Much current research is directed towards reducing pollution formation by burning at lean premixed stoichiometries. Under these conditions flame instability, blow-off and flashback become safety concerns. Buoyancy has been observed to have a significant effect on flame stability and conditions in the far-field burnt gas which, through the pressure field, can effect the flow both upstream and downstream of the flame. We are collaborating with researchers Ian Shepherd, Robert Cheng and Shaheen Tonse of LBNL's EETD to model experimental data numerically and thereby test the models adequacy and also to help elucidate the mechanisms by which buoyancy interacts with the vector and scalar fields of premixed laminar and turbulent flames.
The effects of buoyancy are demonstrated by the overall flame shape of the relative orientation of the flame to the gravitational vector. The flow field may be characterized as predominately hot, light products and cold, dense reactants. For methane flames, the density drops by a factor of 6-8 across flame front. As a result, the buoyancy force accelerates the downstream products and has large impact on the conditions felt by the flame. Buoyancy-induced interaction between products and cold environment produces velocity fluctuations in reactants and flickering of Bunsen flame tip in +1g. This disappears at 0g.
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The figure to the left shows a schlieren photograph of conical, lean premixed, laminar methane/air flame stabilized on one inch burner (courtesy of Ian Shepherd at LBNL's EETD). The flame has equivalence ratio = 0.8, fueling rate of 1.3 m/s from a burner diameter of 25 mm. There is a very small co-annular flow of 0.062 m/s. The central cone is a laminar flame front. Outer structures, showing the interface between the hot products and cold ambient air, exhibit cusping of the interface due to vorticies. Buoyancy induced pressure field fluctuations associated with cusping generates flame tip flicker. Experimental data indicates a 10-15 Hz flicker frequency. |
The adaptive low Mach number model developed by CCSE researchers is used to simulate a simple, two-dimensional, axisymmetric flame similar to the one discussed above, under terrestrial and zero-gravity conditions. Although detailed chemical kinetics and transport are accomodated in the model, a 6-species, 2-step reduced model efficiently predicts heat release profiles. Block-structured hierachical adaptive refinement is used to evolve the system from a non-physical ignition start-up, through to a steady, or quasi-steady solution. Logically rectangular patches of locally structured grids are dynamically created as destroyed as the simulation progresses. AMR affords a large 32x64 cm computational domain. Large computational timesteps are possible due to low Mach model, allowing for long-time integrations of over 2-3 sec. Total resolved flame integration takes less than one week on desktop machine.
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In the figure to the left a representative calculation is shown with overlaid boxes that depict the extent of nested adaptive grid patches. The patches are limited in size to 64 cells across. There are 4-levels of adaptive grid used to dynamically refine the solution, with a factor of 2 or 4 between levels. The base grids cover the entire domain with cell size 1 mm. The finest cells cover 0.5% of the domain (near the flame surface) with cell size 63 microns.
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With gravity, toroidal vorticies develop between products and ambient air cause acceleration in the burnt gas. The plot on the left shows the height of the bunsen cone for the terrestrial case as a function of time. The plot on the right is the same data transformed into frequency space, showing that the peak is at 11 Hz, consistent with experimental data at 10-15 Hz. No toroidal vorticies or flame flicker appears in the zero gravity as observed in experiments. Future work in this area will be to modify software to incorporate partial outflow to acommodate downstream flow obstructions, enabling study of negative gravity cases. We'd also like to investigate effects of numerical domain size and co-flow characteristics. Finally, the work may be extended to include turbulent premixed flame/buoyancy interactions, and other three-dimensional effects.
