Detection of 3-D vortex in the 2-D PIV experiment:analytical solution and application

Nowadays the 2-D PIV is widely used in the field of fluid velocimetry. The study of characteristics of 3-D vortices detected in the 2-D PIV experiment is helpful to deeply analyze measured data and further know the fundamental turbulent physics and the fluid-particle interaction. Based on the vortex identification scheme (the swirling strength criterion), the Euler's rotation theorem and the Burgers vortex model, analytic solutions for the detection of 3-D vortex in the 2-D PIV experiment are derived. The solution demonstrates that two factors (the elevation angle made by the 3-D vortex with the measurement plane and the circulation of the vortex) influence the detection and only when the circulation value is greater than a specified value (a function of the elevation angle), the 3-D vortex could be detected. The direct numerical simulation (DNS) data of fully developed turbulent channel flow is used for the statistical analysis of that detection condition. Results show that in the 2-D PIV experiment, the higher the detection probability is, the larger the elevation angle will be. For examples, 3-D vortex tubes with detection probabilities of 90%, 50% and 10% have elevation angles of 20°, 11° and 5° respectively.