Abstract A new Lagrangian based interpolation scheme is proposed for recovering velocity field data from within masked regions in particle image velocimetry (PIV) experiments. As a first step, the mean field within the masked region is filled through an iterative convolution operation using an optimized kernel. Next, the Lagrangian interpolation scheme estimates velocity field data within the masked region using a weighted average of past and future snapshot data along a mean field streamline from outside of the masked region. The Lagrangian interpolation scheme is compared directly with a traditional bilinear interpolation approach for two datasets: the flow development over a circular cylinder within the laminar vortex shedding regime ( Re D = 150 ) and turbulent vortex shedding regime ( Re D = 3000 ). The results show that for both Reynolds numbers investigated, the Lagrangian approach provides up to a 5 × improvement in average velocity reconstruction error. Application of the proposed interpolation scheme to the estimation of body forces was assessed. For both the momentum and impulse control volume approaches to estimate instantaneous forces, the Lagrangian interpolation scheme provides up to 10 × improvement in the estimation of volume integral contributions to instantaneous drag and lift.

中文翻译：

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PIV 数据的拉格朗日插值算法

摘要 提出了一种新的基于拉格朗日的插值方案，用于从粒子图像测速 (PIV) 实验中的掩蔽区域内恢复速度场数据。作为第一步，使用优化内核通过迭代卷积操作填充屏蔽区域内的平均场。接下来，拉格朗日插值方案使用过去和未来快照数据的加权平均值，沿着来自掩蔽区域外部的平均场流线估计掩蔽区域内的速度场数据。拉格朗日插值方案直接与两个数据集的传统双线性插值方法进行比较：层流涡旋脱落机制（Re D = 150）和湍流涡旋脱落机制（Re D = 3000）内圆柱上的流动发展。结果表明，对于研究的两个雷诺数，拉格朗日方法在平均速度重建误差方面提供了高达 5 倍的改进。评估了所提出的内插方案在体力估计中的应用。对于估计瞬时力的动量和脉冲控制体积方法，拉格朗日插值方案在估计体积积分对瞬时阻力和升力的贡献方面提供了高达 10 倍的改进。