# Experimental and Numerical Study of Swirling Diffusion Flame Provided by a Coaxial Burner: Effect of Inlet Velocity Ratio

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## Abstract

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^{3}dimensions. Numerical flow fields were compared with stereoscopic particle image velocimetry (stereo-PIV) fields for non-reacting and reacting cases. The turbulence was captured using the Reynolds averaged Navier-Stokes (RANS) approach, associated with the eddy dissipation combustion model (EDM) to resolve the turbulence/chemistry interaction. The simulations were performed using the Fluent CFD (Computational Fluid Dynamic) code. Comparison of the computed results and the experimental data showed that the RANS results were capable of predicting the swirling flow. The effect of the inlet velocity ratio on dynamic flow behavior, temperature distribution, species mass fraction and the pollutant emission were numerically studied. The results showed that the radial injection of fuel induces a partial premixing between reactants, which affects the flame behavior, in particular the flame stabilization. The increase in the velocity ratio (R

_{v}) improves the turbulence and subsequently ameliorates the mixing. CO emissions caused by the temperature variation are also decreased due to the improvement of the inlet velocity ratio.

## 1. Introduction

## 2. Experimental Setup

_{i}= 15 mm and inner diameter D

_{in}= 12 mm, which ensured the passage of methane (see Figure 1).

_{e}= 38 mm ensured the passage of air by means of four tubes from the bottom. An injector placed at the end of the central tube had eight uniformly distributed holes (3 mm in diameter) for a lateral injection of the methane across the annular air flow. The fuel injector was used to promote mixing in the vicinity of the burner outlet. The swirler placed in the annular part, 60 mm from the exit burner, ensured the rotation of the air. The swirler used in this work was composed of eight vanes with a fixed angle. The degree of swirl for rotating flows is usually characterized by the non-dimensional swirl number S

_{n}(Boushaki et al. [13]). The swirl number is based on the equation of Beer and Chigier [38]. In this study the swirl number was equal to 1.4. The burner was placed in a combustion chamber of a square section of 48 × 48 and 100 cm

^{3}height, plus a convergent section of 20 cm high with a final circular section of 10 cm. The rigid refractory panels with low thermal conductivity (0.06 W/m k at 200 °C) ensured the insulation and protection of the internal wall of the combustion chamber. The walls were cooled from outside via a flow of water at ambient temperature.

^{2}in physical size (1 pixel = 0.049 mm), with 50% overlap. The vectors of velocity were calculated using the cross-correlation algorithm. For a maximum particle displacement of eight pixels, this corresponded to less than 5% uncertainty in the final velocity obtained.

_{2}particles were used for flow seeding and were injected into the coaxial tube. This choice of Zirconium Oxide particles was due to their very good resistance to the temperature generated by the combustion (melting temperature 2988K), and their good refractive index (2.2), which allows good light scattering, and their small size (1 µm in diameter on average). The particle rate was controlled by valves through the gas flow rate in the seeding line. The particles were dried before measurements, in order to limit agglomerates. The criterion assuring a good track of flow by particles was respected here, since the Stokes number obtained in the case of our experiments was lower than 1 (St << 1). The Stokes number is given by the ratio between the response time of particles (t

_{p}) and a time characteristic of the flow (t

_{f}). Note that the validity of stereo-PIV calibration with high temperature was checked. We compared some data to 2D PIV measurements and also to LDA measurements, the data were similar.

## 3. Numerical Modeling

#### 3.1. Gouverning Equations

#### 3.2. Turbulence Model

#### 3.3. Combustion Modeling

_{R}represents the mass fraction of a particular reactant R, k is the turbulence kinetic energy, ${M}_{\omega}$ is the molecular mass of specie, $\upsilon $ is the stoichiometric coefficient, ${Y}_{P}$ is the mass fraction of any product species P, and A and B are empirical constants fixed to 4 and 0.5 respectively. Two-step reaction mechanisms including six chemical species (CH

_{4}, O

_{2}, CO

_{2}, CO, H

_{2}O, n

_{2}) are used in this work:

_{4}+ 3O

_{2}→ 2CO + 4H

_{2}O

_{2}→2CO

_{2}

#### 3.4. Computational Domain and Boundary Conditions

_{air}was used (see Table 1). At the fuel inlet, CH

_{4}was selected and mass flow inlet boundary condition $\dot{m}$

_{ful}was used (see Table 1). At the outlet, a static pressure was applied. The velocity ratio (R

_{v}) was calculated as the external mean velocity (V

_{e}) to the internal mean velocity (V

_{i}). There are three techniques to modify the velocity ratio; one is to change the external and the internal velocity at the same time, keeping the total mass flow rate of the jets constant. Another method consists of fixing V

_{i}and varying V

_{e}. In the last technique, V

_{e}is kept constant, whereas V

_{i}is modified. In this work, V

_{i}was fixed to 4.98 m/s (fuel velocity), whereas the velocity of the air was modified from 2.8 m/s to 7.47 m/s (see Table 1).

## 4. Results and Discussion

#### 4.1. Model Validation

_{4}, thus it alters the CRZ. Nogenmyr et al. [43] has demonstrated that the complexity of the combustion kinetics affects the degree of agreement between the numerical and experimental reacting flows. The discrepancy between simulation and measurements (Figure 3b) can also be explained by the effect of the presence of the flame, which leads to an important gradient of temperature. Thermal agitation is very important around the reaction zone and the velocity of the flow changes considerably in this region.

#### 4.2. Effect of the Velocity Ratio

#### 4.2.1. Turbulent Kinetic Energy

_{v}= 0.5, R

_{v}= 1 and R

_{v}= 1.5. The plots show that the TKE increases by increasing the velocity ratio. The turbulent kinetic energy reaches its maximum at the region of the swirl jet. Figure 8a–c represents the profile of this parameter for three velocity ratios at different locations downstream of the burner exit (Z = 5, 10, 30 and 60 mm). By increasing the velocity ratio, the TKE profile displays the same behavior at the different locations. It can be seen that the maximum TKE value was reached for a velocity ratio of 1.5.

^{2}/s

^{2}for R

_{v}= 1.5, whereas this value did not exceed 13 m

^{2}/s

^{2}for R

_{v}= 0.5. The high axial velocity of the air jet increased the interactions between reactants, thus improving the mixing. The fluctuations reflect the degree of interaction between the different jets. They are generated by the velocity gradient between the different jets.

#### 4.2.2. Temperature Distribution

_{v}= 0.5), the flame temperature extended into a large area in the computational domain. Figure 9 also shows that the augmentation of the inlet air velocity decreased the flame length and enhanced its stability.

_{v}= 0.5, whereas for R

_{v}= 1.5, the temperature exceeded 2200 K. The addition of air quantity decreased the flame length. It can be seen in Figure 9 that the flame moved to the burner exit when the velocity ratio increased. In addition, the reaction zone was reduced in volume as the velocity ratio increased, which is similar to the decrease in the global equivalence ratio when the velocity of air increases.

#### 4.2.3. Mass Fraction of CH_{4} and O_{2}

_{v}= 0.5) and at a position near the burner exit (Z = 10mm), the mass fraction of the fuel was equal to 0.15 at r = 15 mm. At the same location and for a velocity ratio of 1.5, the fuel mass fraction was equal to 0.1. Figure 11 represents the variation in the fuel mass fraction obtained for three different velocity ratios and for different heights. It can be seen that with different velocity ratios the quantity of CH

_{4}consumed by the combustion reaction depended on the reaction zone displacement. At Z = 60 mm (Figure 11c) the maximum mass fraction equaled 0.018 for R

_{v}= 0.5 and equaled zero for Rv = 1 and Rv = 1.5. This means that at a distance of 60 mm downstream of the burner exit, the methane was completely consumed by the combustion reaction.

_{2}was located at the swirl jet (at r = −20 mm and r = 20 mm). Near the burner exit (Figure 12a), the variation in the mass fraction of the oxygen presents a minimum at the radial position of r between −10 mm and 10 mm, which represents the reactive zone, where the mixing between the fuel and the air is nearly in balance. At Z = 30 mm (Figure 12b), the radial position of the maximum increases when the velocity ratio increases. Thus, the flame becomes thinner by the addition of air. Moving away from the burner exit, at Z = 60 mm (Figure 12c) the mass fraction of the oxygen value is around zero in the flame zone for R

_{v}= 0.5 and Rv = 1, indicating that the quantity of oxygen injected by the burner is completely consumed by the reaction. For R

_{v}= 1.5, it can be seen that the mass fraction of the oxygen in the reactive zone is around 0.1.

#### 4.2.4. Pollutant Emissions

_{CO}distribution takes a V shape like the flame. The maximum CO concentrations are shown in the swirl jet and the central recirculation zone contains only a small quantity. Figure 14 illustrates the profile of the CO variation at Z = 60 mm for three velocity ratios. The results indicate that increasing the velocity ratio decreases CO formation. If the velocity ratio increases from R

_{v}= 0.5 to Rv = 1.5, the mass fraction of CO decreases from 0.008 to 0.001.

_{2}[35].

_{v}= 1 and Rv = 1.5, the maximum NOx concentrations are shown in the reaction zone. The main parameter that affects the NOx emission is the temperature. If the velocity ratio increases from R

_{v}= 0.5 to Rv = 1, the NOx emission increases. This augmentation can be explained by the increases in flame temperature (Figure 10) via the thermal NO mechanism. The highest velocity ratio (R

_{v}= 1.5) causes a decrease in NOx formation because of the decrease in the temperature value in the flame zone at Z = 60 mm (Figure 10c).

## 5. Conclusions

_{n}= 1.4). The stereoscopic particle image velocimetry (stereo-PIV) technique was used to measure the dynamics of non-premixed swirling flows for isothermal and reacting cases. The numerical results were calculated using the RANS turbulence approach, associated with the eddy dissipation combustion model in the reacting case. The numerical models were validated by comparing the computed results with the measurement data obtained for isothermal and reacting cases in the same conditions. The effect of the velocity ratio on the turbulent swirling diffusion flame, particularly in the case where the fuel is injected across the oxidizer, was numerically investigated. The results of this study reveal the following:

- For a fixed inlet fuel velocity, the variation of inlet air velocity in a coaxial burner configuration causes a change in the dynamics of the flame. The increase in the velocity ratio leads to an increase in the turbulent kinetic energy and subsequently improves the mixing.
- The radial injection of fuel induces a partial premixing between reactants, which affects the flame behavior, in particular the flame stabilization.
- Increasing the velocity ratio causes a modification of the flame morphology and the flame becomes well attached to the burner.
- The addition of air decreases the flame length and the height of liftoff and the flame becomes more attached to the burner.
- Pollutant emission results revealed that the increase in the velocity ratio reduced the CO emissions caused by the temperature variation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Obtained numerical profiles of radial mean axial velocity compared to experimental data for non-reacting and reacting cases; (

**a**) non−reacting case; (

**b**) reacting case.

**Figure 4.**Numerical and experimental contours of mean axial velocity under non-reacting and reacting cases; (

**a**) non−reacting case; (

**b**) reacting case.

**Figure 5.**Obtained numerical profiles of the tangential velocity compared to experimental data for non−reacting and reacting cases; (

**a**) non−reacting case; (

**b**) reacting case.

**Figure 6.**Obtained numerical contours of the tangential velocity compared to experimental data for non−reacting and reacting cases; (

**a**) non−reacting case; (

**b**) reacting case.

**Figure 8.**Computed turbulent kinetic energy (m

^{2}/s

^{2}) for three velocity ratios obtained at different height locations; (

**a**) Z = 5 mm; (

**b**) Z = 10 mm; (

**c**) Z = 30 mm; (

**d**) Z = 60 mm.

**Figure 10.**Computed temperature profiles for three velocity ratios obtained at four heights; (

**a**) Z = 5 mm; (

**b**) Z = 10 mm; (

**c**) Z = 30 mm; (

**d**) Z = 60 mm.

**Figure 11.**Radial profiles of the fuel mass fractions obtained for different velocity ratios and at four height locations; (

**a**) Z = 5 mm; (

**b**) Z = 10 mm; (

**c**) Z = 30 mm; (

**d**) Z = 60 mm.

**Figure 12.**Computed radial profiles of oxygen mass fractions for different velocity ratios and at four heights; (

**a**) Z = 5 mm; (

**b**) Z = 10 mm; (

**c**) Z = 30 mm; (

**d**) Z = 60 mm.

**Figure 15.**Radial profiles of NOx mole fractions obtained for different velocity ratios at Z = 60mm.

Cases | Q_{fuel} (Nl/min) | Q_{air} (Nl/min) | $\dot{\mathit{m}}$_{fuel} (kg/s)
| $\dot{\mathit{m}}$_{air} (kg/s)
| V_{i} (m/s) | V_{e} (m/s) | R_{v} | ɸ |
---|---|---|---|---|---|---|---|---|

Case 1: R_{v} < 1 | 15.75 | 150 | 0.00017 | 0.0032 | 4.98 | 2.8 | 0.56 | 1 |

Case 2: Rv = 1 | 15.75 | 266 | 0.00017 | 0.0056 | 4.98 | 4.98 | 1 | 0.56 |

Case 3: Rv > 1 | 15.75 | 400 | 0.00017 | 0.0085 | 4.98 | 7.47 | 1.5 | 0.37 |

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**MDPI and ACS Style**

Chakchak, S.; Hidouri, A.; Zaidaoui, H.; Chrigui, M.; Boushaki, T.
Experimental and Numerical Study of Swirling Diffusion Flame Provided by a Coaxial Burner: Effect of Inlet Velocity Ratio. *Fluids* **2021**, *6*, 159.
https://doi.org/10.3390/fluids6040159

**AMA Style**

Chakchak S, Hidouri A, Zaidaoui H, Chrigui M, Boushaki T.
Experimental and Numerical Study of Swirling Diffusion Flame Provided by a Coaxial Burner: Effect of Inlet Velocity Ratio. *Fluids*. 2021; 6(4):159.
https://doi.org/10.3390/fluids6040159

**Chicago/Turabian Style**

Chakchak, Sawssen, Ammar Hidouri, Hajar Zaidaoui, Mouldi Chrigui, and Toufik Boushaki.
2021. "Experimental and Numerical Study of Swirling Diffusion Flame Provided by a Coaxial Burner: Effect of Inlet Velocity Ratio" *Fluids* 6, no. 4: 159.
https://doi.org/10.3390/fluids6040159