Post-processing of volumetric PIV data based on continuity condition
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摘要: 对粒子图像测速技术(PIV,Particle Image Velocimetry)体空间内三维速度场的后处理技术进行研究,引入不可压缩连续性方程的约束对实验测得流场进行修正,使得修正后流场严格满足差分形式的连续性方程.通过流场修正的后处理技术实现拉格朗日乘数法求解全流场修正速度场二范数的极小值.理论推导严格证明了修正后的速度场在数学上更接近满足连续性方程的真实流场.对解析流场引入高斯噪音来进行人工模拟的测试,其结果进一步验证了修正后流场能更趋近于真实流场,对流场中出现的PIV常见的高斯分布噪音有一定的消弱作用.该技术被成功应用于实验数据的后处理,结果表明其能改善测量速度场的平滑度.Abstract: A new technique of data post-processing was proposed to improve volumetric velocity field of particle image velocimetry (PIV).To make the processed velocity field satisfy the differential form of the continuity equation of incompressible flow, the modification was made on the original experimental data. The correcting velocity field was obtained by solving the minimum problem of its 2-norm using the method of Lagrange multipliers. Mathematical proof was provided to demonstrate that the modified velocity field was a better approximation of the true flow. Simulation of an analytical flow with noise was performed to further prove that the post-processing technique can reduce the common Gaussian noise of PIV measurements. The technique is successfully applied to a volumetric PIV data, which indicates that it can improve the smoothness of the velocity field as well.
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