Abstract
This article derives a method to estimate and correct the bias error of the shift vector's absolute length in the presence of curved streamlines. The main idea is to identify the most likely streamline with constant curvature from the second-order shift vector and its gradient. The work establishes a theoretical framework including the systematic errors of the first-order and second-order shift vector's absolute value and angle. Synthetic images of a stationary vortex are used to validate the proposed method. The curvature-correction is also applied to a synthetic flow field with non-constant curvature to demonstrate its potential for more realistic flow fields. The results reveal that second-order accurate vector fields suffer from a biased shift vector length depending on the streamline's curvature and on the shift vector length. The bias error is negligible for vector fields with a shift vector length below the streamline curvature radius. For large shift vectors or strong curvatures, the bias error can be significantly reduced with the developed method. The approach is very general and can be applied to any vector field obtained from window-correlation particle image velocimetry (PIV), single-pixel ensemble-correlation PIV, particle tracking velocimetry or optical flow methods. It also works for all 3D extensions of the techniques, such as 3D-PTV or tomographic PIV.
Highlights
Particle image velocimetry (PIV) is a non-intrusive measurement technique that estimates the first-order velocity field in a plane, or even in a volume, by measuring the displacement of particles in a certain time interval Dt: Due to the nature of the recording principle, each measured velocity vector represents a volume-averaged mean motion of the discretized and quantized tracer particle’s diffraction images, rather than the actual velocity of the flow (Adrian and Westerweel 2010; Raffel et al 2007)
The results reveal that second-order accurate vector fields suffer from a biased shift vector length depending on the streamline’s curvature and on the shift vector length
The approach is very general and can be applied to any vector field obtained from window-correlation particle image velocimetry (PIV), single-pixel ensemble-correlation PIV, particle tracking velocimetry or optical flow methods
Summary
Particle image velocimetry (PIV) is a non-intrusive measurement technique that estimates the first-order velocity field in a plane, or even in a volume, by measuring the displacement of particles in a certain time interval Dt: Due to the nature of the recording principle, each measured velocity vector represents a volume-averaged mean motion of the discretized and quantized tracer particle’s diffraction images, rather than the actual velocity of the flow (Adrian and Westerweel 2010; Raffel et al 2007). Eckstein and Vlachos (2009) as well as Sciacchitano et al (2012) presented methods to improve the accuracy of PIV evaluation, which results in increased DVR values Another possibility to achieve a large DVR, as well as to get accurate estimations of the velocity and quantities derived from it, especially for low magnifications, is to maximize the particle image shift by selecting a sufficiently large time delay between subsequent illuminations. Since multi-pulse techniques require more expensive equipment, the idea of this paper is to achieve higher-order accuracy from conventional double-pulse recordings by estimating the curvature of the particle path from the second-order shift vector field. For jnj\p; Eq 2.2 can be reduced to n 2 Both the bias of the absolute value and the bias of the angle depend on the radius of the curved path and on the arc’s angle. These quantities are unknown and cannot be measured directly
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