Accuracy analysis of the window overlapping technique for velocity measurements using artificial and real signals

Abstract

The feasibility of using window overlapping processing technique together with cross-correlation method was investigated for measuring instantaneous particle velocities using a fiber optic system. A pair of artificial signal pulses was generated to yield a known velocity field when they were cross-correlated. A parametric analysis was conducted to determine whether the window overlapping technique enhanced the velocity sampling frequency of the fiber optic probe system. The window overlapping technique was found to be effective in improving the accuracy of the instantaneous velocity calculations for relatively shorter data segments (windows). As the length of the window size increased, the efficiency of the window overlapping method diminished. The window overlapping technique was found to be effective only for window sizes up to four times longer than the minimum window size. The minimum window size contains sufficient number of data points that corresponds to the maximum velocity sampling frequency according to the Nyquist Theory. That is, the window overlapping technique could be beneficial for enhancing the velocity sampling frequency only if the velocity data (or the window size used in the cross-correlation function) were sampled at a frequency of four times lower (or better) than the highest frequency in the flow. Due to the hardware limitations, it is not possible to sample data at frequencies high enough to capture the highest frequency velocity fluctuations in a turbulent flow. Therefore, in this study, it was investigated that the velocity sampling frequency of a fiber optic probe could be enhanced by window overlapping technique using data collected from a highly turbulent particle laden pipe flow. The results indicated that the window overlapping technique slightly improved the accuracy of the instantaneous particle velocity measurements. This is believed to be due to the larger window sizes (or low sampling frequencies) relative to the high frequency velocity fluctuations in the flow. Therefore, the particle velocity fluctuations may not be computed accurately using a fiber optic probe due to the nature of the cross-correlation method which filters the velocity variations during the time period of Δ T . In order to obtain reasonably accurate results for measuring the particle velocity fluctuations in real life applications, the time interval (window size) must be sufficiently small such that it corresponds to the frequencies, at most, four times lower than the highest frequency occurring in the flow. The feasibility of using window overlapping processing technique together with cross-correlation method was investigated for measuring instantaneous particle velocities using a fiber optic system. The efficiency of window overlapping technique for enhancing the velocity sampling frequency was evaluated using artificial signals and data obtained from a fiber optic probe ( Fig. 1 ) in a highly turbulent particle laden pipe flow.