A sensitivity analysis of the point reference global correlation (PRGC) technique for spatio-temporal correlations in turbulent flows

The point reference global correlation (PRGC) technique which combines single and global measurements as proposed by Chatellier and Fitzpatrick (Exp Fluids 38(5):563–757, 2005) is of significant interest for the analysis of the turbulent statistics for noise source modeling in jet flows as it allows the 2D spatio-temporal correlation functions to be obtained over a region of the flow. This enables the statistical characteristics including inhomogeneous and anisotropic features to be determined. The sensitivity of the technique is examined in some detail for the specific case of laser doppler velocimetry (LDV) and particle image velocimetry (PIV). Simulated data are used to enable a parametric study of the accuracy of the PRGC technique to be determined as a function of the various measurement parameters. The sample frequencies and the number of samples of both the LDV and PIV signals are shown to be critical to errors associated with the estimated spatio-temporal correlations and that low data rates can lead to significant errors in the estimates. Measurements performed in single stream and co-axial jet flows at Mach 0.24 using PIV and LDV systems are reported and the 2D space–time correlation functions for these flows are determined using the PRGC technique. The results are discussed in the context of noise source modeling for jet flows.     

Phase discrimination method for simultaneous two-phase separation in time-resolved stereo PIV measurements

A phase discrimination method for two-phase PIV is presented that is capable of simultaneously separating the two phases from time-resolved stereoscopic PIV images taken in a particle-laden jet. The technique developed expands on previous work done by Khalitov and Longmire (Exp Fluids 32:252–268, 2002), where by means of image processing techniques, a raw two-phase PIV image can be separated into two single-phase images according to particle size and intensity distributions. The technique is expanded through the use of three new image processing algorithms to separate particles of similar size (up to an order of magnitude better than published work) for fields of view much larger than previously considered. It also addresses the known problem of noisy background images produced by high-speed CMOS cameras, which makes the particle detection and separation from the noisy background difficult, through the use of a novel fast Fourier transform background filter.     

Limits on the resolution of correlation PIV iterative methods. Practical implementation and design of weighting functions

Elsewhere in this volume (Nogueira et al. (2005) Exp Fluids, in press), the conceptual background that explains the possibility of resolving wavelengths smaller than the size of the interrogation window, with no basic restrictions but sampling, has been explained. Here, a practical implementation of the concepts is performed. To achieve this resolution in iterative PIV processing, an appropriate weighting function can be used, as commented in that reference. Here, the constraints for the design of such weighting functions are presented and analysed. This opens a line of work on possible weighting functions to develop, since the weightings used in these iterative methods, like local field correction particle image velocimetry (LFC-PIV) (Nogueira et al. (1999) Exp Fluids 27(2):107–116), have not been optimised yet. As an example, different weighting functions are commented and tested both on synthetic and real images. The results on these new weightings indicate that the current ones can be improved and the optimisation criteria are open for further advancement.     

Full 3D correlation tensor computed from double field stereoscopic PIV in a high Reynolds number turbulent boundary layer

The turbulence structure near a wall is a very active subject of research and a key to the understanding and modeling of this flow. Many researchers have worked on this subject since the fifties Hama et al. (J Appl Phys 28:388–394, 1957). One way to study this organization consists of computing the spatial two-point correlations. Stanislas et al. (C R Acad Sci Paris 327(2b):55–61, 1999) and Kahler (Exp Fluids 36:114–130, 2004) showed that double spatial correlations can be computed from stereoscopic particle image velocimetry (SPIV) fields and can lead to a better understanding of the turbulent flow organization. The limitation is that the correlation is only computed in the PIV plane. The idea of the present paper is to propose a new method based on a specific stereoscopic PIV experiment that allows the computation of the full 3D spatial correlation tensor. The results obtained are validated by comparison with 2D computation from SPIV. They are in very good agreement with the results of Ganapthisubramani et al. (J Fluid Mech 524:57–80, 2005a).     

Limits on the resolution of correlation PIV iterative methods. Fundamentals

The spatial resolution of correlation particle image velocimetry (PIV) is a frequently addressed issue that still raises scientific interest. In conventional non-iterative PIV, the spatial resolution limits are of common knowledge (Willert and Gharib (1991) Exp Fluids 10:181–193; Raffel et al. (1998) ISBN 3-540-63683-8, Springer, Berlin Heidelberg New York, among others). On the contrary, those advanced iterative multipass methods that use image distortion techniques or multigrid techniques present a more complex scenario. One of the concepts that raises more debate is the limiting effect of the interrogation window size. This paper focuses on the subject, trying to clarify key points. The results indicate that iterative algorithms using an appropriate weighting function eliminate the window size from the ensemble of spatial resolution limits.     

Propeller tip and hub vortex dynamics in the interaction with a rudder

In the present paper, the interaction mechanisms of the vortices shed by a single-screw propeller with a rudder installed in its wake are addressed; in particular, following the works by Felli et al. (Exp Fluids 6(1):1–11, 2006a, Exp Fluids 46(1):147–1641, 2009a, Proceedings of the 8th international symposium on particle image velocimetry: Piv09, Melbourne, 2009b), the attention is focused on the analysis of the evolution, instability, breakdown and recovering mechanisms of the propeller tip and hub vortices during the interaction with the rudder. To investigate these mechanisms in detail, a wide experimental activity consisting in time-resolved visualizations, velocity measurements by particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) along horizontal chordwise, vertical chordwise and transversal sections of the wake have been performed in the Cavitation Tunnel of the Italian Navy. Collected data allows to investigate the major flow features that distinguish the flow field around a rudder operating in the wake of a propeller, as, for example, the spiral breakdown of the vortex filaments, the rejoining mechanism of the tip vortices behind the rudder and the mechanisms governing the different spanwise misalignment of the vortex filaments in the pressure and suction sides of the appendage.     

A correction method for measuring turbulence kinetic energy dissipation rate by PIV

The accuracy of turbulent kinetic energy (TKE) dissipation rate measured by PIV is studied. The critical issue for PIV-based dissipation measurements is the strong dependency on the spatial resolution, Δx, as reported by Saarenrinne and Piirto (Exp Fluids Suppl:S300–S307, 2000). When the PIV spacing is larger than the Kolmogorov scale, η, the dissipation is underestimated because the small scale fluctuations are filtered. For the case of Δx smaller than the Kolmogorov scale, the error rapidly increases due to noise. We introduce a correction method to eliminate the dominant error for the small Δx case. The correction method is validated by using a novel PIV benchmark, random Oseen vortices synthetic image test (ROST), in which quasi-turbulence is generated by randomly superposing multiple Oseen vortices. The error of the measured dissipation can be more than 1,000% of the analytical dissipation for the small Δx case, while the dissipation rate is underestimated for the large Δx case. Though the correction method does not correct the underestimate due to the low resolution, the dissipation was accurately obtained within a few percent of the true value by using the correction method for the optimal resolution of η/10 < Δx < η/2.     

Accuracy of the Sampling Moiré Method and its Application to Deflection Measurements of Large-Scale Structures

Measuring accurate displacement distributions for large-scale structures is an important issue and a very challenging task. Recently, a simple and accurate phase measurement technique called sampling moiré method [Exp Mech 50–4:501–508, (2010)] has been developed for small-displacement distribution measurements. In this method, the phase distribution of moiré fringes can be analyzed from a single grating image by simultaneously performing down-sampling image processing and intensity-interpolation to generate multiple phase-shifted moiré fringe images. In addition, the phase of the original grating can also be obtained from the phase of the moiré fringe by adding the phase of the sampling grating. In this study, the measurement accuracy of the sampling moiré method was analyzed through computer simulations and a displacement measurement experiment. Four factors of the sampling moiré method were investigated, including the sampling pitch, the order of the intensity-interpolation, random noise, and the form of grating. The results show that determining the optimal sampling pitch is an important factor for obtaining better results but it is not critical. In addition, a practical application of the sampling moiré method is presented that involves a deflection measurement on a 10-meter-long crane. The experimental results demonstrate that submillimeter deflections of the crane can be successfully detected.     

Use of particle image velocimetry to study heterogeneous drag reduction

Large polymer filaments can form when drag reducing polymers are injected through wall slots. The presence of these structures enhances the performance of the drag reducing function by mechanisms which are not understood. This paper shows how particle image velocimetry (PIV) techniques can be used to study changes in the configuration of the injected polymer and in the structure of the velocity field with increasing drag reduction. The filaments are found to behave as solid bodies which break up in high shear regions close to a boundary. The breakup process provides an explanation of why the filaments are not observed close to a wall and offers the possibility of providing a heterogeneous distribution of small aggregates of polymers which could be more effective than uniformly distributed molecules as suggested by Hoyer and Gyr (J Non-Newton Fluid Mech 65:221–240, 1996; J Fluids Eng 120:818–823, 1998), Dunlop and Cox (Phys Fluids 20:203–213, 1977) and Vlachogiannis et al. (Phys Fluid 15:3786–3794, 2004). PIV measurements show dramatic qualitative changes in the velocity patterns at maximum drag reduction.     

Estimation of power spectral density from laser Doppler data via linear interpolation and deconvolution

Spectral estimation of irregularly sampled velocity data issued from Laser Doppler Anemometry measurements is considered in this paper. A new method is proposed based on linear interpolation followed by a deconvolution procedure. In this method, the analytic expression of the autocorrelation function of the interpolated data is expressed as a linear function of the autocorrelation function of the data to be estimated. For the analysis of both simulated and experimental data, the results of the proposed method is compared with the one of the reference methods in LDA: refinement of autocorrelation function of sample-and-hold interpolated signal method given by Nobach et al. (Exp Fluids 24:499–509, 1998), refinement of power spectral density of sample-and-hold interpolated signal method given by Simon and Fitzpatrick (Exp Fluids 37:272–280, 2004) and fuzzy slotting technique with local normalization and weighting algorithm given by Nobach (Exp Fluids 32:337–345, 2002). Based on these results, it is concluded that the performances of the proposed method are better than the one of the other methods, especially for what concerns bias and variance.     

A comparative analysis of the uncertainty of astigmatism-μPTV,stereo-μPIV,and μPIV

Astigmatism or wavefront deformation, microscopic particle tracking velocimetry (A-μPTV) (Chen et al. in Exp Fluids 47:849–863, 2009; Cierpka et al. in Meas Sci Technol 21:045401, 2010b) is a method to determine the complete 3D3C velocity field in micro-fluidic devices with a single camera. By using an intrinsic calibration procedure that enables a robust and precise calibration on the basis of the measured data itself (Cierpka et al. in Meas Sci Technol 22:015401, doi:, 2011), accurate results without errors due to spatial averaging or bias due to the depth of correlation can be obtained. This method takes all image aberrations into account, allows for the use of the whole CCD sensor, and is easy to apply without expert knowledge. In this paper, a comparative study is presented to assess the uncertainties of two state-of-the-art methods for 3C3D velocity field measurements in microscopic flows: stereoscopic micro-particle image velocimetry (S-μPIV) and astigmatism micro-particle tracking velocimetry (A-μPTV). First, the main parameters affecting all methods’ measurement uncertainty are identified, described, and quantified. Second, the test case of the flow over a backward-facing step is analyzed using all methods. For comparison, standard 2D2C μPIV measurements and numerical flow simulations are shown as well. Advantages and disadvantages of both methods are discussed.     

Application of multivariate outlier detection to fluid velocity measurements

A statistical-based approach to detect outliers in fluid-based velocity measurements is proposed. Outliers are effectively detected from experimental unimodal distributions with the application of an existing multivariate outlier detection algorithm for asymmetric distributions (Hubert and Van der Veeken, J Chemom 22:235–246, 2008). This approach is an extension of previous methods that only apply to symmetric distributions. For fluid velocity measurements, rejection of statistical outliers, meaning erroneous as well as low probability data, via multivariate outlier rejection is compared to a traditional method based on univariate statistics. For particle image velocimetry data, both tests are conducted after application of the current de facto standard spatial filter, the universal outlier detection test (Westerweel and Scarano, Exp Fluids 39:1096–1100, 2005). By doing so, the utility of statistical outlier detection in addition to spatial filters is demonstrated, and further, the differences between multivariate and univariate outlier detection are discussed. Since the proposed technique for outlier detection is an independent process, statistical outlier detection is complementary to spatial outlier detection and can be used as an additional validation tool.     

A simple model for the effect of peak-locking on the accuracy of boundary layer turbulence statistics in digital PIV

A simple model was constructed to study the effect of peak-locking on the accuracy of particle image velocimetry (PIV) turbulence statistics. A crucial parameter is the ratio between the root-mean-square (rms) velocity and the discretization velocity, which reflects the number of peaks distributed over the velocity probability density functions. When the ratio of the discretization velocity, which is set by the PIV setup parameters, to the rms, given by the flow, is larger than two, the maximum errors introduced in the mean and rms values become significant (larger than 1%). The errors introduced also depend on the amplitude, or severity, of the peak-locking, and whether the mean displacement corresponds to an integer or a fractional number of pixels. The peak-locking affects the statistical moments of different order in such a way that the errors are phase shifted. The proposed model can be used to predict errors in the turbulence statistics in a laboratory PIV experiment. According to our model predictions, the most significant influence of peak-locking in a boundary layer type of flow is an overall underestimation of the wall-normal rms. Our predictions are in good agreement with our experimental results from turbulent boundary layers and the recent experimental results from a turbulent channel flow by Christensen (Exp Fluids 36:484–497, 2004) for a case of moderate peak-locking.

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PIV study of near-field tip vortex behind perforated Gurney flaps

The impact of Gurney flaps, of different heights and perforations, on the growth and development of a tip vortex, both along the tip and in the near field of a finite NACA 0012 wing, at Re = 1.05 × 10⁵ was investigated by using particle image velocimetry (PIV). Wind-tunnel force balance measurements were also made to supplement the PIV results. This study is a continuation of the work of Lee and Ko (Exp Fluids 46(6):1005–1019, 2009) on the near-wake measurements behind perforated Gurney flaps. The present results show that along the tip, the overall behavior of the secondary vortices and their interaction with the primary, or tip, vortex remained basically unchanged, regardless of flap height and perforation. The peak vorticity of the tip vortex, however, increased with flap height and always exhibited a local maximum at x/c = 0.8 (from the leading edge). In the near field, the strength and structure of the near-field tip vortex were found to vary greatly with the flap height and perforation. The small flaps produced a more concentrated tip vortex with an increased circulation, while the large Gurney flaps caused a disruption of the tip vortex. The disrupted vortex can, however, be re-established by the addition of flap perforation. The larger the flap perforation the more organized the tip vortex. The Gurney flaps have the potential to serve as an alternative off-design wake vortex control device.     

Non-intrusive temperature measurement using microscale visualization techniques

μPIV is a widely accepted tool for making accurate measurements in microscale flows. The particles that are used to seed the flow, due to their small size, undergo Brownian motion which adds a random noise component to the measurements. Brownian motion introduces an undesirable error in the velocity measurements, but also contains valuable temperature information. A PIV algorithm which detects both the location and broadening of the correlation peak can measure velocity as well as temperature simultaneously using the same set of images. The approach presented in this work eliminates the use of the calibration constant used in the literature (Hohreiter et al. in Meas Sci Technol 13(7):1072–1078, 2002), making the method system-independent, and reducing the uncertainty involved in the technique. The temperature in a stationary fluid was experimentally measured using this technique and compared to that obtained using the particle tracking thermometry method and a novel method, low image density PIV. The method of cross-correlation PIV was modified to measure the temperature of a moving fluid. A standard epi-fluorescence μPIV system was used for all the measurements. The experiments were conducted using spherical fluorescent polystyrene-latex particles suspended in water. Temperatures ranging from 20 to 80°C were measured. This method allows simultaneous non-intrusive temperature and velocity measurements in integrated cooling systems and lab-on-a-chip devices.     

Flow structure and skin friction in the vicinity of a streamwise-angled injection hole fed by a short pipe

The velocity field and skin friction distribution around a row of five jets issuing into a crossflow from short (L/D ≃ 1) pipes inclined by 35° with respect to the streamwise direction, (i.e., “short holes”) are presented for two different jet supply flow directions. Velocity was measured using PIV, while the skin friction was measured with oil-film interferometry. The flow features are compared with previously published data for jets issuing through holes oriented normal to the crossflow and with numerical simulations of similar geometries. The distinguishing features of the flow field include a reduced recirculation region in comparison to the 90° case and markedly different in-hole flow physics. The jetting process caused by in-hole separations force the bulk of the jet fluid to issue from the leading half of the streamwise-angled injection hole, as previously reported by Brundage et al. (Tech Rep ASME 99-GT-35, 1999) and predicted by Walters and Leylek (ASME J Turbomach 122:101–112, 2000). The flow structure impacts the skin friction distribution around the holes, resulting in higher near-hole shear stress for a counter-flow supply plenum (jet fluid supplied by a high speed plenum flowing opposite to the free stream direction). In contrast, the counter-flow supply plenum was previously found to have the lowest near-hole wall shear stress for normal injection holes (Peterson and Plesniak in Exp Fluids 37:497–503, 2004b). Streamwise-angled injection generally reduces the near-hole skin friction due to the reduced jet trajectory resulting from the lower wall-normal jet momentum. Far downstream, the skin friction distributions are similar for the two injection angle cases.     

Flow temporal reconstruction from non-time-resolved data part I: mathematic fundamentals

At least two circumstances point to the need of postprocessing techniques to recover lost time information from non-time-resolved data: the increasing interest in identifying and tracking coherent structures in flows of industrial interest and the high data throughput of global measuring techniques, such as PIV, for the validation of computational fluid dynamics (CFD) codes. This paper offers the mathematic fundamentals of a space--time reconstruction technique from non-time-resolved, statistically independent data. An algorithm has been developed to identify and track traveling coherent structures in periodic flows. Phase-averaged flow fields are reconstructed with a correlation-based method, which uses information from the Proper Orthogonal Decomposition (POD). The theoretical background shows that the snapshot POD coefficients can be used to recover flow phase information. Once this information is recovered, the real snapshots are used to reconstruct the flow history and characteristics, avoiding neither the use of POD modes nor any associated artifact. The proposed time reconstruction algorithm is in agreement with the experimental evidence given by the practical implementation proposed in the second part of this work (Legrand et al. in Exp Fluids, 2011), using the coefficients corresponding to the first three POD modes. It also agrees with the results on similar issues by other authors (Ben Chiekh et al. in 9 Congrès Francophone de Vélocimétrie Laser, Bruxelles, Belgium, 2004; Van Oudheusden et al. in Exp Fluids 39-1:86?C98, 2005; Meyer et al. in 7th International Symposium on Particle Image Velocimetry, Rome, Italy, 2007a; in J Fluid Mech 583:199?C227, 2007b; Perrin et al. in Exp Fluids 43-2:341?C355, 2007). Computer time to perform the reconstruction is relatively short, of the order of minutes with current PC technology.