# Validation of the Lattice Boltzmann Method for Simulation of Aerodynamics and Aeroacoustics in a Centrifugal Fan

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Setup

#### 2.1.1. Fan Characteristics

#### 2.1.2. Fan Test Rig

#### 2.1.3. Aerodynamic Performance Measurements

#### 2.1.4. Acoustic Measurements

#### 2.2. Numerical Setup

#### 2.2.1. Lattice Boltzmann Method

#### 2.2.2. Simulation Model

## 3. Results and Discussion

#### 3.1. Global Performance

#### 3.2. Acoustic Results

#### 3.3. Flow Topology

#### 3.4. Analysis of the Acoustic Field

- ①
- Tongue area;
- ②
- Blade passage;
- ③
- Gap between impeller and housing;
- ④
- Wake of the impeller’s trailing edge.

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BPF | Blade passing frequency |

CFD | Computational Fluid Dynamics |

EXP | Experiment |

FWH | Ffowcs Williams and Hawkings |

LBM | Lattice Boltzmann Method |

LES | Large Eddy Simulation |

LRF | Local Reference Frame |

RANS | Reynolds Averaged Navier Stokes |

SIM | Simulation |

URANS | Unsteady Reynolds Averaged Navier Stokes |

VLES | Very Large Eddy Simulation |

VR | Variable Resolution |

Latin symbols | |

c | Velocity |

D | Outer diameter of impeller |

f | Frequency |

f | Velocity distribution function |

${L}_{p}$ | Sound pressure level |

$Ma$ | MACH Number |

n | Rotational speed |

${n}_{i}$ | Total number of measurement points |

${n}_{j}$ | Total number of frequency bands |

${P}_{E}$ | Electrical power |

p | Pressure |

${p}_{0}$ | Reference sound pressure |

Q | Volume flow |

u | Circumferential velocity at impeller’s outlet |

$x,y,z$ | Cartesian coordinates |

Greek symbols | |

$\mathsf{\Delta}$p | Pressure rise |

$\mathsf{\Delta}$x | Lattice size |

$\rho $ | Density |

$\eta $ | Efficiency |

$\xi $ | Particle velocity |

$\omega $ | Collision frequency |

Subscripts | |

1 | Inflow |

2 | Outflow |

amb | Ambient |

char | Characteristic |

eq | Equilibrium |

i | Measurement point |

j | Frequency band |

m | Motor |

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**Figure 2.**Schematic view of the fan test rig as top view (

**a**) and photograph of the measurement setup inside the anechoic room facility (

**b**).

**Figure 6.**Pressure rise coefficient $\psi $ and efficiency $\eta $ (

**a**) as well as total sound pressure ${\overline{L}}_{p,e}$ (

**b**) as function of volume flow rate $Q/{Q}_{opt}$

**Figure 7.**Acoustic spectra averaged over measurement positions M1 to M11 (shown in Figure 2a); the simulation’s cut-off frequency is marked in gray, the first (1 × BPF) and second (2 × BPF) blade passing frequency are indicated by dotted lines. BPF—blade passing frequency.

**Figure 8.**Total sound pressure ${\overline{L}}_{p,e}$ level in comparison to the first and second BPF peak levels ${L}_{p,{e}_{BP{F}_{1}}}$ and ${L}_{p,{e}_{BP{F}_{2}}}$ extracted from the acoustic spectra averaged over measurement positions M1 to M11 for experiment (EXP) and simulation (SIM).

**Figure 9.**Campbell diagram of rotational speed test for $Q/{Q}_{opt}=1.0$ at microphone position M10 determined by experiment.

**Figure 10.**Acoustic narrow band spectra of variation of rotational speed for $Q/{Q}_{opt}=1.0$ at microphone position M10 determined by simulation.

**Figure 11.**Illustration of the impeller and housing in gray and the evaluation plane through the center of the impeller in red as isometric view (

**a**), in x-direction (

**b**) and y-direction (

**c**); the black arrows in (

**c**) indicate the viewing direction.

**Figure 12.**Instantaneous velocity with respect to the containing reference frame superimposed with projected streamlines on the plane shown in Figure 11; the black arrow mark the stagnation point.

**Figure 13.**Instantaneous vorticity field on the plane shown in Figure 11.

**Figure 14.**Instantaneous isosurface of ${\lambda}_{2}$ values lower than $-5\times {10}^{6}{\mathsf{s}}^{2}$ colored by vorticity magnitude.

**Figure 15.**Isosurface of the pressure fluctuation filtered around BPF with values higher than 115 dB (top) and in a broadband range of 100–2500 Hz with values higher than $127.5$ dB (bottom); the numbers mark the identified main noise source locations: 1 tongue area; 2 blade passage; 3 gap between impeller and housing; 4 wake of the impeller’s trailing edge.

**Figure 16.**Wall sound pressure level of housing filtered around BPF (

**top**) and in a broadband range of 100–2500 Hz (

**bottom**).

**Figure 17.**Wall sound pressure level of impeller filtered around BPF (

**top**) and in a broadband range of 100–2500 Hz (

**bottom**).

Parameters | Settings |
---|---|

Sampling rate | 51,200 Hz |

Signal length | 10 s |

Bandwidth | 6.25 Hz |

Window | Hanning |

Overlapping of windows | 50% |

Averaging | linear |

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**MDPI and ACS Style**

Schäfer, R.; Böhle, M.
Validation of the Lattice Boltzmann Method for Simulation of Aerodynamics and Aeroacoustics in a Centrifugal Fan. *Acoustics* **2020**, *2*, 735-752.
https://doi.org/10.3390/acoustics2040040

**AMA Style**

Schäfer R, Böhle M.
Validation of the Lattice Boltzmann Method for Simulation of Aerodynamics and Aeroacoustics in a Centrifugal Fan. *Acoustics*. 2020; 2(4):735-752.
https://doi.org/10.3390/acoustics2040040

**Chicago/Turabian Style**

Schäfer, Rebecca, and Martin Böhle.
2020. "Validation of the Lattice Boltzmann Method for Simulation of Aerodynamics and Aeroacoustics in a Centrifugal Fan" *Acoustics* 2, no. 4: 735-752.
https://doi.org/10.3390/acoustics2040040