# Analysis of NO Formation and Entropy Generation in a Reactive Flow

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}) was a more influential factor on NO

_{x}formation, as compared with the other chemical and radiative factors in methane diffusion flames. Parkash et al. [8] reported the influence of an outlet gas recirculation on the CO and NO

_{x}formations within a gas turbine combustion chamber. The results demonstrated that by employing outlet gas recirculation, a reduction occurred in NO

_{x}formation, as compared with the air oxidizer emission levels at elevated pressures.

_{X}). Xu et al. [10,11] stated the cylindrical length section and nozzle axis distance of a self-reflux burner can influence oxygen and NOx concentrations.

_{2}and C play a significant role in the destruction of NOx and that NO generation in the primary zone may be seriously diminished by staged combustion. They noticed that the types of re-burning fuel, the ratio of fuel–air in the primary zone, the mass factor of the re-burning fuel in the overall fuel, and the combustion temperature in the re-burning zone, were the major factors which affected NO reduction. Yuan and Naruse [13] studied diffusion combustion within a gas furnace with diluted and greatly pre-heated air. They reported that reducing the concentration of oxygen in the pre-heated air can improve the temperature distribution uniformity and decrease the NOx emission in the furnace.

## 2. Numerical Details

#### 2.1. Governing Equations

#### 2.2. Radiation Modeling

#### 2.3. Calculation of Entropy Generation

#### 2.4. NO Modeling

#### 2.5. Solution Procedures

## 3. Model Combustor and Boundary Conditions

_{2}O

_{3}. The mass flow rate and temperature of propane fixed at $0.0162\mathrm{kg}/\mathrm{s}$ and $293\mathrm{K}$, respectively, is introduced through a gas nozzle placed at the core of the bluff body. The 0.55$\mathrm{kg}/\mathrm{s}$ air flows through the inlet nozzle at 288$\mathrm{K}$ temperature and then exits through the outlet nozzle at a pressure of 1.0 $\mathrm{atm}$.

## 4. Results and Discussion

## 5. Conclusions

- I.
- The prompt NO is mostly produced before the combustion zone, where the air jets of high velocity enter and entropy starts to generate.
- II.
- The main region of NO formation is within the range of $0.125\mathrm{m}\mathrm{X}0.375\mathrm{m}$, in which the maximum total entropy rate of generation and the maximum temperature are also reported.
- III.
- The total entropy generation rate is more sensitive to high temperature (1500–1930 K) than the NO formation rate. With an increase of 28.7% in temperature, entropy generation and NO formation rates augment by 900% and 127%, respectively.
- IV.
- The chemical reactions process is the major cause of the generation of entropy. Moreover, the contribution of other processes toward entropy generation can be arrayed, such as heat conduction, diffusion of mass, and viscous dissipation.
- V.
- The generation of entropy owing to chemical reactions depends on each species, and therefore, NO formation directly affects the entropy generation rate.
- VI.
- The results prove that, in a reactive flow, the distributions of the total entropy generation rate and temperature are defined in practice by the chemical reactions process. The NO formation rate and total entropy generation rate are dependent on temperature. Therefore, by realizing the distribution of each of these three parameters (i.e., entropy generation), the approximate distributions of the other two (i.e., NO concentration and temperature) along with the combustion formation zone, can be predicted.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

List of symbols | |||

${A}_{pn}$ | Surface area of particle | Greek symbols | |

${D}_{i-mix}$ | Mass diffusion coefficient of species | $\alpha $ | Absorption coefficient |

${D}_{pn}$ | Particle diameter | ${\alpha}_{p}$ | Equivalent absorption coefficient |

${e}_{i}$ | Internal energy | ${\gamma}_{i}$ | Species chemical potential(J/kg K) |

${E}_{p}$ | Equivalent emission | $\mathsf{\Gamma}$ | Coefficient of diffusion |

${f}_{i}$ | Body force per unit volume of species $i$ | $\epsilon $ | Kinetic energy dissipation rate |

$I$ | Radiation intensity | ${\epsilon}_{pn}$ | Particle emissivity |

${j}_{i}$ | Mass flux of species $i$ | ${\mathsf{\Omega}}^{\prime}$ | Solid angle |

${k}_{b},{k}_{f}$ | Reaction rate constant | $\rho $ | Density ($\mathrm{kg}/{\mathrm{m}}^{3}$) |

$k$ | Kinetic energy of turbulence | ${\sigma}^{\prime}$ | Stefan-Boltzmann constant |

${k}_{eff}$ | Coefficient of thermal conductivity (W/m K) | ${\sigma}_{p}$ | Equivalent particle scattering factor |

n | Refractive index | ${\sigma}_{pn}$ | Particle scattering factor |

P | Pressure (Pa) | $\tau $ | Viscous stress (N/m^{2}) |

${P}_{ref}$ | Reference pressure | $\mathsf{\Psi}$ | Dependent variable |

${q}_{c}$ | Conduction heat flux | $\dot{{\omega}_{i}}$ | Production rate from chemical reaction |

r | Position vector | $\varnothing $ | Equivalence ratio |

$R$ | Gas constant (J/kg K) | $\eta $ | Phase function |

$R,\theta ,Z$ | Cylindrical coordinates system | $\mathsf{\Phi}$ | Viscous dissipation function |

$\stackrel{\xb4}{s}$ | Scattering direction vector | Subscripts | |

$s$ | Direction vector | $eff$ | Effective |

${s}_{i}$ | Specific entropy of species $i$ | · | Dot product (Multiplication) |

${S}_{\mathsf{\Psi}}$ | Source term | $\nabla $ | Vector differential operator |

${S}^{\u2034}$ | Volumetric generation rate of entropy (W/m^{3} K) | k | Variable type in Equation (1) |

$t$ | Time ($\mathrm{s}$) | Abbreviations | |

$T$ | Mean temperature ($\mathrm{K}$) | CO_{2} | Carbon dioxide |

${u}_{j}$ | Velocity component ($\mathrm{m}/\mathrm{s}$) | DOM | Discrete ordinate model |

V | Volume | EDM | Eddy dissipation model |

${X}_{i}$ | Species mole fraction | EGR | Exhaust gas recirculation |

${x}_{j}$ | Coordinates of Cartesian system | FGR | Flue gas recirculation |

$X,Y,Z$ | Coordinates of Cartesian system | FVM | Finite volume method |

${Y}^{+}$ | Non-dimensional distance | OH | hydroxyl radical |

${Y}_{i}$ | Species mass fraction | MD | Mean deviation |

$u,v,w$ | Velocity components ($\mathrm{m}/\mathrm{s}$) | NO | Nitrogen oxide |

$T$ | Mean temperature ($\mathrm{K}$) | NO_{X} | Nitrogen oxides |

Presumed density function | |||

WGSSM | Weighted sum of gray gases model |

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**Figure 2.**Independence evaluation of grid: (

**a**) mean temperature, (

**b**) NO concentration on center line (Y = 0, Z = 0).

**Figure 4.**Present simulation profiles in comparison with experiment [1] along center line (Z = Y = 0): (

**a**) Mean temperature, (

**b**) X-velocity.

**Figure 6.**Present lateral profiles of X-velocity as compared with experimental data [1], at different positions.

**Figure 7.**Present lateral profiles of mean temperature as compared with experimental data [1], at different positions.

**Figure 8.**Formation rates of (

**a**) prompt NO, and (

**b**) thermal NO, and (

**c**) concentration of NO in model combustor (mid-plane, Z = 0).

**Figure 9.**Present lateral profiles of NO species concentration as compared with experimental data [1], at three different positions.

**Figure 10.**Generation rate of entropy owing to (

**a**) chemical reactions, (

**b**) heat conduction, (

**c**) mass diffusion and (

**d**) viscous dissipation along mid-plane (Z = 0).

**Figure 11.**Distributions of (

**a**) mean temperature, (

**b**) NO concentration and (

**c**) total entropy generation rate along mid-plane (Z = 0).

**Figure 12.**Normalized variable of total entropy generation rate and NO formation rate: (

**a**) mean temperature and (

**b**) along center line (Y = Z = 0).

**Table 1.**Geometrical, flow, and boundary conditions details [1].

Parameter | Amount |
---|---|

Diameter of inlet air ($\mathrm{mm}$) | 50.8 |

Diameter of Fuel inlet ($\mathrm{mm}$) | 8.4 |

Flow rate of air ($\mathrm{kg}/\mathrm{s}$) | 0.55 |

Flow rate of fuel ($\mathrm{kg}/\mathrm{s}$) | 0.0162 |

Inlet Air temperature ($\mathrm{K}$) | 293 |

Inlet fuel temperature ($\mathrm{K}$) | 293 |

Fuel (gas) | Propane (C_{3}H_{8}) |

Conditions of walls | No-slip |

Exit pressure ($\mathrm{atm}$) | 1.0 |

Outlet diameter ($\mathrm{mm}$) | 50.5 |

Name of Grid | Size | $\mathbf{X}\times \mathbf{R}\times \mathsf{\theta}$ |
---|---|---|

(A) | $250,000$ | 165 $\times 33\times 46$ |

(B) | $500,000$ | 215 $\times 40\times 58$ |

(C) | $1,000,000$ | 298 $\times 46\times 73$ |

(D) | $1,500,000$ | 338 $\times 53\times 83$ |

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Mohammadi, M.; Abedinejad, M.S. Analysis of NO Formation and Entropy Generation in a Reactive Flow. *Aerospace* **2022**, *9*, 666.
https://doi.org/10.3390/aerospace9110666

**AMA Style**

Mohammadi M, Abedinejad MS. Analysis of NO Formation and Entropy Generation in a Reactive Flow. *Aerospace*. 2022; 9(11):666.
https://doi.org/10.3390/aerospace9110666

**Chicago/Turabian Style**

Mohammadi, Milad, and Mohammad Sadegh Abedinejad. 2022. "Analysis of NO Formation and Entropy Generation in a Reactive Flow" *Aerospace* 9, no. 11: 666.
https://doi.org/10.3390/aerospace9110666