PIV空间分辨率对湍流多点统计量测量的影响

Effects of the spatial resolution of planar PIV on measured turbulence multi-point statistics

  • 摘要: 粒子图像测速(Particle Image Velocimetry, PIV),尤其是平面PIV,因其技术成熟且能提供瞬时流场,被广泛应用于湍流统计特性实验研究。PIV测量的空间分辨率(实验测量中所能解析的最小流场尺度,由图像处理时问询域窗口大小决定)不能准确分辨湍流中的小尺度运动,导致PIV测量获得的湍流多点统计量的定量信息(如速度结构函数、湍流耗散率等)包含一定误差。为定量分析这一误差,本文采用空间滤波模型模拟PIV测量对单点速度矢量的作用,进而推导出PIV测得的速度结构函数及湍流耗散率随滤波尺度的变化规律。为检验该模型,通过模拟示踪粒子在基于均匀各向同性湍流直接数值模拟(DNS)得到的湍流速度场中的运动及PIV系统对其的成像,获得了计算合成的PIV粒子图像,采用标准PIV算法对该图像进行处理,获得了速度场并计算得到了相关的湍流统计量,将其与基于真实DNS数据计算得到的统计量对比,获得了定量的误差信息,并与模型的预测结果进行了对比。研究结果表明:本文建立的模型反映了PIV测量中空间分辨率对湍流统计量的影响。在冯·卡门旋流系统产生的近似均匀各向同性流场中进行了平面PIV测量,针对测量得到的速度结构函数与K41理论结果的误差,采用基于本文模型得到的结论进行了分析与校正。本文工作为PIV测量得到的湍流统计量(尤其是小尺度多点统计量)给出了一个基于理论指导的修正方案。

     

    Abstract: Particle Image Velocimetry (PIV), in particular planar PIV, has been widely implemented in the experimental study of statistical characteristics of turbulence because of its maturity in technology and capability to provide instantaneous flow fields. The spatial resolution of PIV measurement, i.e., the smallest scale of the flow field resolvable by PIV, is determined by the size of the Interrogation Window (IW) during image processing. Hence, small-scale turbulence fluctuations might not be accurately resolved, which leads to deviations in measured turbulence multi-point statistics, such as velocity structure functions, turbulent dissipation rate and so on. To quantify this deviation, we model the effect of PIV measurement on the instantaneous single-point velocity vectors as spatial filtering, which allows the change of the velocity structure functions and the turbulent dissipation rate measured by PIV with filter size to be derived. To check these predictions, synthetic PIV image pairs were generated based on simulated tracer particle motions following the velocity fields from direct numerical simulation (DNS) of isotropic turbulence, which were then processed by a standard PIV algorithm. Turbulence statistics obtained from such measured velocity fields were then compared with those from the exact DNS data to evaluate quantitative deviations. The results show that our model captures the effect of spatial resolutions on turbulence statistics in PIV measurement. Experimentally, planar PIV measurements were carried out in the center of a von Kármán swirling flow device, where the turbulence is nearly homogeneous and isotropic. The deviation between measured velocity structure functions and the K41 theory was also analyzed and corrected using the aforementioned model prediction. This work provides a theoretical guidance for examing turbulence statistics measured by PIV, especially multi-point statistics at small scales.

     

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