| Abstract: | The analysis of digital PIV data, either derived from CCD technology or through film and then scanned, typically involves two quantization steps: spatial and intensity quantization. The all-optical systems do not introduce these sources of error. For systems which make use of digital technology however, it is of crucial importance to have reliable error bounds and a sufficiently accurate estimate of particle position, taking into consideration both types of quantization. The accuracy demanded by aerodynamicists from PIV has been a major barrier to its practical application in the past. The more recent approach of using the Gaussian profile of the particle images to yield sub-pixel accurate position estimates has resulted in robust measurements being taken to an accuracy of 1/10th pixel and 1% in velocity for the in-plane velocity, in hostile industrial environments. A major problem for 3D PIV estimation has historically been that the out-of-plane velocity error was of the order of 3–4 times larger than in-plane. The out-of-plane velocity estimate can be derived from the change in the ratio of amplitude to variance—known as the depth factor—of the Gaussian form, as a particle traverses the beam profile. However, such measurements are crucially dependent not only on an accurate position estimate but also on an equally accurate estimate of the amplitude and variance. The accuracy of the Gaussian profile fit using a Nelder–Meade optimisation method as developed until now however, is not capable of providing the required accuracies. Therefore, this paper presents a development of the “locales” approach to position estimation to achieve the desired objective of high accuracy PIV measurements. This approach makes use of the fact that by considering all the possible digital representations of the Gaussian particle profile, regions of indistinguishable position can be derived. These positions are referred to as “locales”. By considering the density, distribution, and shape of these locales, the available precision can be estimated and an accurate (no worse than 0.5% error for a typical PIV image) in-plane velocity, accuracy can be obtained; while at the same time providing estimates of the depth factor with an error of approximately 0.8%. This paper describes the implementation of an efficient algorithm to provide velocity estimates to an accuracy of at least 0.5% in-plane, together with a discussion of the required constraints imposed on the imaging. The method was validated by creating a synthetic PIV image with CCD-type noise. The flow being analysed is that of flow past the near wake of a cylinder at a Reynolds Number of 140,000. This image was then analysed with the new method and the velocity estimates compared to the CFD data for a range of signal-to-noise ratios (SNR). For a realistic SNR of 5, the accuracy of the method is confirmed as being at least 0.5% in-plane. Finally, the algorithm was used to map an experimental transonic flow field of the stator trailing edge region of a full-size annular cascade with an estimated error of 0.5%. The experimental results are found to be in good agreement with a previously reported steady state viscous calculation and PIV mapping. |
