ranking the open rotor location and empennage geometries. But it gives more practical information. For instance, the highest shielding effect of 6.5 dB occurs in the flyover band for the 3*BPF maximum with the PS-E_L-Tail configuration. But this latter configuration has a weak shielding effect of 0.4 dB in the sideline band for the same tone maximum. In contrast, at the same frequency, the PS-E_U-Tail configuration gives a more balanced shielding between flyover and sideline (−3.8 dB; −4.5 dB). A general observation is also confirmed, namely that none of the configurations succeed in effectively mitigating the sound radiation of all the harmonics. This is the result of the complexity of the sound directivity of the current CRORs which would require objects with extended shielding. This is one of the difficulties related to CRORs whose interaction tones have complex directivity and whose pylon – particularly in the case of the pusher configuration – makes the noise directivity wider. In the current study, the equal blade number and rotation speed of the propellers concentrate the noise along the CROR axis and away from the cabin and the ground. Suitable shielding for such configurations present new possibilities. This study is a first step to push forward with this challenge by (i) assessing a numerical approach for the calculation of installation effects related to CRORs and (ii) showing that specific empennage geometries enable some acoustic benefit on the ground.

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Table 6.

Maximum sound pressure level on the ground map for each configuration and relative discrepancy with uninstalled/isolated open rotors.

	PS-A_T-Tail		PS-C_T-Tail		PS-E_T-Tail		PS-E_L-Tail		PS-E_U-Tail		PS-E_W-Tail
in dB	Fly.	Sid.	Fly.	Sid.	Fly.	Sid.	Fly.	Sid.	Fly.	Sid.	Fly.	Sid.
BPF	1.8	−1.0	1.0	−0.8	1.8	0.0	−0.4	−0.3	−1.9	−0.7	−0.6	0.3
2*BPF	3.8	−0.1	3.7	−3.2	0.4	−1.5	−2.4	−5.4	−1.4	−4.5	0.8	−0.3
3*BPF	0.8	−0.6	0.5	0.5	−0.1	−0.3	−6.5	−0.4	−3.8	−4.5	0.2	−1.5
4*BPF	4.1	3.5	3.7	1.7	4.1	2.1	−0.6	−1.1	0.7	−0.2	0.9	0.4