# A Porous Media Model for the Numerical Simulation of Acoustic Attenuation by Perforated Liners in the Presence of Grazing Flows

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## Abstract

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## Featured Application

**Passive control devices for combustion noise reduction in gas turbine engines and/or other general flow noises.**

## Abstract

## 1. Introduction

- Where the noise signal propagates in parallel with a perforated liner without a mean flow;
- Where the noise signal propagates in parallel with a perforated liner in the presence of a mean bias flow;
- Where the noise signal propagates in parallel with a perforated liner in the presence of a mean grazing flow;
- Where the noise signal propagates in parallel with a perforated liner in the presence of coexisting bias and grazing flows;
- Where the grazing flow is of higher temperatures.

## 2. Methods

#### 2.1. Background Theory

_{t}is the real liner thickness, d is the diameter of perforations,

_{b}is the bias flow velocity and U

_{ac}represents the acoustic velocity inside the perforations [32].

#### 2.2. Further Development of PVPM Model

#### 2.2.1. Extra Flow Resistance Due to Grazing Flow Effect

_{b}, is directly resolved and accounted for by the current PVPM model, as discussed by Jianguo et al. [32]. The flow resistance due to a bias flow does not need to be imposed in the pressure loss source terms. However, the effect of grazing flows was not included in the original homogenous PVPM model. As a consequence, the overall flow resistance r of a perforated liner represented by the PVPM model is required to be amended by the grazing flow-induced resistance, as shown in Equation (14):

_{b}is the bias flow-induced resistance for the porous media region which is resolved by the PVPM model [32].

#### 2.2.2. Extra Porous Media Region Thickness Corrections Due to Grazing Flows

#### 2.3. Numerical Schemes

#### 2.4. Acoustic Data Processing Method

## 3. Results

#### 3.1. Grazing Acoustic Signal without Flow

#### 3.1.1. Self-Designed Experiment Configuration

#### 3.1.2. Validation of the PVPM Model

#### 3.2. Grazing Acoustic Signal with Bias Flow

#### 3.3. Grazing Flow

#### 3.4. Simultaneous Grazing and Bias Flows

#### 3.5. Effects of Temperature of Grazing Flows

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Mesh distribution for CFD simulations employing the PVPM model: (

**a**) front view; (

**b**) cross-sectional view.

**Figure 5.**CFD and experimental comparison of absorption coefficients in sound grazing incidence conditions with closed cavity.

**Figure 6.**Test rig setup in the experiment by Eldredge and Dowling [21].

**Figure 7.**Numerical and experimental comparison of absorption coefficients at ${\mathrm{M}}_{\mathrm{in}}=0.023$ and zero grazing flow conditions [21].

**Figure 8.**Numerical and experimental comparison of absorption coefficients at ${\mathrm{M}}_{\mathrm{in}}=0.041$ and zero grazing flow conditions [21].

**Figure 9.**Numerical and experimental comparison of absorption coefficients variation with the bias flow speed in zero grazing flow conditions [21].

**Figure 10.**Test rig configuration for the investigation of grazing flow, Jing et al. [23].

**Figure 11.**Numerical and experimental comparison of normalized specific acoustic impedance as a function of the grazing flow Mach number for (

**a**) liner JG1, (

**b**) liner JG2, (

**c**) liner JG3 and (

**d**) liner JG4 [23].

**Figure 12.**Test rig setup in experiment for the investigation of simultaneous bias/grazing flow effect, Sun et al. [22].

**Figure 13.**Numerical and experimental comparison of normalized specific acoustic impedance for liner JGB1 under various bias/grazing flow conditions [22].

**Figure 14.**Numerical and experimental comparison of normalized specific acoustic impedance for liner JGB2 under various bias/grazing flow conditions [22].

**Figure 15.**Numerical and experimental comparison of normalized specific acoustic impedance for liner JGB3 under various bias/grazing flow conditions [22].

**Figure 16.**Schematic view of the test rig configuration in the experiment by Kabral [27].

**Figure 17.**CFD and experimental comparison of normalized specific acoustic impedance (${\mathrm{M}}_{\mathrm{g}}=0.12$) [27].

**Figure 18.**CFD and experimental comparison of normalized specific acoustic impedance (${\mathrm{M}}_{\mathrm{g}}=0.25$) [27].

Liner No. | Hole Diameter (mm) | Liner Circumferential Length (mm) | Liner Axial length (mm) | Pitch-y (mm) | Pitch-x (mm) | Porosity σ |
---|---|---|---|---|---|---|

H1 | 2.0 | 59.4 | 50 | 6.0 | 12 | 0.0338 |

H2 | 3.0 | 59.4 | 50 | 6.0 | 12 | 0.0762 |

H3 | 4.0 | 59.4 | 50 | 6.0 | 12 | 0.135 |

**Table 2.**Geometric specifications of the orifice liners from the experiment by Jing et al. [23].

Liner No. | Hole Diameter (mm) | Liner Thickness (mm) | Number of Orifices | Porosity |
---|---|---|---|---|

JG1 | 3 | 2 | 4 | 2.94% |

JG2 | 4.5 | 2 | 1 | 1.65% |

JG3 | 7 | 0.5 | 1 | 4% |

JG4 | 7 | 2 | 1 | 4% |

**Table 3.**Geometric specifications of the orifice liners, Sun et al. [22].

Liner No. | Hole Diameter (mm) | Liner Thickness (mm) | Number of Orifices | Porosity |
---|---|---|---|---|

JGB1 | 7 | 0.5 | 1 | 4% |

JGB2 | 7 | 2 | 1 | 4% |

JGB3 | 3 | 2 | 4 | 2.94% |

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**MDPI and ACS Style**

Wang, J.; Rubini, P.; Qin, Q.
A Porous Media Model for the Numerical Simulation of Acoustic Attenuation by Perforated Liners in the Presence of Grazing Flows. *Appl. Sci.* **2021**, *11*, 4677.
https://doi.org/10.3390/app11104677

**AMA Style**

Wang J, Rubini P, Qin Q.
A Porous Media Model for the Numerical Simulation of Acoustic Attenuation by Perforated Liners in the Presence of Grazing Flows. *Applied Sciences*. 2021; 11(10):4677.
https://doi.org/10.3390/app11104677

**Chicago/Turabian Style**

Wang, Jianguo, Philip Rubini, and Qin Qin.
2021. "A Porous Media Model for the Numerical Simulation of Acoustic Attenuation by Perforated Liners in the Presence of Grazing Flows" *Applied Sciences* 11, no. 10: 4677.
https://doi.org/10.3390/app11104677