# The Exergy Losses Analysis in Adiabatic Combustion Systems including the Exhaust Gas Exergy

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## Abstract

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## 1. Introduction

## 2. Numerical Modeling

#### 2.1. Eulerian Stochastic Fields Method

#### 2.1.1. Manifold Generation

#### 2.1.2. Coupling FGM to LES

_{Yc}, in Equation (5) is highly nonlinear and remains normally unclosed in an LES context, it is difficult to accurately and correctly represent the thermochemical state only with the LES-filtered values of the controlling variables. Thus, the turbulence–chemistry interaction at the sub-grid scale level must be accounted for. In order to accomplish this task and provide the chemical source term in a closed form, the Eulerian stochastic fields (ESF) method was adopted.

#### 2.1.3. The Eulerian Stochastic Field (ESF) Method

_{sgs}= 0.7 [44]. The linear mean square estimation closure (LMSE) [43,47,48], also reported under the interaction by exchange with the mean model (IEM) [49], was adopted to provide a closure for the molecular diffusion or the micro-mixing term.

_{t}is the micro mixing time scale defined as (e.g., [35,36,37,44,46,47]):

_{Ω}= 2.

_{α}is obtained through the first moment and its sub-grid variance by the second moment as:

#### 2.1.4. Numerical Solution Procedure

^{∗}, which are continuously utilized in all equations to be solved. Following the solution steps explained in [25,44] and preserving the main numerical setup in terms of the different numerical scheme, the momentum predictor, pressure solver and stochastic contribution were not considered in the first phase of solution procedure while the stochastic fields were computed. In the second phase of calculation, when all fields reached convergence, the respective stochastic terms were included [53]. Simulations were performed using adjustable time step ∆t around 10

^{−7}to maintain the CFL-number below unity. As stated in previous works [35,36,37,44], eight stochastic fields are found sufficient to reach the convergence for Sandia flames.

#### 2.2. The Exergy Losses of Adiabatic Turbulent Flame

#### 2.2.1. Exergy Losses during Combustion

_{0}is the ambient temperature and Π

_{g}is the total rate of the entropy generation rate induced by the irreversibilities of the processes involved in the combustion system. The entropy production rate is derived from the filtered transport equation of entropy within the combustion system. Considering the gradient assumption for the entropy diffusion term, according to [22], it yields:

_{m}denotes the diffusion coefficient and τ (a, b) are the second-order SGS moments given by:

_{v}), heat transfer (II

_{q}), mass/diffusion of species (II

_{d}) and chemical reaction (II

_{ch}). Additional modeling is required to provide closure for these terms. In Equation (14), λ, C

_{p}, R

_{k}and μ

_{k}are the thermal conductivity, specific heat capacity, gas constant of species and specific chemical potential of species, respectively. It is worth mentioning that, in Equation (14), the cross-terms in the gradient-based contributions of the entropy production are not considered.

#### 2.2.2. Exergy Losses at the Exhaust Gas

## 3. Results and Discussion

#### 3.1. Experimental and Numerical Setup

^{−11}m

^{−3}in order to enhance the accuracy in computing the flow and scalar gradients, and consequently, the entropy generation rates.

#### 3.2. Validation

#### 3.3. Exergy Losses Analysis

#### 3.3.1. Entropy Generation during Combustion

#### 3.3.2. Exhaust Gases Exergy

_{2}and CO which can also be found in [36,37], the evaluation of these species draws on the evolution of the chemical exergy of exhaust gases. This is also visible in Figure 13 and Figure 14, where the instantaneous contour plots of the mass fraction of CO

_{2}and CO as well as the chemical exergy of exhaust gases for both flames were presented. In terms of values, the chemical exergy of the exhaust gases of flame F is higher than that of flame E, which is related to the exhaust gases species mass fractions. From these results, a strong link can be built between the combustion emissions presented by the exhaust gases and the exergy of the exhaust gases. The chemical exergy of the exhaust gases can give an idea of the combustion emissions, and as its value decreases, these emissions decrease.

## 4. Conclusions

- The exergy destroyed inside the combustion chamber increases with the increase in the mass flow rate along with the Re-number for flame F in comparison to flame E.
- The heat transfer and chemical reaction processes have higher contributions in entropy production compared to those of mass diffusion and viscous dissipation.
- With the increase in the jet velocity for flame F, inducing more concentrations and temperature gradients, further increase in entropy generation was expected compared to flame E. However, the lower predictivity of the ESF in the case of flame F leads to a slight difference in entropy generation, especially for the heat transfer entropy source term.

- The analysis of the chemical exergy content of exhaust gases decreases, going towards the combustion chamber outlet.
- Downstream from the burner, the temperature continues to decrease. The same decrease in the chemical exergy of the exhaust gases can be related to the temperature. This leads to the fact that cooling the exhaust gases can increase the exhaust gases exergy recovery.
- A strong link was found between the combustion emissions and the chemical exergy of the exhaust gases since its evolution follows the mass fractions of exhaust gases species.

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Nishida, K.; Takagi, T.; Kinoshita, S. Analysis of entropy generation and exergy loss during combustion. Proc. Comb. Inst
**2002**, 29, 869–874. [Google Scholar] [CrossRef] - Keenan, J.G. Availability and irreversibility in thermodynamics. Brit. J. Appl. Phys
**1951**, 2, 183–192. [Google Scholar] [CrossRef] - Bejan, A. Fundamentals of exergy analysis, entropy generation minimization, and the generation of flow architecture. Int. J. Energy Res.
**2002**, 26, 545–565. [Google Scholar] [CrossRef] - Som, S.K.; Datta, A. Thermodynamic irreversibilities and exergy balance in combustion processes. Prog. Energy Combust. Sci.
**2008**, 34, 351–376. [Google Scholar] [CrossRef] - Sciacovelli, A.; Verda, V.; Sciubba, E. Entropy generation analysis as a design tool—A review. Renew. Sust. Energ. Rev.
**2015**, 43, 1167–1181. [Google Scholar] [CrossRef] - Caton, J.A. Implications of fuel selection for an SI engine: Results from the first and second laws of thermodynamics. Fuel
**2010**, 89, 3157–3166. [Google Scholar] [CrossRef] - Caton, J.A. A cycle simulation including the second law of thermodynamics for a spark-ignition engine: Implications of the use of multiple-zones for combustion. SAE Tech. Paper
**2002**, 111, 281–299. [Google Scholar] - Javaheri, A.; Esfahanian, V.; Salavati-Zadeh, A.; Darzi, M. Energetic and exergetic analyses of a variable compression ratio spark ignition gas engine. Energy Convers. Manag.
**2014**, 88, 739–748. [Google Scholar] [CrossRef] - Özkan, M.; Özkan, D.B.; Özener, O.; Yılmaz, H. Experimental study on energy and exergy analyses of a diesel engine performed with multiple injection strategies: Effect of pre-injection timing. Appl. Therm. Eng.
**2013**, 53, 21–30. [Google Scholar] [CrossRef] - Taghavifar, H.; Khalilarya, S.; Jafarmadar, S. Exergy analysis of combustion n in VGT-modified diesel engine with detailed chemical kinetics mechanism. Energy
**2015**, 93, 740–748. [Google Scholar] [CrossRef] - Rakopoulos, C.D.; Giakoumis, E.G. Simulation and exergy analysis of transient diesel-engine operation. Energy
**1997**, 22, 875–885. [Google Scholar] [CrossRef] - Sayin, C.; Hosoz, M.; Canakci, M.; Kilicaslan, I. Energy and exergy analyses of a gasoline engine. Int. J. Energy Res.
**2007**, 31, 259–273. [Google Scholar] [CrossRef] - Feng, H.; Liu, D.; Yang, X.; An, M.; Zhang, W.; Zhang, X. Availability analysis of using iso-octane/n-butanol blends in spark-ignition engines. Renew. Energy
**2016**, 96, 281–294. [Google Scholar] [CrossRef] - Teh, K.Y.; Miller, S.L.; Edwards, C.F. Thermodynamic requirements for maximum internal combustion engine cycle efficiency. Part 1: Optimal combustion strategy. Int. J. Engine Res.
**2008**, 9, 449–465. [Google Scholar] [CrossRef] - Teh, K.Y.; Miller, S.L.; Edwards, C.F. Thermodynamic requirements for maximum internal combustion engine cycle efficiency. Part 2: Work extraction and reactant preparation strategies. Int. J. Engine Res.
**2008**, 9, 467–481. [Google Scholar] [CrossRef] - Bhatti, S.S.; Verma, S.; Tyagi, S.K. Energy and exergy-based performance evaluation of variable compression ratio spark ignition engine based on experimental work. Therm. Sci. Eng. Prog.
**2019**, 9, 332–339. [Google Scholar] [CrossRef] - da Costa, Y.J.R.; de Lima, A.G.B.; Filho, C.R.B.; de Araujo Lima, L. Energetic and exergetic analyses of a dual-fuel diesel engine. Renew. Sustain. Energy Rev.
**2012**, 16, 4651–4660. [Google Scholar] [CrossRef] - Li, Y.; Jia, M.; Chang, Y.; Kokjohn, S.L.; Reitz, R.D. Thermodynamic energy and exergy analysis of three different engine combustion regimes. Appl. Energy
**2016**, 180, 849–858. [Google Scholar] [CrossRef] - Sanli, B.G.; Özcanli, M.; Serin, H. Assessment of thermodynamic performance of an IC engine using microalgae biodiesel at various ambient temperatures. Fuel
**2020**, 277, 118108. [Google Scholar] [CrossRef] - Punov, P.; Evtimov, T.; Chiriac, R.; Clenci, A.; Danel, Q.; Descombes, G. Progress in high performance, low emissions, and exergy recovery in internal combustion engines. Int. J. Energy Res
**2017**, 41, 1229–1241. [Google Scholar] [CrossRef] - Safari, M.; Sheikhi, M.R.H.; Janbozorgi, M.; Metghalchi, H.; Sheikhi, R.H. Entropy transport equation in large eddy simulation for exergy analysis of turbulent combustion systems. Entropy
**2010**, 12, 434–444. [Google Scholar] [CrossRef] - Safari, M.; Hadi, F.; Sheikhi, M.R.H. Progress in the Prediction of entropy generation in turbulent reacting flows using large eddy simulation. Entropy
**2014**, 16, 5159–5177. [Google Scholar] [CrossRef] [Green Version] - Pope, S. PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci
**1985**, 11, 119–192. [Google Scholar] [CrossRef] - Pope, S.B. A monte carlo method for the PDF equations of turbulent reactive flow. Combust. Sci. Technol.
**1981**, 25, 159–174. [Google Scholar] [CrossRef] - Agrebi, S.; Dreßler, L.; Nicolai, H.; Ries, F.; Nishad, K.; Sadiki, A. Analysis of Local Exergy Losses in Combustion Systems Using a Hybrid Filtered Eulerian Stochastic Field Coupled with Detailed Chemistry Tabulation: Cases of Flames D and E. Energies
**2021**, 14, 6315. [Google Scholar] [CrossRef] - Ries, F.; Li, Y.; Nishad, K.; Janicka, J.; Sadiki, A. Entropy generation analysis and thermodynamic optimization of jet impinge-ment cooling using large eddy simulation. Entropy
**2019**, 19, 129. [Google Scholar] [CrossRef] [Green Version] - Valencia, G.; Fontalvo, A.; Cárdenas, Y.; Duarte, J.; Isaza, C. Energy and Exergy Analysis of Different Exhaust Waste Heat Recovery Systems for Natural Gas Engine Based on ORC. Energies
**2019**, 12, 2378. [Google Scholar] [CrossRef] [Green Version] - Rosen, M.A.; Dincer, I. On exergy and environmental impact. Int. J. Energy Res.
**1997**, 21, 643–654. [Google Scholar] [CrossRef] - Valero, A.; Usón, S.; Torres, C.; Stanek, W. Theory of Exergy Cost and Thermo-ecological Cost. In Thermodynamics for Sustainable Management of Natural Resources. Green Energy and Technology; Stanek, W., Ed.; Springer: Cham, Switzerland, 2017. [Google Scholar]
- Valero, A.; Valero, A.; Stanek, W. Assessing the exergy degradation of the natural capital: From Szargut’s updated reference environment to the new thermogeological-cost methodology. Energy
**2018**, 163, 1140–1149. [Google Scholar] [CrossRef] - Veiga, J.P.S.; Romanelli, T.L. Mitigation of greenhouse gas emissions using exergy. J. Clean. Prod.
**2020**, 260, 121092. [Google Scholar] [CrossRef] - Vihervaara, P.; Franzese, P.P.; Buonocore, E. Information, energy, and eco-exergy as indicators of ecosystem complexity. Ecol. Model.
**2019**, 395, 23–27. [Google Scholar] [CrossRef] - Wu, J.; Wang, N. Exploring avoidable carbon emissions by reducing exergy destruction based on advanced exergy analysis: A case study. Energy
**2020**, 206, 118246. [Google Scholar] [CrossRef] - Rosen, M.A. Exergy Analysis as a Tool for Addressing Climate Change. Eur. J. Sustain. Dev. Res.
**2021**, 5, 0148. [Google Scholar] [CrossRef] - Prasad, V.N. Large Eddy Simulation of Partially Premixed Turbulent Combustion. Ph.D. Thesis, Imperial College London, University of London, London, UK, 2011. [Google Scholar]
- Jones, W.; Prasad, V. Large eddy simulation of the Sandia flame series (D–F) using the Eulerian stochastic field method. Combust. Flame
**2010**, 157, 1621–1636. [Google Scholar] [CrossRef] - Yifan, D.U.A.N.; Zhixun, X.I.A.; Likun, M.A.; Zhenbing, L.U.O.; Huang, X.; Xiong, D.E.N.G. LES of the Sandia flame series D-F using the Eulerian stochastic field method coupled with tabulated chemistry. Chin. J. Aeronaut
**2020**, 33, 116–133. [Google Scholar] - Bilger, R.W.; Stårner, S.H.; Kee, R.J. On reduced mechanisms for methane-air combustion in non-premixed flames. Combust. Flame
**1990**, 80, 135–149. [Google Scholar] [CrossRef] - Mahmoud, R.; Jangi, M.; Ries, F.; Fiorina, B.; Janicka, J.; Sadiki, A. Combustion characteristics of a non-premixed oxy-flame applying a hybrid filtered eulerian stochastic field/flamelet progress variable approach. Appl. Sci.
**2019**, 9, 1320. [Google Scholar] [CrossRef] [Green Version] - Goodwin, D.; Moffat, H.K. Cantera. Available online: http://code.google.com/p/cantera/ (accessed on 28 June 2021).
- Nicoud, F.; Toda, H.B.; Cabrit, O.; Bose, S.; Lee, J. Using singular values to build a subgrid-scale model for large eddy simula-tions. Phys. Fluids
**2011**, 23, 085106. [Google Scholar] [CrossRef] [Green Version] - Valiño, L. A field monte carlo formulation for calculating the probability density function of a single scalar in a turbulent flow. Flow Turbul. Combust.
**1998**, 60, 157–172. [Google Scholar] [CrossRef] - Dopazo, C.; O’Brien, E.E. Functional formulation of non-isothermal turbulent reactive flows. Phys. Fluids
**1974**, 17, 1968–1975. [Google Scholar] [CrossRef] [Green Version] - Dressler, L.; Filho, F.L.S.; Ries, F.; Nicolai, H.; Janicka, J.; Sadiki, A. Numerical prediction of turbulent spray flame characteristics using the filtered eulerian stochastic field approach coupled to tabulated chemistry. Fluids
**2021**, 6, 50. [Google Scholar] [CrossRef] - Jones, W.P.; Navarro-Martinez, S.; Röhl, O. Large eddy simulation of hydrogen auto-ignition with a probability density function method. Proc. Combust. Inst.
**2007**, 31, 1765–1771. [Google Scholar] [CrossRef] - Avdić, A.; Kuenne, G.; di Mare, F.; Janicka, J. LES combustion modeling using the Eulerian stochastic field method coupled with tabulated chemistry. Combust. Flame
**2017**, 175, 201–219. [Google Scholar] [CrossRef] - Frost, V.A. Model of a turbulent, diffusion-controlled flame jet. Fluid Mech. Soviet Res.
**1975**, 4, 124–133. [Google Scholar] - O’Brien, E.E. The probability density function (pdf) approach to reacting turbulent flows. In Turbulent Reacting Flows; Springer: Berlin/Heidelberg, Germany, 1980; pp. 185–218. [Google Scholar]
- Villermaux, J.; Falk, L. A generalized mixing model for initial contacting of reactive fluids. Chem. Eng. Sci.
**1994**, 49, 5127–5140. [Google Scholar] [CrossRef] - Kloeden, P.E.; Platen, E. Numerical Solution of Stochastic Differential Equations; Springer Science & Business Media: New York, NY, USA, 1992. [Google Scholar]
- Picciani, M.A. Investigation of Numerical Resolution Requirements of the Eulerian Stochastic Fields and the Thickened Sto-chastic Field Approach. Ph.D. Thesis, University of Southampton, Southampton, UK, 2018. [Google Scholar]
- Muradoglu, M.; Jenny, P.; Pope, S.B.; Caughey, D.A. A consistent hybrid finite-volume/particle method for the PDF equations of turbulent reactive flows. J. Comput. Phys.
**1999**, 154, 342–371. [Google Scholar] [CrossRef] [Green Version] - Garmory, A. Micro-mixing Effects in Atmospheric Reacting Flows. Ph.D. Thesis, University of Cambridge, Cambridge, UK, 2008. [Google Scholar]
- Sahoo, B.B.; Dabi, M.; Saha, U.K. A Compendium of Methods for Determining the Exergy Balance Terms Applied to Reciprocating Internal Combustion Engines. J. Energy Resour. Technol.
**2021**, 143, 120801. [Google Scholar] [CrossRef] - Dimitrova, Z.; Marechal, F. Energy Integration on Multi-periods for Vehicle Thermal Powertrains. Can. J. Chem. Eng.
**2017**, 95, 235–264. [Google Scholar] [CrossRef] - Khaliq, A.; Trivedi, S.K. Second Law Assessment of a Wet Ethanol Fuelled HCCI Engine Combined with Organic Rankine Cycle. ASME J. Energy Resour. Technol.
**2012**, 134, 022201. [Google Scholar] [CrossRef] - Salek, F.; Babaie, M.; Ghodsi, A.; Hosseini, S.V.; Zare, A. Energy and Exergy Analysis of a Novel Turbo-compounding System for Supercharging and Mild Hybridization of a Gasoline Engine. J. Therm. Anal. Calorim
**2020**, 145, 817–828. [Google Scholar] [CrossRef] - Ntziachristos, L.; Samaras, Z.; Zervas, E.; Dorlhene, P. Effects of a Catalysed and an Additized Partied Filter on the Emissions of a Diesel Passenger Car Operating on Low Sulphur Fuels. Atmos. Environ.
**2005**, 39, 4925–4936. [Google Scholar] [CrossRef] - Moran, M.J.; Shapiro, H.N.; Boettner, D.D.; Bailey, M.B. Fundamentals of Engineering Thermodynamics; John Wiley & Sons: Hoboken, NJ, USA, 2010. [Google Scholar]
- TNF Workshop. Available online: http://www.ca.sandia.gov/TNF (accessed on 28 June 2021).

**Figure 1.**Mean and RMS mixture fraction at different axial positions: case of flame E. Dashed line: unresolved contribution from LES/ESF to RMS.

**Figure 5.**Instantaneous entropy generation due to heat transfer: (

**a**) flame E; (

**b**) flame F and chemical reaction; (

**c**) flame E; and (

**d**) flame F.

**Figure 6.**Instantaneous entropy generation due to mass diffusion (

**a**) flame E; (

**b**) flame F and viscous dissipation; (

**c**) flame E; and (

**d**) flame F.

**Figure 7.**Radial profile of the volumetric entropy from heat transfer at various axial positions for flame E (red) and flame F (black dashed).

**Figure 8.**Radial profile of the chemical reaction entropy generation source term at different axial positions for flames E and F.

**Figure 9.**Radial profile of the mass diffusion entropy generation source term at various axial positions for flames E and F.

**Figure 10.**Radial profile of the viscous dissipation entropy generation source term at different axial positions for flames E and F.

**Figure 11.**Radial profiles of mean CO

_{2}, CO mass fraction and chemical exhaust gases exergy at various axial locations for Sandia flame E.

**Figure 12.**Radial profiles of mean CO

_{2}, CO mass fraction and chemical exhaust gases exergy at various axial locations for Sandia flame F.

**Figure 13.**Instantaneous contour plots of the chemical exhaust gases exergy, CO

_{2}and CO mass fractions Sandia flame E.

**Figure 14.**Instantaneous contour plots of the chemical exhaust gases exergy, CO

_{2}and CO mass fractions Sandia flame F.

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**MDPI and ACS Style**

Agrebi, S.; Dreßler, L.; Nishad, K.
The Exergy Losses Analysis in Adiabatic Combustion Systems including the Exhaust Gas Exergy. *Entropy* **2022**, *24*, 564.
https://doi.org/10.3390/e24040564

**AMA Style**

Agrebi S, Dreßler L, Nishad K.
The Exergy Losses Analysis in Adiabatic Combustion Systems including the Exhaust Gas Exergy. *Entropy*. 2022; 24(4):564.
https://doi.org/10.3390/e24040564

**Chicago/Turabian Style**

Agrebi, Senda, Louis Dreßler, and Kaushal Nishad.
2022. "The Exergy Losses Analysis in Adiabatic Combustion Systems including the Exhaust Gas Exergy" *Entropy* 24, no. 4: 564.
https://doi.org/10.3390/e24040564