# Pressure Loss in Ducts by Dissipative Splitter Silencers: Comparative Study of Standardized, Numerical and Experimental Results

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Formulation

#### 2.1. The Formulation in ISO 14163

#### 2.2. The Formulation in VDI 2081-1

## 3. Numerical Model

## 4. Experimental Setup

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**A 2D scheme of the studied system, composed of two dissipative splitter silencers embedded in a duct.

**Figure 2.**Geometry of the implemented numerical model with (

**a**) rectangular profiles and (

**b**) semihexadecagonal profiles in the silencer.

**Figure 3.**A 3D model of the test bench setup used for the experimental measurements of pressure loss.

**Figure 4.**(

**a**) Sampling probes for the pressure in the walls of the duct, (

**b**) position of the splitter silencers in the duct.

**Figure 6.**Numerical result of the variation of the flow velocity along the duct as a function of the position and the input face velocity in splitter silencers with (

**a**) rectangular and (

**b**) semihexadecagonal profiles.

**Figure 7.**Pressure loss in splitter silencers with (

**a**) rectangular and (

**b**) semihexadecagonal profiles as a function of the input face velocity, ${U}_{0}$. The dashed black lines show the trend lines followed by the experimental results, used to obtain the fitting equation.

**Figure 8.**Coefficient of determination ${R}^{2}$ between (

**a**) analytical (ISO) and experimental results and (

**b**) numerical and experimental results for the configuration of splitter silencers with rectangular profiles.

**Figure 9.**Coefficient of determination ${R}^{2}$ between (

**a**) analytical (ISO) and experimental results and (

**b**) numerical and experimental results for the configuration of splitter silencers with semihexadecagonal profiles.

**Table 1.**Values of the coefficients for the calculation of the pressure loss coefficient (Equation (5)) in VDI 2081-1.

Thickness of Splitter | ${\mathbf{a}}_{1}$ | ${\mathbf{a}}_{2}$ | ${\mathbf{b}}_{1}$ | ${\mathbf{b}}_{2}$ |
---|---|---|---|---|

100 mm | 0.235 | 0.017 | −2.78 | −2.70 |

200 mm | 0.255 | 0.015 | −2.82 | −2.91 |

300 mm | 0.294 | 0.0167 | −2.83 | −2.95 |

**Table 2.**Reynolds number, Darcy friction factor and major friction loss as a function of the input face velocity.

${\mathbf{U}}_{0}$ [m/s] | $\mathbf{Re}$ | ${\mathbf{f}}_{\mathbf{D}}$ | ${\mathbf{h}}_{\mathbf{f}}$ [m] |
---|---|---|---|

1 | 39,841 | 0.0222 | 0.02 |

2 | 79,681 | 0.0192 | 0.06 |

3 | 119,522 | 0.0178 | 0.14 |

4 | 159,363 | 0.0169 | 0.24 |

5 | 199,203 | 0.0162 | 0.38 |

6 | 239,044 | 0.0158 | 0.54 |

7 | 278,884 | 0.0154 | 0.74 |

8 | 318,725 | 0.0151 | 0.97 |

9 | 358,566 | 0.0148 | 1.22 |

10 | 398,406 | 0.0146 | 1.51 |

11 | 438,247 | 0.0144 | 1.83 |

12 | 478,088 | 0.0142 | 2.18 |

13 | 517,928 | 0.0141 | 2.55 |

14 | 557,769 | 0.0140 | 2.96 |

15 | 597,610 | 0.0138 | 3.40 |

16 | 637,450 | 0.0137 | 3.87 |

17 | 677,291 | 0.0136 | 4.37 |

18 | 717,131 | 0.0136 | 4.90 |

19 | 756,972 | 0.0135 | 5.46 |

20 | 796,813 | 0.0134 | 6.05 |

**Table 3.**Pressure loss (in Pascals) obtained with ISO 14163, VDI 2081-1, FEM and experimental measurements for the system of splitters with rectangular profiles.

${\mathbf{U}}_{0}$ [m/s] | ISO 14163 | VDI 2081-1 | FEM | Experimental |
---|---|---|---|---|

5 | 135 | 114 | 153 | 106 |

10 | 542 | 455 | 604 | 538 |

15 | 1218 | 1023 | 1378 | 1295 |

20 | 2166 | 1818 | 2519 | 2378 |

**Table 4.**Pressure loss (in Pascals) obtained with ISO 14163, VDI 2081-1, FEM and experimental measurements for the system of splitters with semihexadecagonal profiles.

${\mathbf{U}}_{0}$ [m/s] | ISO 14163 | VDI 2081-1 | FEM | Experimental |
---|---|---|---|---|

5 | 77 | 114 | 110 | 98 |

10 | 308 | 455 | 411 | 386 |

15 | 692 | 1023 | 914 | 859 |

20 | 1230 | 1818 | 1640 | 1517 |

**Table 5.**Difference between the predicted pressure loss (in Pascals) obtained with ISO 14163, VDI 2081-1 and FEM with that of experimental measurements for the system of splitters with rectangular profiles.

${\mathbf{U}}_{0}$ [m/s] | ISO 14163 | VDI 2081-1 | FEM |
---|---|---|---|

5 | 29 | 8 | 47 |

10 | 4 | −83 | 66 |

15 | −77 | −272 | 83 |

20 | −212 | −560 | 141 |

**Table 6.**Difference between the predicted pressure loss (in Pascals) obtained with ISO 14163, VDI 2081-1 and FEM with that of experimental measurements for the system of splitters with semihexadecagonal profiles.

${\mathbf{U}}_{0}$ [m/s] | ISO 14163 | VDI 2081-1 | FEM |
---|---|---|---|

5 | −21 | −16 | 12 |

10 | −78 | −69 | 25 |

15 | −167 | −164 | 55 |

20 | −287 | −301 | 123 |

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**MDPI and ACS Style**

Chmielewski, B.; Herrero-Durá, I.; Nieradka, P.
Pressure Loss in Ducts by Dissipative Splitter Silencers: Comparative Study of Standardized, Numerical and Experimental Results. *Appl. Sci.* **2021**, *11*, 10998.
https://doi.org/10.3390/app112210998

**AMA Style**

Chmielewski B, Herrero-Durá I, Nieradka P.
Pressure Loss in Ducts by Dissipative Splitter Silencers: Comparative Study of Standardized, Numerical and Experimental Results. *Applied Sciences*. 2021; 11(22):10998.
https://doi.org/10.3390/app112210998

**Chicago/Turabian Style**

Chmielewski, Bartosz, Iván Herrero-Durá, and Paweł Nieradka.
2021. "Pressure Loss in Ducts by Dissipative Splitter Silencers: Comparative Study of Standardized, Numerical and Experimental Results" *Applied Sciences* 11, no. 22: 10998.
https://doi.org/10.3390/app112210998