Inverse radiation problem of axisymmetric turbulent sooting free flame

An iteration method is extended to reconstruct the time-averaged temperature distribution in turbulent axisymmetric sooting free flame by the multi-wavelength measured data of low time-resolution outgoing emission and transmission radiation intensities. A Gaussian probability density function is used to simulate the turbulent fluctuation of temperature. The reconstruction of time-averaged temperature profile consists of three steps. First, the time-averaged spectral absorption coefficient is retrieved from the time-averaged transmissivity data by iteration method. Then the time-averaged blackbody spectral radiation intensity is estimated from the low time-resolution outgoing spectral emission radiation intensities. Finally, the time-averaged temperature and its standard deviation are approximately reconstructed from the multi-wavelength time-averaged spectral emission radiation data by the least-square method. Both exact and noisy input data have been used to test the performance of the proposed inversion method. The results show that the time-averaged temperature profiles can be estimated with good accuracy by the presented inversion method, even with noisy input data, and the standard deviation of temperature is more sensitive to the measurement errors. In the case of large temperature fluctuation, the errors of estimation for time-averaged temperature profile are large if the turbulent fluctuation is not taken into account.