Numerical prediction of passenger cabin noise due to jet noise by an ultra–high–bypass ratio engine

Journal Pre-proof Numerical prediction of passenger cabin noise due to jet noise by an ultra–high– bypass ratio engine Christopher Blech, Christina K. Appel, Roland Ewert, Jan W. Delfs, Sabine C. Langer PII:

S0022-460X(19)30522-X

DOI:

https://doi.org/10.1016/j.jsv.2019.114960

Reference:

YJSVI 114960

To appear in:

Journal of Sound and Vibration

Received Date: 14 August 2018 Revised Date:

8 September 2019

Accepted Date: 13 September 2019

Please cite this article as: C. Blech, C.K. Appel, R. Ewert, J.W. Delfs, S.C. Langer, Numerical prediction of passenger cabin noise due to jet noise by an ultra–high–bypass ratio engine, Journal of Sound and Vibration (2019), doi: https://doi.org/10.1016/j.jsv.2019.114960. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

Numerical prediction of passenger cabin noise due to jet noise by an ultra–high–bypass ratio engine Christopher Blecha,∗, Christina K. Appelb , Roland Ewertb , Jan W. Delfsb , Sabine C. Langera a Technische b German

Universit¨ at Braunschweig, Institute for Engineering Design, Langer Kamp 8, 38106 Braunschweig, Germany Aerospace Center, Institute of Aerodynamics and Flow Technology, Lilienthalplatz 7, 38108 Braunschweig, Germany

Abstract Within the framework of the Collaborative Research Center 880, future civil transportation aircraft are investigated. One major aim is a drastic reduction of the noise emission to the ground and an appropriate noise immission into the passenger cabin. The latter forms the focus of this contribution with the aim to ensure an equal or lower noise level in the cabin for new aircraft configurations. Numerical methods are applied to establish a multidisciplinary modeling chain resulting in a prediction of cabin noise due to jet noise by two different engine configurations. An ultra–high–bypass ratio engine is compared to a conventional engine on the basis of a preliminary aircraft design used for both configurations. On the basis of flow calculations in cruise flight as operation point, the hybrid Computational Aeroacoustics solver PIANO combined with the Fast Random Particle Mesh method is applied to compute the pressure fluctuations due to jet noise on the outer skin of the fuselage. These loads are applied to a finite element model considering the structure and the fluid of the aircraft cabin. The acoustic model resolving the structure-borne and airborne sound waves is derived from the design data. The results show a lower sound pressure level induced by the ultra–high–bypass ratio engine in the entire frequency range on the outer skin. Within the cabin, the modern engine is still much quieter, though this fact is not generally valid for the entire frequency range as transmission effects of the double wall occur. Keywords: Aircraft Cabin Noise; Jet Noise; Computational Aeroacoustics; Finite Element Method; Vibroacoustics; Ultra–High–Bypass Ratio engine

1. Introduction

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Today’s globalized world is clearly characterized by a great significance of mobility. Beyond certain travel distances, aviation systems have to meet a constantly growing demand of today’s and tomorrow’s society. Within the Collaborative Research Center 880, future civil transportation aircraft concepts with short take-off and landing characteristics, a low fuel consumption and a drastically reduced noise emission are aimed for. The latter enables efficient point-to-point connections between inner-city airports with a minimal noise pollution of the nearby living environment [1]. Another important aspect besides the noise emission to the ground is the passenger cabin as place of noise immission. An increasing number of passengers per year is consequently leading to more and more people exposed to noise during the actual flight. A high noise level during a long time period or many flights in general may lead to health problems, violate legal requirements or simply yield comfort issues by passengers. In contrast, a reduced cabin noise is expected to provide new possibilities as a pleasant flight or an appropriate work environment. These motivations require a consideration of cabin noise during early design stages of future aircraft. With the introduction of new technologies, an appropriate noise level has to be ensured and higher noise levels has to be clearly excluded by noise level estimations. An over-the-wing Ultra-High-Bypass Ratio (UHBR) engine with a bypass ratio of 17 is a possible aircraft propulsion system with great take-off characteristics, a low fuel consumption and a highly reduced noise emission in comparison with a conventional engine with a bypass ratio of 5 (BPR5). A modeling chain has been established [2] considering the aeroacoustics of the jet and the sound transmission into the cabin. In order to compare the two aircraft configurations, containing respectively two BPR5 and two UHBR engines with regard to cabin noise during cruise flight, the modeling chain is applied. The research aircraft’s configuration is presented in Sec. 2 while the modeling chain is further divided into three major steps in Sec. 3. As the UHBR engine has a larger dimension and rotates slower compared to the BPR5 engine, the expected noise emission is significantly smaller. However, the Transmission Loss (TL) of a typical fuselage double wall structure is reduced at lower frequencies which are mainly addressed by UHBR engines. Furthermore, due to aircraft/engine integration ∗ Corresponding

author Email address: [email protected] (Christopher Blech)

Preprint submitted to Journal of Sound and Vibration

September 17, 2019

requirements, the engine is mounted closer to the passenger cabin which finally leads to a non-trivial scientific question concerning the quieter engine. The hypothesis to be investigated in this contribution is stated as follows.

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A propulsion system comprising Ultra-High-Bypass Ratio engines implies a reduced cabin noise compared to a conventional propulsion system. Flow simulations solving the Reynolds-averaged Navier–Stokes equations (RANS) of each jet are conducted which serve as basis for a Computational Aeroacoustics (CAA) simulation. The resulting pressure fluctuations on the outer skin are applied as loads in a mechanical model of the aircraft fuselage. The model is solved by use of the Finite Element Method (FEM). It includes the outer skin, circular frames, the cabin floor, insulation material and the cabin fluid. Fluid- and structural domains are strongly coupled in the fuselage model, directly yielding the sound pressure field within the passenger cabin for each configuration. Using this wave-based approach in comparison to an energy-based approach (e.g. Statistical Energy Method) considers the characteristic footprint of the jet on the outer skin and further enables investigations of innovative passive damping measures [3] within the structure of the fuselage under realistic loadings. Energy-based methods are the current state of the art concerning full aircraft NVH-investigations. In literature, wave-based approaches are rarely represented. In [4], cylindrical structures with frames and stringers are investigated by FE models and compared to experiments up to 1 kHz. Similar comparisons are conducted in [5] resulting in a good agreement up to 200 Hz. In both references [4, 5], the insulation and the cabin sidewall panels have been neglected in order to focus the investigation on a validation of the primary structure. A quite similar model compared to this contribution is presented in [6]. Both references share the application which is a propeller aircraft and a weak coupling of the flow region and the aircraft structure. In [6], the recent status of Airbus is shown modeling the entire cabin fluid but only the back of the aircraft. A solution in frequency domain at harmonics of the blade passing frequency is presented in order to investigate different configurations in early design stages. However, a wave-based approach for full aircraft models still results in massive computational cost. Finally, the model delivers the Sound Pressure Level (SPL) at each seat position enabling a frequency-dependent difference between the two aircraft configurations. On the basis of an auralization or a simple plot per seat, the systems may be assessed. A more general comparison is conducted using the mean square pressure for the entire passenger cabin. As the models are generic due to preliminary aircraft design data, absolute values must be interpreted in a qualified sense. Rather the SPL differences are meaningful results concerning the question in terms of the quieter engine. It is assumed that the SPL differences are not affected significantly by one of the numerous model assumptions applied in this contribution. 2. Investigated aircraft configurations

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A preliminary aircraft design is given within the project. The research aircraft’s mission has a distance of 2000 km, can transport 100 passengers and a total payload of 12000 kg which represents the vision explained above in a technological reference configuration. Both configurations investigated here share the structural dimensions of the fuselage and differ in the applied engine which can be seen in Fig. 1. The conventional BPR5 engine is mounted under the wing while the UHBR engine is mounted over the wing and has a shorter distance to the actual cabin and a different axial position. The potential shielding effect of the wings is not considered within this contribution and will be subject of further studies.

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Figure 1: Investigated aircraft configurations sharing similar fuselage dimensions; a) Conventional propulsion system with BPR5 engines and b) Modern propulsion system with UHBR engines. [7]

The aircraft’s main properties are given in Tab. 1 – further information on the design process by use of the preliminary aircraft design Code of TU-Braunschweig PrADO can be found in [8]. The UHBR engine has a much greater diameter resulting in a significantly higher bypass ratio of µ = 17 and lower rotation speeds. The 2

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conventional engine operates at a bypass ratio of µ = 5 and rotates at higher speeds. The fuselage has a circular cross-sectional area in the center with a maximum diameter of 3.510 m. Concerning the fuselage, the design process delivers the thickness distribution of the outer skin, the dimensions of each circular frame, the entire floor design including stiffener and the two bulk heads. Additionally, all material data is given – the entire primary structure is mainly made of Carbon-Fiber-Reinforced Polymer (CFRP). Table 1: Details on the aircraft fuselage and the two investigated engine configurations.

General Aircraft weight PAX Mach number at cruise flight Range Engine Bypass ratio Max. thrust Max. diameter Geometry Max. Length Max. Width Max. Height Max. Diameter

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Unit

BPR5

UHBR

kg km

45570

kN m

5 2 × 106.884 1.464

44698 100 0.78 2000

m m m m

17 2 × 136.145 2.031

33.176 28.783 9.849 3.510

3. Modeling chain for cabin noise prediction In this contribution, the effect of jet noise on cabin noise at cruise flight conditions is considered only and further noise emitting sources as fan, Turbulent Boundary Layer (TBL) and air-condition systems are neglected. Other sources and especially fan noise will be considered in further studies. However, the process is generally applicable and divided into four main steps in phases A and B as shown in Fig. 2. Phase A

structural data material data

geometry data Preliminary Aircraft Design Code: PrADO Phase B turbulent kinetic energy flow velocities pressure fluctuations 1 | RANS Code: TAU

2 | CAA Code: PIANO/FRPM

3 | FEM Code: elPaSo

Figure 2: Schematic modeling process applying the in-house codes PrADO [8], TAU [9, 10], PIANO/FRPM [11, 12] and elPaSo [13] 80

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The preliminary aircraft design is developed in phase A (Fig. 2 top) and forms the basis for the investigation and is given for this study. The aircraft design fulfills the requirements given within the project (short take-off and landing characteristics, low fuel consumption) – the cabin noise investigation is a subsequent process realized in phase B (Fig. 2 bottom). The applied computational approach for steps 1 and 2 is a hybrid method for broadband jet noise prediction (Ewert et al.[12, 14, 15]). The three main modeling steps in phase B are as follows: 3

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1. RANS computation of underlying flow (Sec. 3.1). Mean flow data and statistical turbulence quantities are calculated for the isolated TBL and the isolated jet, respectively. 2. CAA modeling of fluctuating sound sources (Sec. 3.2). Modeling of fluctuating sound sources derived from the Tam & Auriault [16] cross-correlation model and a 3D CAA prediction step using the previously computed fluctuating sound sources are conducted. The turbulence related sources of jet noise are modeled by means of the Fast Random Particle Mesh (FRPM) method. The important refraction effects by the TBL are considered within the CAA perturbation simulation step. 3. FE modeling of the aircraft’s fuselage (Sec. 3.3). The time-dependent statistically stationary pressure fluctuations are transposed into the frequency domain by the Fast Fourier Transformation (FFT) and interpolated as pressure loads centrally applied to finite shell elements. By applying the loads obtained on a rigid boundary within the CAA calculation (outer skin of the fuselage), the coupling realized is of weak nature – influences by the structure on the flow are neglected. As result, the sound pressure field is directly given as degree of freedom in the passenger cabin. 3.1. RANS computation of underlying flow The applied computational approach is a hybrid method for broadband noise prediction which relies on RANS mean flow data for derivation of turbulence quantities. In the current approach, RANS simulations were performed separately for the fuselage and for the jet. Such simplification allowed for effortless grid generation of superior quality than can be achieved by going a fully unstructured route. The latter may be the necessity when discretizing a volume around the entire aircraft. First, computations were performed for a generic fuselage which employed a quad dominant SOLAR mesh. The near wall refinement comprised 45 grid points in the wall-normal direction in a structured part, ensuring that the boundary layer is well-resolved. The grid had about 1.85 mio. points in total. Second, the RANS solution was obtained for the isolated jet which employed an axisymmetric hexahedral mesh wrapped around the engine. All RANS computations were performed with the DLR’s flow solver TAU(version 2015.2) [9, 10]. TAU is an unstructured solver which can also handle structured grids once they are converted to an unstructured format, meaning that the advantages for aligned flows such as boundary layer or jet flows can still be kept. The symmetry plane and the surface mesh for the fuselage are shown in Fig. 3 along with the Mach number distribution. The RSM-g turbulence model [17] (Reynolds Stress model) was used where the ambient conditions corresponded to cruise conditions as described in the Collaborative Research Center reference configuration [1].

M 1 0.8 0.6 0.4 0.2 0

Figure 3: Mesh used for the isolated fuselage and resulting Mach number M .

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In addition, the RANS computation of the axisymmetric jet was carried out. The geometry was based on a CFM-56 engine, which dimensions were adapted according to the design introduced by the Collaborative Research Center transport aircraft reference configuration [1]. The thermodynamic cycle data was provided by the software GasTurb of the Institute of Jet propulsion and Turbomachinery of Technische Universit¨ at Braunschweig. The design of the UHBR engine was prepared as part in a diploma thesis [18] by means of the codes PrADO, GasTurb and the Noise prediction tool PANAM [19]. The diameters of the UHBR and the conventional engine bypass duct are 1.78 m and 1.568 m respectively. Both designs are depicted in Fig. 4 below. The meshes for both engines were prepared with the Gridgen/Pointwise mesh generator having the resolution of about 200.000 grid points per radial-axial plane and 19 points in the azimuthal direction. In general, it is only necessary to simulate a segment of the engine. In this case, the RANS mesh was revolved around a 15 degree azimuthal slice forming a structured mesh wedge with symmetry conditions applied at the boundaries. This simulation served as input for the stochastic sound sources modeling. Turbulence modeling was done by 4

means of the Menter-BSL (Baseline) turbulence model [20]. The extent of the source grid was 15D in the radial and 30D from the engine outlet in the axial direction while D is the engine diameter. Finally, the source grid was rotated such that it conformed to the RANS segment.

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b) Figure 4: a) UHBR and b) conventional nozzle.

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3.2. CAA modeling of fluctuating sound sources The pressure fluctuations on the fuselage from both bypass configurations are predicted with a hybrid Computational Aeroacoustics (CAA) approach using the structured multi-block (SMB) CAA solver PIANO of the German Aerospace Center (DLR) [11]. The code utilizes the dispersion relation preserving (DRP) scheme of Tam & Webb [21] for spatial discretization and a fourth order accurate explicit Runge-Kutta method for time advancement. The sound propagation is simulated in a three-dimensional volume enclosing main parts of the jet and the considered portion of the fuselage, so that the pressure fluctuations on the fuselage are directly resolved in space and time. Further details of the CAA setup will be given in paragraph 3.2.9 below. The linearized Euler equations (LEE) are used as governing equations to predict acoustic sound generation and radiation at flight conditions. Mean flow and turbulence statistics needed are provided by the precursor RANS simulations. The Fast Random Particle-Mesh (FRPM) module of DLR has been used as a stochastic method to generate in parallel with PIANO the unsteady jet noise source terms on the right-hand side of the linearized Euler equations. The jet noise sources have been modeled stochastically based on the jet mixing noise source model proposed by Tam & Auriault (hereafter abbreviated as T&A). The following paragraphs give a brief summary of the applied CAA methodology as far as it concerns its application in this work. 3.2.1. Tam & Auriault jet noise model The statistical jet noise model of T&A [16] is based on the linearized Euler equations rewritten in cylindrical coordinates as governing acoustic equations. The cylindrical coordinate system (x, r, ϕ) is centered at the nozzle exit (with the x axis coinciding with the jet axis). In the genuine method the spreading of the jet flow is omitted assuming a mean-flow parallel to the jet axis. Consequently, the axial, radial, and azimuthal mean-flow velocity T components (ux0 , ur0 , uϕ0 ) become ux0 = uj (r), ur0 = uϕ0 = 0, and the mean-flow density is taken as a radial function ρ0 (r), whereas the mean pressure p0 is constant. Furthermore, a source term is introduced that can be expressed in terms of the substantial time derivative of a scalar function qs on the left-hand side of the pressure equation,  0  ∂ux ∂u0 ∂ux0 ∂p0 + ur0 x + u0r + = 0 (1) ρ0 ∂t ∂x ∂r ∂x  0  ∂u0 ∂p0 ∂ur + ux0 r + = 0 (2) ρ0 ∂t ∂x ∂r  0  ∂uϕ ∂u0ϕ 1 ∂p0 ρ0 + ux0 + = 0 (3) ∂t ∂x r ∂ϕ   ∂p0 1 ∂(u0r r) 1 ∂u0ϕ ∂u0x D0 qs ∂p0 + ux0 + γp0 + + = . (4) ∂t ∂x r ∂r r ∂ϕ ∂x Dt Here D0 /Dt := ∂/∂t + uj ∂/∂x denotes the substantial time derivative based on the steady mean-flow velocity from RANS1 . 1 In the original model the source term appears as the gradient of q on the right-hand side of the momentum equation. However s as shown in [22], this can be reformulated in the formulation shown here with D0 qs /Dt on the right-hand side of the pressure

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The equation system Eqs. (1-4) can be Fourier transformed into frequency domain. To the latter equation system exists an adjoint equation system, which was used by T&A to derive expressions for the free-space vector Green’s functions. These Green’s functions include mean-flow refraction effects. Numerically they are obtained by solving the adjoint equations in the frequency domain with CAA techniques. Finally, the numerically determined values of the Green’s function are used to approximately solve the integral expression that defines the far-field acoustic spectrum in terms of the noise source space-time correlation   D0 qs (x1 , t1 ) D0 qs (x2 , t2 ) . (5) R12 (x2 − x1 , t2 − t1 ) = Dt1 Dt2 In the above expression, the brackets indicate an ensemble average and xi = (xi , yi , zi ) denotes the spatial coordinates of point i. T&A propose the correlation function Eq. (5) to be described by        D0 qs (x1 , t1 ) D0 qs (x2 , t2 ) |∆x| ln(2)  2 2 2 ˆ = RTA × exp − exp − 2 (∆x − uj ∆t) + ∆y + ∆z . (6) Dt1 Dt2 uj τs ls The variables ∆x = x2 − x1 , ∆y = y2 − y1 , and ∆z = z2 − z1 denote the relative distance between position 1 and position 2, uj indicates the jet convection velocity parallel to the jet axis, and τs and ls indicate a timeand length-scale, respectively. The variance2 2 ˆ TA = qˆc (7) R τs2 is entirely specified by a RANS solution utilizing a two-equation turbulence model. In the T&A [16] model the parameters are specified by 2 qˆc = Aρ0 k, (8) 3 with A = 0.755 and k denotes the turbulent kinetic energy from RANS. The time-scale is obtained from k τs = cτ , 

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(9)

where  denotes the dissipation rate from RANS and cτ = 0.233. The turbulent source length scale is determined by k 3/2 ls = cl , (10)  with cl = 0.256. Hence, three free parameters are introduced into the source model. Note, the RANS solution is independent of time (steady), but turbulent kinetic energy k and dissipation rate  are spatially varying quantities, so that the derived turbulent source length scale from Eq. (10) becomes a spatially variable but steady field as well. The acoustic spectrum at position x derives from the correlation model by means of volume and time integrals over the source domain (coordinate x1 , source volume indicated by Vs ), and time and spatial separations ∆t = t2 − t1 and ∆x = x2 − x1 , respectively, ZZ Z ∞ ˆ S(x, ω) = pˆ∗a (x1 , x, ω)ˆ pa (x2 , x, ω) Vs −∞   D0 qs D0 qs × (x1 , t1 ) (x1 + ∆x, t1 + ∆t) exp [iωτ ] d∆t dx1 d∆x. (11) Dt Dt Here, pˆa (xi , x, ω) indicates the exact spectral Green’s function that includes refraction in the jet shear layer for the angular frequency ω, source position xi , i ∈ {1, 2}, and observer position x. The asterisk indicates the complex conjugate. In the T&A approach, the Green functions are computed numerically for each frequency band and observer position by means of the adjoint equations related to Eqs. (1-4). The integral over time difference ∆t is integrated over all values from minus to plus infinity. The integral over spatial separations runs over entire 3D space. Eventually, the far-field spectrum is obtained from the solution of the previous integral using the cross-correlation model Eq. (6).

equation, by absorbing the source term qs into the pressure variable. The source term decays rapidly away from the jet, so that the modified pressure variable away from the jet yields the same quantitative results as the original formulation. 2 Note, the variable q ˆc combines and replaces the expression qˆs /c used in the original Tam & Auriault paper [16]. To be precise, the variance of source qs , originally denoted by qˆs2 , and the constant c are jointly expressed by qˆc = qˆs /c in the current work as they both show up always in the indicated combination in all expressions to follow.

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The source term of T&A is known to represent only the sound generated by the fine-scale turbulence, which especially radiates in directions normal to the jet axis. This was demonstrated in [16], showing very good agreement between measured and predicted spectra for polar angles in the range between 60◦ and 120◦ . The approach as discussed above is applicable to cold and mildly hot jet configurations. For hot jets a modification of the time correlation function has been proposed by Tam et al. [23]. 3.2.2. Stochastic sound source modeling In some other previous works a primal solution approach for the T&A model has been proposed, which enables a direct (primal) time-domain solution of the jet noise source term by realizing it with a stochastic method [22, 14, 15]. It was demonstrated that a primal approach in the time-domain provides results equivalent to the genuine frequency domain method, provided the same two-point space-time source statistics are generated. A primal approach might have advantages concerning efficiency and regarding its potential to overcome the simplifications introduced in the genuine approach. Especially, an adjoint approach in the frequency domain needs n × m computations for n observer positions and m frequency bands of the adjoint equations related to the LEE in cylindrical coordinates, Eqs. (1-4), to determine the exact spectral Green’s function used in Eq. (11). A broadband CAA approach to solve the primal LEE in the time-domain, on the contrary, allows to obtain the solution for all m frequency bands and n observers with one single computation. Furthermore, the spreading of the jet flow can be considered. This more complex mean-flow can be considered in the cross-correlation model as well. 3.2.3. Fast Random Particle-Mesh Method based primal approach In the extended time domain realization of the T&A jet source model the linearized Euler equations (LEE) with source term on the right-hand side of the pressure equation are solved based on a Cartesian coordinate system x = (x, y, z) to prescribe a more general three-dimensional jet-flow by means of RANS mean-flow variables (ρ0 , u0 , p0 ), where u0 (x) is the mean flow vector with Cartesian velocity components (u0 (x), v0 (x), w0 (x)). The LEE read ∂ρ0 + u0 · ∇ρ0 + u0 · ∇ρ0 + ρ0 ∇ · u0 + ρ0 ∇ · u0 ∂t ∇p0 ∂u0 ρ0 ∇p0 + (u0 · ∇) u0 + (u0 · ∇) u0 + − ∂t ρ0 ρ20 ∂p0 + u0 · ∇p0 + u0 · ∇p0 + γp0 ∇ · u0 + γp0 ∇ · u0 ∂t

=

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(12)

= qp .

The above system corresponds to the governing equations as used by T&A , Eqs. (1-4), providing that the fluctuating source term used is identical with their fine-scale source term, qp ≡

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D0 qs , Dt

(13)

and that a parallel jet mean-flow is applied, i.e. u0 (x) = uj (r(x)), v0 = w0 = 0 for a Cartesian coordinate system centered at the nozzle exit, where the x-axis coincides with the jet.3 The scalar source term qp is realized stochastically with the so called Fast Random Particle-Mesh (FRPM) method, which can be briefly summarized as follows: • The source term is obtained by spatially filtering convective white-noise U(x0 , t) with a Gaussian derived filter kernel of locally variable width, i.e. for a 3D problem it reads Z ˆ 0 ) G(x, x0 ) U(x0 , t) d3 x0 , qp (x, t) = A(x (14) with the filter kernel defined as a function of position vectors x and x0 given by ! 2 2 ln(2) |x − x0 | 0 G(x, x ) := exp − , ls2 (x0 )

(15)

where ls (x0 ) denotes the RANS derived turbulent source length scale, Eq. (10), evaluated in white-noise field position x0 3 The usage of a parallel mean-flow is a limitation of the T&A model that enables to use less expensive 2D CAA simulation of the adjoint LEE to derive the Green’s function. The more general usage of a realistic non-parallel, i.e., spreading 3D jet flow in the primal method applied in this work means to improve the jet noise model by reducing the level of physical simplification involved.

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• The convective white-noise is defined to have vanishing mean and to be delta-correlated in space but colored in time, i.e., hU(x, t)i =

0,

(16) 

∆t hU(x, t)U(x + ∆x, t + ∆t)i = ρ0 (x)−1 exp − τs

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 δ(∆x − u0 ∆t).

(17)

The scaling function Aˆ in Eq. (14) gives the desired variance of qp and is taken as a function of x0 . A solution to the spatio-temporal correlations that results from Eq. (14) in combination with the delta correlated white-noise definition Eq. (17) can be obtained using standard calculation techniques for distributions [24]. It is reasonable to assume all RANS mean-flow quantities–and quantities derived from it such as the turbulent source length scale Eq. (10)–to vary slowly over a spatial extension defined by the turbulent length scale itself, because the variation of mean-flow quantities occurs over a characteristic scale related to the topology of the mean-flow (e.g. related to the jet diameter), which is considerably larger than the length scales associated to turbulent motion. Based on the assumption of slowly variable mean-flow quantities, together with the definition Eq. (14), an analytical expressions for the two-point cross-correlations of the source term qp follows, refer to the detailed discussion in [12, 25]. The analytical expression is given and utilized in paragraph 3.2.5 to discuss the background of the modified length scale scaling introduced in this work. 3.2.4. Numerical discretization For the quadrature of the integral in Eq. (14) the computational domain is formally split into equal sized nonoverlapping control volumes δVk , continuously covering the resolved source domain without holes. A particle is assigned to each control volume. The particles are moving with an advection velocity according to the RANS mean-flow at the particle location. Random variables are associated to each particle that represent the Wiener increment resulting from the spatial white-noise definition Eqs. (16,17) integrated over each control volume. Based on the given definition, an exponential time decay model is accomplished, similar to the time decay function used in the genuine T&A approach. A modification of the time decay model based on a double Langevin procedure has been proposed in [26] to realize the hot-jet extension as introduced by Tam et al. in [23]. Different numerical methods have been applied and discussed in previous work that differ in detail concerning the realization of particle convection and in the realization of the discrete filter step exploiting the properties of the Gaussian filter Eq. (15) to be separable in space. In the 2D Random Particle-Mesh (RPM) method, [27], streamtraces are pre-computed from an initial seeding position. The size of the seeding area and the downstream extension of the streamtraces specifies the domain where random sources are generated. During run time particles are convected along the streamtraces. The filter step is split into an Gaussian filter applied along each streamtrace, followed by a second filter step that distributes pre-filtered values from the streamtrace to the CAA mesh points. The approach has been extended for the description of 3D jet noise using an azimuthal decomposition to the 3D stochastic source term that yields quasi 2D stochastic realizations for each azimuthal mode order, refer to [22, 14]. This approach will be hereafter referred to as RPM-modal. In the framework of the Fast Random Particle-Mesh (FRPM) method an auxiliary Cartesian mesh is utilized for the generation of the unsteady sources [28, 12]. The particle convection is computed on this mesh similar to particle-in-cell (PIC) methods. The filter step is accomplished by a sequence of 1D-filter steps applying a Gaussian filter along each coordinate direction. High-efficient recursive filters from signal processing are used. Details about the seeding of particles can be found in [12]. Both discretization techniques are implemented into the FRPM source module developed at DLR that is executed in parallel to the PIANO code. In the following the notion (F)RPM is used to indicate that the discussion holds for both discretization methods. 3.2.5. (F)RPM cross-correlation model Following the procedure as outlined in paragraph 3.2.3, straight forward calculation provides the 3D crosscorrelation for a parallel jet of velocity uj ,      ln(2)  |∆t| 2 2 2 ˆ exp − 2 (∆x − uj ∆t) + ∆y + ∆z , (18) hqp (x, t)qp (x + ∆x, t + ∆t)i = RFRPM exp − τs ls refer to the more detailed discussion references [12]. This cross-correlation model vastly corresponds with Eq. (6). Using in Eq. (14) a scaling  3/2 s ˆ 4 ln(2) ρ0 RTA Aˆ = (19) π ls3 8

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ˆ TA from Eq. (7), the resulting variance in Eq. (18) corresponds with that of the T&A model, i.e., with R ˆ FRPM = R ˆ TA . R Note, the mean-flow density could be removed from Eq. (19) and definition Eq. (17) without affecting the final result, Eq. (18). However, the mean-density scaling in Eq. (17) inevitably had to be introduced in Ref. [12] to facilitate an extension of the Random Particle-Mesh Method from the incompressible to the compressible flow regime. 3.2.6. (F)RPM cross-correlation model vs. T&A model Both cross-correlation function are similar despite the first exponential function governing turbulent decay at time scale τs , where |∆x|/uj is used in Eq. (6) instead of |τ | in Eq. (18). The cross-correlation map for both on the horizontal functions is shown in Fig. 5 showing the non-dimensional spatial x-separation ∆x∗ = u∆x j τs

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axis (with ∆y = ∆z = 0) and the non-dimensional time separation ∆τ ∗ = 1 R12

on the vertical axis4 .

1 R12

∆x − uj ∆t = 0

∆x − uj ∆t = 0

0.5 ∆τ ∗

0.5 ∆τ ∗

∆t τs

0

−0.5

0

−0.5

−1

−1 −1

−0.5

a)

0 ∆x∗

0.5

−1

1

−0.5

b)

0 ∆x∗

0.5

1

Figure 5: Cross-correlation plot; a) (F)RPM cross-correlation model Eq. (18); b) T&A cross-correlation model Eq. (6); Parameters non-dimensionalized with tref = τs , vref = uj , lref = uj τs , integral length scale lls = 13 . ref

The convective ridge defined by ∆x − uj ∆t = 0,

(20)

(indicated by the dashed diagonal line) represents the cross-correlation in a Lagrangian frame based on the convection velocity uj . In this frame and omitting the dependence on spatial separations which are not flow T aligned, i.e. ∆y = ∆z = 0, and ∆x = (∆x, 0, 0) , the normalised cross-correlations between points x1 = x and x2 = x + ∆x, denoted by R12 , reduces for both models to   |∆x| R12,TA (x2 − x1 , t2 − t1 ) = exp − , (21) uj τs and

265

  |∆t| , R12,FRPM (x2 − x1 , t2 − t1 ) = exp − τs

(22)

respectively. Hence, by using Eq. (20) to substitute ∆t by ∆x/uj in Eq. (22), both cross-correlation functions become equivalent. This result would also directly follow from Taylor’s hypothesis, which is strictly valid for frozen turbulence. However, the previous result in principle also holds for arbitrary decaying turbulence and supports the conjecture that both cross-correlation functions are equivalent. Nevertheless, the far-field spectrum in observer position x and at angular frequency ω = 2πf that results from the cross-correlation model realized by (F)RPM becomes [22, 29] h i ω 2 ls2  32 Z  exp − 2 3 2 π qˆc ls 4 ln(2)c0 ˆ ω) = 2 S(x, |ˆ pa (x1 , x, ω)|2 d2 x1 , (23) 2 τ 2 (1 − M cos θ)2 ln(2) τ s 1 + ω Vs j s 4 Based on a Fourier-transformation of the spatial and time variables, a wave-number-frequency plot similar to Fig. 5 would result.

9

where Mj := uj /c0 indicates the local axial jet Mach number computed with the local axial jet velocity uj and the local speed of sound c0 . Furthermore, θ denotes the polar angle between observer position vector (with origin defined in the the nozzle exit plane center) and the jet axis. On the contrary, the resulting far-field spectrum that follows from the T&A model yields [16] i h ω 2 ls2   32 Z exp − 2 3 4 ln(2)u2j π qˆc ls 2 ˆ ω) = 2 S(x, |ˆ pa (x1 , x, ω)|2 (24) 2 d x1 , 2 2 ln(2) 1 + ω τs (1 − Mj cos θ) V s τs

270

275

280

Both resulting spectra emerge from the integration (superposition) of building-block spectra depending on the local jet-noise source variables multiplied by the square of the Green function pˆa . The main frequency dependence of the building-block spectrum   of the T&A cross-correlation model in Eq. (24) is given by an exponential function exp −π 2 / ln(2) Str2 , i.e. a function of Strouhal number Str = f ls /uj based on the local length scale parameter ls . Additional contributions come from the denominator of Eq. (24) as well as from the frequency dependence of the Green function. However, the latter contributions to the spectrum turn out to be relatively small. ˆ ω) that will exhibit the Hence, the summation of all building-block spectra yields an acoustic spectrum S(x, Strouhal dependence of the dominating building-block constituents.   The building-block spectrum of the (F)RPM model as revealed by Eq. (23) is given by exp −π 2 / ln(2) He2 , hence, depends on Helmholtz number He = f ls /c0 . That is, the sound spectrum from the T&A cross-correlation model is Strouhal similar, whereas the FRPM cross correlation model, although approximately equivalent to the T&A correlation model function, provides an acoustic spectrum which is a function of Helmholtz number. Since the fine scale jet noise contribution is expected to be Strouhal similar, the previous result highlights a significant deviation from the expected scaling behavior if the cross-correlation function Eq. (18) is being used unmodified. 3.2.7. Velocity correction for zero jet co-flow speed The previous results indicate a possibility to realize with the cross-correlation model Eq. (18) the proper buildingblock spectrum as being used in the genuine T&A model, Eq. (24), by scaling the length scale in the (F)RPM cross-correlation function with the local jet Mach number Mj = uj /c0 . To be precise, a modified length scale is introduced defined by stretching the initial length scale from RANS by the local jet Mach number, ls∗ = ls Mj−1 ,

or,

c∗l = cl Mj−1 .

As a consequence, the (F)RPM building block spectrum defined by Eq. (23) changes, viz " #   ω 2 ls2 ω 2 ls∗ 2 exp − → exp − , 4 ln(2)c20 4 ln(2)u2j

(25)

(26)

and the proper Strouhal scaling is established. However, as a further side effect, the initial variance qˆc2 ls3 /τs in Eq. (23) is also changed due to the replacement ls∗ → ls . To compensate this unwanted side effect on variance, the target variance has to be re-calibrated as well. Specifically, using a variance (ˆ qc2 )∗ = Mj3 qˆc2 ,

285

290

(27)

the initially intended variance can be conserved. The approach was successfully validated against experimental data for a single-stream jet in a resting medium and against the predictions of the genuine T&A model, further details can be found in [14, 15, 30, 31, 32, 33]. The difference in the resulting spectra stems from the moduli present in Eqs. (21) and (22) that cause different ’kinks’ in the contour lines visible in Fig. 5 a) and b). 3.2.8. Velocity correction for non-zero co-flow velocity The previous correction method is suitable for a jet in a medium at rest. For the prediction of jet noise during cruise a modification to the discussed correction is proposed in this paper. Approximately, the effect of a comoving flow e.g. on noise emission can be taken into account by using the difference velocity between jet and co-flow uj − u0 rather than the jet velocity alone uj as the crucial characteristic velocity. Following this reasoning, as a suitable velocity it has been found in this work that the difference Mach number, ∆Mj (x) :=

|uj (x)| − αc Mc , c0

(28)

represents a suitable value to be used in Eqs. (25) and (27) for a non-zero co-flow velocity. Here, uj (x) = u0 (x), x ∈ Ωp , indicates the local jet flow velocity from RANS in the FRPM domain Ωp where sound sources are 10

300

SPL (dB re 2e-5 Pa)

305

evaluated. The quantities Mc and c0 indicate the undisturbed co-flow velocity and speed of sound, respectively. Note, the original Tam and Arriault model assumes a axial jet velocity with single axial component uj . As pointed out in the discussion related to Eq. (12), the stochastic approach allows to generalise the original approach by taking into account the actual three-dimensional RANS jet velocity field. The parameter αc is a order one parameter that was adjusted in this work based on numerical results for single stream jets. A value of αc ≈ 0.9 was found suitable to give a good qualitative and quantitative spectral prediction. For vanishing co-flow Mc → 0 the scaling yields identical results to the standard static method. Fig. 6 compares single stream jet predictions for static and co-flow conditions between the newly proposed approach and experimental data from the literature. In Fig. 6(a) the result for a static jet at Mach number Mj = 0.7 reveals very good agreement between the CAA prediction (solid line) and experimental results from Seiner [16] up to the CAA mesh cut off at a jet Strouhal number Str = f Dj /(Mj c0 ). The result confirms the proposed methodology in the limit Mc → 0. 90

90

80

80

70 60 50 40 −2 10

a)

SPL (dB re 2e-5 Pa)

295

Seiner Jet PIANO, 90◦ 10−1

100 Str

70 60 50 40 −2 10

101 b)

Measurement T&A genuine model PIANO ∆Mj correction 10−1

100

101

Str

Figure 6: Single-stream jet noise prediction using FRPM with new scaling model for Mj = 0.7; a) Co-flow Mach number Mc = 0; b) Co-flow Mach number Mc = 0.5; predictions and experimental data taken from [16, 34].

310

315

320

325

330

Fig. 6(b) provides a comparison of spectra for Mj = 0.73 and co-flow Mc = 0.5. Shown are results from the genuine T&A model (black solid lines), experimental data (black symbols) from reference [34], and predictions with the newly proposed extended scaling (red solid line). A fairly good agreement in terms of level is observable. Some deviations are visible for higher frequencies Str = f Dj /(Mj c0 ). However, in total a reasonably good agreement of the spectrum with the reference data is achieved. For future work it is planned to replace the (F)RPM correlation model with a kink-free model for the Lagrangian correlations Eqs. (21) and (22) to mitigate the need for an extra scaling model to correct for the mean-flow effect. 3.2.9. CAA setup In Fig. 7, the computational domain for the UHBR configuration is shown. Originally the CAA mesh consists out of 16 blocks with about 47 mio points. For parallelization purposes the blocks have been split of into 578 small blocks. The maximal resolved frequency of the CAA mesh is 2 kHz. According to this point sampling positions at the fuselage surface are defined, which allow an appropriate spatial resolution. In total ca. 53000 sampling points are specified for the UHBR configuration. The conventional configuration requires 83000 positions due to the larger extend of the CAA mesh. For the conventional case, the CAA mesh consists of 72 mio points and provides the same mesh and frequency resolution as the UHBR mesh with an average full-scale mesh spacing of about 21 mm. The FRPM patch for both cases has a resolution of 5.5 mio points and about 5.5 mio particles are used. A test with increased particle densities has confirmed a particle-number independent solution. 3.2.10. CAA simulation of pressure fluctuations on the fuselage Fig. 8 reveals the pressure fluctuations on the fuselage as predicted by PIANO/FRPM using the newly proposed scaling method. Qualitatively, it can be observed on the fuselage that the pressure fluctuations are significantly lowered in terms of amplitude and spatial extension compared to the BPR5 reference engine. Furthermore, the visible dominant wave length appears to be slightly larger for the BPR5 configuration. The results are further confirmed in Fig. 9 that depicts evaluated sound pressure spectra for one selected microphone position and both configurations. The spectrum indicates a significant broadband reduction of

11

TKE (m2 s−2 ) 2000 1750 1500 1250 1000 750 500 250 0 Figure 7: CAA domain for the UHBR engine presented together with a slice showing the turbulence kinetic energy (TKE) distribution from RANS downstream of the jet engine; the grey coloured area indicates the sampling positions at the fuselage surface.

p0 (Pa) 1 ·10−4

0

a) UHBR nozzle

−1

b) Conventional nozzle Figure 8: Pressure fluctuations p0 on the fuselage from PIANO/FRPM simulation.

sound pressure level exceeding 12 dB. Furthermore, the maximum for the BPR5 configuration is slightly shifted to smaller wave numbers.

SPL (dB re 2e-5 Pa)

80

60

40 PIANO BPR5 PIANO UHBR G similarity spectrum 20 −2 10

10−1

100

101

Str Figure 9: Predicted spectra for the BPR5 and UHBR configuration at the same microphone position from RPM-modal simulation.

335

The predicted spectra are compared to a fine scale similarity spectrum (G-Spectrum [16])) adjusted for each simulation case (black solid line). The slightly steeper roll-off seen in the numerical simulations might be attributable to the more complex jet flow present for the bypass nozzles that causes deviations from the general spectral shape as expected for a single stream jet, which is well described by a G-Spectrum. 12

340

345

3.3. FE modeling of the aircraft’s fuselage The data available by the preliminary design process includes a static finite element model of the entire aircraft which has been applied in standardized load cases [35] in order to dimension the outer skin, the circular stiffeners, the floor and the bulk head. The obtained thicknesses and cross-sections serve as basis information for the wave resolving mechanical model in frequency domain. In Fig. 10, an overview of all parts is shown. Structural parts are orange, fluid parts are blue. Additionally, an insulation (glass wool), the cabin fluid itself (air) and typical sidewall panels (honeycomb sandwich) are considered in the model. The model underlies the following general assumptions: 1. 2. 3. 4.

350

355

Linearity Stationarity regarding the response in cruise flight Symmetry with inversely phased excitation by the two identical engines in cruise flight Neglection of the aircraft’s structural front partition (cockpit to wing box)

In real flights, neither the response is stationary nor both engines generate symmetric loads. For this investigation, the SPL differences between the two configurations are of interest. Hence, as the mentioned assumptions are expected to introduce systematic modeling errors, the influences can be neglected. The latter assumption helps realizing manageable solution times and memory efforts. The jet noise excitation mainly affects the rear part of the aircraft and the wing box brings a reflecting impedance jump into the system which are justifications for the third assumption. The second assumption leads to a much smaller problem dimension, as symmetric boundary conditions can be applied instead of solving the entire domain. All domains are discretized by finite elements and solved by the working group’s in-house code elPaSo [13]. The code uses PETSc as algebra package and MUMPS (MUltifrontal Massively Parallel sparse direct Solver) as solver.

Cabin 3D Continuum Ideal fluid

Insulation 3D Continuum Equivalent fluid

Stiffener Shell Linear elastic Orthotropic

Sidewall panel 3D Continuum / Shell Linear elastic Floor Orthotropic Shell y z Linear elastic x Orthotropic

Bulk head Shell Linear elastic Orthotropic Outer skin Shell Linear elastic Orthotropic

Figure 10: Mechanical model of the fuselage including structural domains (orange) and fluid domain (blue). 360

365

The outer skin of the fuselage is made of orthotropic CFRP with ten layers by which homogenized values are derived using the classical laminate theory. A quadrilateral 9-node shell element with quadratic polynomial ansatzfunctions is applied, combining structural disc and plate (Reissner-Mindlin) formulations. Hence, in-plane waves and bending waves are represented which is necessary for the complex cylindrical structure. Nevertheless, bending waves are expected to dominate the behavior of the thin structures which is determining the necessary mesh size. The outer skin is quite thin compared to all other parts which yields the smallest bending wave length λmin in the entire aircraft structure. The thinnest outer skin field within the area of excitation has a thickness of tmin = 0.0015 m. λmin at the highest frequency fmax can be estimated by Eq. (29) for an infinite homogeneous plate [36]. s B 2π 4 (29) λmin = √ ρ 2πfmax s tmin Et3

370

min is the constant bending stiffness (with the Young’s modulus E and the Poisson’s ratio ν) and ρs is B = 12(1−ν) the structural density. This estimation is conservative as the circular stiffener at the boundary of each segment

13

375

380

(see Fig. 10) increases the stiffness of the system and so λmin . Further, the minimum bending wave length is estimated for the thinnest skin field. The mesh size is directly derived by this value and taken for all parts of the fuselage resulting in a well structured mesh with coincident nodes at the interfaces between fluid and structural domains. The estimated wave lengths for the outer skin (thinnest field), the floor, the sidewall panel, the cabin fluid and the insulation are depicted in Fig. 11. The grey lines indicate the minimum wave length which can be resolved by the finally chosen mesh sizes 0.200, 0.150 and 0.100 m. The remaining numerical error can be assessed by comparing the three meshes (see Sec. 4). For the sidewall panel, which is a sandwich structure explained below, again, the classical laminate theory is applied to roughly estimate the bending wave length. It can be stated with a high degree of certainty that the wave length in that structure is not crucial within the entire frequency range. Between 100 and 200 Hz an intersection between the wave lengths of the insulation and the sidewall panel occurs. At this coincidence frequency, a high sound transmission into the cabin can be expected as the sound radiation is maximal.

Wave length λ (m)

101 Cabin fluid Insulation Sidewall Panel Floor Outer skin 100 200 mm mesh 150 mm mesh 100 mm mesh 10−1

102

103 Frequency (Hz)

Figure 11: Conservatively estimated wave lengths λ for different domains of the fuselage and resolved maximum wave length λ according to the applied mesh sizes (grey horizontal lines).

385

The floor, the rear bulk head and all stiffeners are similarly made of orthotropic CFRP and represented by 9-node shell elements in the model. In these parts, a thickness distribution is also applied in dependence on the given preliminary aircraft design data. Damping in all structural parts is generally considered by setting a global loss factor of η = 0.01 which is an approximation for complex structures with many joints [36]. Again, due to systematic modeling errors coming along with such simplifications, a valid comparison of the two configurations is still expected. The Young’s modulus E of the linear elastic materials in all structures becomes complex according to Eq. (30). E = E(1 + iη)

390

395

(30)

The generic sidewall panel consists of a typical sandwich structure made of an aramid honeycomb core surrounded by glass fiber reinforced plastic (GFRP). Instead of resolving each comb in the core, an approach by Estorff [37] is applied. The honeycomb core is modeled with a homogenized 3D continuum formulation while the GFRP layers are represented by shell sharing the 3D FE nodes. The cross section of the sandwich panel is depicted in Fig. 12 in which the grey elements are 27-node hexahedrons sharing their nodes with the orange 9-node shells. Material data for the two domains in the sandwich structure is taken from literature [38, 39]. 3D Continuum Linear elastic Orthotropic Homogenized core

GFRP Layer Shell Linear elastic Isotropic

Figure 12: FE model of the generic sidewall panel (sandwich) with 3D continuum (grey) and two GFRP layers (orange).

For both, the cabin fluid and the insulation, the Helmholtz equation is applied as model and discretized by 27-node hexahedrons with quadratic ansatzfunctions using an acoustic pressure formulation. The speed of sound cf and the density ρf of the fluid are complex and frequency-dependent in the equivalent fluid model which is applied for the glass wool in order to model the poro-elastic and damping characteristics. Material data 14

400

is taken from literature [40]. For the cabin fluid, real values are applied as first approach whereby a damped fluid and a realistic modeling of the passenger cabin is planned in future work. A strong coupling is applied between the adjacent structural (outer skin, sidewall panel and floor) and fluid domains (insulation and cabin). As shear stresses are neglected in both the equivalent and the ideal fluid domain, the normal displacement ξ n of the shells is taken into account as stated in Eq. (31) [41]. ρf ω 2 ξ n =

405

410

∂p ∂n

(31)

Here, ω is the angular frequency and ρf is the fluid density. The coupled degrees of freedom (dof) are the normal displacement ξ n and the acoustic pressure p. p is the complex amplitude of the pressure fluctuation in the frequency domain while p0 is generally used for the instantaneous pressure fluctuation in the time domain. In the FE formulation, the shell domain (Eq. (32)) and the fluid domain (Eq. (33)) are linked by means of the coupling matrix C (Eq. (34)) which is evaluated at the interface Γ. C is calculated applying the ansatzfunctions of the adjacent (here: coincident) structural element Ns and the fluid element Nf for the relevant dofs ξ (i) and p(i) , respectively.

Kf −


Ks − ω 2 Ms ξ (i) = Cp(i) !

(32)

p(i) = ρf ω 2 CT ξ (i)

(33)

ω2 Mf c2f

Z C=

NT s Nf dΓ

(34)

In the Eq. (32) and (33), Ks (Kf ) is the stiffness (compressibility) matrix, Ms (Mf ) is the mass matrix and cf is the speed of sound in the fluid domain. Inserting the coupling, the bandwidth of the system matrix is increased significantly. Due to the double wall structure, four interfaces must be considered: 415

420

1. 2. 3. 4.

Outer surface – insulation Outer GFRP layer of sidewall panel – insulation Inner GFRP layer of sidewall panel – cabin Floor – cabin

This leads to a highly complex problem with high computational costs compared to a solution of each single domain. Corresponding solution times and memory requirements are depicted in Tab. 2. If finer meshes shall be investigated in future work, a different solver strategy is necessary as the required memory of the direct solver increases exponentially. The numerical error of the model decreases with finer meshes. A finer mesh size Table 2: Discretisation levels of the fuselage model, according solution times per frequency sample (direct mumps solver at single cpu on phoenix cluster (TU Braunschweig)) and needed memory (direct mumps solver).

Mesh size DOF Solution time per sample Required memory per sample

425

(m) (1000) (min) (GB)

0.200 462 12 10

0.150 769 30 20

0.100 1681 165 57

affects not only the resolution of waves, but also the load input by the fluctuating pressure. The input power converges with a finer mesh as a constant value is assumed per element. For each shell element’s central node of the outer skin, frequency-dependent amplitude and phase values are calculated on the basis of a next neighbor search within the CAA results. The CAA results at these points are transformed into the frequency domain by a Fast Fourier Transformation (FFT). 4. Results

430

435

Finally, the modeling chain introduced in Sec. 3 delivers the sound pressure distribution over frequency in the passenger cabin fluid. Serving as example, in Fig. 13, the SPL at seat 35 (ear-height) is shown for both engine configurations. The small picture indicates the position of this exemplary chosen seat. Comparing the UHBR engine aircraft configuration with the BPR5 engine aircraft configuration, a much smaller SPL at seat 35 is estimated by the model in the entire frequency range. An obvious increase can be observed at f ≈ 140 Hz and at f ≈ 540 Hz. The transmission loss of a similar structure (equal data basis) has been investigated in [42] and shows minima in these frequencies as well. The first increased SPL corresponds with the typical minimum 15

440

of the transmission loss curve and is also predicted as coincidence frequency between the sidewall panel and the insulation (see Fig. 11). In [42], a fuselage section is investigated with a mean value for the outer skin’s thickness instead of the thickness distribution applied here. The second pressure peak in Fig. 13 at f ≈ 540 Hz particularly corresponds to the second local minima in the TL curve of the investigation in [42]. In this case, the outer skin’s bending wave length matches the insulation’s wave length which lead to a high sound transmission into the cabin at this frequency. However, this is an indicator as the mean value of the outer skins thickness matches. 100 BPR5 cabin UHBR cabin SPL (dB re 2e-5 Pa)

80

60

40 Seat 35 20 100

200

300

400

500 600 Frequency (Hz)

700

800

900

1000

Figure 13: SPL as a function of frequency at seat 35 for both engine configurations; Cabin noise results calculated with the finest mesh (he = 100 mm).

445

As stated in Sec. 3.3, the mechanical model of the fuselage underlies a couple of assumptions introducing systematic errors in particular. In Fig. 14, the difference between the two configurations ∆SPL(f) (see Eq. (35)) is shown for seat 35 in third octave bands for the three applied meshes. ∆SPL(f ) = SPLUHBR (f ) − SPLBPR5 (f )

Due to the mesh refinement, a change of these values can be observed without a clear convergence. In further studies, finer meshes will be investigated to show a convergence of the numerical error in the model. Nevertheless, the cabin noise induced by jet noise is much quieter for UHBR engines compared to conventional BPR5 engines of the second generation. The sound reduction potential can be expected at around 20 dB above 50 Hz. In lower frequency ranges, the sound reduction is smaller but still around 10 dB. 0 ∆SPL (dB)

450

(35)

200 mm 150 mm 100 mm

−10 −20 −30 100

200

300

400

500 600 Frequency (Hz)

700

800

900

1000

Figure 14: ∆SPL (according to Eq. (35) corresponding to the benefit by the UHBR engine) in third octave band at seat 35 for three different meshes.

Comparing each seat is not representative for the entire cabin, particularly since damping is not yet considered within the cabin fluid leading to local effects. A clear dominance of mode shapes in the cabin yields a high

16

455

dynamic in the frequency response. Therefore, the mean square sound pressure p2 (f ) of all seats Nseats is calculated, according to Eq. (36). The level SPL(f ) is calculated according to Eq. (37).

p2 (f ) =

2 PNseats (f ) p i=1 i

SPL(f ) = 10log10

460

(36)

Nseats p2 (f ) p2ref

! (37)

Accordingly, in Fig. 15, the SPL(f ) in the cabin of the two engine configurations is shown. Furthermore, the maximum occurring SPL on the outer skin (CAA excitation) is plotted over frequency giving an impression of the sound transmission loss. As expected, the difference between the outer excitation and the occurring SPL in the cabin increases with frequency. The pressure differences on the outer skin are not similarly transferred into the cabin. Rather, depending on the double wall sound transmission characteristics and the loading, the curves are pretty close in lower frequency regions and constantly different (≈ 20 dB) above 200 Hz. BPR5 outer skin BPR5 cabin UHBR outer skin UHBR cabin

SPL (dB re 2e-5 Pa)

100

80

60

40 100

200

300

400

500 600 Frequency (Hz)

700

800

900

1000

Figure 15: SPL as a function of frequency for both engine configurations; Cabin noise results calculated with the finest mesh (he = 100 mm).

In addition, ∆SPL(f ) is depicted in Fig 16 for different meshes in third octave bands. Due to the mean values over all seats, a mesh refinement has less influence on this more general curve. Comparing with Fig. 14, the fluctuations are smaller. Nevertheless, the sound reduction performance by the UHBR engine is similar.

∆SPL (dB)

0 200 mm 150 mm 100 mm

−10 −20 −30 100

200

300

400

500 600 Frequency (Hz)

700

800

900

1000

Figure 16: ∆SPL as a function of frequency in third octave band for three different meshes. 465

In Fig. 17, all seats are shown with a corresponding difference in the sum level. In addition, the maximum occurring excitation in dependence on x is plotted on the outer skin. As the engines are mounted differently, the maximum excitation is shifted to the back of the aircraft in case of the UHBR engine. As the top view is plotted, the distance of the two engines cannot be seen in Fig. 17. In fact, the two engine’s axes have the 17

470

475

same distance to the cabin’s center. Hence, as the UHBR engine has a larger diameter, the turbulent shear layer by the jet is closer to the outer surface. However, by introducing an UHBR engine instead of a BPR5 engine, the overall sum level is decreased between 21 and 24 dB, according to the applied models. This value is highly dominated by the large reduction at high frequencies. The previous graphs and interpretations have emphasized a much lower difference at frequencies below 100 Hz. Finally, it can be stated that the jet noise by an UHBR engine configuration in general induced much less cabin noise compared to a conventional engine configuration which confirms the hypothesis of that contribution. The mainly systematic modeling errors are not expected to change this clear tendency. SPLΣ (dB re 2e-5 Pa) 130 120 UHBR

110

BPR5 -22.4 -21.9 -22.4 -23.0 -23.0 -23.0 -22.8 -22.2 -22.2 -22.0 -23.3 -23.0 -22.8 -21.6 -21.5 -21.7 -23.3 -22.2 -20.8 -21.5 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

y

100 90

x

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -21.9 -22.0 -22.7 -22.3 -22.7 -22.7 -22.8 -21.8 -22.0 -23.4 -23.5 -23.4 -23.6 -23.7 -24.6 -24.0 -22.9 -23.8 -21.9 -21.1

Figure 17: Sum level reduction of UHBR engine configuration at each seat and circumferential maximum sum level max(SPLΣ (x)) at the outer skin in dependence on x coordinate; Solid: BPR5 engine; Dashed: UHBR engine.

5. Conclusion

480

485

490

495

500

In this contribution, a numerical modeling chain is presented for the simulation of cabin noise in dependence on jet noise. The numerical methods are applied for the comparison of an Ultra-High-Bypass Ratio engine configuration with a conventional engine configuration. The jet is considered as noise source for both configurations, respectively. The two configurations are investigated in two individual Computational Aeroacoustics simulations. A novel approach to investigate Ultra-High-Bypass Ratio engines with non-zero co-flow conditions is introduced and applied successfully. Using the difference velocity between jet and co-flow enables a solution of both engine configurations. By use of PIANO [11] in combination with the Fast Random Particle Mesh method FRPM [12], pressure fluctuations on the outer skin of a research aircraft are computed. The resulting pressure values are much higher in the setup with the conventional engine. RANS computations of the outer flow conducted with TAU [9, 10] serve as basis. Considering a weak coupling, a finite element model of a research aircraft fuselage is excited by the received pressure on the outer skin and solved by the in-house code elPaSo [13]. Besides the outer skin and circular stiffeners, the model includes the insulation, the sidewall panels and the cabin fluid. Main assumptions for the FE model are linearity, stationarity, a symmetric loading and response and a neglected front partition of the aircraft. However, the results show a much lower sound pressure level in the cabin at all seat positions for the Ultra-High-Bypass Ratio engine. In sum levels, the reduction is between 21 and 24 dB. The authors expect the potential modeling errors to be mainly systematic and that the major sound source for cabin noise in future aircraft with UHBR engines during cruise flight may be within the turbulent boundary layer. On the basis of this model, future work will be conducted. First, a deeper investigation of some applied model assumptions (e.g. strong coupling and damping models for the cabin fluid) in the entire modeling chain is planned. Second, further application cases such as different noise sources (e.g. turbulent boundary layer) and a propeller engine will be investigated. Finally, the uncertainties of the complex noise transmission problem are planned to be quantified for which the basics are shown in [42]. Acknowledgement

505

The authors would like to thank the Collaborative Research Center 880 of the German Research Foundation and its graduate research program Graduate College for the financial support.

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