A constrained particle image velocimetry algorithm for flow measurement using Euler and Lagrange approaches

The measurement of the momentum of a liquid fluid such as water in a river remains a key issue in the prediction of natural disasters caused by the variation of water velocity in a flow. The article presents a more robust image processing kinematics based on Particle Image Velocimetry by analogy of two approaches (Lagrangian and Eulerian) for better monitoring of the behaviour of flowing fluid in a river. This approach led to the creation of a virtual observer that replicates the Lagrangian and Eulerian approaches. The obtained results demonstrate the limitations of the Lagrangian approach in comparison with the Eulerian one, which offers more detailed information on the behaviour of certain fluid particles in flow. Highlights : • A flow measurement and detection based on local observers has been implemented. • Eulerian and Lagrangian observers, hence, approaches have been used and compared in order to enhance and better recover flow conditions. • The Radon transform has been used to discriminate the content of images for detecting, even, small variations. • The ROC metric has been adopted to verify the relationship between both approaches in terms of specificity and sensivity. • Euler observer displays better results than Lagrangian one.