On the velocity of ghost particles and the bias errors in Tomographic-PIV

Abstract

The paper discusses bias errors introduced in Tomographic-PIV velocity measurements by the coherent motion of ghost particles under some circumstances. It occurs when a ghost particle is formed from the same set of actual particles in both reconstructed volumes used in the cross-correlation analysis. The displacement of the resulting ghost particle pair is approximately the average displacement of the set of associated actual particles. The effect is further quantified in a theoretical analysis and in numerical simulations and illustrated in an actual experiment. It is shown that the bias error does not significantly affect the measured flow topology as deduced in an evaluation of the local velocity gradients. Instead, it leads to a systematic underestimation of the measured particle displacement gradient magnitude. This phenomenon is alleviated when the difference between particles displacement along the volume depth is increased beyond a particle image diameter, or when the reconstruction quality is increased or when the accuracy of the tomographic reconstruction is improved. Furthermore, guidelines to detect and avoid such bias errors are proposed.

Scanning tomographic particle image velocimetry applied to a turbulent jet

“…The ghost particles cause a bias which tends to reduce this velocity gradient. 16 However, for our jet flow the mean velocity gradients are much weaker than in the near-wall region of the boundary layer and we do not expect significant bias of this type. We also use image deformation during the multi-step correlations, which has been shown to reduce such bias.…”

“…These ghost particles decrease the signal-to-noise ratio of the correlation and their presence can potentially have severe effects on the fine scale fidelity of the correlated vector fields, if they exist in both reconstructions of an image pair. Typically, the number ratio of ghost to real particles is estimated by 16 …”

“…The implications of increased seeding density are severe for the full illumination case where ghost particles in the center of the jet are formed from pairs from a set of slow moving real particles on the jet periphery. Since coherent ghost particles (i.e., ghost particles that are present in both images in the correlation) are generally displaced by the average of the particles that form them 16 the correlation will be heavily biased towards the velocity of the slow moving peripheral particles. The effect on spatial gradients is also severe as the slow moving ghosts smooth out all the fine-scale information.…”

Particle imaging techniques for volumetric three-component (3D3C) velocity measurements in microfluidics

“…Point-wise illumination was generated by using a lamp and an aperture at the time it was invented (Minsky Fig. 4 Schematic of the tomographic imaging and the appearance of ghost particles (left) and possible solutions of the reconstruction out of the two camera images (right), according to Elsinga et al (2011) 1961). Nowadays, focused laser beams are most often used for the illumination and the technique is often referred to as confocal laser scanning microscopy (CLSM).…”

Full 3D-3C velocity measurement inside a liquid immersion droplet

“…This is due to ghost particles outside the measurement domain (Elsinga et al 2010). In the case of tomographic PIV, the intensity information from actual and ghost particles both contribute to the crosscorrelation.…”