Error-based dynamic velocity range of PIV processing algorithms

Abstract The ability of PIV processing algorithms to accurately determine velocity vectors across the range of motion present in PIV images is characterized by the algorithm’s dynamic velocity range (DVR). Conventionally, the DVR of PIV is defined using the ratio between the maximum and minimum resolvable particle displacements, with the minimum based on the uncertainty in the location of a single particle in the optical system. In this work, it is demonstrated that this definition is inadequate in practice, as it ignores many factors which affect the accuracy of an algorithm when determining small displacements, and the error in vectors with small magnitudes in actual flows is often many times larger than the theoretical minimum. A more useful criterion for determining the DVR of a PIV setup is proposed that depends on conditional errors, using synthetic data to produce a known ground truth. The introduced error-based DVR accounts for the effect of multiple flow velocity scales present in a PIV experiment as well as multi-particle effects. It is found that the practical, error-based DVR of cross-correlation-based PIV is highly experiment-dependent and much lower than the widely accepted value of $$\mathcal {O} \left( {10^2} \right)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>2</mml:mn> </mml:msup> </mml:mfenced> </mml:mrow> </mml:math> , typically $$\mathcal {O} \left( {10^0} \right) - \left( {10^1} \right)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>0</mml:mn> </mml:msup> </mml:mfenced> <mml:mo>-</mml:mo> <mml:mfenced> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>1</mml:mn> </mml:msup> </mml:mfenced> </mml:mrow> </mml:math> . The findings from the synthetic data results are corroborated using experimental PIV data to approximate the DVR via a deviation-based approach when the ground truth is unknown.