Particle Image Velocimetry in a High-Pressure Turbine Stage at Aerodynamically Engine Representative Conditions


 Particle Image Velocimetry (PIV) is a well-established technique for determining the flow direction and velocity magnitude of complex flows. This paper presents a methodology for executing this non-intrusive measurement technique to study a scaled-up turbine vane geometry within an annular cascade at engine-relevant conditions. Custom optical tools such as laser delivery probes and imaging inserts were manufactured to mitigate the difficult optical access of the test section and perform planar PIV. With the use of a burst-mode Nd: YAG laser and Photron FASTCAM camera, the frame straddling technique is implemented to enable short time intervals for the collection of image pairs and velocity fields at 10 kHz. Furthermore, custom image processing tools were developed to optimize the contrast and intensity balance of each image pair to maximize particle number and uniformity, while removing scattering and background noise. The pre-processing strategies significantly improve the vector yield under challenging alignment, seeding, and illumination conditions. With the optical and software tools developed, planar PIV was conducted in the passage of a high-pressure stator row, at mid-span, in an annular cascade. Different Mach and Reynolds number operating conditions were achieved by modifying the temperature and mass flow. With careful spatial calibration, the resultant velocity vector fields are compared with Reynolds Averaged Navier Stokes (RANS) simulations of the vane passage with the same geometry and flow conditions. Uncertainty analysis of the experimental results is also presented and discussed, along with prospects for further improvements.


Dedicated to my wife, Hannah, for all the time and support she gave me regardless of her
impossibly busy schedule in medical school; and to our families, who selflessly put both of our needs above their own.

ACKNOWLEDGMENTS
The author would like to acknowledge Dr. Guillermo Paniagua and the entire PETAL team for their dedication and guidance throughout this work. The author would also like to acknowledge the Rolls-Royce Corporation for their technical and financial support.

INTRODUCTION
With the advancement of turbomachinery design and optimization, improvements in the performance of turbines are measured in fractions of points of efficiency. The quantification of secondary and tip flow phenomena is central to understanding the principal loss mechanisms of each turbine stage. Horseshoe, passage and tip leakage vortices play a large role in the performance of turbine airfoils and their efficiency. If the behavior of these flow features is not well understood, it can lead to incorrect performance predictions and ultimately sub-optimal designs. As the aviation and power generation industries trend more toward small core turbines, these secondary flows become proportionally more important in determining efficiency and can occur at even higher frequencies. This inspired the first objective of this work, which is to develop the tools needed to assess a new vane geometry and turbine tip for small engine cores.
CFD is frequently used to predict the behavior of these environments, but until these solutions exceed the accuracy of empirical measurements, higher resolution and less invasive diagnostic techniques are required. Physical probes can be used to anchor CFD simulations to a degree, but their discrete nature leads to low spatial resolution, and their finite size means that they inherently disturb the flow they are made to measure. This is especially true in small core turbines, where rake sizes can be significant compared to the size of the airfoils themselves. The basic process to perform PIV begins with the injection of tracer particles into the flow upstream of the region of interest. A laser sheet, like the one depicted in Figure 1.1, is used to illuminate the particles within that region of interest so that they can be captured in an image. With a very short pulse width, the image resolves an instantaneous array of the tracer particles. With a series of images taken, the frames are divided into subregions and the displacement of the particles within these regions between two consecutive images can be determined through a crosscorrelation algorithm. The known time between the laser pulses is then used to convert the displacement into velocity.
The resolution of the velocity measurements is dictated by the size of subregions, which is a parameter known as the window size and is selected by the user. A displacement vector is produced for each window; hence, greater spatial resolution is achieved by minimizing the size of the window. Conversely, smaller windows can decrease the quality of the correlation signal as they become more sensitive to variations in image intensity. Aside from increasing the uncertainty of the particle displacement, the cross-correlation program can fail to resolve the displacement vector if the differences are too great. According to Raffel et al. [1], non-uniform illumination creates noise in the correlation plane and the correlation peaks are skewed by the brightest particles.
Xue et al. [2] affirm that the strength of the signal-to-noise ratio governs the accuracy and uncertainty of the cross-correlation and the resulting velocity measurements. To normalize the particle intensity and improve the quality of the cross-correlation signal, several different image pre-processing techniques such as background subtraction, image binarization, intensity capping, and filtering have been explored [1]. Due to the added challenges posed by operating PIV in an annular turbine test section, a tailored image enhancement tool was implemented in the processing of the images acquired for this investigation.

Review of Previous Experimentation
In lower Reynolds number experimentation, low repetition rates on the order of 10 Hz are used to investigate time-averaged flow structures with high-resolution cameras. Bloxham [3] conducted Velocity measurements axial to the flow direction were obtained at multiple locations within the passage and aft of the passage through the use of a low-repetition-rate double pulse laser and two PCO 1600 cameras fitted with Scheimpflug adapters to correct for the camera lens plane not being parallel to the image plane. [6] reports a laser sheet thickness of 1.5 mm to limit the average inplane particle movement between exposures to less than 30% of the sheet thickness.
For higher Reynolds number applications in annular cascades and rotating rigs, PIV is performed at frequencies of 1 kHz or faster to try to resolve unsteady phenomenon. Peter et al. [7] performed time-averaged and time-resolved SPIV at 5 kHz on a compressor annular cascade to investigate rotating instability at a chord based Reynolds number of 3x10 5 . Two Photron FASTCAMS SA1.1 operating at 10 kfps on tilt mounts were used to capture multiple 3D velocity fields tangential to the stator hub, which was coated with rhodamine b-doped paint to minimize light scattering. Time-resolved pressure data was collected in parallel with the SPIV measurements to serve as a reference for the correlation algorithm and to support the spectral analysis of the optical results. Time-resolved SPIV was also implemented by Anderson et al. [8] to characterize the unsteadiness of the HSV system in a low aspect ratio pin-fin array at a Reynolds number of 2.0x10 4 . Two high speed cameras and a dual-head laser were used to produce vector fields at a sampling frequency of 1 kHz.
A comprehensive review of recent PIV measurements in rotating turbomachinery applications was performed by Woisetschläger and Göttlich [9], with a special focus on the facilities at Graz University of Technology and at German Aerospace Center DLR. The transonic test turbine facility at Graz University features 24 stator and 36 rotor blades rotating at 10,600 rpm, while the centrifugal compressor at German Aerospace DLR features 13 main and 13 splitter blades rotating at up to 50,000 rpm. Both facilities utilize a periscope-type laser delivery probe to deliver a laser sheet into the laser complex geometric environment, as well as a large optical window to allow two cameras to image the plane of interest so that SPIV can be performed. This configuration is illustrated in Figure 1.2.  however, total temperature measurements were acquired at a rate of almost 100 kHz to resolve the energy separation. To study small core turbine designs, Cuadrado et al. [11] have developed a modular two-stage turbine rig that is capable of operating at rotational speeds of over 15,000 rpm.
The Purdue Small Turbine Aerothermal Rotating Rig (STARR) will couple optical and intrusive measurements to precisely characterize stator and rotor flowfields at engine representative conditions. Based on previous experimentation, optical measurements will need to be acquired at frequencies in excess of 100 kHz to accurately characterize the unsteady phenomena present in small core turbines. One of the proposed optical measurement techniques presented in [11] is further detailed in this paper.
Due to the limited access of annular turbine rigs, endoscopic PIV was developed so that optical access can still be provided for the imaging equipment without the need for a large viewing window. Kegalj and Schiffer [12] demonstrated the viability of acquiring PIV data in a 1.5 stage axial low-pressure turbine rig while imaging through a borescope. An axial (setup R) and tangential (setup C) plane were captured in the turbine annulus between the first rotor row and second stator row, illustrated in Figure 1.4, using the LaVision Imager ProX 2m camera and a 15 Hz dual cavity Nd:YAG laser. The results were time-averaged to overcome non-uniform illumination of the area of interest. A drawback to imaging through a borescope is that it bottlenecks the amount of light that reaches the camera chip, so the distance between the borescope and laser sheet must be minimized at the cost of the field of view. The signal to noise ratio was also improved by using larger seeding particles on the order of 2-3 μm. Reeves and Lawson [13] present a method for evaluating and correcting the perspective errors associated with endoscopic PIV, with applications to stereoscopic arrangements.

Research Methodology
To achieve the objectives, first the optical setup and data processing tools needed to perform non-intrusive measurements in an annular rig were developed. Conducting PIV in this environment required optical access to the region of interest, seeding in the desired portion of the annulus, precisely aligned optics, synchronized imaging, and a custom image pre-processing system to maximize the vector yield from the acquired images.
This optical setup is then applied to an annular scaled-up small core turbine vane passage at aerodynamically engine representative conditions. An initial validation of the experimental design is performed on a set of turbine vanes referred to as vane1. After troubleshooting the procedures, the methodology is then applied to a second set of vanes, vane2, and compared to CFD

DEVELOPMENT OF MEASUREMENT TECHNIQUE
The diagnostic complexities demanded a thorough approach to the instrumentation development, as well as the experimental design. This processed began with a review of the optical access provided by the annular test section to select the velocity plane of interest. Based on the available access, a custom optical tool was developed to deliver the laser to desired location in the form of a thin sheet. Alignment procedures were then created to establish an accurate and consistent method of delivering the laser to the interrogation plane, in addition to ensuring the laser sheet and camera imaging plane are coplanar. Finally, an image post-processing tool was generated that enhances the quality of the PIV images to improve the detection of particles in the crosscorrelation software.

Facility Review
To assess the abatement of secondary flows, a stationary annular cascade (BRASTA) was developed at PETAL [14]. The facility is three times larger than the designed scale to facilitate    In attempt to minimize the contamination of the test section by the seeding oil, local seeding was the first location evaluated. Two separate ports, indicated by A and B in Figure 2.3, were assessed at 11.3 kg/s and 278 K. A sample frame from one of the image sets collected with seeding through port A is shown in Figure 2.4 (left). Not only is the seeding limited to the upper left portion of the window, it is also too dense to distinguish individual particles. Additionally, the seeding is not well mixed as revealed by the streamlike flow structures found within the atomized mineral oil. To ensure this outcome was not a consequence of the local seeding port selection, a second set of tests was conducted with the seed particles entering the test section through port B. As can be seen in Figure 2.4 (right), a similar result was attained: the seeding is not well mixed, it is limited to a median height of the window, and individual particles are hard to differentiate. Due to the proximity of the local seeding ports to the optical access window, the particles did not have sufficient time to disperse into the whole stator passage and thus were concentrated too highly in smaller regions of the flow. These limitations in particle mixing impede the collection of highquality data. Alternative local seeding approaches could have been pursued, such as injecting the seed particles into ports A and B simultaneously or manufacturing a dispersion nozzle, but the former does not resolve the mixing problem and the latter creates an obstruction in the flow just upstream of the stator passage. To minimize particle interference from injection and ensure proper seeding density, the seeder was interfaced into the wind tunnel in the settling chamber upstream of the test section. In this way, the particles are mixed into the bulk flow during flow conditions, and a uniform density of particles is delivered to the test article. As observed in Figure 2.2, around 25% of the annular cascade was properly seeded with particles. A sample image of the seeded vane passage, again at 11.3 kg/s and 278 K, is shown below in Figure 2.5. Unlike local seeding, semiglobal seeding resulted in uniform particle distribution across the entire window, with distinct and identifiable particles.
The laser used to illuminate the particles for this investigation is a quasi-continuous burstmode Nd:YAG laser that was custom-built by Slipchenko et al. [15] and produces 150 mJ per pulse at 10 kHz . The fundamental output of this laser is 1064 nm, but the 2 nd harmonic of 532 nm was used as this wavelength is in the visible light spectrum, which can be imaged directly by a Photron FASTCAM camera and can be aligned without the use of detector cards. The nominal repetition rates of the laser are 10 and 20 kHz, but it can be modified to achieve a range of rates from 5 kHz to 100 MHz. For all the data sets explored in this paper, a repetition rate of 10 kHz was used with a pulse-burst duration of 10 ms. This frequency was chosen since the max frequency that the FASTCAM can operate at full-frame is 20 kHz and the laser fires two pulses per cycle in doublet mode. The doublets have a set spacing that is timed such that the pulses occur during two separate image frames, so the laser frequency needs to be half the camera frequency for this system.

Design of Laser Delivery Probe
For the validation of this experimental design, the region of interest is a mid-span cut through the vane passage. This location was chosen as the flow is more uniform and steadier than that of planes nearer to the endwalls, which serves as a more stable target to compare against while troubleshooting the technique. This region also contains large velocity and flow angle gradients, which will test the technique's ability to resolve the flowfield features that are typically used to detect and characterize secondary flows. An example of this plane is illustrated in Figure 2  To allow access for a laser sheet in the vane passage, a laser delivery system capable of surviving high temperatures, pressures, and vibrations was designed and built. The design, which is pictured in Figure 2.7, consists of a stainless-steel structure integrated into one of the plugs for the optical access holes that is fixed in place by a shaft collar. A lens tube for 0.5 in. optics is located in the lower portion of the structure to allow for sheet forming optics to be installed within the probe. The configuration shown below has a cylindrical plano-concave (PCV) lens with a negative focal length installed at the bottom of the lens tube and is the configuration used for the majority of the test campaign. Below the lens tube is a permanent window that seals the inside of the probe. Underneath this window is a prism mirror that utilizes a coated hypotenuse to reflect over 98% of the 532 nm wavelength laser pulse (Thorlabs MRA10-K13). The original probe design used a total internal reflection prism, but due to the unconventional geometry of aligning a laser sheet through a vane passage with a high stagger angle in an annulus, it was replaced with the prism mirror to provide more consistent reflectance at non-zero incidence angles. The body of the probe is adjustable in rotation angle and depth as indicated by the yellow and green arrows, respectively, to allow for adjustment of the laser delivery location. A seal is achieved between the probe body and the optical access plug through internal piston O-rings. The shaft collar is tightened to the probe body and bolted to the optical plug to secure the probe after alignment is finalized. The prism mirror at the end of the probe allows the laser to be turned perpendicularly and directed toward the region of interest. This prism mirror is adjustable in pitch, indicated by the purple arrow, giving the laser beam path the final necessary degree of freedom to deliver a laser sheet into the vane passage. Once the prism is in place, set screws retain its position and prevent displacement during testing.

Experimental Methodology
For this research, two different aerodynamically representative conditions were investigated in the wind tunnel facility. The first one, referred to as the cold condition, is obtained by flowing through the cold line (bypassing the heater) such that the flow is expanded from its reservoir conditions. The second condition referred to as the hot condition, combines flow through both the cold and the hot lines, achieving a higher flow total temperature at the test section inlet.
These conditions and their main flow parameters within the test section are summarized in Table   2.1. A schematic of the flow path with the test section location is shown in Figure 2  While the laser alignment external to the probe was straightforward, careful alignment procedures were needed within the annular turbine rig where access was limited. A calibrated alignment tool was constructed to provide a reference between the geometry of the rig and overlap of the laser sheet and camera focus location. The alignment tool was set such that it could be inserted through one of the optical access holes and held at the midspan of the first stage vane in view of the camera. The tool contained a calibration grid to focus the camera and create a reference for relating camera pixels to the real-world reference frame. The tool also contained a target to ensure that the laser sheet would overlap with the focal plane of the camera. Since there was no outside optical access for viewing the location of the laser during alignment, a digital borescope was inserted into the test section to view the laser and make adjustments until the sheet was precisely aligned with the calibration target. Based on a target average particle travel distance between frames of ~7 pixels [1] and the expected flow velocity in the region of interest, the required laser pulse doublet spacing for the design mass flow rate in this work is ~3 s. Given that the camera is operated at 20 kHz for these experiments (i.e., a frame-to-frame temporal spacing of 50 s), the frame straddling technique is employed to record images with a very short time spacing. This technique consists of timing the first laser pulse of each doublet at the end of the exposure of one frame and the second pulse at the beginning of the next frame. The timing scheme, which is controlled by a digital delay pulse generator, is depicted in Figure 2.10. Given that the pulse width of each laser pulse is on the order of 10 nanoseconds, the two images appear to have a time interval equal to the doublet spacing (3 s in this case) regardless of the frame rate. As this approach requires two frames per velocity field, the effective velocity field measurement rate is 10 kHz. For a narrower field of view and/or reduced spatial resolution, this same setup can be used with a camera frame rate of 200 kHz to produce PIV data up to 100 kHz. PETAL's custom-built burst-mode laser systems [9] have successfully produced PIV data up to 1 MHz [10] in other experiments.

Development of Data Processing Tool
To improve the detection of particle movement within the PIV region of interest, a tool was developed in MATLAB to modify the display properties of each individual frame. First, the range of useful images is extracted from each data set based on the presence of the laser in both images of each frame straddling pair. Due to a significant variation in the mean intensity of each frame across a data set, highlighted in Figure 2.13, frame-by-frame background subtraction is performed using images from a no-flow data set and matching each frame to its corresponding image with the flow. To aid in the explanation of the image pre-processing tool, a flowchart of the process can be found in Figure 2.14. After subtracting the background images, a geometric mask is created based on a reference image showing the window outline that bounds the useful data. Next, each image is optimized for the number of centroids (particles) by varying the contrast cutoff level from high to low. The optimization is truncated if camera noise found within a portion of the frame with no particles exceeds a designated limit. For this tool, camera noise is defined as centroids detected by the program that are not seed particles. For the image sets in this study, a corner of the frame outside the optical window was used as this area could never contains seed particles, nor could it be illuminated by the laser pulse or any scattering. If light scattering exists within the region of interest after background subtraction, a second limit is assigned based on the maximum expected number of centroids. Like camera noise, light scattering within the region of interest appears at low contrast cutoff levels and contributes greatly to the number of centroids. Image pairs with low scattering can be used to identify the expected number of centroids for an image set. This limit prevents the data set from being polluted by too many false centroids. After identifying the contrast level that produces the greatest number of centroids for both images in an image pair, if the number of centroids across the pair differs by more than the allowed amount, the contrast cutoff level of the more centroid-dense image is increased so that the number of observed particles is decreased and the established limit is satisfied. This boundary was added because during the development of this software, it was discovered that when simply maximizing each image's number of centroids, the velocity vector yield was often worse if the two images of a correlation pair greatly differed in number of particles. Lastly, the resulting images are binarized so that the intensity of each particle is normalized. This eliminates any bias created by the differences in mean intensity between the two images in a pair that was highlighted in Figure 2.13.  However, the percent difference between the two images is less than 25%, so the contrast limits that yielded the max number of centroids for each image are applied to both, respectively, before binarizing the images. The enhanced images are then processed in LaVision's DaVis PIV code as a time-series of double frames. Sequential cross-correlation of frame pairs is performed via a multi-pass vector calculation involving 3 passes of a 64x64 pixel square window with 75% overlap, followed by 2 final passes of a 32x32 pixel circular window with 50% overlap. Allowable vector ranges, peak ratios, and universal outlier detection are used to remove outliers, but no vectors were replaced through interpolation to fill or smooth the vector field. The vectors fields were then converted from pixel displacement to velocity based on calibration images of the test article geometry and time spacing between successive laser pulses.

First Application of Technique
Because the laser sheet enters the test section at a different circumferential location than the vane passage to align with the stagger angle of the vanes, one of the most difficult aspects of the alignment is matching the angle of the laser sheet with the midspan plane. For the initial experiments, the sheet forming PCV lens was located just outside the laser delivery probe to allow for easier adjustment of the sheet angle. This alternate configuration is depicted in Figure 3.1. The PCV lens is set in a rotating mount, which gives the user the ability to rotate the orientation of the sheet to match the region of interest and align with the test article geometry. This setup configuration was used only for establishing alignment procedures and experimental practices and is presented here to highlight the potential challenges in achieving optimal imaging conditions and the utility of the custom pre-processing algorithms under non-ideal imaging conditions.    To verify that the cross-correlation program was accurately resolving the velocities from the image pairs, the correlation maps of one of the instantaneous velocity fields from vane1 image set used in Figure 3.3 were evaluated. Figure 3.4 displays the velocity field on the left along with a red box highlighting the vector location for the correlation map shown on the right. The 3D map illustrates the correlation value of the pixel window with respect to the displaced location. The origin is the location that the program identified as the correct displacement, which is why a peak with a maximum correlation value of 1 exists at this point. The surrounding points are the correlation values for the window if it was displaced by the indicated number of pixels away from the estimated location. As there are no large peaks beyond the origin and the PPM is greater than 5, this correlation map indicates that the program is able to extract particle displacements with certainty. Moreover, the narrow width of the center peak is a good indication of precision in the estimation of the true displacement. This is only a qualitative assessment of the uncertainty of the measurement technique, but it is enough to justify the application of the methodology to the vane2 configuration. After the development of laser alignment procedures, the PCV lens was moved back into the laser delivery probe to its original design position. In this location, adjustment of the PCV lens orientation becomes more difficult, but the proximity to the prism mirror prevents the clipping shown above and allows the laser sheet to span the entire width of the interrogation region.

Time-Averaged Flowfield Analysis
The following flowfield analysis is based on 101 averaged PIV vector fields of the vane2 configuration and compared to the CFD results for both the cold and hot-gas experiments. is located close to the front suction side of the adjacent airfoil. Hence, the observed velocity gradient is consistent with the velocity difference usually existing between the pressure and suction side. While the velocity profiles are similar for the measured and computed velocity fields, the mean velocity appears to be higher in the CFD calculations. Even though the PIV maybe matching the trend of Mach number, which is generally well-predicted by CFD, the slight mismatch in the magnitude of velocity can be due to a difference between the temperature considered for CFD versus the experimental case. An assessment of the flow topology can also be made based on the direction of the streamlines. These lines appear to be rather straight on the top-left quarter of the measured region, while towards the bottom right quarter the streamlines have a notable curvature. This is due to the presence of the more significant wall curvature in the front portion of the suction side. These qualitative features, found both experimentally and numerically, can be further verified by comparing the flow angle. Figure 3.6 shows the contours of the tangential flow angle. The experimental and CFD data show good agreement in terms of the time-averaged values and spatial distribution of the flow angles. As it is observed in the contour plots, the turning is slightly higher in the CFD prediction, but not exceeding the measured 70° angle in the trailing edge zone. In the hot experimental conditions, higher velocities are observed than in the cold conditions, as expected, with the average measured velocities being slightly less than CFD 44 predictions. The lower measured velocities in both cases could be an indication that the seed particles are not fully tracking the flow, a phenomenon known as particle lag. For the results shown in Figure 3.7, the low velocity patch in the top right corner may be due in part to the scattering of light from inside the rig.

Assessment of High-Frequency Capabilities
The frame straddling technique produces time resolved data at 10 kHz with a camera frame rate of 20 kHz. A time series of flow angle contours for the vane2 configuration at cold test conditions is depicted in Figure 3.10. Given that the region of interest was selected for its steadiness, there is little expected variation between frames. In this series of 6 time-steps, the flow angle is nearly constant apart from minor fluctuations near the PS and SS of the window.
Furthermore, there are no unexpected structures present in any of velocity fields. The resolution of the vectors in this set could be further improved by increasing the window size, but it comes at the cost of decreased spatial resolution. These cold test results demonstrate that the current optical diagnostic setup can acquire high-frequency velocity measurements of a turbine flowfield.  The cold test case in Figure 3.11A shows that the PIV processing algorithm can produce a velocity vector at nearly all times and across nearly the entire measured region. The edges of the measured region are expected to be less consistent because of the possibility of losing a particle's initial or final position in an image pair. The areas with computed vectors of 80 or less indicate that the intensity of the laser sheet was too weak in that region to illuminate the particles in some of the frames. As the sheet is expanded from a Gaussian beam profile, the sheet profile was similarly Gaussian in intensity. Due to the setup constraints from the annular geometry, the sheet had a limited distance to expand so the lower intensity tails of the Gaussian profile persist at the edges of the sheet within the vane passage. As the laser sheet is delivered diagonally across the region from top-right to bottom-left, the top-left and bottom-right portions of the interrogation region are at risk of lower particle illumination. Figure 3.11B shows that the vector yield is lower for the hot test conditions. This may be due to lower particle number densities or the scattering interferences noted earlier. However, an anomalous dip in the vector yield is observed in the center of the measured region where one would expect relatively ideal imaging conditions. One possible cause is that there is a non-uniform illumination of the vane passage between images. The pre-processing code enhances the image based on the particle resolution across the entire frame, so the quality of some regions may be decreased in order to improve the image as a whole. The images are optimized for the surrounding lower intensity particles, which can cause the apparent size of the higher intensity particles to be increased. This distortion of the particles can be significant enough to prevent the correlation software from determining their displacement. To improve the vector yield, the pre-processing code would need to be modified to enhance images by regions as opposed to the entire frame; however, this will greatly increase the computation cost of the tool.

Uncertainty Analysis
According to Sciacchitano [18], the effects of all the sources of error are fundamentally captured in the acquired images. Even so, not all the error sources can be quantified during the correlation process. Most of these are systematic errors and they include "tracer particle response, hardware timing and synchronization, perspective errors, and calibration errors" [18]. To minimize some of these errors such as the perspective and calibration errors, LaVision employs a selfcalibration routine and a series of sub-pixel interpolation and correlation peak-finding routines [19]. Still, many of the uncertainty sources are quantifiable such as "particle image size and shape, camera noise, seeding density, illumination intensity variation, particle motion and image interrogation" [18]. LaVision calculates the uncertainty from these remaining sources using a correlation statistics-based method that analysis each pixel's contribution to the shape of the crosscorrelation peak to produce a displacement error [19].
To evaluate this error contribution, the pixel displacement error was extracted from the  After reviewing the sample standard deviation of the velocities across the set, reproduced in Figure 3.13, it was discovered that the region of peak uncertainty is collocated with a region of unsteadiness in the velocity field. This variability could be due to true fluctuations in the assumed steady region or the result of the low repeatability with the intensity spike, but it is clear that the increase in uncertainty shown in the previous figure is a consequence of increased precision error as opposed to bias error.

DEVELOPMENT OF OPTICAL SETUP FOR TIP FLOW MEASUREMENTS
To facilitate the assessment of the tip flow control designs, a modular two-stage rotating turbine rig was developed by the PETAL team. A layout of the module installed in the highpressure facility used for BRASTA is shown in Figure 4.1. A motor coupled with a dynamometer is attached to the shaft of the rig to allow for rotation of up to 15,000 rpm and high precision torque measurements to support the determination of turbine efficiency. To aid in the evaluation of the novel tip designs, an optical setup has been designed that adapts the evaluated methodology from 2D to 3D velocity measurements and allows the technique to be implemented in an even more optically restricted environment.  spacing of the blades. The thickness of the laser sheet will be increased in comparison to the measurements taken parallel to the flow direction to ensure particles are retained in the sheet between image frame as the particles are travelling normal to the laser plane. Based on the average flow velocity within the plane of interest, the thickness of the laser sheet will be chosen such that the average particle movement between laser pulses is less than 30% of the laser sheet thickness, the limit imposed by [6].

Development of Endoscopic PIV in Annular Environment
Having established an experimental procedure for conducting PIV in an annular test section, endoscopic PIV will first be implemented in BRASTA for appraisal. To investigate the secondary flows that are fundamental to managing blade and vane loss mechanisms, the most prioritized The primary difficulty with pursuing this plane of interest is that optical access does not exist on BRASTA that would allow for a camera to capture this region directly. For this reason, the camera needs to be coupled to a borescope so that endoscopic PIV can be performed. A configuration of the laser sheet and borescope that would allow for the HSV formation to be imaged is presented in Figure 4  Due to the adjustability of the laser delivery probe, it can be directly applied to this configuration; however, the borescope and its mounting system needed to be purchased or machined. To survive the harsh testing conditions of the aerodynamically engine representative facility, a custom high-temperature borescope capable of withstanding up to 300° C and 10 bar  This is just one of many additional planes that can be investigated in BRASTA with the developed methodology. Nonetheless, it will help establish the application of endoscopic PIV to this facility, which is crucial to the development of optical diagnostic techniques for STARR.

Evolution of Setup for 3D Velocity Measurements
To install the borescopes into the traverse ring on the rotating rig, a mounting system has been designed based on the apparatus that was successfully implemented with BRASTA for PSP measurements. It again features a shaft collar that provides identical freedom of movement, but an  Finally, to deliver a laser sheet into the blade passage in the form of a radial plane, an insert was designed to provide direct over blade optical access. The insert features a large window at the bottom of the outer body that matches the curvature of the inner radius so that it can be flush mounted and not interfere with the sensitive blade passage flow. A window brace sits inside the outer body to fasten the optical window and seal it against the gasket, but it has a very low profile within the body to maximize the optical access for the incoming laser sheet. Both the outer body and window brace shown in Figure 4.6 have been machined out of stainless steel for the first and second rotor stages so that they are able to survive the harsh operating conditions of this rotating annular rig. Due to the proximity of the insert to the interrogation region, the sheet forming optics can be located outside of the laser delivery insert without concern of clipping the laser sheet. The establishment of this methodology also served as a building block for the development of endoscopic SPIV in STARR to aid in the non-intrusive characterization of tip flows in a rotating environment for assessing novel rotor tip designs. An experimental design for demonstrating the feasibility of endoscopic PIV in PETAL facilities and capturing the unsteady formation of the HSV system on the leading edge of the new vane design is also described. With the custom optical components presented, the two proposed experimental setups are equipped to be implemented.