Post-phase averaged PIV, OH-Luminescence and LIF measurements using acoustic time series

Abstract

With common optical measurement techniques it is easy to get time averaged flow images of a combustion chamber. If there is an interest in the temporal development of periodic flow, phase resolved images are often helpful. Thereby the sound waves, generated by the flow can be used as a reference signal providing phase and frequency. Of course this requires a parallel measurement of an acoustic time series using microphones. Than the oscillation of the flow can be analyzed within a time centered window around the image trigger. In this window not only the frequency but also the phase of the acoustical data stream in respect to the trigger position is important. First tests applying a Fourier analysis failed, because the phase resolution correlates with the frequency resolution that again depends on window length. To achieve an acceptable phase resolution the necessary window is usually too large, so that the oscillation frequency is not sufficiently constant within the window. Furthermore, the Fourier transformation only derives a time-fixed frequency expansion with time-fixed amplitude and phase. Therefore, the Hilbert Huang transformation (HHT) was applied, because this transformation derives functions for amplitude and phase depending in time within the chosen window. The HHT combines the Hilbert transformation and the empirical mode decomposition (EMD). The EMD is a method that decomposes wide banded signals into a set of band limited functions, so called intrinsic mode functions (IMF). These intrinsic mode functions have in contrast to wide banded signals the advantage to be Hilbert transformable. Additionally a preprocessing Fourier filter of the acoustical data was investigated in order to remove unwanted high frequencies and to save computational time. This directly provides an IMF within the expected frequency region. Using this complete algorithm phase resolved averaging of for example OH-chemiluminescence pictures is possible with reasonable results.