# Investigation of Slot-Burner Aerodynamics with Recessed-Type Nozzle Geometry

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Modelling

^{2}·T

^{−2}), e.g., m

^{2}/s

^{2}. ε is the turbulence eddy dissipation and has dimensions of k per unit time (L

^{2}T

^{−3}).

_{μ}= 0.09 is a k-ε turbulent model constant. The values of k and ε come directly from the differential transport equations for the turbulence kinetic energy and turbulence dissipation rate.

_{ε1}= 1.44, C

_{ε2}= 1.92, σ

_{ε}= 1.3 are the k-ε turbulent model constants. P

_{k}is the shear production due to turbulence, which for incompressible flow is given by the following equation. Here, U

^{T}is the transpose of the velocity vector matrix.

_{ε1}is replaced by the function C

_{ε1RNG.}The transport equation for the turbulence dissipation becomes:

_{ε1RNG}= 1.42 − f

_{n}, where f

_{n}is the RNG k-ε model coefficient and is given by,

_{ij}is the pressure strain correlation, and P, the exact production term, is given by:

_{ij}. The pressure strain correlations can be expressed in the general form:

## 3. Physical Structure and Burner Geometry

^{5}. Compared to the previous three geometries, flow development in the Geometry D cavity was more complex. For momentum flux ratios of one, all three jets were separated from the lower, short face with the secondary jets attached to the side and upper faces. The primary jet is separated from the upper face, but this separation is not always obvious at the unity momentum flux ratio. Fluid is entrained from the surroundings into the separated regions and into the base regions between the jets. Geometrically-similar jets exhibit similar behaviour when the Reynolds number is above 2.5 × 10

^{4}[15]. Therefore, the model burner jets should exhibit an aerodynamic behaviour similar to a full-sized burner jet, taking into consideration the previous comments on the effects of compressibility and temperature, as well as the isolated nature of the model burners compared to the a real burner, which experiences cross-flow due to neighbouring burners and the furnace’s central vortex.

## 4. Boundary Conditions

## 5. Grid Analysis

_{ce}, of the primary jet. A change in the calculated profiles was found with each successive grid refinement. The finer grids tended to predict less diffusive jets with higher centreline velocity and steeper ∂u/∂y and ∂u/∂z profiles. The 32 × 32 grid gave a very close prediction to that of the 16 × 16, especially in the high shear region of y/D

_{eq}≥ 0.5, and only a three percent difference between the two centrelines velocities’ prediction. The difference between the 16 × 16 and 32 × 32 predictions was small enough to suggest that any further grid refinement would yield the same profile in this plane. Based on this, the 32 × 32 grid was not used, as the extra computational cost associated with the extra cells did not yielded significantly more accurate results.

## 6. Validation of the Study

## 7. Results and Discussion

#### 7.1. Pressure Distributions

#### 7.2. Comparison of Different Turbulence Model

#### 7.3. Velocity Distributions

## 8. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 8.**Pressure distribution on the symmetry plane. (

**a**) mean pressure; (

**b**) instantaneous pressure.

**Figure 9.**Mean wall static pressure distribution in (

**a**) the recess and (

**b**) iso-surface of instantaneous positive and negative pressure.

**Figure 12.**Velocity profiles in the xy plane for the primary jet for the Reynolds Stress Model (RSM).

Name | Description |
---|---|

Geometry A | A nearly square primary jet flanked above and below by rectangular secondary jets, discharging orthogonally from a wall into a large room. |

Geometry B | Same as Geometry A, but the jets make an angle of 60° to the wall. |

Geometry C | Same as Geometry B, but with jets discharging into a straight-walled recess before exiting into the open atmosphere. |

Geometry D | Same as Geometry C, but with a diverging recess. This was geometrically similar to the recessed burner used in the furnace. |

Property | Yallourn Nozzle | Model Nozzle |
---|---|---|

Primary jet | ||

Reynolds number | 4.6 × 10^{5} | 1.3 × 10^{5} |

Slot width | 1020 mm | 37.5 mm |

Height | 800 mm | 29.0 mm |

Gas velocity | 39.2 m·s^{−1} | 60 m·s^{−1} |

Secondary jet | ||

Reynolds number | 3.8 × 10^{5} | 9.3 × 10^{4} |

Slot width | 1020 mm | 37.5 mm |

Height | 565 mm | 17.0 mm |

Gas velocity | 32.5 m·s^{−1} | 60 m·s^{−1} |

Base between jets | ||

Base height | 1020 mm | 37.5 mm |

Width | 380 mm | 14.0 mm |

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**MDPI and ACS Style**

Bhuiyan, A.A.; Karim, M.R.; Hart, J.T.; Witt, P.J.; Naser, J.
Investigation of Slot-Burner Aerodynamics with Recessed-Type Nozzle Geometry. *Fluids* **2016**, *1*, 10.
https://doi.org/10.3390/fluids1020010

**AMA Style**

Bhuiyan AA, Karim MR, Hart JT, Witt PJ, Naser J.
Investigation of Slot-Burner Aerodynamics with Recessed-Type Nozzle Geometry. *Fluids*. 2016; 1(2):10.
https://doi.org/10.3390/fluids1020010

**Chicago/Turabian Style**

Bhuiyan, Arafat Ahmed, Md. Rezwanul Karim, James T. Hart, Peter J. Witt, and Jamal Naser.
2016. "Investigation of Slot-Burner Aerodynamics with Recessed-Type Nozzle Geometry" *Fluids* 1, no. 2: 10.
https://doi.org/10.3390/fluids1020010