Direct numerical simulations of the interaction of a premixed flame with driven , subsonic , homogeneous , isotropic , Kolmogorov-type turbulence in an unconfined system are used to study the mechanisms determining the turbulent flame speed , S _ { T } , in the thin reaction zone regime .
High intensity turbulence is considered with the r.m.s .
velocity 35 times the laminar flame speed , S _ { L } , resulting in the Damköhler number Da = 0.05 .
The simulations were performed with Athena-RFX , a massively parallel , fully compressible , high-order , dimensionally unsplit , reactive-flow code .
A simplified reaction-diffusion model , based on the one-step Arrhenius kinetics , represents a stoichiometric H _ { 2 } -air mixture under the assumption of the Lewis number Le = 1 .
Global properties and the internal structure of the flame were analyzed in an earlier paper , which showed that this system represents turbulent combustion in the thin reaction zone regime .
This paper demonstrates that : ( 1 ) The flame brush has a complex internal structure , in which the isosurfaces of higher fuel mass fractions are folded on progressively smaller scales .
( 2 ) Global properties of the turbulent flame are best represented by the structure of the region of peak reaction rate , which defines the flame surface .
( 3 ) In the thin reaction zone regime , S _ { T } is predominantly determined by the increase of the flame surface area , A _ { T } , caused by turbulence .
( 4 ) The observed increase of S _ { T } relative to S _ { L } exceeds the corresponding increase of A _ { T } relative to the surface area of the planar laminar flame , on average , by \approx 14 \% , varying from only a few percent to as high as \approx 30 \% .
( 5 ) This exaggerated response is the result of tight flame packing by turbulence , which causes frequent flame collisions and formation of regions of high flame curvature \gtrsim 1 / \delta _ { L } , or “ cusps , ” where \delta _ { L } is the thermal width of the laminar flame .
( 6 ) The local flame speed in the cusps substantially exceeds its laminar value , which results in a disproportionately large contribution of cusps to S _ { T } compared with the flame surface area in them .
( 7 ) A criterion is established for transition to the regime significantly influenced by cusp formation .
In particular , at Karlovitz numbers Ka \gtrsim 20 , flame collisions provide an important mechanism controlling S _ { T } , in addition to the increase of A _ { T } by large-scale motions and the potential enhancement of diffusive transport by small-scale turbulence .