# Computational Simulation of Entropy Generation in a Combustion Chamber Using a Single Burner

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Computational Model

_{f}, r

_{i}, r

_{o}were of the order of 0.004, 0.006, and 0.01, respectively.

#### 2.1. Mathematical Formulation

_{i,r}, given as follows:

#### 2.2. Combustion and Reaction Mechanism

_{2}:50% C

_{3}H

_{8}) is considered. It is established in Reference [29] that hydrogen reduces the emission of some unsafe components; pure hydrogen fuel combustion avoids CO or unburned HC production.

#### 2.3. Entropy Generation Rate

#### 2.4. Numerical Tools

## 3. Simulation Results

#### 3.1. Operating Values and Validation

_{F}and Y

_{O}represent the fuel and oxidizer mass fractions, respectively. The subscript st refers to stoichiometric conditions.

#### 3.2. Physical Fields

#### 3.2.1. Reaction Rates

#### 3.2.2. Temperature Distribution

#### 3.2.3. Entropy Generation and Bejan Number

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Latin Symbols | |

Be | Bejan number |

CFD | Computational fluid dynamics |

Cμ, Cε1, Cε2 | Coefficients in k–ε turbulence model |

f_{k,j} | Specific force of volume acting on the species K in the direction i |

H | Enthalpy |

h_{k} | Specific enthalpy of the species k |

h_{s,k} | Heat transfer coefficient, sensible enthalpy of species |

K | Turbulent kinetic energy |

L | Length of burner |

LCV | Lower calorific value |

P | Pressure |

RNG | Renormalization group |

R | Radial distance |

${r}_{i}$ | Inner radius of air inlet |

${r}_{0}$ | Outer radius of air inlet |

${s}_{gen}^{\u2034}$ | Volumetric entropy generation rate |

T | Temperature |

u_{i} | Velocity in direction i |

V_{k,i} | Velocity diffusion of the species k in direction i |

Y_{k} | Mass fraction of the species k |

Greek Symbols | |

${\delta}_{ij}$ | Kronecker delta |

$\epsilon $ | Turbulent energy dissipation rate |

$\varphi $ | Equivalence ratio |

$\Phi $ | Viscous dissipation |

$\lambda $ | Air excess ratio |

$\mu $ | Dynamic viscosity |

$\rho $ | Density |

$\theta $ | Tangential direction |

${\rho}_{k}$ | Density of the species k |

${\sigma}_{ij}$ | Tensor of the constraint in plan i and the direction j |

${\dot{\omega}}_{k}$ | Production rate of the k species. |

$\dot{Q}$ | Heat transfer rate |

${\tau}_{ij}$ | Tensor of the viscous constraints |

Subscripts | |

F | Fuel |

K | Species |

N | Total number of species number |

O | Oxidant |

P | At constant pressure |

S | Sensibility (enthalpy) |

V | At constant volume |

R | Radial |

X | Axial |

Amb | Ambient |

Air | Air |

Eff | Effective |

Fric | Friction |

Heat | Heat transfer |

i,j | Indices of tensor notation |

In | Inlet |

## References

- BP 2011 Statistical Review of World Energy; The British Petroleum Company: London, UK, 2011.
- Bejan, A. Entropy Generation Through Heat and Fluid Flow; Wiley: New York, NY, USA, 1982. [Google Scholar]
- Bejan, A. Entropy Generation Minimization; CRC Press: New York, NY, USA, 1995. [Google Scholar]
- Som, S.K.; Datta, A. Thermodynamic irreversibilities and exergy balance in combustion processes. Prog. Energy Combust. Sci.
**2008**, 34, 351–376. [Google Scholar] [CrossRef] - Oztop, H.F.; Al-Salem, K. A review on entropy generation in natural and mixed convection heat transfer for energy systems. Renew. Sustain. Energy Rev.
**2011**, 16, 911–920. [Google Scholar] [CrossRef] - Ko, T.H.; Wu, C.P. A numerical study on entropy generation induced by turbulent forced convection in curved rectangular ducts with various aspect ratios. Int. Commun. Heat Mass Transf.
**2009**, 36, 25–31. [Google Scholar] [CrossRef] - Gazzah, M.H.; Belmabrouk, H. Local entropy generation in coflowing turbulent jets with variable density. Int. J. Numer. Methods Heat Fluid Flow
**2014**, 24, 1679–1695. [Google Scholar] [CrossRef] - Gazzah, M.H.; Belmabrouk, H. Directed co-flow effects on local entropy generation in turbulent heated round jets. Comput. Fluids
**2014**, 105, 285–293. [Google Scholar] [CrossRef] - Elkaroui, A.; Ben Haj Ayech, S.; Hichem Gazzah, M.; Mahjoub Saïd, N.; Le Palec, G. Numerical study of local entropy generation in a heated turbulent plane jet developing in a co-flowing stream. Appl. Math. Model.
**2018**, 62, 605–628. [Google Scholar] [CrossRef] - Elkaroui, A.; Hichem Gazzah, M.; Mahjoub Saïd, N.; Bournot, P.; Le Palec, G. Entropy generation concept for a turbulent plane jet with variable density. Comput. Fluids
**2018**, 168, 328–341. [Google Scholar] [CrossRef] - Mahmud, S.; Fraser, R.A. The second law analysis in fundamental convective heat transfer problem. Int. J. Thermal Sci.
**2003**, 42, 177–186. [Google Scholar] [CrossRef] - Akih-Kumgeh, B. Toward improved understanding of the physical meaning of entropy in classical thermodynamics. Entropy
**2016**, 18, 270. [Google Scholar] [CrossRef] - Kostic, M.M. The elusive nature of entropy and its physical meaning. Entropy
**2014**, 16, 953–967. [Google Scholar] [CrossRef] - Yilbas, B.S.; Shuja, S.Z.; Rashid, M. Confined swirling jet impingement onto an adiabatic wall. Int. J. Heat Mass Transf.
**2013**, 46, 2947–2955. [Google Scholar] - Shuja, S.Z.; Yilbas, B.S.; Budair, M.O. Local entropy generation in an impinging jet: Minimum entropy concept evaluating various turbulence models. Comput. Methods Appl. Mech. Eng.
**2001**, 190, 3623–3644. [Google Scholar] [CrossRef] - Demirel, Y.; Kahraman, R. Entropy generation in a rectangular packed duct with wall heat flux. Int. J. Heat Mass Transf.
**1999**, 42, 2337–2344. [Google Scholar] [CrossRef][Green Version] - Bouras, F.; Soudani, A.; Si Ameur, A. Thermochemical study of internal combustion engine. Energy Procedia
**2012**, 18, 1086–1095. [Google Scholar] [CrossRef] - Bouras, F.; Attia, M.E.H.; Khaldi, F. Entropy generation optimization in internal combustion. Engine Environ. Process.
**2015**, 2, 233–242. [Google Scholar] [CrossRef] - Zimmermann, S.; Tiwari, M.K.; Meijer, I.; Paredes, S.; Michel, B.; Poulikakos, D. Hot water cooled electronics: Exergy analysis and waste heat reuse feasibility. Int. J. Heat Mass Transf.
**2012**, 55, 6391–6399. [Google Scholar] [CrossRef] - Dunbar, W.R.; Lior, N. Sources of combustion irreversibility. Combust. Sci. Technol.
**1994**, 103, 41–61. [Google Scholar] [CrossRef] - Goodarzi, M.; Safaei, M.; Hakan, R.; Oztop, F.; Karimipour, A.; Sadeghinezhad, E.; Dahari, M.; Kazi, S.N.; Jomhari, N. Numerical study of entropy generation due to coupled laminar and turbulent mixed convection and thermal radiation in an enclosure filled with a semitransparent medium. Sci. World J.
**2014**, 2014, 8. [Google Scholar] [CrossRef] [PubMed] - Chen, S. Analysis of entropy generation in counter-flow premixed hydrogen air combustion. Int. J. Hydrog. Energy
**2010**, 35, 1401–1411. [Google Scholar] [CrossRef] - Chen, S.; Li, J.; Han, H.; Liu, Z.; Zheng, C. Effects of hydrogen addition on entropy generation in ultra-lean counter-flow methane-air premixed combustion. Int. J. Hydrog. Energy
**2010**, 35, 3891–3902. [Google Scholar] [CrossRef] - Chen, S.; Han, H.; Liu, Z.; Li, J.; Zheng, C. Analysis of entropy generation in non-premixed hydrogen versus heated air counter-flow combustion. Int. J. Hydrog. Energy
**2010**, 35, 4736–4746. [Google Scholar] [CrossRef] - Chen, S.; Liu, Z.; Liu, J.; Li, J.; Wang, L.; Zheng, C. Analysis of entropy generation in hydrogen-enriched ultra-lean counter-flow methane-air non-premixed combustion. Int. J. Hydrog. Energy
**2010**, 35, 12491–12501. [Google Scholar] [CrossRef] - Morsli, S.; El Ganaoui, M.; Sabeur, A. Numerical investigation of diffusion turbulent propane/air flame. Energy Environ. Biol. Biomed.
**2014**, 232, 18–23. [Google Scholar] - Morsli, S.; Sabeur, A.; El Ganaoui, M. Simulation of a burner with different fuels and analysis based on entropy generation. Energy Procedia
**2017**, 139, 631–638. [Google Scholar] [CrossRef] - Magnussen, B.F.; Hjertager, B.H. On mathematical models of turbulent combustion with special emphasis on soot formation and combustion. In Proceedings of the 16th Symposium (International) on Combustion, Cambridge, UK, 15–20 August 1976; The Combustion Institute: Pittsburgh, PA, USA, 1997. [Google Scholar]
- Ilbas, M.; Yılmaz, I.; Kaplan, Y. Investigations of hydrogen and hydrogen–hydrocarbon composite fuel combustion and NO
_{x}emission characteristics in a model combustor. Int. J. Hydrogen Energy**2005**, 30, 1139–1147. [Google Scholar] [CrossRef] - Fluent Inc. FLUENT 6.3.26 User’s Guide; Fluent Inc.: New York, NY, USA, 2006. [Google Scholar]
- Launder, B.E.; Spalding, D.B. Lectures in Mathematical Models of Turbulence; Academic Press: London, UK, 1972. [Google Scholar]
- Poinsot, T.; Veynante, D. Theoretical and Numerical Combustion; RT Edwards Inc.: Philadelphia, PA, USA, 2005. [Google Scholar]
- Pinho, C.E.L.; Delgado, J.M.P.Q.; Pilão, R.; Conde, J.; Pinho, C. Defect and diffusion. In Diffusion in Solids and Liquids III; Öchsner, A., Murch, G.E., Eds.; Trans Tech Publications: Zurich, Switzerland, 2008; Volume 273, pp. 144–149. [Google Scholar]
- Morsli, S.; Sabeur, A.; El Ganaoui, M. Numerical simulation of entropy generation in hydrogen-air burner. FDMP
**2015**, 4, 342–353. [Google Scholar] - Yapici, H.; Kayataş, N.; Albayrak, B.; Baştürk, G. Numerical study of burner effect of oxygen fraction on local entropy generation in a methane-air. Sadhana
**2004**, 29, 641–667. [Google Scholar] [CrossRef]

**Figure 2.**Contours of reaction rates for different values of the equivalence ratio ϕ and oxygen percentage in air.

**Figure 3.**Variations of temperature at the axis of the burner depending on the axial distance for (

**a**) ϕ = 0.5 and (

**b**) ϕ = 1.0, at different values of γ.

**Figure 4.**Logarithmic volumetric local entropy generation rate contours for ϕ = 0.5, 0.7, and 1.0, at different values of γ.

U Air (m/s) | |||
---|---|---|---|

$\lambda (\%)$ | ϕ = 0.5 | ϕ = 0.7 | ϕ = 1 |

10 | 56.436 | 40.312 | 20.218 |

20 | 28.614 | 20.439 | 14.307 |

30 | 19.340 | 13.814 | 9.670 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Morsli, S.; Sabeur, A.; El Ganaoui, M.; Ramenah, H.
Computational Simulation of Entropy Generation in a Combustion Chamber Using a Single Burner. *Entropy* **2018**, *20*, 922.
https://doi.org/10.3390/e20120922

**AMA Style**

Morsli S, Sabeur A, El Ganaoui M, Ramenah H.
Computational Simulation of Entropy Generation in a Combustion Chamber Using a Single Burner. *Entropy*. 2018; 20(12):922.
https://doi.org/10.3390/e20120922

**Chicago/Turabian Style**

Morsli, Souad, Amina Sabeur, Mohammed El Ganaoui, and Harry Ramenah.
2018. "Computational Simulation of Entropy Generation in a Combustion Chamber Using a Single Burner" *Entropy* 20, no. 12: 922.
https://doi.org/10.3390/e20120922