Turbulent premixed combustion: A flamelet formulation and spectral analysis in theory and IC-engine experiments

A flamelet formulation for premixed combustion has been derived based on a scalar field equation describing the instantaneous flame front location in the turbulent flow field. This partial differential equation is equivalent to the local kinematic balance between fluid flow velocity, burning velocity and flame propagation velocity. If the burning velocity depends locally on flame stretch and flame front curvature, an additional length scale, the Markstein length is introduced into the problem. A spectral closure of the problem has been performed on the basis of a two-point correlation. The transformation of the scalar field equation into wavenumber-space leads to the definition to a spectrum function for the fluctuations of the turbulent flame front. The cut-off of the inertial subrange occurs at the Gibson scale. The scalar spectrum function can be determined experimentally by taking the power spectral density from fourier-transformation of flame contours. To obtain flame contours at high turbulence levels, 2D-lasersheet-images of turbulent flame fronts have been taken in a VW transparent engine. Mie-scattering from tobacco smoke-particles in the unburnt mixture was recorded via a non-intensified CCD-camera with direct digital storage of image sequences, yielding a high resolution of the length scale range. The evaluation of flame contours, extracted from the original images by digital image processing, shows the spectral behavior that was predicted by the flamelet formulation.