Multi-tomographic flame analysis with a schlieren apparatus

Optical tomographic measurement techniques are powerful non-invasive methods for combustion diagnostics, delivering the spatial distributions of gas concentration, absorption and refractive index, emissivity, density and temperature. In this paper the well known schlieren effect is combined with emission/absorption methods leading to tomographic projections of gas flames from which the temperature fields inside the flames are reconstructed. The measurement object is modelled by the three distributions of emissivity, extinction coefficient and refractive index and is determined by different measurement conditions (multi-tomographic) in a schlieren arrangement. Considering the different physical effects leading to different mathematical types of interaction between the light beams and the flame, the equations of projection can be derived analytically. The tomographic reconstruction of the three projected fields has to be performed by scalar, attenuated scalar and vectorial Radon or Abel inversion techniques. By means of these fields other not directly accessible distributions can be calculated, for example the temperature either by the Gladstone-Dale formula from the refractive index or by absorption/emission pyrometry in the presence of light-emitting soot particles. Tomograms of weakly illuminating free jet gas flames have been taken within 10 ms with the help of the schlieren effect and temperature fields have been reconstructed in good agreement with thermocouple measurements (maximum error 10%). Luminously absorbing, rotationally symmetric flames were also measured and reconstructed, showing the superiority of Gladstone-Dale pyrometry compared to the emission/absorption method. The method is suitable to measure laminar as well as turbulent flames.