Polynomial element velocimetry (PEV): a technique for continuous in-plane velocity and velocity gradient measurements for low Reynolds number flows

摘要

Particle image velocimetry (PIV) selects the maximum of the cross-correlation map to represent the modal displacement, and a wealth of information stored in the cross-correlation is discarded. We introduce a novel method, termed polynomial element velocimetry (PEV), which results in continuous velocity and velocity gradient measurements. PEV utilizes the extra information stored in the cross-correlation to determine continuous velocity measurements with low levels of measurement noise. In contrast to PIV, the continuous nature of velocity measurements facilitates the direct determination of the velocity gradient. The PEV method is applied to two laboratory flows: flow in a channel and flow behind a circular cylinder at Reynolds number, Re = 30, and is shown to greatly reduce the noise in the measurements. In addition, the accuracy of PEV is validated using two computer-generated synthetic flows: parabolic flow in a channel and flow past a square cylinder at Re = 30. In these cases, PEV is shown to reduce the velocity measurement error by up to 45% and the vorticity estimation error by up to 77% when compared to PIV. A key benefit of the PEV method is that it is capable of calculating continuous measures for flow gradient with greatly reduced bias errors. In particular, PEV provides a more accurate measurement of the vorticity near interfaces such as a cylinder wall or channel wall where PIV methods only provide measurement data at half the sampling window size from the wall. Since PEV utilizes the entire shape of the cross-correlation map to determine a local map for the underlying velocity, minimal random error is transmitted to the estimated flow gradient. This feature of the PEV method makes it optimal for flows where flow gradients are well defined and there are insufficient pixels to fully resolve structures in the flow using PIV.