Dual-plane stereo particle image velocimetry measurements of velocity gradient tensor fields in turbulent shear flow. I. Accuracy assessments

Abstract

Results are presented from quantitative assessments of the accuracy of velocity gradients measured by a dual-plane stereo particle image velocimetry (DSPIV) technique that allows direct, highly resolved, nonintrusive measurements of all nine simultaneous components of the velocity gradient tensor fields ∂ui/∂xj∂ui∕∂xj at the quasi-universal intermediate and small scales of turbulent shear flows. The present results systematically determine the sources of errors in DSPIV measurements and the resulting accuracy of velocity gradients obtained from such measurements. Intrinsic errors resulting from asymmetric stereo imaging are found by synthetic particle imaging to be no larger than 0.8%. True particle imaging in finite-thickness light sheets is found from single-plane imaging tests to produce net errors in measured velocity differences of 6% for in-plane components and 10% for out-of-plane components. Further errors from limits on the accuracy of independent dual light sheet generation and positioning are found from coincident-plane imaging tests to produce overall errors of 9% and 16% in the in-plane and out-of-plane velocity differences. Practical DSPIV velocity gradient component measurements are found from separated-plane imaging tests in a turbulent shear flow to show excellent similarity in on-diagonal (i = j)(i=j) and off-diagonal (i ≠ j)(i≠j) components of ∂ui/∂xj∂ui∕∂xj, as well as mean-square gradient values showing agreement within 1%–4% of ideal isotropic limit values. The resulting measured divergence values are consistent with overall rms errors obtained from the coincident-plane imaging tests. Collectively, these results establish the accuracy with which all nine simultaneous components of the velocity gradient tensor fields ∂ui/∂xj∂ui∕∂xj can be obtained from DSPIV measurements at the quasi-universal intermediate and small scales of turbulent shear flows.