Wavelet-based optical velocimetry for oil spill flow rate estimation

Abstract

Flow rate estimation of an underwater oil spill is challenging due to the complex flow dynamics of an oil spill. Existing techniques such as particle image velocimetry (PIV) and feature tracking velocimetry (FTV) were unable to accurately estimate the flow rate of the oil spill in the Macondo well incident, with the most accurate technique being optical plume velocimetry (OPV). OPV estimates the velocity field based on temporal averaging algorithm, which has a better temporal resolution compared to PIV and FTV. This is useful for flow estimation where the temporal evolution of turbulent flow is significant. However, the classical temporal cross correlation algorithm used in OPV is not appropriate to deal with multi-scale flow behaviour associated with a turbulent flow such as that of oil spills. Several methods were previously used to multi-scale representation, such as Short-Time Fourier Transform, Wavelet Transform (WT) and Empirical Mode Decomposition. Among all of these methods, wavelet transform (WT) is more appropriate for turbulent flow applications, since the interesting point is the presentation of flow spectral changes over time. This is because the wavelet convolution has the ability to balance between temporal and frequency information. This paper proposed an alternative technique called wavelet-based optical velocimetry (WOV). WOV estimates the velocity field based on cross correlation of wavelet coefficients. Continuous wavelet transform was first utilized to transform two intensity signals into the wavelet domain. The Fast Fourier Transform (FFT) algorithm was then used for wavelet coefficient correlation, from which the velocity was estimated. To validate the accuracy of the WOV technique, a turbulent jet flow was experimentally simulated at Reynold's number ranging from 1847 to 11,656 at the nozzle. In our experimental work, WOV estimated the nozzle flow rate with an error of 8.3%, while the OPV estimated the nozzle flow rate with an error of 19.7%. The better estimation of WOV technique is due to its advantage to deal with the multi-scale behaviour of turbulent flow, since the WT has a multi-resolution scheme. The accuracy of WOV algorithm, however is sensitive to the selection of wavelet scaling, as well as the wavelet function. A significant influence was observed for the wavelet scaling, due to the difference of the frequency bandwidth width of WT, while the influence of wavelet function is less significant.