Measurement of the conditioned turbulence and temperature field of a premixed Bunsen burner by planar laser Rayleigh scattering and stereo particle image velocimetry

The turbulence and temperature field of Bunsen-type turbulent lean methane/air flames has been investigated using planar laser Rayleigh scattering (PLRS) and stereo particle image velocimetry (stereo PIV). Temporally averaged reaction progress variable plots have been computed from PLRS measurements in order to provide a basis with regards to the verification of computational fluid dynamics (CFD) models. Turbulence was characterised by stereo PIV in one plane for all three velocity components. Averaged velocity fields have been calculated, as well as Reynolds-decomposed fluctuation vector fields. Conditioned root mean square (RMS) values of the turbulent fluctuations in terms of unburnt and burnt gas could be determined by making use of the information gained from a threshold setting procedure in the PIV raw images. Furthermore, several length scales were measured indirectly from PIV vector plots. In this context, all integral length scales being accessible with stereo PIV were computed separately for the burnt and unburnt regions and were compared to each other. It could be observed that all integral length scales increased in the burnt zone. Additionally, the conditioned Taylor and Kolmogorov lengths have been extracted from the PIV field data, derived either from the zero-radius curvature of the correlation function or from common turbulence theory relations.     

A model-based validation framework for PIV and PTV

The utility of particle image velocimetry (PIV) for measurement of velocity fields in many fluid flows is well established. This has created interest in overcoming difficulties with the technique when applied to increasingly larger fields of view where there exists a significant range of velocities and spatial velocity gradients are large. In this regard, a major deficiency with standard cross-correlation PIV is the inherent link between the density of vectors in the measurement field and the maximum measurable displacement. Several schemes exist to reduce this link. These iterative hierarchical/multiresolution schemes are strongly dependent on vector validation routines to remove spurious vectors. Here the design of a new framework for vector validation is described. This framework is general enough for use with both regular and irregularly spaced vector fields to make it applicable to particle image velocimetry (PIV), particle tracking velocimetry (PTV), and hybrid methods. It is based on the determination of a smoothed displacement field that robustly characterizes the measured field such that invalid vectors are attenuated more than valid vectors. In this particular study a thin-plate spline model is incorporated within an iterative regularized weighted least-squares routine to find a smoothed version of the displacement field that maintains pertinent velocity gradient information. The utility of the methodology is demonstrated for a complex flow profile containing four vortices where the valid displacement ranges from ?1/4 to +1/4 of the area of interest (AOI) dimension. Results indicate that this validation strategy can discriminate between valid and invalid vectors remarkably well over a range of parameter settings. In the example presented a flow field with significant velocity gradients and having a high number of invalid vectors (25%) is accurately validated.     

A correlation-based central difference image correction (CDIC) method and application in a four-roll mill flow PIV measurement

An experiment is conducted in a four-roll mill to verify a novel particle image velocimetry (PIV) recording evaluation method that combines the advantages of central difference interrogation and an image correction technique. Simulations and experiments in the four-roll mill geometry demonstrate that the central difference image correction method described in this paper can not only avoid the bias error resulting from the curvature and high-velocity-gradient flow but also effectively reduce the random error resulting from particle image distortion. Two image correction schemes and two base algorithms are discussed. A four-point image correction scheme is suggested on the basis of the traditional correlation-based interrogation algorithm to enable a fast, high-accuracy evaluation of PIV recordings in complex flows. In addition, the PIV experiment accurately determines the velocity field in the four-roll mill and confirms the linear distributions of the velocity components and the roller speed.     

A method for automatic estimation of instantaneous local uncertainty in particle image velocimetry measurements

The uncertainty of any measurement is the interval in which one believes the actual error lies. Particle image velocimetry (PIV) measurement error depends on the PIV algorithm used, a wide range of user inputs, flow characteristics, and the experimental setup. Since these factors vary in time and space, they lead to nonuniform error throughout the flow field. As such, a universal PIV uncertainty estimate is not adequate and can be misleading. This is of particular interest when PIV data are used for comparison with computational or experimental data. A method to estimate the uncertainty from sources detectable in the raw images and due to the PIV calculation of each individual velocity measurement is presented. The relationship between four error sources and their contribution to PIV error is first determined. The sources, or parameters, considered are particle image diameter, particle density, particle displacement, and velocity gradient, although this choice in parameters is arbitrary and may not be complete. This information provides a four-dimensional “uncertainty surface” specific to the PIV algorithm used. After PIV processing, our code “measures" the value of each of these parameters and estimates the velocity uncertainty due to the PIV algorithm for each vector in the flow field. The reliability of our methodology is validated using known flow fields so the actual error can be determined. Our analysis shows that, for most flows, the uncertainty distribution obtained using this method fits the confidence interval. An experiment is used to show that systematic uncertainties are accurately computed for a jet flow. The method is general and can be adapted to any PIV analysis, provided that the relevant error sources can be identified for a given experiment and the appropriate parameters can be quantified from the images obtained.     

PIV through moving shocks with refracting curvature

Particle image velocimetry (PIV) is applied to moving millimeter shock waves whose density jump and small radii of curvature make refraction significant. The motion of the shock front is also much larger than the motion of the corresponding mass at the front. A Lagrangian model of particle displacement in response to a moving shock is developed to investigate the relationship between particle displacements and the actual mass velocity behind the shock. Errors in PIV measurements due to light refraction across a curved, moving shock are investigated in terms of both position and velocity errors using a refraction model developed from geometrical optics. The model is experimentally validated and applied to 1-D slices of data extracted from PIV vector fields, and the resulting measurement errors are quantified.     

Evaluation of aero-optical distortion effects in PIV

Aero-optical distortion effects on the accuracy of particle image velocimetry (PIV) are investigated. When the illuminated particles are observed through a medium that is optically inhomogeneous due to flow compressibility, the resulting particle image pattern is subjected to deformation and blur. In relation to PIV two forms of error can be identified: position error and velocity error. In this paper a model is presented that describes these errors and particle image blur in relation to the refractive index field of the flow. In the case of 2D flows the model equations can be simplified and, furthermore, the background oriented schlieren technique (BOS) can be applied as a means to assess and correct for the optical error in PIV. The model describing the optical distortion is validated by both computer simulation and real experiments of 2D flows. Two flow features are considered: one with optical distortion normal to the velocity (shear layer) and one with optical distortion in the direction of the flow (expansion fan). Both simulation and experiments demonstrate that the major source for the velocity error is the second derivative of the refractive index in the direction of the velocity vector. The aero-optical distortion effect is less critical for shearing interfaces in comparison with compression/expansion fronts, the most critical case being represented by shock waves. Based on the results from the simulated experiments, it is concluded that for the 2D flow case the BOS method allows a measurement of the mean velocity error in PIV and can reduce it to a large extent.     

Planar flow field measurements in atmospheric and pressurized combustion chambers

The investigation of velocity fields in complex combustor flows is an important and necessary subject of propulsion technology. A persisting problem in computational fluid dynamics (CFD) modeling is that current numerical design tools have a number of deficiencies in accurately predicting the complex combustor flow. Using planar techniques such as planar Doppler velocimetry (PDV) or particle image velocimetry (PIV) it is possible to provide detailed information of the flow field inside the combustor. This paper reports on the applicability of PIV in combustor flows at realistic operating conditions.     

3-Component acceleration field measurement by dual-time stereoscopic particle image velocimetry

In this article, a multiplane stereo-particle image velocimetry (PIV) system was implemented and validated to measure the three-component acceleration field in a plane of turbulent flows. The employed technique relies on the use of two stereoscopic particle image velocimetry (SPIV) systems to measure pairs of velocity fields superimposed in space but shifted in time. The time delay between the two velocity fields enables the implementation of a finite difference scheme to compute temporal derivatives. The use of two synchronized SPIV systems allows us to overcome the limited acquisition rate of PIV systems when dealing with highly turbulent flows. Moreover, a methodology based on the analysis of the spectral error distribution is described here to determine the optimal time delay to compute time derivatives. The present dual-time SPIV arrangement and the proposed analysis method are applied to measure three-component acceleration fields in a cross section of a subsonic plane turbulent mixing layer.     

Stereoscopic PIV on multiple color-coded light sheets and its application to axial flow in flapping robotic insect wings

Non-scanning volume flow measurement techniques such as 3D-PTV, holographic and tomographic particle image velocimetry (PIV) permit reconstructions of all three components (3C) of velocity and vorticity vectors in a fluid volume (3D). In this study, we present a novel 3D3C technique termed Multiple-Color-Plane Stereo Particle-Image-Velocimetry (color PIV), which allows instantaneous measurements of 3C velocity vectors in six parallel, colored light sheets. We generated the light sheets by passing white light of two strobes through dichroic color filters and imaged the slices by two 3CCD color cameras in Stereo-PIV configuration. The stereo-color images were processed by custom software routines that sorted each colored fluid particle into one of six gray-scale images according to its hue, saturation, and luminance. We used conventional Stereo PIV cross-correlation algorithms to compute a 3D planar vector field for each light sheet and subsequently interpolated a volume flow map from the six vector fields. As a first application, we quantified the wake and axial flow in the vortical structures of a robotic insect (fruit fly) model wing. In contrast to previous findings, the measured data indicate strong axial flow components on the upper wing surface, including axial flow in the leading-edge vortex core. Collectively, color PIV is robust against mechanical misalignments, avoids laser safety issues, and computes instantaneous 3D vector fields in a fraction of the time typical for other 3D systems. Color PIV might thus be of value for volume measurements of highly unsteady flows.     

Coherent structure identification from wavelet analysis of particle image velocimetry data

 A new technique based on wavelet transform is applied to bidimensional velocity fields obtained by particle image velocimetry (PIV) measurements, in order to extract and characterize swirling motion associated with coherent structures. The proposed technique is based on the selectivity property of the wavelet transform and permits the detection of regions of the flow field associated with coherent structures and their spatial localization. Furthermore, being the method based on the analysis of the local energy content at separated scales, it is possible to extract the typical wavenumber associated with structures and therefore the typical length-scale. The procedure is validated by the application to velocity vector fields obtained from PIV measurements in different flow conditions and turbulence levels. Results are compared with those obtained by other more standard procedures, and the advantages and limitations of the proposed method are then discussed. Received: 16 October 2000 / Accepted: 18 June 2001 Published online: 29 November 2001     

On the effect of particle image intensity and image preprocessing on the depth of correlation in micro-PIV

The depth of correlation (DOC) is an experimental parameter, introduced to quantify the thickness of the measurement volume and thus the depth resolution in microscopic particle image velocimetry (μPIV). The theory developed to estimate the value of the DOC relies on some approximations that are not always verified in actual experiments, such as a single thin-lens optical system. In many practical μPIV experiments, a deviation of the actual DOC from its nominal value can be expected, due for instance to additional components present in the optical path of the microscope or to the use of image preprocessing before the PIV evaluation. In the presented paper, the effect of real particle image intensity distribution and image preprocessing on the thickness of the measurement volume is investigated. This is performed studying the defocusing of tracer particles and the DOC-related bias error present in μPIV measurements in a Poiseuille flow. The analysis shows that the DOC predicted using the conventional formulas can be significantly smaller than its actual value. To overcome this problem, the use of an effective NA determined experimentally from the curvature of the image autocorrelations is proposed. The accuracy of this approach to properly predict the actual size of DOC is discussed and validated on the experimental data. The effectiveness of image preprocessing to reduce the DOC-related bias error is tested and discussed as well.     

Construction of three-dimensional flow structure out of two-dimensional steady flow field velocity measurements

 Two-dimensional particle image velocimetry (PIV) is used to obtain a set of parallel vector maps in spanwise direction over the delta wing configuration ELAC. The out-of-plane velocity component is then constructed by application of continuity equation. This yields the whole three-dimensional separated flow field over the leeward side of the model. The spatial resolution of the measurements enables a detailed examination of the three-dimensional flow structure. The growth and the helical structure of primary vortex as well as smaller flow structures caused by secondary separation can be observed. Accuracy of the constructed velocity component is estimated with help of a numerically obtained three-dimensional dataset of the flow field around this configuration. The reconstruction procedure was applied to this data set taking the experimental uncertainty and the grid spacing of the PIV measurements into consideration. A comparison of reconstructed out-of-plane component and data of the numerical solution of Navier–Stokes equations results in a promising low error. A statistical analysis of different procedures allows interpretation of reconstruction capabilities. Received: 15 April 1998 / Accepted: 15 September 1998     

Two-color particle image velocimetry technique for an internal combustion engine

A two-color particle image velocimetry (PIV) technique has been applied to a single-cylinder motored research engine. Two-color PIV is a quantitative planar velocity measurement technique that can unambiguously determine the velocity magnitude and direction.

The work includes the development of an interrogation system, a series of computer simulations to determine the performance of the technique under various conditions, the comparison of these results to similar ones obtained for an autocorrelation PIV system, and a test of the technique by reconstructing the velocity field of a uniform jet flow.

The technique was then applied to the in-cylinder flow field of a motored single-cylinder, cup-in-head, research engine. A total of 27 instantaneous velocity fields were obtained at a single measurement plane for a single operating condition of the engine. The data were analyzed to yield ensemble-averaged velocity and velocity fluctuation.     

Pseudo turbulence in PIV breaking-wave measurements

 The particle image velocimetry (PIV) technique was employed to measure the instantaneous velocity distribution under nonbreaking and breaking water waves. The corresponding turbulence intensity was calculated by the ensemble average of repeated measurements. The pseudo turbulence found was large enough to affect the accuracy of the turbulence measurements. We follow Prasad et al.'s (1992) approach to demonstrate that the pseudo turbulence is related to the bias error, which is the discrepancy between the true position of the particle image and the position calculated from the pixel array data with inadequate pixel resolution. To reduce the bias error (or the pseudo turbulence), we first calculate it from a turbulence-free flow with the same experimental set-up as that used for the targeted experiments (i.e., we use the same size of field of view, seeding particles, seeding density, lens aperture, and laser wavelength in both experiments). Then we minimize the bias error from the turbulence measurements in the actual experiments. To demonstrate the procedure, the evolution of a breaking wave is investigated. Received: 30 January 1998/Accepted: 28 October 1999     

Development of fiberscope PIV system by controlling diode laser illumination

Because of the inherent small size of optical fiberscopes, they provide access and relative handling ease in given closed vessels, which are hardly equipped with extra windows for conventional flow visualization. The use of an optical fiberscope in conjunction with a conventional particle image velocimetry/particle tracking velocimetry (PIV/PTV) system without optimization can lead to degraded transmission of images. The present study proposes a processing technique to filter background noise contained within the coarse bundle image by subtracting the original image of the bundle as reference image. Additionally, efforts were made to increase the reliability of vector processing using particle streak images via judicious pulse interval and duration adjustments. As an applications test we measured classic jet flow using the developed system and using established conventional measurement techniques. Our tests confirmed that our fiberscope PTV system provides vector fields with sufficient accuracy.     

Theory of non-isotropic spatial resolution in PIV

The spatial resolution of the PIV interrogation technique is discussed from an analytical standpoint and assessed with Monte Carlo numerical simulation of particle image motion. The PIV measurement error associated with lack of spatial resolution is modelled associating the cross-correlation operator to a moving average filter. The error associated with the "low-pass filtering" effect is investigated by adopting a second-order polynomial expression for the velocity spatial distribution. According to the present error analysis, the measurement error is proportional to the second-order spatial derivative of the velocity field and increases with the square of the window linear size. The strategy for the selection of the window size and properties (aspect ratio and orientation) so as to minimize the error is discussed. The principle is based on nonisotropic interrogation windows of elliptical shape, with a constant area and elongated in the direction of the largest curvature radius. The nonisotropic parameters are defined as eccentricity and orientation, which are based on the local eigenvalues/vectors of the Hessian tensor of the displacement spatial distribution. The technique is implemented in a recursive PIV interrogation method. The performance of nonisotropic interrogation technique is assessed by means of synthetic PIV images, which simulate three situations: first, a one-dimensional sinusoidal shear displacement, which allows comparison of the cross-correlation spatial response with the transfer function of linear filters. Second, the stream-wise exponential velocity decay is simulated, which simulates the particle tracers decelerating downstream of a shock wave and gives an example of a flow with main velocity differences aligned with the velocity direction. The results show that keeping the image density fixed, the error caused by insufficient spatial resolution can be reduced by a factor two when a preferential direction is found in the flow field. Finally, a Lamb–Oseen vortex flow is presented, which shows the complex pattern formed by the interrogation windows in a two-dimensional case. In this case, the improvement in interrogation performance is limited due to the isotropic nature of the velocity spatial fluctuation.     

Measurements of the orthogonal blade–vortex interaction using a particle image velocimetry technique

This paper describes the results of application of a particle image velocimetry (PIV) technique to an orthogonal blade–vortex interaction experiment. To help resolve the problem of vortex meander during the tests, two PIV systems were used, which produced two velocity vector maps closely separated in time. During the PIV analysis an image-based vector validation scheme was used, which was shown to reduce significantly the number of wild vectors reaching the vector map. Preliminary results from the tests showed that, close to the blade, a significant radial outflow was superimposed on the vortex flow field. The radial flow is thought to be due to the dispersion of the vortex axial core flow during vortex cutting, which distorts the vortex flow field and enlarges the vortex. Further away from the blade, no significant radial flow was detected and the vortex remained undisturbed. Received: 26 April 1999/Accepted: 9 November 1999     

Time-resolved particle imaging velocimetry for the investigation of rotating stall in a radial pump

The operating range of turbomachines is limited in terms of the low flow rate by instabilities appearing in flow-leading parts of the machinery resulting in the creation of vortices. If the flow is further throttled, stall cells can start to propagate in the impeller at a fraction of the rotor speed. This article presents an investigation of rotating stall at different flow rates in a radial pump using time-resolved particle imaging velocimetry (PIV). This technique was used to investigate the flow field at the same position in every channel of the impeller during several revolutions. Frequency analysis was applied to the measured velocities to calculate the angular speed of the rotating stall in the impeller. The interest of time-resolved PIV to understand rotating stall is demonstrated, as it allows measurement of transient, irregularly appearing flow fields.     

A variational filtration and interpolation technique for PIV employing fluid dynamical constraints

A variational method for post-processing of the velocity fields obtained by particle image velocimetry (PIV) is described. This method allows one to effectively reconstruct the flow field in the areas of the domain where the spurious vectors were discarded either by other filters or manually. If the spurious vectors cannot be removed, they are smoothed in with the surrounding field so that their effect is significantly reduced. The method is based on the application of dynamical constraints such as continuity, smoothness and matching to the original data. The results of the application of the developed algorithm to the velocity fields obtained by PIV in laboratory experiments with quasi-two-dimensional vortex dipoles are discussed.     

Evaluation of instationary flow fields using crosscorrelation in image sequences

In order to investigate the temporal behavior of dynamic flow processes, a movie version of particle image velocimetry (PIV) with a high framing capability has been developed. The experimental setup includes a copper vapor laser capable to produce pulse sequences with more than 100 pulses with a repetition rate of up to 30 kHz and a rotating drum camera to record the Mie scattering signals from the particles seeded to the flow. With this setup, image sequences with a number of consecutive images (40–70 depending on the image size) of a dynamic process can be taken on high resolution 36 mm film.To evaluate the 2-dimensional velocity vector fields, an algorithm based on the crosscorrelation of subareas in consecutive images has been developed and optimized in terms of computing time. The technique was applied to resolve the instationary flow field in a single cylinder spark ignition (SI) engine during the compression stroke.