An accelerated BEM for simulation of noise control in the aircraft cabin

Aerospace Science and Technology 23 (2012) 418–428

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An accelerated BEM for simulation of noise control in the aircraft cabin V. Mallardo a,∗,1 , M.H. Aliabadi a , A. Brancati a , V. Marant b a b

Department of Aeronautics, Imperial College London, South Kensington, SW7 2BY, UK ACUSTTEL Acustica y Telecomunicaciones SL, Pol. Ind. Benieto – C/Transport n12, Gandia (Valencia), Spain

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 4 October 2010 Received in revised form 9 September 2011 Accepted 2 October 2011 Available online 8 October 2011 Keywords: Boundary Element Method Noise control Aircraft

In this paper passive noise control in the aircraft cabin by using nanofibre textiles is investigated. The acoustic performance of the aircraft cabin under different noise sources and with various seat textiles is tested experimentally and analysed numerically. The numerical results are obtained by means of the three-dimensional Boundary Element Method (BEM) accelerated by the Adaptive Cross Approximation (ACA) and the Generalised Minimum Residual (GMRES) solver. Some numerical analysis are carried out in order to assess the accuracy of the numerical model in comparison with experimental results. A new nanofibre textile with excellent acoustic properties in the low frequency range is modelled and its performance assessed. Finally, a new shape of the seats’ headrest, aimed at reducing further the noise disturbance, is proposed and analysed. © 2011 Elsevier Masson SAS. All rights reserved.

1. Introduction The interior noise of aircraft cabin is an important concern due to its influence on passenger comfort and many researchers have investigated the best way to soften it (see for instance [5, 9,14,16,17]). In order to reduce the noise, the designer must pay close attention to the response of the cabin from various acoustic sources. The complex shape of the cabin does not allow for an analytic solution. The mathematical resolution becomes more difficult when the designer applies acoustically absorptive materials not equally distributed on the cabin surface. There are many techniques available for modelling interior sound fields, including modal expansions, method of images, finite element (FEM) and boundary element (BEM) methods. The modal expansion method [8,13] is based on the analysis of the acoustic motion in terms of the normal modes of the enclosure. A good approximation in the interior can be obtained by using the acoustic modes for the rigid wall enclosure. Such a solution is not correct in the region near the boundaries. The FEM and the BEM [1,18] are both based on the discretisation of the Helmholtz wave equation for simpleharmonic waves. Regarding internal problems, the main difference is in the dimension adopted: FEM requires the discretisation of the entire volume under analysis whereas BEM meshes the boundary only. For external (i.e. infinite) problems BEM is capable to automatically satisfy the Sommerfield radiation condition without any

*

Corresponding author. E-mail addresses: [email protected] (V. Mallardo), [email protected] (M.H. Aliabadi), [email protected] (A. Brancati), [email protected] (V. Marant). 1 On leave from the Department of Architecture, University of Ferrara, Italy. 1270-9638/$ – see front matter doi:10.1016/j.ast.2011.10.001

© 2011 Elsevier Masson

SAS. All rights reserved.

domain discretisation. An application of BEM to nonlinear acoustics is given in [12]. Many papers have dealt with the computation of the approximate solution of the Helmholtz equation by FEM and BEM. On this regard the BEM seems to be more efficient particularly in 3D and when coupled with fast procedures such as Fast Multipole Method (FMM) [15] and Hierarchical Matrix format plus Adaptive Cross Approximation (ACA) approach [2]. In [7] an edge-based smoothed FEM approach for analysing acoustic problems is proposed in order to overcome the inaccuracy in the FEM solution with increasing wave number, i.e. the numerical dispersion errors. In [6] a cost comparison between BEM and FEM in acoustics is performed, but the comparison does not keep into account the recent improvements of BEM in conjunction with fast procedures such as FMM and ACA. There is a large number of papers concerning the application of BEM to 3D and 2D acoustic fields. Many references can be found in [18]. A BE/FE method to reduce the interior noise in the aircraft cabin is developed in [4] where the structure is dealt with FEM and coupled to the acoustic cavity modelled by BEM. This paper presents some results obtained in the project “Smart tEchnologies for stress free Air Travel (SEAT)” under the 6th Framework Programme. The main goal of the paper is to numerically investigate the acoustic performance of a new textile material which was developed in the project. Such a textile is a nanofibre web with excellent absorptive properties in the frequency range 200–1000 Hz and it can be used as upholstery to reduce the noise in the aircraft cabin. All the numerical results are obtained by direct BEM and they are given in terms of pressure/velocity on the boundary. As the corresponding governing matrix is nonsymmetric and fully populated, the numerical solution would be

V. Mallardo et al. / Aerospace Science and Technology 23 (2012) 418–428

419

Fig. 1. Experimental mockup. Internal views.

extremely time consuming. In the present paper the generation of the governing matrix and of the right-hand side vector is sped up by the ACA approach whereas the resolution of the system of equations is accelerated by the GMRES. The value at any internal point can be determined in the post-processing step on the basis of the knowledge of the solution on the boundary. The adopted elements are linear of quadrilateral/triangular type and the mesh is set in order to have 8–10 elements per wavelength. The numerical experiments are aimed at investigating the reduction of noise level inside the aircraft cabin which may be obtained by adopting new nanofibre textiles and different headrest geometries. The geometry under investigation coincide with an actual aircraft cabin. The absorbing properties of the panels of the cabin are determined on the basis of both the scientific literature [3] and some experimental results obtained by Acusttel (one of the partners of the project). The included numerical results have two goals: 1) to recover the experimental tests, 2) to probe the influence of new nanofibre textiles and headrest geometries on the noise control.

Fig. 2. Experimental signal spectrum – takeoff.

2. The experimental test The numerical model was first tested by some experimental results obtained at the laboratory of Thales (Toulose, France). An aircraft cabin mockup (1/1 real scale – see Fig. 1) was set up and subjected to different acoustic sources reproducing the internal noise produced by typical flight operations. Some microphones were also located in order to measure the sound pressure level (SPL) in proximity of the passengers’ ears. The experimental source was obtained by a dodecahedral speaker located in the middle of the corridor, 0.37 m from the rear plane and 1.42 m from the floor. Such a type of speaker was necessary in order to create a diffuse acoustic field inside the cabin. The speaker was modelled as a monopole in the numerical model. The acquisition system, including microphones, analyser and wires, is of class I, i.e. the most precise possible. The sample frequency was 51 200 Hz and the acquisition was real-time and simultaneous in several microphone positions. Finally, the microphone calibration was checked before and after the tests. Four microphones (two of them are visible in Fig. 1(a)) were positioned in order to measure the SPL. The experiments were performed with different acoustic signals, i.e. with three signals reproducing the noise which occur internally during the takeoff, the landing and the cruise conditions. In other words, first the noise arising inside the aircraft cabin during three different typical flight operations was recorded, then, it was suitably reproduced by using an internal speaker located in the corridor of the cabin. The spectrum signal referred to the takeoff is given in Fig. 2. In most applications the signal frequency content (or the frequency

Fig. 3. Experimental results at the microphones – takeoff noise.

spectrum) is investigated. There are two primary reasons for obtaining frequency information about a signal. First, the response of the ear and the sensation of sound in humans is strongly dependent on the frequency. Second, the physical processes of sound emission, propagation, diffraction and transmission are all frequency dependent. The experimental results detected at the microphones are depicted in Figs. 3–5 where the position of the four microphones (A, B, C and D) is given in Table 1 (in millimetres and with ref-

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Fig. 6. Position of the microphones. Fig. 4. Experimental results at the microphones – landing noise.

Table 1 Coords of the microphones in the numerical model. Microphone

X

Y

Z

A B C D

818 818 1618 1618

1723 311 1723 326

1045 1045 1045 1045

It must be pointed out that both the spectrum signals and the experimental results at the microphones were filtered by a frequency A-weighting. 3. The numerical model

Fig. 5. Experimental results at the microphones – cruise noise.

erence to the origin located as depicted in Fig. 6). The numerical response was tested for the takeoff signal. For clarity’s sake the value measured experimentally at the microphones with reference to the takeoff signal are listed in Table 2.

The numerical response of the aircraft cabin model under the above source can be obtained by a multifrequency ACA-GMRES accelerated BEM analysis. The procedure provides the numerical response in terms of pressure/velocity at the central frequency of each octave band. The amplitude of the numerical monopole (unique value common to all the frequencies under investigation) was set on the basis of the experimental SPL. The experimental results were used to validate the numerical model. The propagation of time-harmonic acoustic waves in a homogeneous isotropic acoustic medium (either finite or infinite) is described by the Helmholtz equation:

∇ 2 p (x) + k2 p (x) = 0

(1)

under the typical boundary conditions:

Table 2 Experimental SPL (in dB) measured at the microphones (takeoff signal). f [Hz] A f [Hz] A

31.5 57.6 200 77.3

40 69.5 250 85.6

50 75.1 315 78.9

63 76.3 400 66

80 87.5 500 66.1

100 90.2 630 61.8

125 83.5 800 65.5

160 88.4 1000 55.3

f [Hz] B f [Hz] B

31.5 56 200 76.8

40 67 250 80.7

50 71.4 315 73.6

63 68.9 400 70.0

80 86.1 500 74.1

100 92.5 630 64.9

125 87.8 800 69.0

160 90.2 1000 62.0

f [Hz] C f [Hz] C

31.5 58.6 200 86.9

40 72.5 250 88.4

50 76.2 315 79.6

63 71.4 400 75.9

80 89.1 500 73.3

100 92.7 630 61.6

125 83.8 800 58.6

160 85.4 1000 55.4

f [Hz] D f [Hz] D

31.5 61.6 200 89.1

40 68.1 250 86.9

50 71.1 315 81.1

63 77.1 400 76.9

80 91.4 500 76.1

100 96.4 630 69.7

125 91.1 800 71.3

160 91.9 1000 62.8

V. Mallardo et al. / Aerospace Science and Technology 23 (2012) 418–428

q∗ (ξ , x) = −

1 4π



1 r2

+

ik r

421



e −ikr r,n

(4b)

where r = x − ξ  is the distance between the collocation point ξ and the field point x. The conventional BEM numerical procedure is based on two steps: first, the discretisation of the boundary Γ , second, the collocation of Eq. (3) at each node provides a final system of equations in the unknown p and q on the boundary, i.e.:

Hp = Gq

(5)

After the application of the boundary conditions, such a system can be re-written as:

Ay = b

where y collects the unknowns on the boundary. After solving the system of equations the pressure at any internal point X can be computed as post-processing step by applying the following relation:

Fig. 7. Geometric model.

p (x) = p (x)

x ∈ Γ1

q(x) = p (x),n = q(x)



(2a) x ∈ Γ2

(2b)

α p (x) + β q(x) = γ x ∈ Γ3

(2c)

where p is the acoustic pressure, k = ω/c with ω = angular frequency and c = sound velocity, α , β and γ are constants (α and β different from zero), comma indicates partial derivative, Γ1 ∪ Γ2 ∪ Γ3 = Γ , Γ is the boundary of the domain Ω under analysis, n = n(x) is the outward normal to the boundary in x, q is the flux and the barred quantities indicate given values. The initial geometric model consisted of two lines of three seats (with passengers) surrounded by the aircraft fuselage (see Fig. 7). Such a geometry was simplified in order to reduce the computational effort, i.e. the passengers were not included (the experimental results were available without passengers). The surfaces were meshed with linear quadrilateral and triangular elements. The investigation was carried out in the frequency range 31.5–1000 Hz as the authors’ goal was to investigate the behaviour of the textile in such a frequency range. Furthermore, two panels, one at the front (which was not included in the figures showing the results for the sake of clarity) and the other one at the rear of the cabin, were added to the model in order to obtain an “internal closed surface” to be correctly described by a numerical approach. The acoustic source was located in the middle of the corridor (the exact position was given in the previous section), therefore it was possible to take into account the symmetry with respect to the vertical plane.

The boundary value problem described by Eq. (1) under the boundary conditions given in Eqs. (2) can be transformed into the following integral representation (see [1,18] for details):



q∗ (ξ , x) p (x) dΓ (x) −

Γ



p ∗ (ξ , x)q(x) dΓ (x) = 0

Γ

(3) where c (ξ ) occurs in the limiting process from the internal point to the boundary point, being equal to 0.5 for boundary points where the boundary is smooth. The fundamental solutions p ∗ and q∗ are given by:

p ∗ (ξ , x) =

1 4π r

e −ikr

p (X) =

p ∗ (X, x)q(x) dΓ (x) −

Γ



q∗ (X, x) p (x) dΓ (x)

(7)

Γ

The numerical simulations were performed by using the LMS Virtual Lab software [11] coupled with in-house routines: the former was adopted to import the geometric model and to build the boundary mesh whereas the construction of the A matrix and its resolution was performed by in-house routines developing the ACA and GMRES techniques. In order to speed up the solution time of the simulations, the ACA approach along with the Hierarchical matrix (H-matrix) format and the GMRES technique is here utilised. It is well known that the BEM generates fully populated and non-symmetric matrices, H and G in Eq. (5), which heavily increase the CPU time required by the matrix and right-hand side assembly and by the resolution of the discrete system of equations. In the recent past a number of techniques have been explored in order to overcome such drawbacks. The ACA is a pure algebraic technique widely investigated in the recent past and recently applied to the Helmholtz equation by [2]. Such a technique decreases enormously the solution time as it permits to calculate only a small part of the original matrix on the basis of its division into two groups of blocks, full rank and low rank blocks. The former blocks are entirely determined in the classical way whereas the latter blocks are substituted by a few entries which result to be capable to represent the original ones, i.e.: ¯

Ca  Ck =

k 

al · blT

(8)

l =1

3.1. The governing integral equations and the BEM

c (ξ ) p (ξ ) +

(6)

(4a)

The solution is adaptively approximated maintaining a required level of accuracy. Matrices C a and C k denote the admissible and the approximated block, respectively, ai and b i the columns and the rows of the approximated block, respectively. It should be noted that the value k¯ is, in general, much smaller than the rank of the original block. The admissibility condition leading the existence of a low rank block is based on the consideration that the integrals of contiguous elements due to a single collocation point have almost the same values; the same consideration is valid for the integrals of a single element due to a number of contiguous source points. The admissibility condition can be written as follows:

min(diam Ωx0 , diam Ωx )  η · dist(Ωx0 , Ωx )

(9)

where Ωx0 denotes the cluster of elements containing the discretisation nodes corresponding to the row indices of the considered

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Fig. 10. New headrest shape with lateral caps.

Fig. 8. Block-wise representation of the ACA generated matrix.

block and Ωx the set of elements over which the integration is carried out to compute the coefficient corresponding to the column indices. The parameter η > 0 influences the number of admissible blocks and the convergence speed of the adaptive approximation of low rank blocks. Hence, the matrix assembly time as well as the storage requirements are both strongly reduced. Moreover, the matrix–vector multiplication is accelerated by the block-wise representation of the low rank block. An example of such a representation for the whole matrix is shown in Fig. 8 where the dark grey and the light grey represent the full rank and the low rank blocks, respectively. In particular, the more the light grey the lower the rank of the blocks.

whereas the latter in the range 125–1000 Hz. Both meshes were sufficient to guarantee 6–8 elements per wavelength. Two further triangular meshes (with about 20 200 and 32 280 nodes, respectively) were also used to verify the accuracy of the results obtained by using the mesh of 13 806 nodes with regard to the frequency of 1000 Hz. The numerical analyses were also aimed at measuring the influence of the lateral caps on the noise level in the cabin. A new shape of the seat’s headrest was designed in order to reduce the noise disturbance perceived by the passenger: two absorbing panels were inserted laterally to the passenger’s head as depicted in Fig. 10. Two new meshes (one for the frequencies up to 100 Hz, the other one for the range 125–1000 Hz) were therefore considered (see Fig. 11) in order to include the lateral caps. Such meshes were formed by around 12 000 and 20 000 nodes, respectively. The external panels and the seats were all modelled as absorbing surfaces with different impedance values, i.e. the model was subdivided into the following panels: left, front and rear panels, floor, ceiling, seats with their armrests and supports. Each panel constituting the model, except the seats supports considered perfectly rigid, were supposed to be absorbing surfaces, i.e. by setting a boundary condition of the type:

q(x) = 3.2. Discretisation and boundary conditions In order to obtain the numerical results, the model needs to be meshed and the boundary conditions are to be set properly. Two initial meshes were adopted: the coarse mesh (see Fig. 9(a)) and the fine mesh (see Fig. 9(b)) formed by 9876 nodes and 13 806 nodes, respectively. The former was used up to 100 Hz

−i ρω p (x) Z

(10)

where ρ is the density and Z is the impedance value (in general a complex number). It must be pointed out that the impedance value Z is to be given on each surface involved in the numerical model. The present analysis is mainly aimed at investigating the behaviour of a new textile. Such a textile, made of nanofibres (from now on

Fig. 9. Coarse mesh (a), fine mesh (b).

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423

Fig. 11. Model with lateral caps located at the headrests: coarse mesh (a), fine mesh (b). Table 3 Values of the absorption coefficient in the range 8–50 Hz. f [Hz]

α

FLOOR REAR FRONT CEILING ARMRESTS SEATS

8

10

12.5

16

20

25

31.5

40

50

0.002 0.002 0 .1 0.001 0.001 0.05

0.003 0.004 0 .1 0.003 0.001 0.05

0.005 0.007 0 .1 0.005 0.002 0.05

0.01 0.01 0 .1 0.005 0.002 0.05

0.015 0.014 0 .1 0.01 0.003 0.05

0.02 0.018 0 .1 0.01 0.004 0.065

0.025 0.02 0 .1 0.01 0.005 0.075

0.03 0.03 0 .1 0.02 0.005 0.075

0.05 0.04 0.15 0.03 0.005 0 .1

Table 4 Values of the absorption coefficient in the range 63–400 Hz. f [Hz]

α

FLOOR REAR FRONT CEILING ARMRESTS SEATS

63

80

100

125

160

200

250

315

400

0.09 0.05 0. 2 0.05 0.006 0.14

0.12 0 .1 0 .3 0.07 0.008 0.175

0.15 0.15 0 .6 0 .1 0.01 0.210

0.25 0 .2 0 .9 0.15 0.02 0.49

0.275 0.23 0.95 0.175 0.021 0.509

0 .3 0.26 0.95 0 .2 0.023 0.533

0.325 0 .3 0.95 0.225 0.025 0.565

0.35 0.34 0.95 0.25 0.029 0.614

0.375 0.37 0.95 0.275 0.036 0.689

indicated as “nanofibre textile”), was designed by Aitex (Instituto Tecnologico Textil, Spain) inside the SEAT project. It is produced by a special apparatus, the Nanospider, protected under the patent [10] and it has demonstrated to be particularly absorptive even in the low frequency range. The absorption properties of the nanofibre textile as well as of the common textile (i.e. the textile usually adopted as upholster on the seats of the aircraft cabin, from now on named “common textile”), were determined experimentally by the reverberation chamber method, i.e. the random incident absorption coefficients were obtained. It must be underlined that the authors’ intention was to furnish results which were valid for a typical aircraft and not only for the mockup under analysis. Therefore it seemed to be more correct to set the boundary conditions of all the panels involved in the numerical model except, as above detailed, the textile adopted for the seats, on the basis of the values available in the technical literature. On the other hand, the main references (see for instance [3], pp. 944–945) provide the absorption coefficient α , and not the impedance value, for many of the materials used in the aircraft cabin. Such a coefficient includes both absorption and transmission, it does not contain information on the variation of the absorption properties with the phase and it can be written in terms of Z by the following relations:

Table 5 Values of the absorption coefficient in the range 500–1000 Hz. f [Hz]

α

FLOOR REAR FRONT CEILING ARMRESTS SEATS

α = 1 + r p 2 Z = Z0

1 + rp 1 − rp

500

630

800

1000

0 .4 0.4 0.95 0 .3 0.05 0. 8

0.45 0.45 0.95 0.325 0.06 0.817

0.5 0.5 0.95 0.35 0.08 0.84

0 .6 0 .6 0.95 0.375 0 .1 0.88

(11a) (11b)

where r p is the (complex) reflection coefficient and Z 0 is the impedance of the air ( Z 0 = ρ c). From the above relations it is clear that two different values of Z correspond to a given value of α , but only the part of the curve which is after the peak is to be considered physically meaningful. The absorbing coefficients adopted in the numerical model for each surface of the cabin as well as for the common textile covering the seats (see row “seats”) are reported in Tables 3–5.

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V. Mallardo et al. / Aerospace Science and Technology 23 (2012) 418–428

Fig. 12. Comparison between experimental (dashed circle) and numerical (line with circle) results at the microphones A and B.

Fig. 13. Comparison between experimental (dashed circle) and numerical (line with circle) results at the microphones C and D.

Fig. 14. Experimental signal (takeoff) – noise reduction at the microphones A and B. Q Nanofibre textile A. × Nanofibre textile B. " Headrests with lateral caps.

4. Numerical results

4.1. Comparison with the experimental results

Two groups of numerical results are presented. The first group is aimed at showing the comparison between experimental and numerical results at the microphones A, B, C and D. The second group of results measure the influence of both the absorption property of the seat textile and the shape of the seat headrest on the noise reduction in the cabin. For such a group two different signals were adopted: the first one is coincident with the takeoff signal of the experimental test, the second one is a typical white noise.

In this section the comparison between experimental and numerical results is presented. Acoustic source, type of signal, geometry and boundary conditions of the numerical model were detailed in the previous sections. The comparison is depicted in Figs. 12, 13. In the range 125–1000 Hz the difference is relatively low (from 0 to 15%) but it increases in the low frequency range 31.5–100 Hz. The higher difference in the low frequency range is related to the fact that the low frequency response is mainly driven by the geometry of the model and not by the boundary condi-

V. Mallardo et al. / Aerospace Science and Technology 23 (2012) 418–428

425

Fig. 15. Experimental signal (takeoff) – noise reduction at the microphones C and D. Q Nanofibre textile A. × Nanofibre textile B. " Headrests with lateral caps.

Fig. 16. Experimental signal – overall SPL in the range 500–1000 Hz. (a) Common textile, (b) nanofibre textile A, (c) nanofibre textile B, (d) headrests with lateral caps, (e) legend.

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V. Mallardo et al. / Aerospace Science and Technology 23 (2012) 418–428

Table 6 SPL in dB at the passengers’ ears in the range 125–1000 Hz.

A1 A2 B1 B2 C1 C2 D1 D2 E1 E2 F1 F2

C.T.

A

B

Caps

63.1 60.6 60.5 62.3 65.5 67.4 67.5 65.2 66.4 68.1 71.3 73.8

62.8 60.4 60.1 62.0 65.3 67.2 67.3 65.1 66.3 68.0 71.2 73.8

62.6 60.1 59.6 61.7 65.1 67.1 67.1 65.0 66.1 67.9 71.1 73.7

62.1 59.7 59.1 61.4 64.5 66.7 66.8 64.7 65.9 66.1 70.9 73.5

Table 7 SPL in dB at the passengers’ ears in the range 500–1000 Hz. Fig. 17. Sensors located close to the passengers’ ears.

tions. In fact, only a slight difference in the numerical results was observed when fictitiously changing the impedance at the low frequency range. 4.2. Passive noise control A sensitivity analysis of the noise reduction in the cabin due to the seat’s cover and to the headrest’s shape was performed. The noise reduction related to a change in the seat textile was investigated. The analysis drew on the excellent absorption properties, even in the low frequency range, of the nanofibre textile developed in SEAT. Furthermore, the influence of the new designed shape of the seat’s headrest on the cabin noise level was probed. All the simulations were performed with reference to the same position of the acoustic source used in the experimental test. The experimental tests carried out on the nanofibre textiles showed that the absorption coefficient’s improvement with respect to the common textile (whose acoustic properties are listed in Tables 3–5 at the row “seats”), in the frequency range under analysis, goes from 10% to 20%. Therefore, two nanofibres textiles, in the remaining figures indicated as nanofibre textile A and nanofibre textile B, were tested, the former 10% more absorptive than the common textile, the latter 20% more absorptive than the common textile. The comparison was carried out by numerically measuring the noise reduction (in dB) obtained by the two nanofibre textiles with respect to the common textile. Such a comparison is depicted in Figs. 14, 15 with regard to the takeoff noise. It is clear how the seat textile can influence the noise level in the cabin. The presence of the caps located laterally to the headrests is able to guarantee the best noise control. As it could be expected, the passive noise control is more effective for higher frequencies where it is possible to obtain up to 8 dB of reduction. The comparison can be also performed with regard to the overall response. The total SPL, i.e. the sound pressure level calculated as sum of squared pressure modulus at different frequencies, is depicted in Fig. 16 with reference to the 500–1000 Hz interval. The noise reduction due to the different textiles and in the range 8–1000 Hz is not shown as it is negligible. The performance improves if the comparison is performed in a range which excludes the lowest frequencies, as is evident, for instance, in Fig. 16. The noise reduction corresponding to the experimental signal in the range 8–1000 Hz can be better visualised by investigating some points close to the passengers’ ears. If A 1 , A 2 , B 1 , B 2 , C 1 , C 2 and D 1 , D 2 , E 1 , E 2 , F 1 , F 2 are located as depicted in Fig. 17, Tables 6, 7 provide the total SPL at those points for the different configurations, i.e. for the common textile (column C.T.), the

A1 A2 B1 B2 C1 C2 D1 D2 E1 E2 F1 F2

C.T.

A

B

Caps

44.9 50.5 50.6 52.0 57.2 57.8 46.7 54.6 51.2 53.2 53.2 57.5

44.3 49.8 49.6 51.3 56.7 57.6 46.7 54.3 50.9 52.9 53.0 57.5

43.1 48.6 48.0 50.2 55.9 57.3 46.9 53.9 50.7 52.4 52.5 57.5

43.0 47.9 46.3 50.2 54.3 56.8 46.9 52.9 50.7 51.9 52.1 55.6

nanofibre textile A, the nanofibre textile B and the headrest with caps (last column). The noise reduction goes up to 1.5 dB (around 3% of the initial SPL) in the range 125–1000 Hz, up to 2.5 dB (around 5% of the initial SPL) in the range 500–1000 Hz. The noise reduction at the points located close to the loudspeaker (F 1 and F 2 ) is negligible when compared to the other points as F 1 and F 2 are directly illuminated by the acoustic source. The acoustic performance of the aircraft cabin was also tested for a typical white noise, with polar acoustic amplitude A (where the volume acceleration Q˙ in m3 /s2 is given by Q˙ = 4π A /ρ0 ) of the monopole equal to 0.01 kg/m2 . The comparison on the entire range 8–1000 Hz does not show any improvement in the noise reduction, but focusing the results on higher frequencies points out that adopting improved textiles on the seats or a different shape of the headrests may improve the noise reduction properties of the system. In Fig. 18 the SPL at the level of the passengers’ ears is depicted with regard to the 500–1000 Hz range. 5. Conclusions The analysis of the noise reduction in the aircraft cabin obtained by intervening on seats’ upholster and shape has been carried out. The investigation has drawn on a new suitably designed nanofibre textile with excellent acoustic absorption even in the low frequency range (from 0 to 1000 Hz). Some experimental tests have been carried out on a mockup cabin with different signals reproducing various flight operations. A numerical model has been built and some numerical investigations have been performed by using an accelerated (ACA and GMRES) 3D-BEM. The noise reduction related both to the acoustic absorption performance of the nanofibre textile on the seats and to the shape of the seat’s headrest has been investigated. The numerical results have shown that a reduction of the noise level inside the aircraft cabin is possible, even in the frequency range below 1000 Hz, by adopting suitably designed nanofibre textiles.

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Fig. 18. White noise – overall SPL in the range 500–1000 Hz. (a) Common textile, (b) nanofibre textile A, (c) nanofibre textile B, (d) headrests with lateral caps, (e) legend.

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