# Validating Confined Flame Noise Simulation Using External Sensor

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Methods

_{4}and air into a burner (Figure 1) which was placed in confined space. The diagram of the setup is shown in Figure 2, and photographs of the experiment are shown in Figure 3. An external sensor (model UMIK-1 USB measurement-calibrated microphone) and a sound pressure level (SPL) meter (model Larson Davis 831) were placed a distance $\overrightarrow{r}=$ (3, 3, 6) inches from the center line of the outlet plane. The placement of the sensor can affect the amplitude of the measurements, particularly at the lower frequencies that are produced by combustion. The microphone must be placed in the far-field for its position which is accurately measured to be modeled with the acoustic analogy. The microphone was connected to the computer, and it simultaneously recorded the sound and measured the SPL spectrum using the REW software [17]. The SPL meter recorded the internal memory, then, the recorded data were transferred to the computer.

_{2}was used to purge the system post-combustion to remove any combustible gases from the setup and for calibrating the Bronkhorst mass flow controllers: 10 L/min for the air and 1 L/min for the CH

_{4}. The mass flow controllers were pre-loaded with the capability for measuring the liter per minute of air and CH

_{4}. The lean mixture was delivered with an air-to-fuel equivalence ratio $\mathsf{\lambda}$ = 1.05 at a flow rate of 7.7 L/min. The burner was placed in a (1.5 × 2.5 × 0.25) inch square pipe that was made from stainless steel 304 with rounded corners. The viewing chamber was aluminum with quartz windows. A digital single reflex lens (DSLR) camera was placed to record video and photos of the flame. The area from the base of the viewing chamber to the outlet of the square pipe was 27.5 inches. The burner outlet was a standard Bunsen burner design with a stabilizer, and it was positioned 7 inches from the bottom of the experimental duct.

## 3. Computational Methods

#### 3.1. Burner Geometry and Computation Grid

#### 3.2. Simulation Settings

^{−10}to resolve the small pressure perturbations, but not to slow down the simulation too greatly. The time step was set to 10 $\mathsf{\mu}\mathrm{s}$ to ensure stability and to reduce the computational time.

^{+}for the burner interior was consistently less than 5, with there being a maximum of 6.8. The y

^{+}for the burner exterior and pipe wall was less than 1 for all of the cells. A compressible wall function was utilized to calculate the thermal diffusivity based on the turbulent viscosity and turbulent Prandtl number.

^{−6}, and the kinetic energy and turbulent dissipation can be estimated from the burner geometry, and with these the mixing constant was estimated, ${C}_{mix}\approx $ 0.1.

## 4. Results and Discussion

#### 4.1. Flow Visualization

#### 4.2. Noise Results

## 5. Concluding Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Conflicts of Interest

## Nomenclature

${C}_{mix}$ | PaSR model mixing coefficient |

$k$ | Turbulent kinetic energy |

$\overrightarrow{r}$ | Distance vector |

$\dot{V}$ | Volumetric flow rate |

${y}^{+}$ | Dimensionless wall distance |

${\alpha}_{t}$ | Thermal diffusivity |

$\u03f5$ | Turbulent dissipation |

$\lambda $ | Fuel Equivalence Ratio |

${\nu}_{t}$ | Turbulent viscosity |

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**Figure 1.**(

**a**) Image of a Bunsen burner stabilizer, (

**b**) dimensional drawing of the stabilizer from the top, (

**c**) section view of the Bunsen burner revealing the small openings in the annulus, and (

**d**) the inverted flow domain for the simulation.

**Figure 5.**Still images from the video recordings demonstrating the wrinkling of the burner’s flame cone.

**Figure 6.**Contour of the flame temperature: (

**a**) LES and (

**b**) URANS in comparison with (

**c**) the experiment.

**Figure 7.**The y–z plane cut of the LES simulation for (

**a**) x-component velocity, (

**b**) y-component velocity, and (

**c**) pressure.

**Figure 8.**The y–z plane cut of the URANS simulation for (

**a**) x-component velocity, (

**b**) y-component velocity, and (

**c**) pressure.

**Figure 9.**The SPL spectrum for combustion in a solid blue line, air flow only in a dotted orange line, and no flow conditions in the dashed green line.

**Figure 10.**The SPL frequency spectrum for the measured noise (solid blue line) in comparison with the LES modeled noise (orange dashed line) and URANS modeled noise (green dash dotted line).

PIMPLE | nOuterCorrectors | 1 |

nCorrectors | 2 | |

nNonOrthogonalCorrectors | 1 | |

Solvers | rho | diagonal PBiCGStab|DILU PCG|DIC |

U|h|k|epsilon|Yi | ||

P | ||

Numerical Schemes | ddtSchemes | Euler |

gradSchemes | linear | |

divSchemes | limitedLinear |

Boundary | Pressure (Pa) | Temperature (K) | Velocity U (m/s) |
---|---|---|---|

Initial Field | uniform 101325 | uniform 300 | uniform (0 0 0) |

outlet | fixedValue | zeroGradient | pressureInletOutletVelocity |

inlet | zeroGradient | uniform 300 | flowRateInletVelocity |

wallPipe | zeroGradient | externalWallHeatFluxTemperature | noSlip |

wallBuner | zeroGradient | zeroGradient | noSlip |

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**MDPI and ACS Style**

Williamson, A.J.; Srivastava, S.; Sallam, K.A. Validating Confined Flame Noise Simulation Using External Sensor. *Sensors* **2022**, *22*, 8039.
https://doi.org/10.3390/s22208039

**AMA Style**

Williamson AJ, Srivastava S, Sallam KA. Validating Confined Flame Noise Simulation Using External Sensor. *Sensors*. 2022; 22(20):8039.
https://doi.org/10.3390/s22208039

**Chicago/Turabian Style**

Williamson, Andrew J., Shubham Srivastava, and Khaled A. Sallam. 2022. "Validating Confined Flame Noise Simulation Using External Sensor" *Sensors* 22, no. 20: 8039.
https://doi.org/10.3390/s22208039