Material acceleration estimation by four-pulse tomo-PIV

Abstract

A tomographic PIV system is introduced for the instantaneous measurement of the material acceleration (material derivative of velocity). The system is conceived to operate with short temporal separation (microseconds) and is therefore suitable for applications up to the high-speed flow regimes. The method of operation consists of tomographic imaging of a measurement volume using three arrays of four CCD cameras and two double-pulse laser systems. Advantages and shortcomings of the approach with respect to the most commonly used method based on light polarization are discussed. Various approaches are compared to determine the optimal utilization of four-pulse data to measure the material acceleration: Eulerian and Lagrangian schemes are compared to the recently introduced fluid trajectory correlation (FTC) technique from the authors. A synthetic image test case of a translating vortex is used to compare the schemes with and without the presence of noise. The truncation errors and sensitivity to random noise for each scheme are highlighted. A discussion is also given on the dynamic range of the schemes. The four-pulse tomographic system is used to measure the separated wake of an axisymmetric truncated base with afterbody at a Reynolds number of 68 000. The system calibration accuracy and the baseline measurement uncertainty of the velocity are evaluated with a zero-time delay test. A novel criterion is introduced to establish the relative accuracy of the material derivative measurement, based on the curl of the material acceleration field. The results indicate that the four-pulse tomo-PIV approach suits the measurement of the material acceleration using a variety of estimation schemes. In particular, the FTC technique gives the lowest error levels and is well-suited to perform accurate material acceleration measurements.