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ABSTRACT
This research employs a more detailed radiation treatment to improve the accuracy of the velocity-turbulent frequency-composition joint probability density function (PDF) methods in numerical solution of the turbulent non-premixed flames. The radiation heat transfer in the traditional velocity-frequency-composition joint PDF methods has been disregarded or treated simply using an emission-only radiation model, even though radiation is important in the combustion systems. In the present PDF method, radiation is modeled using the P1-approximation and the radiative properties are calculated by the weighted-sum-of-gray-gases (WSGG) model. The results of present method are first validated by solving a laboratory turbulent piloted jet flame and comparing them with the measured data. Then, two constructed large-scale flames are modeled and simulated. Results reveal that reabsorption of emitted radiation increases from 2.98% in a laboratory-scale flame to 56.8% in the scaled-up flame and has a strong effect on the temperature distribution in the scaled-up flame. It is shown that reabsorption of emitted radiation increases the peak temperature on the flame axis by 119 degrees. Furthermore, radiation becomes more significant with the increase of the flame scales, so that the radiation fraction increases from 4.15% in the small-scale flame to 16.6% in the large-scale flame.
Nomenclature
| Variables | = | |
| = | weighting factor corresponding to the gray gas j | |
| ap,i | = | Planck mean absorption coefficient for species i, 1/atm.m |
| = | the mass-weighted joint probability density function | |
| Gj | = | incident radiation corresponding to the gray gas j, W/m2 |
| Gη | = | spectral incident radiation, W/m |
| h | = | enthalpy, J/kg |
| = | total black-body intensity, W/m2 | |
| = | spectral intensity of black-body (Plank function), W/m | |
| = | radiation intensity corresponding to the gray gas j, W/m2 | |
| = | spectral radiative intensity, W/m | |
| J | = | total number of gray gases |
| = | absorption coefficient corresponding to the gray gas j, 1/m | |
| = | spectral absorption coefficient, 1/m | |
| L | = | path length, m |
| = | mass flow rate of the fuel, kg/s | |
| = | boundary surface unit normal vector | |
| Ns | = | number of chemical species |
| Nφ | = | number of composition variables |
| pi | = | partial pressure of species i in the gas mixture, atm |
| q | = | heat flux vector, W/m2 |
| s | = | direction vector, m |
| S | = | source term, W/m3 |
| = | chemical reaction source term for the αth composition variable (α = 1, 2, … , Nϕ) | |
| T | = | temperature, K |
| t | = | time, s |
| Tb | = | background temperature, 273 K |
| U | = | velocity vector, m/s |
| u | = | fluctuating velocity vector, m/s |
| = | mean velocity components, m/s | |
| V | = | sample space variable corresponding to U, m/s |
| = | sample space variable corresponding to u, m/s | |
| W | = | isentropic scalar-valued Wiener process, s1/2 |
| Wi | = | the i-th component of an isotropic vector-valued Wiener process, s1/2 |
| x | = | position vector, m |
| = | position components, m | |
| Yi | = | species mass fractions |
| Greek-letter variables | = | |
| = | solid angle | |
| = | heat of combustion, J/kg | |
| = | Kronecker delta function ( | |
| = | total emissivity | |
| = | boundary emittance | |
| θ | = | sample space variables corresponding to ω, 1/s |
| ρ | = | density, kg/m3 |
| σ | = | Stefan-Boltzmann constant, 5.669e-08 W/m2K4 |
| Φ | = | composition vector |
| ψ | = | sample space variables corresponding to Φ |
| ω | = | turbulent frequency, 1/s |
| Subscripts | = | |
| rad | = | radiation |
| η | = | wavenumber, 1/m |
| ω | = | turbulent frequency, 1/s |
| Operators and accents | = | |
| = | volume (Reynolds)-averaged | |
| ˜ | = | mass (Favre)-averaged |
| A|B | = | the conditional probability of event A, given that the event B occurs |
Acknowledgements
The authors would like to thank the support received from the Deputy of Research and Technology in Sharif University of Technology. It is greatly acknowledged.
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No potential conflict of interest was reported by the author(s).
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All authors whose names appear on the submission:
1. made substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data; or the creation of new software used in the work;
2. drafted the work or revised it critically for important intellectual content;
3. approved the version to be published; and
4. agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.
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