Numerical Study of Methane–Oxygen Premixed Flame Characteristics in Non-adiabatic Cylindrical Meso-Scale Reactors with the Backward-Facing Step

  • Mohammadreza BaigmohammadiEmail author
  • Sadegh Tabejamaat
  • Zeinab Javanbakht
Research Paper


In the present study, the effects of reactor diameter, inlet velocity, velocity profile, equivalence ratio (Phi, Ф), and outer wall convective and radiative heat transfer coefficients on flame characteristics in cylindrical non-adiabatic meso-scale reactors with the backward-facing step were investigated numerically. The results showed that these parameters could strongly affect the mole fraction of radical species within the flame zone. Also, it was shown that as compared to the reactor with 3 mm inner diameter, increasing the inlet velocity in the reactor with 5 mm inner diameter may lead to the opposite effect on the flame location. In addition, it was observed that the velocity profile could sensibly affect the flame location, temperature, and the species mole fractions in the meso-scale reactors. Moreover, it was demonstrated that the effect of equivalence ratio on the flame characteristics was more crucial for the reactors with smaller diameters. Furthermore, it was maintained that the outer wall convective and radiative heat transfer coefficients could cause the flame instability in the meso-scale reactors because of decreasing the mole fraction of important species such as O, H, and OH in the vicinity of the reactor inner wall.


Numeric Reactor Premixed Meso-scale Methane Oxygen 

List of symbols


Area (m2)


Heat capacity at constant pressure (J/kg K)


Molar concentration of species j in reaction r (kgmol/m3)


Mass diffusivity (m2/s)


Reactor outer diameter (m)


Emissivity coefficient


Specific enthalpy (J/kg)

\( h_{i}^{ \circ } \)

Standard-state enthalpy (kJ/kgmol)


Outer wall convective heat transfer coefficient (W/m2 K)


Thermal conductivity (W/m K)

kf or s

Thermal conductivity of fluid or solid (W/m K)

kf, r

Forward rate constant for reaction r

kb, r

Backward rate constant for reaction r


Molecular weight (kg/mol)


Total number of chemical species


Number of reaction


Pressure (pa, patm = 101,325 pa)

\( \dot{q} \)

Heat generation rate per unit of volume (W/m3)


Rate of reaction (kgmol/m3 s)


Temperature (K)


x-direction velocity (m/s)


y-direction velocity (m/s)

\( v^{\prime}_{i,r} \)

Stoichiometric coefficient of reactant species

\( v^{\prime\prime}_{i,r} \)

Stoichiometric coefficient of product species


Axial coordinate (m)


Monatomic value of thermal conductivity (W m−1 K−1)




Equivalence ratio


Lateral direction (m)


Mass fraction


Dynamic viscosity (N s/m2)

\( \gamma_{j,r} \)

Third-body efficiency of the ith species in the rth reaction


Density (kg/m3)


Lennard–Jones characteristic length (Angstroms)


Shear stress (Pa)


Reduced collision integral


Analogous reduced collision integral


Species mass generation rate per unit volume


The net effect of third bodies on the reaction rate

\( \eta^{\prime}_{j,r} \)

Rate exponent for reactant species j in reaction r

\( \eta^{\prime\prime}_{j,r} \)

Rate exponent for product species j in reaction r



Outer surface of the reactor wall


Species ith


Species i in the mixture


Species i in species jth




ith species in rth reaction


Species jth



xx, yx, xy, yy

Tensor index



Supplementary material

40997_2018_144_MOESM1_ESM.doc (2.9 mb)
Supplementary material 1 (DOC 2924 kb)


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Copyright information

© Shiraz University 2018

Authors and Affiliations

  • Mohammadreza Baigmohammadi
    • 1
    Email author
  • Sadegh Tabejamaat
    • 2
  • Zeinab Javanbakht
    • 2
  1. 1.Department of Physics, Faculty of Science and TechnologyUmeå UniversityUmeåSweden
  2. 2.Combustion and Turbulence Laboratory (CTL), Center of Excellence on Computational Aerospace Engineering, Department of Aerospace EngineeringAmirkabir University of Technology (Tehran Polytechnic)TehranIran

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