# Acoustical Treatments on Ventilation Ducts through Walls: Experimental Results and Novel Models

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## Abstract

**:**

## 1. Introduction

## 2. Theory

## 3. Method

^{2}mock-up wall can be constructed (Figure 4a). The experimental part in [2] tested three different types of walls. Lab measurements yielded ${R}_{w}$ of 35, 46, and 54 dB according to ISO 717-1:2013 [41] and $STC$ of 35, 46, and 53 dB according to ASTM E413-16 [42]. The edges, between the mock-up wall and the heavy wall, were covered with sealant on all sides.

- External lagging with 50 mm stone wool, density of 100 kg/m
^{3}, closest to the wall with a length of 600 mm. - External lagging with 50 mm stone wool, density of 100 kg/m
^{3}, closest to the wall with a length of 1200 mm. - External lagging with 50 mm stone wool, density of 100 kg/m
^{3}, closest to the wall with a length of 1800 mm. - External lagging with 50 mm stone wool, density of 100 kg/m
^{3}, along the whole duct. - External lagging with 100 mm stone wool, density of 100 kg/m
^{3}, closest to the wall with a length of 1800 mm. The rest of the duct is covered with 50 mm stone wool, density of 100 kg/m^{3}.

- Wall A. Sound reduction index: ${R}_{w}=35\mathrm{dB}$ or sound transmission class: $STC=35\mathrm{dB}$
- Wall B. Sound reduction index: ${R}_{w}=46\mathrm{dB}$ or sound transmission class: $STC=46\mathrm{dB}$
- Wall C. Sound reduction index: ${R}_{w}=54\mathrm{dB}$ or sound transmission class: $STC=53\mathrm{dB}$

## 4. Theoretical Models with External Lagging

#### 4.1. Theoretical Models with External Lagging for Circular Ducts

#### 4.1.1. Theoretical Models When Circular Ventilation Ducts Are Partly Wrapped

#### 4.1.2. Theoretical Models When Circular Ventilation Ducts Are Completely Wrapped

#### 4.2. Theoretical Models with External Lagging for Rectangular Ducts

#### 4.2.1. Theoretical Models When Rectangular Ventilation Ducts Are Partly Wrapped

#### 4.2.2. Theoretical Models When Rectangular Ventilation Ducts Are Completely Wrapped

## 5. Results

#### 5.1. Measurement Results Compared to the Developed Theoretical Models

#### 5.2. Suspended Absorbent Ceilings: Estimated Calculations

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Theoretical models compared to measurements with external lagging as acoustic treatment. Ventilation duct with Ø315 mm through wall A with a sound reduction index of ${R}_{w}=$ 35 dB. External lagging is mounted at a partial length of 0.6 m (Treatment 1) with 50 mm stone wool, density of 100 kg/m

^{3}, closest to the wall.

**Figure A2.**Theoretical models compared to measurements with external lagging as acoustic treatment. Ventilation duct with Ø315 mm through wall B with a sound reduction index of ${R}_{w}=$ 46 dB. External lagging is mounted at partial lengths of 0.6–1.2 m (Treatment 1 and 2) with 50 mm stone wool, density of 100 kg/m

^{3}, closest to the wall.

**Figure A3.**Theoretical models compared to measurements with external lagging as acoustic treatment. Ventilation duct with Ø315 mm through wall A with a sound reduction index of ${R}_{w}=$ 35 dB. External lagging is mounted at partial lengths of 0.6–1.2 m (Treatment 1 and 2) with 50 mm stone wool, density of 100 kg/m

^{3}, closest to the wall.

**Figure A4.**Theoretical models compared to measurements with external lagging as acoustic treatment. Ventilation duct with Ø315 mm through wall B with a sound reduction index of ${R}_{w}=$ 46 dB. External lagging is mounted at partial lengths of 0.6–1.8 m (Treatment 1–3) and full length (Treatment 4) with 50 mm stone wool, density of 100 kg/m

^{3}, closest to the wall.

**Figure A5.**Theoretical models compared to measurements with external lagging as acoustic treatment. Ventilation duct with dimension: 700 × 250 mm through wall B with a sound reduction index of ${R}_{w}=$ 46 dB. External lagging is mounted at partial lengths of 0.6–1.8 m (Treatment 1–3) with 50 mm stone wool, density of 100 kg/m

^{3}, closest to the wall.

**Figure A6.**Estimated theory with suspended absorbent ceiling, Ceiling A, as acoustical treatment. Ventilation duct with dimensions of: Ø315, Ø630 and 700 × 250 mm through wall B with a sound reduction index of ${R}_{w}=$ 46 dB.

**Figure A7.**Estimated theory with suspended absorbent ceiling, Ceiling B, as acoustical treatment. Ventilation duct with dimensions of: Ø315, Ø630 and 700 × 250 mm through wall B with a sound reduction index of ${R}_{w}=$ 46 dB.

## Appendix B

Variable | Unit, SI |
---|---|

a | m |

b | m |

c_{0}, c_{L} | m/s |

d | m |

L | m |

M_{duct}, M_{wall} | m^{2} |

P | m |

q_{wrap} | kg/m^{2} |

S, S_{wall} | m^{2} |

Variable | Value: |

${f}_{1,315}$ | 638 Hz |

${f}_{1,630}$ | 319 Hz |

${f}_{1,700}$ | 245 Hz |

${f}_{e,315}$ | 336 Hz |

${f}_{e,630}$ | 168 Hz |

${f}_{R,315}$ | 5108 Hz |

${f}_{R,630}$ | 2554 Hz |

${f}_{L,700}$ | 1465 Hz |

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**Figure 1.**Illustration model of how sound travels from the sending room to the receiving room if only the surface area affects the sound transmission.

**Figure 2.**Illustration model of how sound travels from the sending room to the receiving room if the surface area and air diffusers affects the sound transmission.

**Figure 3.**Illustration model of how sound travels from the sending room to the receiving room if the surface area and air diffusers affects the sound transmission. Two areas on the ventilation duct in the sending room are marked with blue and green colors together with the letters a and b that describe different areas for acoustical treatments.

**Figure 4.**Pictures from the measurements in [2]: (

**a**) The finished mounted wall; (

**b**) Foam lining for rectangular duct; (

**c**) Cover cap for the circular duct: rubber lining, gypsum boards and sealant around the border; (

**d**) Cover cap for the rectangular duct: foam lining and gypsum boards.

**Figure 5.**Pictures from the measurements in [2] in one of the rooms: (

**a**) Circular 630 mm duct, treatment according to case 3; (

**b**) Circular 630 mm duct, treatment according to case 5; (

**c**) Circular 315 mm duct, treatment according to case 4; (

**d**) Rectangular duct, 700 × 250 mm, treatment according to case 4.

**Figure 6.**Theoretical models compared to measurements with external lagging as acoustic treatment. Ventilation duct with Ø315 mm through wall C with a sound reduction index of ${R}_{\mathrm{w}}=$ 54 dB. External lagging is mounted at partial lengths of 0.6–1.8 m (Treatment 1–3) and full length (Treatment 4) with 50 mm stone wool, density of 100 kg/m

^{3}, closest to the wall.

**Figure 7.**Theoretical models compared to measurements with external lagging as acoustic treatment. Ventilation duct with Ø630 mm through wall C with a sound reduction index of ${R}_{\mathrm{w}}=$ 54 dB. External lagging is mounted at partial lengths of 0.6–1.8 m (Treatment 1–3) and full length (Treatment 4 and 5) with 50 mm and 100 mm stone wool, density of 100 kg/m

^{3}, closest to the wall.

**Figure 8.**Theoretical models compared to measurements with external lagging as acoustic treatment. Ventilation duct with dimension: 700 × 250 mm through wall C with a sound reduction index of ${R}_{\mathrm{w}}=$ 54 dB. External lagging is mounted at partial lengths of 0.6–1.8 m (Treatment 1–3) and full length (Treatment 4 and 5) with 50 mm and 100 mm stone wool, density of 100 kg/m

^{3}, closest to the wall.

**Figure 9.**Estimated theory with a suspended absorbent ceiling, Ceiling A, as acoustical treatment. Ventilation duct with dimensions of Ø315, Ø630 and 700 × 250 mm through wall C with a sound reduction index of ${R}_{\mathrm{w}}=$ 54 dB.

**Figure 10.**Estimated theory with a suspended absorbent ceiling, Ceiling B, as acoustical treatment. Ventilation duct with dimensions of Ø315, Ø630 and 700 × 250 mm through wall C with a sound reduction index of ${R}_{\mathrm{w}}=$ 54 dB.

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**MDPI and ACS Style**

Nilsson, E.; Ménard, S.; Bard Hagberg, D.; Vardaxis, N.-G.
Acoustical Treatments on Ventilation Ducts through Walls: Experimental Results and Novel Models. *Acoustics* **2022**, *4*, 276-296.
https://doi.org/10.3390/acoustics4010017

**AMA Style**

Nilsson E, Ménard S, Bard Hagberg D, Vardaxis N-G.
Acoustical Treatments on Ventilation Ducts through Walls: Experimental Results and Novel Models. *Acoustics*. 2022; 4(1):276-296.
https://doi.org/10.3390/acoustics4010017

**Chicago/Turabian Style**

Nilsson, Erik, Sylvain Ménard, Delphine Bard Hagberg, and Nikolaos-Georgios Vardaxis.
2022. "Acoustical Treatments on Ventilation Ducts through Walls: Experimental Results and Novel Models" *Acoustics* 4, no. 1: 276-296.
https://doi.org/10.3390/acoustics4010017