This paper has been withdrawn by the authors due to a fatal error in the analysis. The manuscript was submitted to Chemical Engineering Science. To clarify the situation, we copy the main comment from an anonymous referee here: To my understanding, t
he authors analyze i = 1 ... 63 time series and calculate their mean and standard deviation. These time series correspond to individual, single ignition processes. Is this correct? If yes, these processes, as Fig. 3 shows very clearly, are not stationary, and the pressure difference (i.e., the signal) quickly decays to zero. In this case both the mean and the standard deviation are poorly defined, for example because both depend in a trivial fashion on the observation period T. I am not aware of any study (including those cited by the authors) which allows for any conclusion from such non-stationary signals. The results of Menezes and Barabasi are strictly only valid for stationary time series, and they cannot be applied at all in this case. We agree with this insightful comment that our data are not stationary and the method adopted in our manuscript does not apply. We do not see any possibility to correct this error and decide to withdraw it. We would like to thank gratefully the referee and apologize for any inconvenience caused by our oversight.
On a laboratory-scale testing platform of impinging entrained-flow gasifier with four opposed burners, the flame images for diesel combustion and gasification process were measured with a single charge coupled device (CCD) camera. The two-dimensional
multifractal detrended fluctuation analysis was employed to investigate the multifractal nature of the flame images. Sound power-law scaling in the annealed average of detrended fluctuations was unveiled when the order $q>0$ and the multifractal feature of flame images were confirmed. Further analyses identified two multifractal parameters, the minimum and maximum singularity $alpha_{min}$ and $alpha_{max}$, serving as characteristic parameters of the multifractal flames. These two characteristic multifractal parameters vary with respect to different experimental conditions.
