American Institute of Aeronautics and Astronautics

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Coupled FEM/BEM Vibroacoustic Modeling of

Turbopropeller Cabin Noise

Javier Rodríguez Ahlquist1

Airbus Military, Spain

Pierre Huguenet2 and José Ignacio Palacios Higueras

3

SENER Ingeniería y Sistemas, Spain

A vibroacoustic numerical model of the cabin of an Airbus Military C295, a medium-

weight turboprop aircraft, was developed with the purpose of operational acoustic level

prediction and acoustic package optimization with focus on the first three propeller acoustic

tones. The model includes a detailed finite element model (FEM) of the fuselage structure

and a representation of the interior and exterior acoustic domains using boundary elements

(BEM). Acoustic loading was modeled by means of point sources with directivity fitted to

experimental data. A summary of the activities is presented together with selected validation

results.

I. Introduction

he Airbus Military CN235 and C295 are both turboprop military transport aircraft conceived for tactical airlift

capable of operating on short and semi-prepared runways. Typical missions include transport of troops and

cargo, medical evacuation, humanitarian missions and maritime patrol. The CN235 and C295 present structural

commonalities, with the latter featuring a stretched fuselage and upgraded powerplant. Propeller rotational speed can

be adjusted in both aircraft according to flight regime.

Cabin noise in military transport aircraft has been traditionally put behind other considerations in terms of

aircraft performance, transport capacity and ability to endure rough operating conditions. This picture has changed,

as more of these aircraft are equipped with surveillance systems for maritime patrol. Where previously only cargo

and troops were carried for an eventual short lift, now system consoles are installed requiring human operators.

Maritime patrol missions typically extend over several hours and cabin noise levels in the vicinity of the propeller

plane can be significant in high-power high-speed cruise conditions. To ensure communication requirements and

compliance with health regulations regarding exposure to noise, cabin personnel is provided with

intercommunication headsets featuring active noise control, offering excellent acoustic performance to weight.

Existing and prospective operators of this type of aircraft nevertheless demand lower cabin noise levels.

This motivated Airbus Military (by then EADS-CASA) to initiate in 2006 a development program with the aim

of reducing cabin noise in C295 and CN235 aircraft. The focus was put on interior noise and how propeller noise

propagates to the cabin, for which extensive experimental and numerical activities were launched. Being a

development on an already existing aircraft, actuation on the powerplant was not considered. The efforts regarding

exterior noise were limited to experimental characterization.

Following the requirements of Airbus Military, a vibroacoustic numerical model of the cabin of a C295 was

developed by SENER, an engineering consultancy firm with established experience in noise and vibration, with the

purpose of operational acoustic level prediction and acoustic package optimization. Modeling activities focused on

the first three propeller Blade Passing Frequency (BPF) tones, up to 400 Hz. The model includes a detailed finite

element model (FEM) of the fuselage structure and a representation of the interior and exterior acoustic domains

using boundary elements (BEM). The referred vibroacoustic model was validated against aircraft measurements

using synthetic structural and acoustic sources (electrodynamic shakers, loudspeakers) with satisfactory results at

1 Aeroelasticity and Structural Dynamics, Ed. T1 1

st floor, Pº John Lennon s/n, 28906 Getafe (Madrid), Spain.

2 Noise and Vibration Technological Area, C/ Provença 392, 5

th floor, 08025 Barcelona, Spain.

3 Noise and Vibration Technological Area, C/ Provença 392, 5

th floor, 08025 Barcelona, Spain.

T

16th AIAA/CEAS Aeroacoustics Conference AIAA 2010-3948

Copyright © 2010 by Airbus Military. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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least up to 150 Hz. Beyond this frequency the structural modal base rapidly increases, which results in prohibitively

long computational lead-times when solving the coupled problem. In any case this frequency limit is high enough to

encompass the fundamental BPFx1 frequency. This limitation, related to computational expense, could be overcome

in the future as vibroacoustic coupling at higher frequencies is less significant and more straightforward decoupled

solutions prove to be sufficiently representative.

In a second testing phase, aircraft operational data was gathered using a flyable high channel count acquisition

system, simultaneously retrieving fuselage

vibration, interior and exterior sound

pressure distributions using state-of-the-art

test technology. Operational data was

collected using multiple transducer

arrangements on ground and a limited set in

flight. The effects of powerplant torque,

propeller speed and flight altitude in cruise

conditions were evaluated. The results of this

test phase served to derive a model for

propeller exterior noise, as well as validation

data in form of vibration amplitude and

phase, and sound pressure at multiple

locations throughout fuselage and cabin.

The acoustic loads induced by the

propellers were introduced in the aircraft

FEM/BEM model by means of a

deterministic point source model fitted to

operational data. This approach yielded

satisfactory results, superior to considering

the exterior sound field as an acoustic

constraint, which requires extrapolation in

the usual case of reduced number of exterior

transducer locations. The results, expressed

in terms of structural response and cabin

sound pressure distribution, were compared

to aircraft measurements, showing

satisfactory agreement in frequency, level

and spatial distribution.

The selected FEM/BEM approach made possible reproducing the structural and acoustic response of cabin and

fuselage, and incorporating a simplified, yet sufficiently representative, model of propeller noise.

II. Propeller Noise

Propeller noise is dominated by tonal components associated to the propeller blade passing frequency and its

harmonics. Propeller noise has been the subject of extensive research, of which a recent overview can be found in

Ref. 1. Different modeling techniques exist for its prediction both in far-field and near-field, in time and in

frequency domain. Theoretical models require consideration of the propeller geometry and kinematics, and use of

aerodynamic codes for the determination of blade loading. More advanced models can consider nonuniform inflow

conditions, nonlinear terms and effect of propeller installation, for which they require considerable computational

power.

Different physical phenomena participate in the generation of propeller noise. The universal mathematical model

used in the propeller industry is based on the Ffowcs-Williams-Hawkings2 (FW-H) acoustic analogy. According to

it, primary sources of propeller noise can be related to (1) blade thickness, (2) blade loading and (3) nonlinear or

quadrupole sources. All three can be further categorized in steady and unsteady, periodic and aperiodic. Steady and

periodic sources produce tonal noise.

Thickness noise is generated by the volume displaced by each propeller blade, and is said to be of a monopole

type, whose strength is strongly dependent of the helical tip speed, but also of the blade geometry: sweep, chord, and

thickness distribution. The directivity of the thickness noise peaks near the plane of the propeller disk.

CN235/300 C295 Maximum Take-off Weight kg 16,500 23,200

Maximum Payload kg 6,000 9,250 Powerplant 2 x GE CT7-9C3 2 x PW127G

Max. Cont. Power SHP 1750 2645 Propeller Speed (Np) rpm 1384 1200

Np variability range in flight % 86-100 80/90/95/100 Propeller blades 4 6

Propeller diameter mm 3678.9 3932 BPF variability range Hz 79.3-92.3 96-120

Figure 1. Airbus Military C295 and CN235/300 main features.

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Loading noise depends on the blade surface pressure, and is said to be of a dipole type. Steady loading is related

to propeller net thrust and torque. Oscillations in blade effective angle of attack result in periodic blade loading,

which in time result in generation of acoustic tones. The directivity of the loading noise peaks out of the propeller

disk.

Finally, quadrupole or nonlinear sources are relevant for propellers operating in transonic and supersonic

regimes, as it is the case of high speed propellers and propfans. For general aviation and conventional turboprop

aircraft quadrupole terms can normally be considered negligible.

Practical near-field predictions for isolated subsonic propellers in axial flow indicate that the fundamental tone

and usually the second harmonic are dominated by the steady loading contribution3. As harmonic number increases,

the thickness contribution becomes increasingly dominant. Propeller noise is affected by aircraft installation.

Aircraft configuration may affect inflow reaching the propeller. At high frequencies and close to normal angle of

incidence, local sound pressure can go up as a result of fuselage presence. Nonnormal incidence results in acoustic

scatter and thereby in lower acoustic levels. Wing and fuselage originate acoustic shielding, which may be

dependent on propeller sense of rotation relative to the airframe.

III. Interior Noise Problem

Propeller noise can be transmitted to the cabin through the air (airborne path) and through the structure

(structure-borne path). Conventional metallic fuselages are essentially rib-stiffened cylindrical structures, with an

outer skin reinforced by means of longitudinal stringers and transversal annular frames, joined together by means of

riveting. The fuselage interior is lined using thermoacoustic insulation, usually glass-fiber based, on top of which

rigid composite panels or flexible quilted liners are installed. Damping materials may be locally applied onto the

skin for reducing radiated noise. In the case of turboprop aircraft, specific devices may be installed for addressing

propeller related tones. These may be passive, such as mass-spring vibration dampers, or active, including active

noise and vibration control.

At the propeller noise fundamental frequency

(BPFx1), typically between 60 and 140 Hz,

fuselage structural response and cabin acoustic

response can show vibroacoustic coupling:

structural dynamic response is affected by the

characteristics of the acoustic pressure distribution

of the receiving acoustic cavity and vice versa.

Fuselage response in this frequency range is

usually driven by frame dynamic behavior.

Providing significant acoustic insulation by means

of interior lining materials is difficult without

incurring into prohibitive added weight and cabin

space reductions.

At the first harmonic of propeller noise

(BPFx2), or double the fundamental frequency,

skin panel dynamic response usually becomes

relevant. Skin response is conditioned by frame

and stringer spacing. Skin stiffening caused by

cabin pressurization may be significant. Cabin

differential pressure normally varies with flight

altitude.

The contribution of higher harmonics typically decreases as the insulation becomes more effective with

increasing frequencies. On-board noise sources, mainly those associated with cabin environmental control

(pressurization, ventilation, air conditioning) and equipment cooling, may become dominant at medium to high

frequencies.

In spite of its shortcomings, cabin noise levels are usually expressed in terms of A-weighted sound pressure level

(SPL). The use of A-weighting aims at integrating noise levels in the audible range, giving preponderance to the

frequency range where the human ear is more sensitive. Low frequency noise, to which the human ear is less

sensitive, is thereby given a relatively lower contribution compared to noise between 1 and 4 kHz, where human

sensitivity peaks. The contribution of lower propeller tones to overall levels are considerably affected by the use of

A-weighting.

Figure 2. View of C295 cabin with microphone array

installed along the propeller plane. A surveillance system

console is installed aft of propeller plane.

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On the CN235, with a BPF between 79 and 92 Hz, cabin A-weighted levels are driven by BPFx2 and higher

frequencies. Participation of BPFx1 is strongly penalized (weighted down) by the use of A-weighting.

The C295, with a higher BPF (between 96 and 120 Hz), combined with higher power and reduced clearance

between propeller and fuselage, cause cabin A-weighted levels to be driven by BPFx1 and BPFx2, at least for high

power flight conditions where interior noise is maximum.

IV. Modeling Approach

Numerical simulation focused on solving the coupled vibroacoustic problem, combining fuselage structural

response and cabin acoustic response. Practical implementation requires the acoustic field and the structural

response to be simultaneously solved in an iterative process. This is done using a finite element model (FEM) for the

structural representation and either FEM or a boundary element model (BEM) for the representation of the acoustic

space(s) 5-7

.

The election of FEM/FEM or FEM/BEM

depends on whether the problem is interior or

exterior and on the size of model, related to

physical dimensions and frequency range. Coupled

FEM/FEM simulation is usually preferred for

interior problems and smaller models. FEM/FEM

requires a full volumetric mesh of the acoustic

spaces, which for large structures and for exterior

problems results in very large models.

For FEM/BEM models, on the other hand, the

process of model creation and modification is

comparatively very efficient. It is not required to

mesh the entire acoustic spaces. This makes

FEM/BEM preferable for large structures.

A disadvantage of FEM/BEM simulation is

that the small number of elements of the BEM

mesh does not imply a higher computational

efficiency. The acoustic matrices of the equations

defining the problem are fully populated, complex

and frequency dependent. A second limitation of

coupled FEM/BEM simulation in existing

commercial implementations is the difficult

integration of acoustic treatments, characterized by

their Transmission or Insertion Loss, and the effect

of material multilayers.

Two different approaches can be used with

BEM models: direct and indirect, referring to the

different methods of solving the integral equations

of the problem. For the Direct BEM approach, the

variables of interest at the boundaries (surfaces)

are pressure and normal velocity. The direct BEM approach is commonly used for closed domains, and most solvers

allow only one side of the closed surface to be considered for calculation (interior or exterior). In the case of the

Indirect BEM approach, the variables of interest at the boundaries are differential pressure and differential normal

velocity. For the indirect approach, both sides of the surface can be simultaneously considered (interior and exterior

problem are simultaneously solved), and the boundary does not require to be closed: it is applicable to any given

arbitrary surface (open, closed, with junctions, etc.).

Indirect BEM was used for this study, as it allowed incorporating radiating open elements (ribs, frames, trim

panels, etc.) to the acoustic model, and typical computation lead-times are shorter than direct BEM for models of

comparable size.

Figure 3. C295 vibroacoustic FEM model.

Figure 4. C295 vibroacoustic FEM model – Section of

interest.

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The aircraft structural FE model contains a fine

mesh for a fuselage section comprising ten frames

that include the propeller plane. The element size

of this mesh was dimensioned for reproducing

structural dynamic behavior up to 400 Hz

(approximately 25 mm). A coarser mesh based on

a existing dynamic model8 was used for the rest of

the aircraft for the purpose of improving boundary

conditions at the extremes of the section of

interest, which lead to improved correlation with

experimental results. The complete FEM model

contained approximately 200,000 elements and

800,000 degrees of freedom. A snapshot of the

complete FE model of the aircraft is given in

Figure 3 and Figure 4.

Correlation analysis conducted between

numerical and experimental results showed a

reasonable degree of correlation up to 150 Hz. The number of normal modes obtained with the complete aircraft

structural FE model is given in Figure 5, reaching approximately 2,000 modes up to 250 Hz.

The boundary element representation used for the coupled FEM/BEM model was created based on the C295

internal cabin geometry of the aircraft used for testing. System consoles and equipment racks were included in the

model. Sub-domains were created based on the geometrical position of the floor and roof panels. Views of the

complete BEM model of the aircraft are given in Figure 6.

Depending on the localization of the noise source and the model, not all the structure in contact with the interior

fluid needs to be coupled to the acoustic domain. Theoretically, only the critical zone which shows the largest

contribution to the global interior noise needs to be coupled, thus significantly reducing the computation time

compared to a fully coupled geometry. On the other hand, careful considerations regarding noise transmission path

and structural contribution to interior noise are needed before determining the reduced coupling zone. For the

coupled vibroacoustic simulations of the C295, the coupling zone or “wetted surface” was considered to stretch over

five frames encompassing the propeller plane, as shown in Figure 6. The surrogate mesh is defined as a transition

mesh where structural data is transferred to the acoustical mesh through a node-to-node mesh mapping process,

ensuring the transfer of vibration data estimated on the FE model to the BE model as vibrating boundary conditions.

Coupled vibroacoustic simulations presented in this paper were all performed using LMS Sysnoise and LMS

Virtual.Lab “Acoustic Harmonic Toolbox” pre- and post-processing capabilities. The choice of this solver and

interface was based on the experience of SENER in the field of acoustic simulation using LMS software, and earlier

references where LMS software was used for coupled FEM/BEM simulations of similar structures9-12

. Modal

analysis of FE models were performed using MSC.NASTRAN and the well-known Lanczos method. The frequency

range of interest for the coupled simulation was set up to 150 Hz, while the structural normal modes of the aircraft

were calculated up to 250 Hz.

Figure 5. Accumulated number of modes of full aircraft

FEM model of the aircraft until 250 Hz.

Figure 6. Representation of the different meshes used in LMS Virtual.Lab and LMS Sysnoise for coupled

FEM/BEM simulations.

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V. Exterior Acoustic Source Model

Even when recent developments allow integrating aeroacoustic solvers together with classical FE and BE

acoustic models, the computational expense is still very important. Model complexity, already high for adequate

representation of structure and acoustic spaces, would additionally require three-dimensional modeling of blade

geometry and consideration of airflow characteristics for different operating conditions. Two factors were

determinant in disregarding this path. Firstly,

implementing an aeroacoustic model of the propellers

would make difficult solving the problem for conditions

differing substantially from the narrow margin where the

propeller operates. A frequency sweep covering not just

the variability range of propeller rotating speed, but a

broader one in order to help evaluating structural response

would be computationally very expensive.

Representativeness would decay as conditions differ

significantly from propeller nominal conditions.

Discerning between the effects of propeller load and

vibroacoustic response would greatly hamper the

analysis.

Secondly, being this a study where the aircraft already

existed and no substantial modification of the powerplant

was foreseen, the value of aeroacoustic modeling was

limited. It was decided instead to implement a simpler

deterministic model, fitted to experimental data,

providing representative loading conditions without

scaling model complexity.

Different point source models were evaluated with characteristics of amplitude, directivity and location.

Computation time was thereby not significantly increased compared to trivial vibroacoustic loads. In addition, the

procedure allowed conducting the analysis throughout a wide frequency range, providing a more complete

perspective for the analysis of structural and acoustical response beyond the nominal variability range of the BPF.

Experimental data collected by means of flush-mounted microphones installed on the fuselage in the vicinity of

the propeller plane made possible adjusting the point source parameters for different powerplant and aircraft

operating conditions. Results presented in this paper are derived from engines runs on ground only. In total, 30

different locations were measured along the fuselage. Flight test data is available for a reduced set of locations. The

best results were obtained by assigning the point source the directivity pattern of a dipole oriented along the

aircraft’s longitudinal axis. One dipole per propeller was placed in each propeller disk at approximately 90% of the

propeller radius in a position minimizing distance with the fuselage. The simulated external pressure field together

with the agreement between measured and predicted exterior noise levels at BPFx1 is shown in Figure 8.

Figure 8. Left: simulated exterior pressure field obtained by means of described directive point sources.

Right: Measured (□) vs. predicted (∆) SPL on fuselage exterior using directive point sources.

Figure 7. Exterior microphones mounted onto the

C295 fuselage.

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VI. Experimental Results and Model Validation

Experimental activities were highly focused on full-scale aircraft tests, with the purpose of characterizing

fuselage dynamic response and the complex interior and exterior acoustic fields in real or close to real operation.

An extensive test campaign allowed surveying cabin noise distributions in flight on a number of CN235 and

C295 in various configurations. Well-defined test points and flight conditions made possible obtaining repetitive and

comparable results. On a given highly instrumented C295 aircraft, vibroacoustic instrumentation included

accelerometers (up to 90) distributed throughout the fuselage (frames, stringers, skin and rigid interior panels), a

movable microphone array covering the cabin section (24 microphones), and exterior flush-mounted microphones

(6). Various transducer locations were chosen throughout various tests, while monitoring repeatability.

Instrumentation was concentrated in the section of interest containing the propeller plane, where both structural and

acoustic response was higher. Throughout the test campaign, various acoustic solutions, jointly developed with

qualified suppliers, were integrated and evaluated (results are not reported in this document).

In addition to operational tests (flight and ground engine runs), other tests were conducted where

structural/acoustic excitation was generated by means of controllable synthetic sources (e.g. electrodynamic shakers

and loudspeakers). These tests provided valuable results for model validation, as known inputs replaced the

uncertainties related to propeller excitation and other operational sources. Selected results are presented for

frequencies close to BPFx1 in powerplant max cruise conditions. Both cabin sound pressure distribution (see Figure

9) and fuselage dynamic response (see Figure 10) show satisfactory agreement in terms of frequency and spatial

distribution.

This validated aircraft FEM/BEM vibroacoustic model using synthetic sources was then completed with the

previously described propeller source model. This allowed comparison of structural and acoustic response in

operational conditions. Figure 11 and Figure 12 show measured and predicted frame vibration and cabin acoustic

levels for engine operation during ground runs (C295, max cruise propeller speed). Frame/stringer/skin vibration

was experimentally determined on a total of 460 fuselage locations during subsequent engine ground runs. Cabin

noise distribution was determined using a combination of 6 reference microphones at occupant head level in the

section of interest and a 24-microphone array installed at propeller plane. The agreement between measured and

predicted levels in operational conditions is considered satisfactory in terms of amplitude, frequency and spatial

distribution.

Measured

Predicted (FEM/BEM)

Figure 9. FEM/BEM model acoustic validation: measured vs. predicted cabin sound pressure distribution

(propeller plane) determined at BPFx1 frequency (C295 max cruise) using a synthetic acoustic source

(loudspeaker).

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Predicted (FEM): 113 Hz

Measured (GVT): 110 Hz

Figure 10. FEM model structural validation: measured (GVT) vs. predicted (FEM) fuselage dynamic

response at frequencies close to BPFx1 (C295 max cruise).

Figure 11. Left: measured fuselage operational deflection shape (ODS) at BPFx1 determined during engine

ground runs. Right: comparison of predicted (red dashed line) vs. measured (solid blue line) fuselage frame

vibration amplitude using directive point sources reproducing propeller noise.

Figure 12. Left: Predicted cabin noise distribution in propeller plane at BPFx1 frequency using C295

FEM/BEM model with operational sources. Right: Comparison of predicted vs. measured SPL for a number

of reference locations (C295 engine ground run in max cruise power conditions).

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VII. Conclusion

Results are presented corresponding to experimental and simulation activities aimed at characterizing cabin noise

on a C295 aircraft. A-weighted SPL in max cruise conditions is driven in this aircraft by the fundamental propeller

noise frequency (BPFx1). Agreement between measured and predicted levels was found to be reasonable, at least up

to BPFx1, both for fuselage dynamic response and cabin sound pressure distribution. Validation encompassed

synthetic structural and acoustic load cases, with known excitation, and real aircraft operation, where propeller noise

was reproduced in the model by means of a deterministic point source fitted to measured sound pressure on the

fuselage exterior. Presented results correspond to engine ground operation, for which more test information was

gathered. Even if results can not be directly extrapolated to in-flight conditions, they constitute an important first

step in modeling propagation of propeller noise to the cabin interior.

The presented results constitute a small fraction of what was obtained in the scope of a development program

stretching during several years. Different acoustic solutions were engineered and evaluated on aircraft, resulting in

considerable reduction of cabin noise levels. Development is to be continued, looking for performance-weight

optimization of acoustic solutions capable of withstanding rough operating conditions.

As what simulation activities is concerned, two lines of development are to be followed. On one hand, robust

procedures are to be implemented for incorporating the effect of acoustic treatments and anti-vibration devices into

the aircraft model. Secondly, numerical simulation needs to be brought into the important medium frequency range,

where structural modal response is still too significant to apply a statistical approach, but the size of the modal base

is so high that originates problems of computational power.

Acknowledgments

This program enjoyed partial funding in various phases from the European Union and the regional government

of Madrid (Spain) through the INNOVA program.

Acknowledgments are made to the Laboratory of Acoustical and Mechanical engineering (LEAM) of the

Polytechnic University of Catalonia (UPC) for support given to simulation activities.

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