The relationship between dilatation, displacement speed, flame tangential strain rate and flame normal velocity gradient for a premixed turbulent flame in a corrugated/wrinkled flame regime is analyzed. The decomposition of dilatation into the flame tangential and normal strains and their relationship with curvature is studied. Three-dimensional, fully compressible direct numerical simulations (DNS) of premixed flames in a cube have been performed using a uniform 256^3 grid. For the turbulent case, decaying isotropic homogeneous turbulent velocity field is considered with an initial turbulence spectrum imposed. Simple single-step chemistry with an Arrhenius reaction rate is used. This simplification is valid as the flame considered is in the corrugated/wrinkled regime where the flame thickness is smaller than the smallest scales of turbulence. A single laminar flame is initially inserted into the turbulent field. A strongly linear relationship between dilatation and curvature has been seen which is due to the high correlation of displacement speed with curvature. The correlation between tangential strain rate and curvature is shown to be negative with a breakdown due to the curvature reaching the scale of the flame thickness at the cusps. To isolate the effect of heat release and turbulence, cases of a laminar sinusoidal wrinkled flame and a turbulent
𝛕=0 flame have been carried out. For a laminar sinusoidal wrinkled flame, a negative correlation between a^𝛕 and curvature was seen. This contradicts previous hypotheses (Haworth and Poinsot, 1992) (Chakraborty and Cant, 2004) where the negative correlation between a^𝛕 and curvature was explained to be due to different turbulence levels in front and behind the flame. Turbulence and alignment of flame surface with expansive tangential strains is shown to be responsible for the scatter seen in a^n and a^𝛕 relationships with curvature. Changing the peak reaction location towards the front of the flame did not change the trend in the plots of dilatation, tangential and normal strain rates versus curvature, confirming that dilatation relationship with curvature in particular is not due to any curvature distortion of the flame interior. However, it did thicken the flame and reduce the dilatation (and consequently its components, an and at) plot versus curvature and the magnitude of their curvature dependence. / Thesis / Master of Applied Science (MASc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/22381 |
| Date | 12 1900 |
| Creators | Shahbazian, Nasim |
| Contributors | Tullis, S., Mechanical Engineering |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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