# Sound Pressure Level Analysis of a Liquid-Fueled Lean Premixed Swirl Burner with Various Quarls

^{*}

## Abstract

**:**

## 1. Introduction

_{X}); thus, the operation of the combustion chamber lies close to the flame blowout by design [3,4]. Consequently, a high understanding of combustion dynamics, especially thermo-acoustic oscillations [5], is required to prevent operational failures [6]. There are numerous papers available on the investigation of blowout using various time series analyses [7,8,9]. Typically, OH* and/or acoustic measurements are performed to detect oscillations at a few hundred Hz, which characterizes the flame in V-shaped mode. Their relative intensity is monitored, which shows an increase prior to blowout [6,10]. The majority of acoustical studies focus on common fossil fuels; however, it was shown earlier that stability limits are significantly affected by fuel type and combustion conditions [11]. By installing a quarl on the burner, the stable operating regime can be significantly extended [12]; hence, burner design is investigated in great detail in this paper.

## 2. Materials and Methods

#### 2.1. Experimental Setup

^{3}/h steps in rotameter reading. Since the atomizing air flow rate can be calculated using an adiabatic expansion at the atomizer nozzle [43], the second rotameter was used only for validation.

#### 2.2. Burner Design and Atomization

_{0}= 0.4 mm inner diameter fuel pipe, and the atomizing air is accelerated in a concentric annular nozzle (0.8 mm inner and 1.6 mm outer diameter). The mixing tube is 75.5 mm long, measured from the atomizer tip, and its inner radius is R = 13.4 mm. In this study, the atomizing gauge pressure, p

_{g}, was varied from 0.3 to 1.6 bar. The uncertainty of pressure measurement was below 1 kPa. The burner was used in a Capstone C30 micro gas turbine while the quarls were manufactured in the local workshop.

_{A}is the Weber number of the atomizing air as follows:

_{A}is the density of atomizing air at the nozzle, w

_{A}is the atomizing air discharge velocity, and σ is the surface tension of the utilized standard diesel oil (EN 590:2014). Table 1 summarizes the principal parameters of atomization, considering a constant fuel flow rate since the combustion power was uniformly 15 kW for all the cases. Ma = a/w

_{A}is the Mach number, where a is the speed of sound of the fully expanded jet. The notable fuel properties are summarized in Table 2.

#### 2.3. Swirl Characterization and Observed Flames

_{φ}is the axial flux of the angular momentum, G

_{x}is the axial thrust, and R is the radius of the mixing tube. By assuming the conservation of momentum, the geometric swirl number is usually calculated by Equation (5), based on the inlet conditions of the burner [49] since the spatial distribution of the pressure and velocity of the burner is rarely available in practice:

_{x}is the thrust at the inlet; hence, the pressure field can be omitted, and average velocity can be used for S’ estimation. This calculation method of the geometric swirl number was criticized by, e.g., Galley et al. [50], and Durox et al. [9]. Nevertheless, the cited results are limited for a different burner, and its generalization to the present burner is not possible. Hence, Equation (5) is used as the definition of the swirl number. Since the swirl vanes were fixed, the swirl number varied with the combustion air flow rate. The axial thrust is significantly increased by the increasing atomizing air flow rate at elevated p

_{g}, leading to low S’. G’

_{x}was calculated by Equation (6):

_{φ}is estimated as:

_{C}= 0.52 kg/m3 is the density of combustion air, and

_{x}is the mixture discharge velocity at the mixing tube outlet. ρ

_{x}is the density of the mixture, and µ

_{x}is its dynamic viscosity. The Reynolds number values varied between 6800 and 18680; therefore, the combustion was always in the turbulent regime.

## 3. Results and Discussion

_{g}= 0.3 bar, highlighting the characteristic effect of the combustion air flow rate on the combustion noise. Thirdly, the effect of the combustion air flow rate on OASPL with Z-weighting is analyzed, emphasizing the V-shaped flames. Lastly, the trends in the previous results are combined to conclude a general noise emission characteristic of the investigated swirl burner.

#### 3.1. Spectral Analysis of the Flame

_{g}= 0.3 bar with S’ = 0.48. The increase in combustion air flow rate, hence, in tangential momentum due to the fixed 45° swirl vanes, led to a random breakdown and merging of the precessing vortex core, called the transitory regime. A stable, V-shaped flame was then observable until blowout, shown in Figure 4. Note that certain setups reached neither the transitory state nor the subsequent V-shaped operation. They were the ones with high atomizing pressures and quarls, which provided no or low effect on flame stability. The spectrum of the straight flame was dominated by frequencies between 3 and 4 kHz. This band starts to fade as the flame approaches the transitory regime with the increasing combustion air flow rate, and hence S’. By increasing the air flow rate further, the average occurrence ratio of the two flame shapes starts to tend to the V-shaped flame; therefore, the amplitude at > 3 kHz decreases and low-frequency bands start to emerge, especially at 500 and 220 Hz. The V-shaped regime is characterized by lower amplitudes, and the energy density of the reacting flow is concentrated into the sub-1 kHz regime until blowout and contains no peak in the 3–4 kHz band.

#### 3.2. OASPL at p_{g} = 0.3 bar

_{g}was uniformly set to 0.3 bar. The results are presented for both A- and Z-weighting functions, indicating the various flame shapes by using different marker types. The combined expanded uncertainty ranges from 3% to 7.5% for S’ at 95% level of significance, which is 5%–6.5% for λ. The higher values characterize low flow rates, while the lower values are typically close to the blowout. The discussed uncertainty ranges incorporate all cases, including the later discussed ones. Hence, the corresponding error bars are omitted from all figures containing measurement data for better visibility.

#### 3.3. Effect of Quarls

_{g}s. Hence, data of various quarls are shown in separate diagrams, evaluating only the OASPL with Z-weighting as a function of S’.

_{g}[12]. At the initial combustion air flow rates, the flow was governed by the atomizing air jet at the center; hence, the flow was attached to the quarl wall later. The flow separation here was acceptable since the operation was far from the blowout. As the combustion air flow rate was increased, the increasing S’ resulted in flow attachment to the wall, allowing flame stabilization through the appearing boundary layer. The 45° quarl provided a sufficient flow attachment at lower p

_{g}; however, its half cone angle was too large for higher p

_{g}where the central regime was notably affected by the atomizing air jet. Therefore, the detached flow resulted in similar flame blowout characteristics as the baseline burner had. The flow was always separated from the 60° quarl; it only provided some protection against cold air entrainment. The blowout characteristics were close to the baseline and 0° configurations.

_{g}= 0.3 bar for the baseline burner configuration and up to 0.6 bar for the 0° quarl. Therefore, further analyses are limited to the mentioned configurations where a stable V-shaped flame was achieved for at least two consequent measurement points, excluding 45° and 60° quarls. Figure 7c,d showed stable V-shaped operation for all p

_{g}s, showing a nearly linear decrease in OASPL while increasing S’.

_{g}. In this state, the higher p

_{g}results in higher OASPL. The intersection of the trends is due to the enhanced thrust, generated by the elevated p

_{g}, hence, the denominator of Equation (5) was high. Therefore, the increased combustion air flow rate caused a smaller increase in S’ while the OASPL notably decreased in the case of V-shaped flames. As for straight flames, the higher p

_{g}leads to higher OASPL for all cases due to the enhanced shear induced by the atomizing jet. The noise under hot conditions was about 20 dB higher due to the following reason. The fuel first mixes with atomizing air; hence, the conditions of ignition could be satisfied here, which lead to a rapid expansion inside the shearing flow structure, significantly enhancing the generated noise by the high-velocity atomizing air jet.

#### 3.4. Linearity Analysis of the OASPL trends of V-shaped Flames

_{g}= 0.45 bar.

_{g}. In Figure 9a, the coefficient of determination is 0.878 and 0.796 for Z- and A-weighting functions, respectively. The results as a function of λ, are shown in Figure 9b; the corresponding R

^{2}values are 0,832 and 0,713, respectively. The data scattering at p

_{g}= 1.6 bar originated from the following phenomenon. The deviation from the fitted line is attributed to the lower frequency components in the case of the 30° quarl, which is amplified by the A-weighting function, leading to a steeper decreasing trend. However, the 15° quarl featured higher frequencies where the A-weighting function has a positive gain. Nevertheless, the deviation is close to the trend line in the case of Z-weighting. Considering the logarithmic scaling of the OASPL, the discussed result covers a wide range of operating conditions. The use of concluded decreasing derivatives with elevated p

_{g}might contribute to advanced combustion chamber designs for decreased noise emission and a healthier environment for the operators and affected personnel.

## 4. Conclusions

_{g}.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Latin letters | ||

a | (m/s) | Speed of sound |

AFR | (–) | Air-to-fuel mass flow ratio |

B | (mm) | Height of the swirl slots |

D | (mm) | Diameter of the circular slots |

d_{0} | (mm) | Fuel pipe inner diameter |

G_{φ} | (Nm) | Axial flux of the angular momentum |

G_{x} | (N) | Axial thrust |

G’_{x} | (N) | Axial thrust for the geometric swirl number calculation |

h | (mm) | Width of the swirl slots |

$\dot{m}$ | (kg/s) | Mass flow rate |

Ma | (–) | Mach number |

p_{g} | (bar) | Atomizing gauge pressure |

R | (m) | Mixing tube inner radius |

Re | (–) | Reynolds number |

S | (–) | Swirl number |

S’ | (–) | Geometric (estimated) swirl number |

s | (mm) | Slot-to-slot distance in the circumference of the mixing tube |

SMD | (µm) | Sauter Mean Diameter |

OASPL | (dB) | Overall Sound Pressure Level |

T | (K) | Temperature |

w | (m/s) | Velocity |

We | (–) | Weber number |

y | (piece) | Number of circular slots in the cylindrical surface of the mixing tube |

z | (piece) | Number of swirl slots in the cylindrical surface of the mixing tube |

Greek letters | ||

α | (°) | Swirl vane angle |

λ | (–) | Air-to-fuel equivalence ratio |

µ | (Pa·s) | Dynamic viscosity |

ψ | (–) | Blockage factor |

ρ | (kg/m^{3}) | Density |

σ | (N/m) | Surface tension |

Subscripts | ||

A | Atomizing air | |

air | Sum of air | |

C | Combustion air | |

F | Fuel | |

S | Air passing through the swirl vanes | |

sto | Stoichiometric | |

x | Mixture |

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**Figure 3.**Straight flame at the end of the transitory regime (

**left**, p

_{g}= 0.3 bar, λ = 1.1, and S’ = 0.82), stable V-shaped flame (

**middle**, p

_{g}= 0.3 bar, λ = 1.23, and S’ = 0.91), and V-shaped flame with a 45° quarl (

**right**, p

_{g}= 0.3 bar, λ = 1.25, and S’ = 0.92).

**Figure 4.**Spectrogram of a single measurement at p

_{g}= 0.8 bar, using a 15° quarl. The shaded areas indicate the changeover between two points with distinct flame characteristics. Blowout is indicated by the vertical black line, beyond which the spectrum of the cold flow noise is visible.

**Figure 6.**(

**a**,

**c**) OASPL with Z- and (

**b**,

**d**) A-weighting functions using the baseline burner and various quarls as a function of S’ (

**a**,

**b**) and λ (

**c**,

**d**) all at p

_{g}= 0.3 bar. Symbols: straight flame (○), transitory flame (

**×**), and V-shaped flame (◊).

**Figure 7.**OASPL of the (

**a**) baseline burner and (

**b**–

**f**) 0°–60° quarls at six p

_{g}s as a function of S’, using Z-weighting. Symbols: straight flame (○), transitory state (×), and V-shaped flame (◊).

**Figure 8.**Flame images with various quarls. (

**a**) 15° (

**b**) 30° qualrs, showing attached flame to its wall. (

**c**) 45° with detached flame in V-shaped mode and (

**d**) straight flame also detached from the quarl wall.

**Figure 9.**The derivative of the fitted linear trend lines as a function of the atomizing pressure. (

**a**) geometric swirl number, (

**b**) air-to-fuel equivalence ratio.

p_{g} (bar) | SMD (µm) | We_{A} (–) | AFR (–) | ρ_{A} (kg/m_{3}) | T_{A} (K) | Ma (–) |
---|---|---|---|---|---|---|

0.3 | 21.6 | 779 | 0.778 | 1.27 | 277 | 0.62 |

0.45 | 16.2 | 1121 | 0.948 | 1.31 | 268 | 0.75 |

0.6 | 13.4 | 1438 | 1.089 | 1.34 | 261 | 0.85 |

0.8 | 11.1 | 1830 | 1.249 | 1.39 | 252 | 0.95 |

1.1 | 9.17 | 2363 | 1.451 | 1.45 | 241 | 1.08 |

1.6 | 7.44 | 3143 | 1.725 | 1.54 | 227 | 1.25 |

Property | Value |
---|---|

Thermal power | 15 kW |

Lower heating value | 43 MJ/kg |

Fuel flow rate | 0.35 g/s |

Dynamic viscosity | 3.45 mPa·s |

Density | 830 kg/m^{3} |

Surface tension | 28 mN/m |

**Table 3.**The coefficient of determination of linear fit lines for A- and Z-weighting functions as a function of S’ and λ.

Quarl | p_{g} (bar) | R^{2} (S’, dB(Z)) | R^{2} (S’, dB(A)) | R^{2} (λ, (dBZ)) | R^{2} (λ, (dBA)) |
---|---|---|---|---|---|

Baseline | 0.3 | 0.944 | 0.970 | 0.971 | 0.988 |

0° | 0.3 | 0.885 | 0.924 | 0.926 | 0.955 |

15° | 0.3 | 0.963 | 0.996 | 0.993 | 0.993 |

0.45 | 0.989 | 0.997 | 0.995 | 0.987 | |

0.6 | 0.988 | 0.965 | 0.979 | 0.947 | |

0.8 | 0.974 | 0.964 | 0.966 | 0.955 | |

1.1 | 0.999 | 0.999 | 0.998 | 0.998 | |

1.5 | 1.000 | 1.000 | 1.000 | 1.000 | |

30° | 0.3 | 0.802 | 0.934 | 0.853 | 0.967 |

0.45 | 0.763 | 0.722 | 0.793 | 0.739 | |

0.6 | 0.983 | 0.980 | 0.970 | 0.966 | |

0.8 | 0.987 | 0.994 | 0.978 | 0.989 | |

1.1 | 0.993 | 0.998 | 0.989 | 0.995 | |

1.5 | 0.994 | 0.990 | 0.992 | 0.987 |

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## Share and Cite

**MDPI and ACS Style**

Novotni, G.I.; Józsa, V. Sound Pressure Level Analysis of a Liquid-Fueled Lean Premixed Swirl Burner with Various Quarls. *Acoustics* **2020**, *2*, 131-146.
https://doi.org/10.3390/acoustics2010010

**AMA Style**

Novotni GI, Józsa V. Sound Pressure Level Analysis of a Liquid-Fueled Lean Premixed Swirl Burner with Various Quarls. *Acoustics*. 2020; 2(1):131-146.
https://doi.org/10.3390/acoustics2010010

**Chicago/Turabian Style**

Novotni, Gergely I., and Viktor Józsa. 2020. "Sound Pressure Level Analysis of a Liquid-Fueled Lean Premixed Swirl Burner with Various Quarls" *Acoustics* 2, no. 1: 131-146.
https://doi.org/10.3390/acoustics2010010