# Influence of a Central Jet on Isothermal and Reacting Swirling Flow in a Model Combustion Chamber

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup and Flow Regimes

#### 2.1. Combustor

#### 2.2. PIV Measurements

## 3. Computational Details

## 4. Results

#### 4.1. Mesh Convergence

^{6}control volumes with approximately 130, 290, and 280 cells in radial, axial, and azimuthal directions. The central area along the symmetry axis was subjected to the highly dense mesh due to central jet effects. The refinement procedure, which splits each hexahedral cell of $m1$ in x directions producing 2 smaller hexahedra, was employed in the critical area $r/D<0.8$ and $-1<x/D<1$, including the outer shear layer and part of the domain inside the nozzle. The $m2$ mesh contained 5.4 × 10

^{6}cells, serving as a compromise between accuracy and overall simulation time. In the same region of interest as above, the $m2$ mesh was refined in r and $\theta $ directions yielding 4 smaller cells and resulting in a $m3$ mesh with 13.4 × 10

^{6}cells total. Meshes $m1$ and $m2$ were used for isothermal mesh convergence studies, while $m2$ and $m3$ were utilized in reacting flow cases. These computational grids are visualized in Figure 3 (bottom row). Figure 3 (top row) demonstrates a x-r plane in the near-nozzle area, as well as the time-averaged axial velocity fields for the isothermal and reacting cases without the central jet for Cases 1 and 3 documented in Table 1 with the corresponding Fourier transform of the axial velocity signal. Both cases show that neither the size nor shape of the recirculation zone is affected by the refinement procedure indicating mesh convergence of the results. The results for the reacting case are slightly more sensitive to refinement, demonstrating small changes of the flow inside the recirculating region. The $\Delta {x}^{+}$, $\Delta {y}^{+}$, $\Delta {z}^{+}$ distributions were computed and showed a gradual decline with mesh refinement levels increasing, with values typically in the range from 1 to 25, reaching their maximum near the outer radius of the swirler nozzle.

#### 4.2. No Central Jet

#### 4.3. Central Jet Effect

#### 4.4. Proper Orthogonal Decomposition

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

PVC | Precessing vortex core |

LES | Large-eddy simulation |

PIV | Partice image velocimetry |

PLIF | Planar laser-induced fluorescence |

FGM | Flamelet-generated manifold |

POD | Proper orthogonal decomposition |

(r, $\theta $, x) | Cylindrical coordiante system components |

(x, y, z) | Cartesian coordiante system components |

D | diameter of the swirler nozzle |

$\mu $ | dynamic viscosity |

${\mu}_{t}$ | turbulent viscosity |

f | frequency in Hz |

${U}_{b}$ | bulk velocity calculated through the swirler nozzle |

${U}_{b}^{pilot}$ | bulk velocity calculated through the pilot nozzle |

St | Strouhal number |

${Q}_{air}^{main}$ | volumetric flow rate for air supplied in the air channel |

${Q}_{fuel}^{pilot}$ | volumetric flow rate for fuel supplied in the pilot nozzle |

$\rho $ | density |

${u}_{i}$ | velocity component |

p | pressure |

${Y}_{c}$ | progress variable |

Z | mixture fraction |

${\overline{u}}_{i}$ | time-averaged velocity component |

${\tilde{u}}_{i}$ | Favre-averaged velocity component |

${R}_{ij}$ | subgrid-scale stresses tensor |

$S{c}_{t}$ | Schmidt number |

m | POD mode |

${\lambda}_{m}$ | energy in m POD mode |

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**Figure 2.**Computational domain of the combustion chamber model and Cartesian and cylindrical coordinate systems.

**Figure 3.**Cell centers for $m1$ and $m2$ meshes are demonstrated in the near-nozzle area in the x-r plane. Contour plots in the middle show the time-averaged axial velocity field for the isothermal Case 1 (obtained on $m1$ and $m2$) and reacting Case 3 (obtained on $m2$ and $m3$) (see Table 1). The Fourier transform of the axial velocity ${U}_{x}/{U}_{b}$ signal in auxiliary units (a.u.) is presented for Case 1 (red—$m1$, blue—$m2$) and Case 3 (red—$m2$, blue—$m3$), measured at 4 points defined as $(x,r)=(0.13D,0.40D)$ (distributed by $\pi /2$ along $\theta $ direction). The bottom row provides a three-dimensional illustration of $m1$, $m2$, and $m3$ meshes.

**Figure 4.**Experimental (e) and numerical (s) time-averaged velocity components and streamwise component of the Reynolds stresses in the x-r plane for the isothermal case with no central jet (see Case 1 in Table 1). Bottom row presents mean profiles at $x/D=0.27$ (LES—solid line, PIV—⊙ markers).

**Figure 5.**Instantaneous velocity and pressure fields for the isothermal case with no central jet (see Case 1 in Table 1) are presented in the x-r plane to highlight the PVC near the nozzle. We employ Cartesian coordinates, where $({U}_{x},{U}_{y},{U}_{z})$ correspond to the streamwise, ‘radial’ and ‘azimuthal’ components in cylindrical coordinates (see Figure 2). The pressure field P is plotted with respect to the pressure at the origin ${P}_{0}$.

**Figure 6.**Experimental (e) and numerical (s) time-averaged velocity components and streamwise component of the Reynolds stresses in the x-r plane for the reacting case with no central jet (see Case 3 in Table 1). Bottom row presents mean profiles at $x/D=0.27$ (LES—solid line, PIV—⊙ markers).

**Figure 7.**Instantaneous velocity and pressure fields for the reacting case with no central jet (see Case 3 in Table 1) are presented in the x-r plane to highlight the PVC near the nozzle. For this image we employ Cartesian coordinates where $({U}_{x},{U}_{y},{U}_{z})$ correspond to the streamwise, ‘radial’, and ‘azimuthal’ components in cylindrical coordinates (see Figure 2). The pressure field P is plotted with respect to the pressure at the origin ${P}_{0}$.

**Figure 8.**Comparison of all four cases without and with the central jet. Time-averaged and instantaneous axial velocity field for isothermal and reacting cases.

**Figure 10.**The spectra of (

**left**) $Ux/{U}_{b}$ time history for the same points as in Figure 3 and (

**right**) temporal POD modes # 1 (red), 2 (blue), 3 (orange) for all four cases and in auxiliary units (a.u.).

**Figure 11.**The left plot shows the part of energy ${\lambda}_{i}^{2}/\sum {\lambda}_{k}^{2}$ and time-history ${a}_{1}\left(t\right)$ of a particular POD mode #i for all cases. The right image demonstrates the spatial distribution of the axial component ${\Phi}_{1,x}(y,z)$ at the station $x/D\approx 0.4$ for the largest eigenvalue for all cases. A dashed circle shows the diameter of the nozzle D.

**Table 1.**Description of flow cases with the corresponding values of air and fuel flow rates [$\mathrm{L}/\phantom{\rule{-0.166667em}{0ex}}min\phantom{\rule{0.277778em}{0ex}}]$ and bulk velocities [$\mathrm{m}/\phantom{\rule{-0.166667em}{0ex}}\mathrm{s}\phantom{\rule{0.277778em}{0ex}}]$.

Case | ${\mathit{Q}}_{\mathit{air}}^{\mathit{main}}$ | ${\mathit{Q}}_{\mathit{fuel}}^{\mathit{main}}$ | ${\mathit{U}}_{\mathit{b}}$ | ${\mathit{Q}}_{\mathit{air}}^{\mathit{pilot}}$ | ${\mathit{Q}}_{\mathit{fuel}}^{\mathit{pilot}}$ | ${\mathit{U}}_{\mathit{b}}^{\mathit{pilot}}$ | Type |
---|---|---|---|---|---|---|---|

Case 1 | 398 | 0 | 4.82 | 0 | 0 | 0 | isothermal |

Case 2 | 398 | 0 | 4.82 | 29.2 | 0 | 17.18 | isothermal |

Case 3 | 398 | 10.8 | 4.9 | 0 | 3.2 | 1.91 | reacting |

Case 4 | 398 | 10.8 | 4.9 | 26.0 | 3.2 | 17.18 | reacting |

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## Share and Cite

**MDPI and ACS Style**

Palkin, E.V.; Hrebtov, M.Y.; Slastnaya, D.A.; Mullyadzhanov, R.I.; Vervisch, L.; Sharaborin, D.K.; Lobasov, A.S.; Dulin, V.M.
Influence of a Central Jet on Isothermal and Reacting Swirling Flow in a Model Combustion Chamber. *Energies* **2022**, *15*, 1615.
https://doi.org/10.3390/en15051615

**AMA Style**

Palkin EV, Hrebtov MY, Slastnaya DA, Mullyadzhanov RI, Vervisch L, Sharaborin DK, Lobasov AS, Dulin VM.
Influence of a Central Jet on Isothermal and Reacting Swirling Flow in a Model Combustion Chamber. *Energies*. 2022; 15(5):1615.
https://doi.org/10.3390/en15051615

**Chicago/Turabian Style**

Palkin, Egor V., Mikhail Yu. Hrebtov, Darya A. Slastnaya, Rustam I. Mullyadzhanov, Luc Vervisch, Dmitriy K. Sharaborin, Aleksei S. Lobasov, and Vladimir M. Dulin.
2022. "Influence of a Central Jet on Isothermal and Reacting Swirling Flow in a Model Combustion Chamber" *Energies* 15, no. 5: 1615.
https://doi.org/10.3390/en15051615