Evaluation of wavelet-based optical flow for high-resolution velocimetry in primary breakup

Abstract The primary breakup process of an atomizing spray is an intriguing area of research, for which the fluid mechanics governing primary breakup at liquid–gas interfaces (LGIs) remain largely under-resolved. This work evaluates the performance of wavelet-based optical flow velocimetry (wOFV) for measuring velocities at the LGI during the primary breakup process of an atomizing liquid jet. Sequential 2D scalar images, rendered from a direct numerical simulation (DNS) of a temporally evolving atomizing liquid jet, are used as ground-truth data to quantify wOFV accuracy at different stages of breakup. The sharp interfacial intensity gradients inherent to spray images enable wOFV to achieve good accuracy with an error down to 6.5% for the images analyzed. Two regularization terms are assessed (first-order Horn &amp; Schunck and second-order Laplacian) and yield comparable error magnitudes, likely due to the flow exhibiting a strong principal flow direction. Accuracy improves markedly as breakup progresses due to increasing interfacial corrugation and reduced local regions of motion ambiguity. In this work, wOFV is shown to provide 20–40% higher accuracy than cross-correlation-based methods with superior vector resolution. This application of wOFV shows better accuracy compared to previous optical flow investigations involving diffuse scalar fields. The reduced motion ambiguity from sharp interfacial intensity features of the LGI results in accuracy levels closer to those achieved for discrete particle images. A simple warping-based procedure is introduced to provide an estimate of wOFV accuracy in the absence of ground-truth data. This procedure is tested on both synthetic images as well as experimental images of a turbulent jet undergoing primary breakup. Findings show good agreement with error metrics from ground-truth data and can provide valuable guidance in $$\lambda$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> </mml:math> selection and in estimating the uncertainty of wOFV. Findings demonstrate the proficiency of wOFV to resolve velocity estimates along interfaces with high-resolution and acceptable accuracy, providing promising opportunities to study the fluid mechanics of primary breakup, which will be presented in future studies. Graphical abstract