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ABSTRACT
The flame surface density (FSD) based reaction rate closure is one of the most important methodologies of turbulent premixed flame modeling in the context of Large Eddy Simulations (LES). The transport equation for the Favre-filtered reaction progress variable needs closure of the filtered reaction rate and the subgrid scalar flux (SGSF). The SGSF in premixed turbulent flames has both gradient and countergradient components, where the former is typically modeled using eddy diffusivity and the latter can be modeled either on its own or in combination with the filtered reaction rate term using an appropriate wrinkling factor. The scope of the present work is to identify an explicit SGSF closure for the optimum performance in combination with an already established LES FSD model. The performance of different SGSF models for premixed turbulent combustion has been assessed recently by the authors using a Direct Numerical Simulation (DNS) database of freely propagating turbulent premixed flames with a range of different values of turbulent Reynolds number. The two most promising models have been implemented in the LES code. The modeling methodology identified based on a priori DNS analysis is assessed further a posteriori by comparing the LES simulation results of turbulent methane Bunsen flames with the well-documented experimental data. A significant change of the overall flame speed is not observed for different SGSF models. However, the flame shape and thickness respond to the modeling of SGSF. Considering the fact that the SGSF models have very different characteristics, the overall effect on the LES results in this work is smaller than expected. An extension of a previous a priori DNS analysis provides detailed explanations for the observed behavior.
Nomenclature
| c | = | reaction progress variable, [-] |
| CR | = | combustion model constant, [-] |
| D | = | fractal dimension, [-] |
| Da | = | Damköhler number, [-] |
| k | = | turbulent kinetic energy, m2/s2 |
| Ka | = | Karlovitz number, [-] |
| l | = | integral length scale of turbulence, m |
| lF | = | laminar flame thickness, m |
| Le | = | Lewis number, [-] |
| Ma | = | Markstein number, [-] |
| M | = | Mach number, [-] |
| p | = | pressure, Pa |
| Pr | = | Prandtl number, [-] |
| Re | = | Reynolds number, [-] |
| st | = | turbulent flame speed, m/s |
| = | unstretched laminar flame speed, m/s | |
| sL | = | stretched laminar flame speed, m/s |
| Sij | = | shear stress tensor, 1/s |
| Sct | = | Schmidt number, [-] |
| t | = | time, s |
| T | = | temperature, K |
| u’ | = | rms turbulent velocity, m/s |
| ui | = | velocity component, m/s |
| U | = | bulk velocity at inlet, m/s |
| xi | = | spatial coordinate i, m; |
| Greek | = | |
| α | = | diffusivity, m2/s |
| δt | = | turbulent flame brush thickness, m |
| δth | = | thermal flame thickness, m |
| Δ | = | filter size, m |
| ε | = | cutoff scale, m |
| Φ | = | equivalence ratio, [-] |
| η | = | Kolmogorov length scale, m |
| κ | = | flame stretch rate, 1/s |
| κs | = | flame strain rate, 1/s |
| μ | = | dynamic viscosity, kg/ms |
| ν | = | kinematic viscosity, m2/s |
| ρ | = | density, kg/m3 |
| Σ | = | flame surface density, 1/m |
| τ | = | heat release factor, [-] |
| Ξ | = | flame wrinkling factor, [-] |
| = | turbulent reaction source term, kg/m3s | |
| Subscripts | = | |
| ad | = | adiabatic |
| b | = | burned |
| i | = | inner |
| o | = | outer |
| res | = | resolved |
| sgs | = | subgrid scale |
| t | = | turbulent |
| tot | = | total |
| 0 | = | unburnt |
| Δ | = | filter size as length scale |
Nomenclature
| c | = | reaction progress variable, [-] |
| CR | = | combustion model constant, [-] |
| D | = | fractal dimension, [-] |
| Da | = | Damköhler number, [-] |
| k | = | turbulent kinetic energy, m2/s2 |
| Ka | = | Karlovitz number, [-] |
| l | = | integral length scale of turbulence, m |
| lF | = | laminar flame thickness, m |
| Le | = | Lewis number, [-] |
| Ma | = | Markstein number, [-] |
| M | = | Mach number, [-] |
| p | = | pressure, Pa |
| Pr | = | Prandtl number, [-] |
| Re | = | Reynolds number, [-] |
| st | = | turbulent flame speed, m/s |
| = | unstretched laminar flame speed, m/s | |
| sL | = | stretched laminar flame speed, m/s |
| Sij | = | shear stress tensor, 1/s |
| Sct | = | Schmidt number, [-] |
| t | = | time, s |
| T | = | temperature, K |
| u’ | = | rms turbulent velocity, m/s |
| ui | = | velocity component, m/s |
| U | = | bulk velocity at inlet, m/s |
| xi | = | spatial coordinate i, m; |
| Greek | = | |
| α | = | diffusivity, m2/s |
| δt | = | turbulent flame brush thickness, m |
| δth | = | thermal flame thickness, m |
| Δ | = | filter size, m |
| ε | = | cutoff scale, m |
| Φ | = | equivalence ratio, [-] |
| η | = | Kolmogorov length scale, m |
| κ | = | flame stretch rate, 1/s |
| κs | = | flame strain rate, 1/s |
| μ | = | dynamic viscosity, kg/ms |
| ν | = | kinematic viscosity, m2/s |
| ρ | = | density, kg/m3 |
| Σ | = | flame surface density, 1/m |
| τ | = | heat release factor, [-] |
| Ξ | = | flame wrinkling factor, [-] |
| = | turbulent reaction source term, kg/m3s | |
| Subscripts | = | |
| ad | = | adiabatic |
| b | = | burned |
| i | = | inner |
| o | = | outer |
| res | = | resolved |
| sgs | = | subgrid scale |
| t | = | turbulent |
| tot | = | total |
| 0 | = | unburnt |
| Δ | = | filter size as length scale |
Acknowledgments
UA and MP thank ITIS for cosponsoring this work. NC is grateful to EPSRC, UK, for financial assistance.