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An empirical formula to predict the overall irreversibility of counter-flow premixed flames of methane and its mixtures

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Abstract

A novel method for estimating the non-equilibrium entropy generated in a premixed stretched methane flame is proposed. Counter-flow premixed methane flames were numerically investigated. The flame structure in terms of species, species production rate, and temperature was modeled using the San Diego mechanism with multicomponent diffusion. The local entropy generation of flames due to heat conduction, mass diffusion, viscous dissipation, and chemical reaction and the total irreversibility induced were analyzed for flames with various equivalence ratios at various temperatures, pressures, and counter-flow strain rates. The strain rate had a weak effect on the mass diffusion irreversibility and thermal conduction irreversibility but a strong effect on the chemical irreversibility. The overall irreversibility was highest at the equivalence ratio of 1.1. The heat conduction irreversibility, mass diffusion irreversibility, and chemical irreversibility all increased as the pressure was increased, and the chemical irreversibility increased as the temperature was increased. In all studied cases, the flame thickness decreased as the pressure or temperature was increased, and the flame thickness was inversely related to the non-equilibrium irreversibility. An empirical formula for predicting the irreversibility as a function of flame thickness was derived. The formula is valid not only for pure methane premixed flames but also for binary or triply blended fuel mixtures of methane, carbon monoxide, and hydrogen.

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Abbreviations

a :

Strain rate (s−1)

D :

Diffusivity (m2s−1)

F :

Function of x denotes axial velocity

G :

Function of x denotes radial velocity

H :

Pressure derivative in radial

h :

Specific enthalpy (kJ kg−1)

i :

Specific irreversibility (kJ kg−1)

I :

Total specific irreversibility (kJ kg−1)

P :

pressure (atm)

R :

Universal gas constant (kJ K−1 kmol−1)

r :

Radial direction

s :

Specific entropy (kJ kg−1 K−1)

T :

Temperature (K)

u :

Axial velocity of counter-flow premixed flame (m s−1)

v :

Radial velocity of counter-flow premixed flame s−1

W :

Molar weight (g mol−1)

X :

Molar fraction

x :

Axial direction

Y :

Mass fraction

δ :

Flame thickness (mm)

λ :

Thermal conductivity (W m−1 K−1)

μ :

Chemical potential (kJ kg−1)

ρ :

Density (kg m−3)

τ :

Viscous stress tensor

ϕ :

Equivalence ratio

ω :

Reaction rate (kmol m−3 s−1)

0:

Properties at standard state

chem:

Chemistry

cond:

Conduction

diff:

Mass diffusion

flame:

Flame

in:

Reactants at inlet

k:

Species k

max:

Maximum

mix:

Mixtures

visc:

Viscosity

x:

Axial direction of the counter-flow burner

‧ :

Dot over symbol denotes time rate

_ :

Bar over symbol denotes average

T :

Thermal

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Acknowledgements

This research was supported by the Ministry of Science and Technology, Taiwan, under Grant no. MOST 110-2221-E-006 -093. We thank Research Center for Energy Technology and Strategy, National Cheng King University, for providing computational resources.

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    Chien-Ru Yu & Chih-Yung Wu

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Yu, CR., Wu, CY. An empirical formula to predict the overall irreversibility of counter-flow premixed flames of methane and its mixtures. J Therm Anal Calorim 147, 14587–14599 (2022). https://doi.org/10.1007/s10973-022-11573-4

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