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Research Papers: Fuel Combustion

# Modeling of Entropy Generation in Turbulent Premixed Flames for Reynolds Averaged Navier–Stokes Simulations: A Direct Numerical Simulation Analysis

[+] Author and Article Information
Nilanjan Chakraborty

School of Mechanical and Systems Engineering,
Newcastle University,
Newcastle-Upon-Tyne,
NE1 7RU, UK
e-mail: nilanjan.chakraborty@ncl.ac.uk

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received March 31, 2014; final manuscript received September 9, 2014; published online October 21, 2014. Assoc. Editor: Reza H. Sheikhi.

J. Energy Resour. Technol 137(3), 032201 (Oct 21, 2014) (13 pages) Paper No: JERT-14-1093; doi: 10.1115/1.4028693 History: Received March 31, 2014; Revised September 09, 2014

## Abstract

The modeling of the mean entropy generation rate $S·"' gen¯$ due to combined actions of viscous dissipation, irreversible chemical reaction, thermal conduction and mass diffusion (i.e., $T¯1,T¯2,T¯3$, and $T¯4$) in the context of Reynolds averaged Navier–Stokes (RANS) simulations has been analyzed in detail based on a direct numerical simulation (DNS) database with a range of different values of heat release parameter $τ$, global Lewis number Le, and turbulent Reynolds number $Ret$ spanning both the corrugated flamelets (CF) and thin reaction zones (TRZ) regimes of premixed turbulent combustion. It has been found that the entropy generation due to viscous dissipation $T¯1$ remains negligible in comparison to the other mechanisms of entropy generation (i.e., $T¯2,T¯3$, and $T¯4$) within the flame for all cases considered here. A detailed scaling analysis has been used to explain the relative contributions of , and $T¯4$ on the overall volumetric entropy generation rate $S·"' gen¯$ in turbulent premixed flames. This scaling analysis is further utilized to propose models for $T¯1,T¯2,T¯3$, and $T¯4$ in the context of RANS simulations. It has been demonstrated that the new proposed models satisfactorily predict $T¯1,T¯2,T¯3$, and $T¯4$ for all cases considered here. The accuracies of the models for $T¯1,T¯2,T¯3$, and $T¯4$ have been demonstrated to be closely linked to the modeling of dissipation rate of turbulent kinetic energy and scalar dissipation rates (SDRs) in turbulent premixed flames.

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## Figures

Fig. 1

Variations of T1¯×αT/(ρ0cpSL2), (broken line), T2¯×αT/(ρ0cpSL2) (solid line), T3¯×αT/(ρ0cpSL2) (line with + symbol), T4¯×αT/(ρ0cpSL2) (line with circles), and S·¯gen×αT/(ρ0cpSL2) (line with stars) with c˜ across the flame brush for cases: (a) A, (b) B, (c) C, (d) E, (e) F, (f) G, (g) H, and (h) L

Fig. 2

Variations of T1¯×αT/(ρ0cpSL2) (solid line) and res(T1¯)×αT/(ρ0cpSL2) (broken line) with c˜ across the flame brush along with the prediction of Eq. (8c) (model) (line with circles) for cases: (a) A, (b) B, (c) C, (d) E, (e) F, (f) G, (g) H, and (h) L

Fig. 3

Variations of T2¯×αT/(ρ0cpSL2) (solid line) and 0.1×res(T2¯)×αT/(ρ0cpSL2) (broken line) with c˜ across the flame brush along with the prediction of Eq. (10) (line with circles) and Eq. (12) (line with stars) for cases: (a) A, (b) B, (c) C, (d) E, (e) F, (f) G, (g) H, and (h) L

Fig. 4

Variations of T3¯×αT/(ρ0cpSL2) (solid line) and res(T3¯)×αT/(ρ0cpSL2) (broken line) with c˜ across the flame brush along with the prediction of Eq. (13) (Model) (line with circles) for cases: (a) A, (b) B, (c) C, (d) E, (e) F, (f) G, (g) H, and (h) L

Fig. 5

Variations of T4¯×αT/(ρ0cpSL2) (solid line) and res(T4¯)×αT/(ρ0cpSL2) (broken line) with c˜ across the flame brush along with the prediction of Eq. (15) (model) (line with circles) for cases: (a) A, (b) B, (c) C, (d) E, (e) F, (f) G, (g) H, and (h) L

Fig. 6

Variations of S·"' gen¯×αT/(ρ0cpSL2)=(T1¯+T2¯+T3¯+T4¯)×αT/(ρ0cpSL2) (solid line) with c˜ across the flame brush along with the predictions of Eqs. (8c), (12), (13), and (15) (model) (broken line) for cases: (a) A, (b) B, (c) C, (d) E, (e) F, (f) G, (g) H, and (h) L

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