# Numerical Steady and Transient Evaluation of a Confined Swirl Stabilized Burner

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Combustor Domain Investigated

#### Swirl Flow Structure

## 3. Experimental Setup

## 4. Mesh Generation

## 5. Numerical Approach

#### 5.1. Boundary Conditions Applied

#### 5.2. Turbulence-Chemistry Models

## 6. Results

#### 6.1. Cold Flow

#### 6.2. Hot Flow Using Combustion Models

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

d | Flame length above burner exit (mm) |

D | Burner exit diameter (mm) |

${f}_{D}$ | Frequency shift of laser light (Hz) |

U | Velocity magnitude (m/s) |

u | Axial velocity component (m/s) |

V | Tangential velocity component (m/s) |

$\lambda $ | Air/fuel ratio (-) |

$\Phi $ | Equivalence ratio (-) |

CFD | Computational Fluid Dynamics |

DES | Detached Eddy Simulation |

DLE | Dry-Low Emission |

DO | Discrete Ordinates |

ED | Eddy Dissipation |

FGM | Flamelet Generated Manifold |

FM-DGV | Frequency Modulated Doppler Global Velocimetry |

IRZ | Inner Recirculation Zone |

LES | Large Eddy Simulation |

LIV | Laser Interferometric Vibrometry |

ORZ | Outer Recirculation Zone |

Probability Density Function | |

PIV | Particle Image Velocimetry |

QUICK | Quadratic Upstream Interpolation for Convective Kinematics; |

RANS | Reynolds-averaged Navier–Stoke |

SAS | Scale Adaptive Simulation |

SLF | Steady Laminar Flamelet |

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**Figure 2.**Vortex core overview. (

**left**) current combustor; (

**right**) sketch of flow patterns in a confined, premixed swirl stabilized combustor [22].

**Figure 3.**Vortex structure of PVC [21].

**Figure 5.**Axial velocity field comparison between k-$\u03f5$ ${y}^{+}$ = 3 (

**left**) and k-$\u03f5$ ${y}^{+}$ = 1 (

**right**).

**Figure 8.**Axial velocity profile for the cold flow case with RNG k-$\u03f5$ turbulence model (

**a**) and axial profile 2D plot set at the inlet of the combustion simulations (

**b**).

**Figure 9.**Velocity magnitude profile for the cold flow case with RNG k-$\u03f5$ turbulence model at the z-plane = 5 mm (

**a**) and velocity magnitude profile 2D plot along the black line on z-plane = 5 mm (

**b**).

**Figure 10.**Flow comparison-temperature profile shown for (

**a**) experiments, (

**b**) FGM premixed with RNG k-$\u03f5$, (

**c**) FGM premixed with k-$\omega $ and (

**d**) LES.

**Figure 11.**Snapshot of isosurfaces at temperature T = 1600 °C (

**left**) and isovorticity surface $\omega =2000$ s${}^{-1}$ (

**right**) for LES.

**Figure 12.**Flow comparison heat release profile shown for (

**a**) OH* chemiluminescence experiments, (

**b**) FGM premixed with RNG k-$\u03f5$, (

**c**) FGM premixed with k-$\omega $ and (

**d**) LES.

**Figure 13.**Flow comparisons-axial velocity profile shown for the combustion model ED and different turbulence models: (

**a**) RNG k-$\u03f5$, (

**b**) k-$\omega $ and (

**c**) SST.

**Figure 14.**Flow comparisons-tangential velocity profile shown for the combustion model ED and different turbulence models: (

**a**) RNG k-$\u03f5$, (

**b**) k-$\omega $ and (

**c**) SST.

**Figure 15.**Flow comparisons-axial velocity profile shown for FGM premixed and different turbulence models: (

**a**) RNG k-$\u03f5$, (

**b**) k-$\omega $ and (

**c**) SST.

**Figure 16.**Velocity magnitude profile for combustion model ED with (

**a**) RNG k-$\u03f5$, (

**b**) k-$\omega $ and FGM with (

**c**) RNG k-$\u03f5$ and (

**d**) k-$\omega $.

${\mathit{y}}^{+}=3$ | k-$\mathbf{\u03f5}$ | k-$\mathbf{\omega}$ |
---|---|---|

$S-D/4$ | 0.5684 | 0.4548 |

$S-D/2$ | 0.53625 | 0.54065 |

${\mathbf{y}}^{+}=1$ | k-$\mathbf{\u03f5}$ | k-$\mathit{\omega}$ |
---|---|---|

$S-D/4$ | 0.48035 | 0.4278 |

$S-D/2$ | 0.43935 | 0.40995 |

Eddy Dissipation | k-$\mathbf{\u03f5}$ | k-$\mathbf{\omega}$ | SST |

S | 0.38505 | 0.605785 | 0.3929925 |

Steady Flamelet | k-$\mathbf{\u03f5}$ | k-$\mathbf{\omega}$ | SST |

S | 0.36569 | 0.27741 | 0.36799 |

FGM Premixed Flamelet | k-$\mathbf{\u03f5}$ | k-$\mathbf{\omega}$ | SST |

S | 0.378645 | 0.5313975 | 0.3744125 |

FGM Diffusion Flamelet | k-$\mathbf{\u03f5}$ | k-$\mathbf{\omega}$ | SST |

S | 0.3799175 | 0.523415 | 0.374775 |

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**MDPI and ACS Style**

Farisco, F.; Castellanos, L.; Woisetschläger, J.; Sanz, W.
Numerical Steady and Transient Evaluation of a Confined Swirl Stabilized Burner. *Int. J. Turbomach. Propuls. Power* **2021**, *6*, 46.
https://doi.org/10.3390/ijtpp6040046

**AMA Style**

Farisco F, Castellanos L, Woisetschläger J, Sanz W.
Numerical Steady and Transient Evaluation of a Confined Swirl Stabilized Burner. *International Journal of Turbomachinery, Propulsion and Power*. 2021; 6(4):46.
https://doi.org/10.3390/ijtpp6040046

**Chicago/Turabian Style**

Farisco, Federica, Luisa Castellanos, Jakob Woisetschläger, and Wolfgang Sanz.
2021. "Numerical Steady and Transient Evaluation of a Confined Swirl Stabilized Burner" *International Journal of Turbomachinery, Propulsion and Power* 6, no. 4: 46.
https://doi.org/10.3390/ijtpp6040046