# Experimental and Numerical Investigation of Novel Acoustic Liners and Their Design for Aero-Engine Applications

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## Abstract

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## 1. Introduction

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_{X}and noise), which impact people’s quality of life in the vicinity of airports and beyond. These emissions occur at all phases of the flight, with highest nuisance during take-off and landing. One way to reduce the noise emissions is to optimize the geometry of the fan, respectively the whole engine, which may interfere with contrary optimization requirements for fuel efficiency or other aircraft design criteria. Currently, an important part of the reduction of the emitted engine noise is obtained by liners (usually an array of cells covered by a perforate) installed in the nacelle intake and at other locations of the engine. To increase propulsive efficiency and reduce the gaseous emissions as well as the noise emissions, the increase of engine bypass ratios has proven to be very successful. While delivering the same thrust, larger fans rotate slower than the smaller ones which leads to lower rotor-stator interaction frequencies. To reduce the emitted tonal and broadband noise, standard liners would require a larger volume and increased depth to address the tonal components at lower frequency, which is conflicting with the limited design space and aerodynamic requirements. Most standard liners for aero-engine applications consist of a perforated face sheet, which is attached to a lightweight core structure and a rigid back plate underneath. This type of liner is called a single-degree-of-freedom liner, as each cell can be modeled individually as a simple spring-and-mass system—usually considered as a Helmholtz resonator (HR). To extend their relatively small first resonance bandwidth, several concepts for multi-degree-of-freedom liners exist. These include multi-layer liners consisting of two cell layers with a septum or “mesh cap” in between [1,2,3,4]. While these concepts offer a more broadband damping, they cannot lower the system’s first resonance frequency. In contrast, different concepts, such as folded cavities [1,2,3,4], active elements [5,6,7,8] or attached mass elements [6,9], offer the possibility for low frequency damping, with certain drawbacks and limitations connected to each of these concepts.

## 2. Acoustic Analysis of Helmholtz Resonator with Flexible Walls and Results

#### 2.1. Experimental Setup for the HR

^{2}and a depth of 50 mm when used as a normal Helmholtz resonator. This configuration of the resonator exhibits a Helmholtz resonance between 600–700 Hz. The one-quarter wave resonance frequency due to the cavity depth would be 1715 Hz but is altered by the presence of the face sheet yielding the above Helmholtz resonance frequency. The walls and back cavities can be attached parallel or orthogonal to the DUCT-R main axis and to each other due to the nearly cubical form. The presented modular setup therefore offers the possibility to change the shape of the flexible wall; the material and thickness of the flexible wall; the position of the flexible wall with respect to the resonator (and thereby the main duct); the size of the back cavity; and the number of flexible walls and back cavities attached to the main resonator. The investigated materials with their Young’s modulus and different thicknesses are shown in Table 1.

#### 2.2. Results of Experimental Investigations of the FHR Design

_{res}/V

_{cav}= 1, which does not correlate with the observed trend for other cavity sizes. This shift can be explained by a different thickness distribution over the investigated film area, which is caused by the manufacturing process.

## 3. Semi-Analytical Parameter Studies for FHR and PR Liner Concepts

#### 3.1. Result and Discussion of Parameter Studies for the FHR Concept

#### 3.2. Result and Discussion of Parameter Studies for PR Liner Concept

## 4. Structural Mechanics Analysis and Results

#### 4.1. Structural Design

#### 4.2. Materials

#### 4.3. Modeling and Numerical Implementation

#### 4.4. Constraints and Load Cases

- global pressure loads due to pressure differences between the face sheet and the back side of the back sheet
- local loads due to maintenance

#### 4.5. Results of the FEA

## 5. Design and Manufacturing Feasibility Study for Curved Acoustic Liners

#### 5.1. Design and Manufacturing Concept HR-Liner

#### 5.2. Design and Manufacturing Concept of Curved PR-Liner

## 6. Conclusions

#### 6.1. Experimental Investigation

#### 6.2. Models and Parameter Studies of FHR/PR Liner

#### 6.3. Structural Mechanical Analysis

#### 6.4. Design Concepts and Production

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Holistic approach of the presented research to analyze novel acoustic liners concepts considering experimental, analytical modeling, structural mechanical and manufacturing aspects.

**Figure 3.**(

**a**) ① Assembly of resonator, ② holder with film, ③ back cavity (here ~0.5 of resonator volume) and ④ back plate at the ⑤ DUCT-R; (

**b**) holder with square cut-out and (TPU) film.

**Figure 4.**Comparisons of different aspects in the dissipation in dependence of (

**a**) materials and thicknesses (constant back cavity and circular shaped cut-out), (

**b**) the size of the back cavity in relation to the resonator volume (same material and rectangular shaped cut-out), (

**c**) orientation of the back cavity in relation to the Duct (same material and circular shaped cut-out) and (

**d**) the shape of the cut-out (TPU_03 and same back cavity size).

**Figure 6.**Results of the parameter study of the Helmholtz resonator with flexible walls, (

**a**) variation of Young’s modulus $E$ and loss factor $\eta $, (

**b**) variation of plate thickness ${h}_{p}$, (

**c**) variation of plate diameter ${d}_{p}$, (

**d**) variation of second cavity height ${h}_{sc}$.

**Figure 8.**Results of the parameter study of the plate silencer, (

**a**) variation of Young’s modulus $E$ and loss factor $\eta $, (

**b**) variation of plate thickness ${h}_{p}$, (

**c**) variation of plate length ${l}_{p}$, (

**d**) variation of cavity height ${h}_{c}$.

**Figure 9.**(

**a**) Conventional HR liner and detailed honeycomb, (

**b**) Resonator liner with square honeycombs detail of the square cells with film (turquoise).

**Figure 11.**Workload of the perforated face sheets of the liner models (

**a**) HR liner, (

**b**) FHR liner with carbon fiber, (

**c**) FHR liner with PA6-GF.

**Figure 13.**Distribution plot of the principal stresses of the core walls for the (

**a**) HR-Liner; (

**b**) FHR-Liner type 1; (

**c**) FHR-Liner type 2 with ${t}_{sc}=1\mathrm{mm}$ and ${l}_{scP}=5\mathrm{mm}$; (

**d**) FHR-Liner type 2 with ${t}_{sc}=0.25\mathrm{mm}$ and ${l}_{scP}=5\mathrm{mm}$.

**Figure 14.**(

**a**) Process of cutting the components of the resonator cavity out of sheet material, i.e., water jet or laser cutting, (

**b**) curved frame with slits, the stringer with and without cut-outs for the flexible film.

**Figure 15.**(

**a**) Process of pretension the film using a force-controlled set-up including clamps and weights and the subsequent conservation of the resulting stress state by applying a fixing frame, (

**b**) necessary components for ultrasonic welding including welding die, lower support carrying the stringers and the pre-tensioned film, (

**c**) rectangular sonotrode with its cross-section as well as the final setup for ultrasonic welding of the film and the stringer, (

**d**) stringers with attached films.

**Figure 16.**Design study of a curved FHR liner with the perforated face sheet including active and passive cavities, the covering face sheet and the strip slotted cavity structure.

**Figure 17.**(

**a**) Schematic thermoforming process of the resonator cavity, (

**b**) joining process of the curved and pre-tensioned film and the cavity, (

**c**) cavity support with functional elements such as the drainage channel and mounts for attaching the guard panel, (

**d**) design concept of the barrel-shaped PR-liner.

Thickness mm | Aluminum (Alu) 70,000 MPa | Poly Propylene (PP) 1600 MPa | Thermoplastic Polyurethan (TPU) 16 MPa | Polyamide 6 (PA6) 800 MPa | Polyphenylene Sulphide (PPS) 2400 MPa | Polyether Ether Ketone (PEEK) 2800 MPa |
---|---|---|---|---|---|---|

0.001 | x | |||||

0.01 | x | x | x | x | x | |

0.02 | x | |||||

0.03 | x | |||||

0.04 | x |

Parameter | Symbol | Unit | Value, Value Range | Design Point |
---|---|---|---|---|

Common parameters for both concepts | ||||

Duct height | ${h}_{\mathrm{d}}$ | mm | 60 | 60 |

Duct width | ${w}_{\mathrm{d}}$ | mm | $\infty $ | $\infty $ |

Young’s modulus | $E$ | MPa | $E\in \left[{10}^{1};{10}^{4}\right]$ | $14$ |

Poisson ratio | $\nu $ | - | $0.48$ | $0.48$ |

Loss factor | $\eta $ | - | $\eta \in \left[0.65;0.008\right]$ | $0.53$ |

Density | $\rho $ | kg/m^{3} | $1080$ | $1080$ |

Plate thickness | ${h}_{\mathrm{p}}$ | mm | ${h}_{\mathrm{p}}\in \left[0.1;0.5\right]$ | 0.3 |

FHR specific parameters | ||||

Plate diameter | ${d}_{\mathrm{p}}$ | mm | ${h}_{\mathrm{p}}\in \left[12;18\right]$ | 15 |

Cell cross Section | ${A}_{\mathrm{cell}}$ | mm^{2} | $19\times 19$ | $19\times 19$ |

Face sheet porosity | $\sigma $ | - | 2.6% | 2.6% |

Face sheet thickness | ${h}_{\mathrm{fs}}$ | mm | 2 | 2 |

Main cavity height | ${h}_{\mathrm{mc}}$ | mm | 40 | 40 |

Second cavity height | ${h}_{\mathrm{sc}}$ | mm | ${h}_{\mathrm{sc}}\in \left[5;20\right]$ | 10 |

Liner length | ${l}_{\mathrm{liner}}$ | mm | $200$ | 200 |

PR specific parameters | ||||

Cavity length | ${l}_{\mathrm{c}}$ | mm | ${l}_{\mathrm{c}}\in \left[30;90\right]$ | 65 |

Cavity height | ${h}_{\mathrm{c}}$ | mm | ${h}_{\mathrm{c}}\in \left[5;35\right]$ | 30 |

Cavity width | ${w}_{\mathrm{c}}$ | mm | $\infty $ | $\infty $ |

**Table 3.**Structure component, corresponding materials and thickness of the acoustic liner configuration.

Component | Face Sheet | Core | Back Plate | Cell Geometry | Mass [kg] | ||
---|---|---|---|---|---|---|---|

HR liner | 2/2 Twill Weave * CFRP (0.2 mm) | Aramid Paper (Nomex) (0.194 mm) | 10 UD-plies CFRP Orientation: $[0/0/45/90/-45{/}_{s}]$(1 mm) | 2 UD-plies GFRP Orientation: $[0/90$] (0.2 mm) | Honeycomb | 0.218 | |

FHR-Type 1 | Square Cells | 0.240 | |||||

FHR-Type 2 | PA6-GF–2/2 Twill Weave (1 mm) | PA6-GF–2/2 Twill Weave (1 mm) | PA6-GF–2/2 Twill Weave (1 mm) | PA6-GF–2/2 Twill Weave (1 mm) | Square Cells | 0.573 |

Material | Nomex with Phenolic Resin | PVC-Rigid Foam Core | Carbon Fiber with Epoxy Resin–Unidirectional- (Woven Fabric) | PA6-GF E-Glass | Glass Fiber with Epoxy Resin |
---|---|---|---|---|---|

Youngs Modulus ${E}_{1}$ [MPa] | 6034 | 70 | 129,000 (61,000) | 18,000 | 29,700 |

Youngs Modulus ${E}_{2}$ [MPa] | 5263 | 70 | 7380 (61,000) | 18,000 | 29,700 |

Youngs Modulus ${E}_{3}$ [MPa] | 4427 | 70 | 7380 (6900) | 22,000 | 8600 |

Poisson’s ratio ${\nu}_{12}$ | 0.316 | 0.3 | 0.319 (0.04) | 0.17 | 0.17 |

Poisson’s ratio ${\nu}_{13}$ | 0.327 | 0.3 | 0.319 (0.3) | 0.17 | 0.17 |

Poisson’s ratio ${\nu}_{23}$ | 0.317 | 0.3 | 0.4 (0.3) | 0.49 | 0.17 |

Shear Modulus ${G}_{12}$ [MPa] | 2142 | 27 | 4480 (3300) | 7692 | 5300 |

Shear Modulus ${G}_{13}$ [MPa] | 1588 | 27 | 4480 (2700) | 7692 | 3070 |

Shear Modulus ${G}_{23}$ [MPa] | 1865 | 27 | 2636 (2700) | 7382 | 3070 |

Density $\rho $ [$\mathrm{kg}/{\mathrm{m}}^{3}$] | 1185 | 60 | 1560 (1420) | 1800 | 2200 |

Fiber processing type | - | - | Unidirectional (Twill Weave 2/2) | Twill 2/2 | Twill 2/2 |

Stress limits | |||||

Tensile Strength ${R}_{1}^{\left(+\right)}$ [MPa] | 62.3 | 1.5 | 2553 (805) | 380 | 367 |

Tensile Strength ${R}_{2}^{\left(+\right)}$ [MPa] | 48.2 | 1.5 | 42 (805) | 380 | 367 |

Tensile Strength ${R}_{3}^{\left(+\right)}$ [MPa] | 48.2 | 1.5 | 42 (50) | - | 128 |

Compression Strength ${R}_{1}^{\left(-\right)}$ [MPa] | −85 | 0.96 | 1239 (509) | - | 549 |

Compression Strength ${R}_{2}^{\left(-\right)}$ [MPa] | −78 | 0.96 | 199 (509) | - | 549 |

Compression Strength ${R}_{3}^{\left(-\right)}$ [MPa] | −78 | 0.96 | 199 (170) | - | 39 |

Shear strength ${R}_{12}$ [MPa] | 71.8 | 0.93 | 138 (125) | 64 | 97 |

Shear strength ${R}_{13}$ [MPa] | 71.8 | 0.93 | 138 (65) | 64 | 97 |

Shear strength ${R}_{23}$ [MPa] | 71.8 | 0.93 | 138 (65) | 64 | 97 |

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**MDPI and ACS Style**

Neubauer, M.; Genßler, J.; Radmann, V.; Kohlenberg, F.; Pohl, M.; Böhme, K.; Knobloch, K.; Sarradj, E.; Höschler, K.; Modler, N.;
et al. Experimental and Numerical Investigation of Novel Acoustic Liners and Their Design for Aero-Engine Applications. *Aerospace* **2023**, *10*, 5.
https://doi.org/10.3390/aerospace10010005

**AMA Style**

Neubauer M, Genßler J, Radmann V, Kohlenberg F, Pohl M, Böhme K, Knobloch K, Sarradj E, Höschler K, Modler N,
et al. Experimental and Numerical Investigation of Novel Acoustic Liners and Their Design for Aero-Engine Applications. *Aerospace*. 2023; 10(1):5.
https://doi.org/10.3390/aerospace10010005

**Chicago/Turabian Style**

Neubauer, Moritz, Julia Genßler, Vincent Radmann, Fleming Kohlenberg, Michael Pohl, Kurt Böhme, Karsten Knobloch, Ennes Sarradj, Klaus Höschler, Niels Modler,
and et al. 2023. "Experimental and Numerical Investigation of Novel Acoustic Liners and Their Design for Aero-Engine Applications" *Aerospace* 10, no. 1: 5.
https://doi.org/10.3390/aerospace10010005