## Abstract

A high-speed infrared camera is used to measure the temperature of blade tips in a cooled high-pressure turbine operating at corrected engine conditions in The Ohio State University short duration Turbine Test Facility. These experiments create a challenging problem for infrared imaging since the rotor turns at over 13,000 rpm with tip speeds on the order of 300 m/s, and the surface temperature of the airfoils is on the order of 350 K. This means that the camera needs to capture a low-intensity signal in a very short time period. This article reviews the design and operation of a measurement procedure to accomplish this difficult task along with the postprocessing steps necessary to extract useful data. Raw infrared images are processed by deblurring the images using a nonblind Wiener filter and mapping the two-dimensional data onto the three-dimensional blade. This article also describes experiments covering a range of cooling flowrates and main flow temperatures. In addition, several tests with no main flow and only cooling flow were performed at lower speeds to reduce motion blur and enable the separation of internal and external heat transfer information. Results show that the infrared data are consistent and can provide quantitative comparisons of cooling performance even at the high rotation speed. This article presents the lessons learned for high-speed infrared measurement along with the representative data to illustrate the repeatability and capability of the measurement scheme as well as suggested improvements to guide further development.

## 1 Introduction

In the world of turbine research, one area of interest is the heat load of components in the hot gas path and the performance of different turbine cooling technologies. Engineers constantly push for higher temperatures and efficiencies, but there are still a number of challenges remaining to improve these components. Bunker posed a number of questions about cooling technology including how to ensure uniform internal cooling, how can cooling hole shapes be improved, how can microcooling technologies be effectively implemented, and how can secondary flow systems be used to cool components [1]. These questions all have a common theme: to answer them, more detailed information is needed about those cooling flows, particularly where the cooling flows are most efficient. One way to gather these necessary data is through experiments utilizing spatial measurement techniques where temperature distributions of an entire surface can be recorded at once. In the current work, infrared (IR) thermography is used to take measurements of a transonic turbine operating at corrected engine conditions and collect spatial temperature measurements that can be used to address these questions about hot section cooling.

Infrared measurements have been increasing in use as cameras have become faster and cheaper, and computers are more capable of processing the large amounts of data the cameras produce. The advantages of IR temperature measurements are undeniable. They increase spatial resolution and are nonintrusive. As such, they are becoming increasingly common in turbine research in both cascade and rotating experimental rigs. There is an immense amount of work performed using IR cameras in stationary or cascade tests, but this article focuses only on work where IR cameras are used in conjunction with rotating test articles with particular attention devoted to how the issue of motion blur is addressed.

Motion blur is an inherent problem with any imaging due to small vibrations in the camera or target object, but the effect of motion blur is much more significant when imaging a moving object, such as capturing images of a rotating turbine. When preparing an imaging system, there are two important lengths of time associated with a camera: integration time and frame rate. Integration time is analogous to shutter speed or exposure time; it is how long the camera is capturing the signal from the target. The magnitude of motion blur is directly affected by the integration time. Having a lower integration time reduces the time it takes to capture the image and therefore lowers the amount of movement that occurs and thereby reducing the motion blur. The frame rate is how often a camera can capture an image. This is determined by the combination of the integration time and the time needed to save the image to memory. Increasing the frame rate does not reduce motion blur rather it increases the number of images that can be captured.

The earliest use of optical measurements was pyrometers in the 1960s. Due to the extreme temperatures in an operating gas turbine, most instrumentation would not survive. Therefore, nonintrusive pyrometers were used to make optical temperature measurements. Uguccini and Pollack used pyrometers to make 2D scans of a blade providing a rough temperature map paving the way for future full surface measurements [2].

Recent works have shown optical infrared measurements being used in a variety of rotating applications. In 2002, Astarita et al. used a line scan infrared camera to reconstruct the temperature distribution of a heated disk rotating at a speed of 100–2000 rpm [3]. In this study, radial temperature profiles were measured at a sampling rate of 2.5 kHz, while simultaneously recording the angular position of the disk. By using these profiles, a time-averaged thermal image could be recreated. In a line scan method, a one-dimensional image is captured. This greatly reduces the amount of processing that the camera has to complete before the next image can be captured allowing for higher frame rates. Motion blur is reduced even though the integration time is not changed, but rather the camera captures one line and then saves the image rather than capturing the entire field of view and then saving.

Mori et al. investigated the variation of heat transfer due to rotation for rotating hollow turbine blades [4]. An infrared camera was used to capture the temperature distribution along the pressure surface, and their study was confirmed using numerical calculations. The rotation speed of this rig was approximately 1500 rpm, and the integration time of their camera was 100 μs. At this speed, the rotor traverses 0.009 deg during the image capture process. This would create a negligible amount of motion blur assuming the rotor was of reasonable size.

Rotating passages mimicking turbine blades have also been a subject of interest. Wang et al. measured the heat transfer in a turbulated two-pass serpentine passage rotating at approximately 500 rpm [5]. An infrared camera was used to capture the interior wall temperature and was synchronized to the rotating arm. The authors did not mention the processing of the images, so it is assumed that motion blur was insignificant.

An interesting method to reduce motion blur caused by rotating objects was presented in the study by Lang et al. and elaborated in the study by Raffel and Heineck [6,7]. In these experiments, a mirror reflected the image of the rotating target blade, in this case, a NACA0015 airfoil. The mirror rotates at half the speed of the rotor. As a result, for small angles of mirror rotation, the reflected image appears as a stationary object to the camera. This technique artificially removes the movement from the image capture process, reducing motion blur.

The final work reviewed was the study by Lazzi-Gazzini et al. [8]. This study investigated heat transfer on heated rotor endwalls. At steady operation, the surface temperatures of heated rotor endwalls were measured using a FLIR SC7300L IR camera. Two sets of images were captured. For one set, the integration time of the camera was 10 μs, and for the second set, the integration time was 50 μs. The short integration time introduced more noise in the images but produced a crisper image. With a longer integration time, the appropriate temperature scale was captured but with more motion blur. A blind deblurring algorithm was employed to process the long exposure images and identified deblurring artifacts such as ringing through the frequency analysis of both images. Finally, high- and low-pass filters were applied to eliminate the white noise and ringing.

It should also be noted that infrared imaging is a common practice in proprietary engine testing, but the authors are not aware of a public record of these efforts. The high temperatures of an operational engine make it possible to use very short integration times and significantly reduce blur compared to lower temperature turbine rigs.

All these studies use imaging on rotating rigs, and different methods are used to approach the challenge of motion blur. If possible, motion blur should be avoided or minimized, but image reconstruction can be done if motion blur is unavoidable. The current study describes the process of incorporating an infrared camera into an existing rotating turbine rig and the efforts made to synchronize the camera to the rotor, reduce motion blur, and reconstruct clear images from blurred inputs. It also presents sample measurements from the blade tip measurement campaign.

## 2 Experiment Setup

An infrared camera is integrated into the second build of the high-pressure turbine innovative cooling experiment. This collaborative effort incorporates components from a Honeywell engine including the high-pressure vane, high-pressure blades, shroud, and tangential onboard injector (TOBI) into a turbine rig constructed at The Ohio State University (OSU). The rig is designed to operate in the Turbine Test Facility (TTF) at OSU, which can match the operating conditions of the nondimensional engine for a brief period of time. Previous measurements performed for this turbine are reported in the study by Nickol et al. [911]. The IR camera is focused on the blade tips and synchronized with the rotor to capture images of the same blades in each rotation.

A schematic of the experimental setup is shown in Fig. 1. A large reservoir (not shown) supplies high-pressure air and is connected to the expansion nozzle through a fast-acting valve. The turbine rig is located within a large dump tank that starts at a vacuum during experiments. The rig is composed of an inlet nozzle, combustion emulator, and engine flow path hardware including the high-pressure vane, high-pressure rotor, shroud, and TOBI. An experiment begins with accelerating the rotor to just below the design speed, approximately 13,000 rpm. Once the desired speed is reached, the cooling airflow is initiated to give the coolant time to fill the internal volumes of the rig and establish the friction-driven forward and aft purge flows. Next, the main fast-acting valve opens to allow air to flow through the yellow expansion nozzle into the dump tank. A normal shock forms in front of the rig inlet nozzle where a portion of the flow (black arrows) passes through the experimental setup, and the remainder passes around the model. After the inlet nozzle, the flow passes through a combustion emulator, which heats the flow to the desired temperature and then proceeds through the vane and the rotor before exiting the model into the dump tank. The normal shock in front of the rig inlet nozzle provides a constant mass flow through the test section for the duration of that normal shockwave, approximately 120 ms. During this period, the turbine will accelerate freely with nearly constant inlet conditions after a brief startup period. A quasi-steady period of four revolutions is selected where the corrected speed, the stage pressure ratio, the flow function, and the temperature ratios match engine design conditions. During the experiment, the target blade temperatures will start at room temperature and increase by approximately 20–25 K. A more detailed description of the TTF and previous experimental programs are presented in the study by Dunn and Mathison [12].

Fig. 1
Fig. 1
Close modal

The IR camera used in these tests is the FLIR X6901sc SLS. It is selected because of its sensitivity and speed. The camera detector is a cooled strained layer superlattice sensitive to wavelengths between 7.5 and 10.5 µm, which is ideal for the near room temperature experiments where peak emission is around 9 μm. The maximum frame rate is 1004 Hz when capturing images with the full resolution of 640 by 512 pixels, but the frame rate can be increased by subwindowing the image to capture a reduced field of view. The maximum frame rate will put a limit on the number of images captured during each revolution. In this study, three images were captured each revolution, one for each of the IR target blades. The blades were spaced unevenly, so the frame rate varied between images, but the maximum frame rate required was approximately 900 Hz. This is well below the 1004 Hz full window maximum, and with subwindowing, the maximum allowable frame rate is increased to about 1600 Hz.

In addition to the repetition rate of the camera, it is important to address the effect of integration time on the image quality. This value is the digital equivalent of exposure time in traditional cameras, and the performance considerations are the same. For very short integration times, the image will be noisy unless there is a very intense source (high-temperature object). Long integration times make it possible to obtain noise-free images of lower temperature objects, but if the object moves during that period, the image will be blurred. Therefore, it is quite difficult to image the rotor in this experiment, which is rotating at 13,000 rpm with relatively low surface temperatures around 275–400 K. Using the minimum integration time of the camera, 270 ns, would be effective in eliminating motion blur, but the image would be dominated by noise and have limited temperature resolution because the detector well is less than 10% filled. Instead, a preliminary experiment utilizing a small rotor mounted to a machine tool was used to determine the optimal trade-off between signal intensity and motion blur. This led to the selection of an integration time of 47.6 μs.

This integration time is still long enough to allow significant motion blur, but image deblurring algorithms are used to correct for the motion of the object. Common methods used by other authors take advantage of unique circumstances that limit their applicability for this study. First, the high rotation speeds make motion blur a significant factor that cannot be neglected or eliminated. The temperature cannot be increased to lower the camera’s integration time without impacting the other instrumentation. Operating in a short-duration facility means the data captured will be inherently transient, and steady-state methods will not be applicable. Using existing engine hardware precludes designing a mirror rotation system in the facility since optical access through the aft of the rig is not feasible. Thus, the remaining route is postprocessing of the IR images using deblurring algorithms, which will be covered in a later section.

Optical access to the rotor is provided through the turbine shroud, as shown in Fig. 2. The camera looks radially inward through a nonreflective optical pipe that passes through the thick casing of the rig. It is oriented, so that it can image the tip, pressure surface, and rotor platform of selected blades. One segment of the turbine shroud is replaced with a specially machined part that holds a Zinc Selenide (ZnSe) window, as shown in Fig. 3.

Fig. 2
Fig. 2
Close modal
Fig. 3
Fig. 3
Close modal

The inner surface of the ZnSe window is precisely machined to match the conical cross section of the shroud segment without disrupting the airflow. The exterior surface of the window is shaped to minimize the refraction of the radiation traveling through the window. This is done by applying Snell’s law across the interior and exterior surface and iteratively altering the surface parameters to minimize the net refraction of the incident rays. The window is also coated to improve the transmissivity for the mid and long-wave infrared spectra, 2–14 µm.

The camera is synchronized to the passing of specific blades by setting it to only capture single images when it is triggered by an outside source. A simple logic circuit is then used to interrogate the output signal from a 1000 pulse per revolution optical encoder mounted on the rotor shaft. This circuit counts each encoder pulse and then sends a trigger pulse to the camera when the counter reaches a predetermined value. When the counters receive a once-per-revolution index pulse, their count resets to zero, and the process repeats. The current setup uses three parallel counting circuits to capture images of three different target blades. The cards can be easily reprogrammed to trigger at different encoder counts. This system ensures that each picture is taken when the rotor is at the same angular position.

Three IR target blades are selected to provide imagery for three different cooling hole schemes. There is a blade with round film cooling holes, advanced shape film cooling holes, and a solid blade with no cooling. The two cooled blades have a surface-mounted resistance temperature detector (RTD), on the pressure surface for use as a reference temperature. Blades with a fan-shaped film cooling holes were not imaged, but they were instrumented with other sensors, and the results are presented in the study by Celestina et al. [13]. The details of these cooling schemes are not provided here because the tip cooling scheme is identical among all cooled blade types, and the uncooled blade has the same tip geometry with the holes filled by epoxy. The metering section of the cooling holes should be the same for all blades to ensure a consistent mass flowrate, but small changes in the installed flowrate or geometric differences from one blade to the next still introduce differences.

These three blades are coated with a thin ceramic polymer coating, which improves the emissivity to 0.92 and decreases reflections from the ambient. The value for emissivity was determined experimentally by comparing the surface in question to another surface with a known emissivity, while both are in thermal equilibrium. This coating is also applied to the components in the optical access path to reduce reflections. The view angles between the camera and the surface normal vectors range from 0 deg to 15 deg for the platform and tip to 70 deg on the pressure surface. Elfner et al. examined several matte black paints and found that for view angles less than 50 deg, it is not necessary to make directional emissivity corrections [14]. Similar tests were performed on the coating used in this study with similar results, so it is only necessary to track directional variation in emissivity for the pressure surface.

### 2.2 Experimental Matrix.

The experiments conducted in this study vary the cooling flow conditions and rotation speed while still matching the corrected engine speed, the stage pressure ratio, and the flow function. The rotor incorporates blades with four different film cooling schemes to be able to compare the performance of the different blade types with each other. In addition to the regular experiments operating at corrected engine conditions, complementary experiments were performed with no main flow and at a reduced speed. These cooling-only experiments are intended to help isolate the influence of heat transfer due to the internal cooling flows. Table 1 provides a summary of the selected runs that will be considered in this article. Each experiment is classified as having low, nominal, high, or very high cooling. These groupings are based on the cooling flowrates, which are presented as a percentage of the main flow. In addition, the temperature of the main flow had two levels: high and low. The temperature is presented as the deviation from the high-temperature levels. The rotation speed of the rotor is also shown for each run. In the cooling-only experiments, there is no main flow, but the cooling flowrates would match their corresponding main flow experiments.

Table 1

Summary of experimental runs utilized in this paper

RunCooling conditionCooling flowrate (% of main flow)Main flow temperature deviation (%)Rotation speed (rpm)
15Low5.62.413,600
16Low5.2−5.813,000
30Low5.4−0.213,500
31Low5.3−7.613,000
3Nominal6.81.613,400
23Nominal6.9−5.713,000
38Nominal7.30.913,500
18High7.90.613,500
19High7.7−7.513,000
13Very high8.50.313,500
14Very high8.5−7.413,000
26Very high9.20.713,400
27Very high8.8−6.413,000
39No cooling0−8.412,900
Cooling-only runs
17Lown/an/a4700
32Lown/an/a4600
33Lown/an/a8600
10Nominaln/an/a6900
24Nominaln/an/a4800
40Nominaln/an/a2400
41Nominaln/an/a5000
42Nominaln/an/a8800
20Highn/an/a5000
36Highn/an/a5000
37Highn/an/a8800
28Very highn/an/a5200
29Very highn/an/a8800
RunCooling conditionCooling flowrate (% of main flow)Main flow temperature deviation (%)Rotation speed (rpm)
15Low5.62.413,600
16Low5.2−5.813,000
30Low5.4−0.213,500
31Low5.3−7.613,000
3Nominal6.81.613,400
23Nominal6.9−5.713,000
38Nominal7.30.913,500
18High7.90.613,500
19High7.7−7.513,000
13Very high8.50.313,500
14Very high8.5−7.413,000
26Very high9.20.713,400
27Very high8.8−6.413,000
39No cooling0−8.412,900
Cooling-only runs
17Lown/an/a4700
32Lown/an/a4600
33Lown/an/a8600
10Nominaln/an/a6900
24Nominaln/an/a4800
40Nominaln/an/a2400
41Nominaln/an/a5000
42Nominaln/an/a8800
20Highn/an/a5000
36Highn/an/a5000
37Highn/an/a8800
28Very highn/an/a5200
29Very highn/an/a8800

## 3 Data Reduction

Once the IR images are captured during the test, they must go through a reduction process to convert the raw images into useful data. The raw IR data are presented as a 2D image where each pixel is represented as a digital count value output by the camera, and the final temperature map is a cloud of points with spatial coordinates, a time value, and the temperature value. The data reduction process has six distinct steps: locating the image, conditioning, predicting the motion blur, deblurring, projecting the 2D image onto the 3D blade, and applying final corrections. This is illustrated in the flowchart in Fig. 4.

Fig. 4
Fig. 4
Close modal

### 3.1 Locating the Image.

The first step in data processing is to locate the position of the IR image with respect to a known geometry feature. In this case, the ZnSe window in the turbine shroud serves as the fixed reference, along with the orientation and position of the camera with respect to the turbine rotor. The window is located by identifying the circular shape that it casts in the IR image. It is assumed that the camera is fixed in space with relation to the window. In addition to anchoring the position of the IR image, locating the window enables the identification of the blurred data. All the pixels located within the window are moving during the image capture and subject to motion blur. These are the pixels of interest, so future processing steps will use only the data within the window and ignore the image outside the window. This reduces the effects of the stationary data in the deblurring process.

### 3.2 Conditioning the Image.

Next, the IR data need to be conditioned to reduce deblurring artifacts. Conditioning involves adjusting the boundary conditions of the image. In this case, the borders of the rectangular image and the borders of the circular data region will be conditioned.

Image conditioning is important because portions of the image outside of the field of view contribute to the blurred image. Imagine a camera taking an image of a moving object, such as the sample turbine blade in Fig. 5. During the image capture process, the blade starts at the pink position and travels to the green position. The camera will only capture whatever is inside the viewing window indicated by the red dashed line. The bottom portion of the pink blade, which was not initially captured by the camera moved into the view window while the image was being taken. The final blurred image is affected by any part of the image in the view window even if it is not seen during the entire integration time. Conditioning is done to estimate the unknown portions of the blurred image outside the view window. Adding more information will improve the deblurring results by reducing the boundary effects, which will be discussed later. Unfortunately, this problem of missing information outside of the view window is inevitable with finite image size.

Fig. 5
Fig. 5
Close modal

There are several ways to treat the boundary conditions of the image edges such as ignoring the boundaries, assuming the boundaries are periodic, or assuming the boundaries are mirror images of the blurred image [15]. The common theme with these boundary conditions is they only use the information available from the blurred image and approximate what the camera would see outside the view window.

In this study, the boundaries around the blurred data within the window are treated in four steps. First, the pixels outside the window are set to the mean value of the data within the window. Second, the data are periodically repeated where the adjacent turbine blades are expected to be. Third, a simulated motion blur, mimicking the actual rotor motion, is applied to the image to reduce the sharp gradient between the mean value pixels and the data within the window. The final step is to reinsert the unaltered data into the image. This preserves the data within the view window but still accomplishes the conditioning of the image outside of the view window. With this conditioned image, only data outside of the view window have been altered. Pixels within the view window remain unaffected.

### 3.3 Predicting the Motion Blur.

Knowledge of the object motion significantly improves the effectiveness of deblurring algorithms. Because the camera is fixed in space and the turbine can only rotate about its axis, motion blur can be determined by manipulating a computer-aided design model of the blade and camera system.

Determining the motion of the turbine blades is done using 3D models of the blades and particle image velocimetry software. First, the blade is converted into a stereolithography (.stl) file format, with the coordinate system origin located at the rotor axis. This represents the blade as a collection of triangular faces and their associated vertices. Using a rotation matrix, the blade vertices are rotated about the turbine axis in the same motion they would experience during operation. At each angular position, the 3D cloud of blade vertices is projected onto the 2D camera plane. This creates a series of 2D images where the blade vertices are rotated through the camera’s field of view.

These 2D images are fed into the pivlab software package, which treats each vertex as a particle to determine the motion of each point from one rotor position to the next position [16]. Figure 6 presents the mean magnitude (black) and direction of motion (red) for all vertices as a function of blade position in the window. At blade position 0, the blade is just entering view, and at position 1, the next blade is coming into view. The mean direction of the blur at the different rotor positions is nearly constant at 150 deg, so the blur is approximated as purely linear motion. The magnitude of blur is also relatively constant, and the slight decrease is due to tip surface vertices, which translate more, leaving the view window. Units of the blur magnitude are pixels traversed per degree of rotor rotation during the integration time. The magnitude of a blur for a given time-step changes slightly depending on the angular position of the rotor, but an approximate value of the mean magnitude is used. It is also assumed that the blur is spatially invariant across the whole image, which would be applicable since the data are focused on the tip region only.

Fig. 6
Fig. 6
Close modal

The magnitude and the direction of motion blur are used to estimate the point spread function (PSF), which mathematically describes the motion blur and can later be used to remove motion blur. The PSF is generated using the magnitude and direction results and the matlab function fspecial.

### 3.4 Deblurring.

Image deblurring is a deconvolution process where an ideal image is recovered from a blurred image. The deblurring problem can be expressed as shown in Eq. (1) [15].
$Ax+e=B$
(1)
where A is the point spread function, x is the ideal image, B is the blurred image, and e is additive noise

Deblurring is a linear problem that is complicated because the blurred image is a combination of the convoluted ideal image and a random noise term. The naive solution is to neglect the noise term and solve for the ideal image by multiplying each side of Eq. (1) by the inverse of the PSF, but this only amplifies the noise, rendering the resulting image meaningless. Proper image deblurring requires the noise term to be filtered out from the blurred image in the deconvolution process.

Knowledge of the PSF is helpful but not required in the deblurring process. If there is a priori knowledge of the motion blur, then the process is known as nonblind deblurring. Conversely, if the magnitude and the type of blurring are unknown, then it is known as blind deblurring. Both blind and nonblind deblurring algorithms exist, but for this study, nonblind methods are utilized.

The most common tool used in image deblurring is singular value decomposition (SVD), which decomposes the blurred image into a series of component images similar to how a Fourier transform decomposes a signal into component frequencies. A detailed derivation of the SVD tool is beyond the scope of this work, but it is presented by Björck [17]. Filtering algorithms use SVD to decompose an image into component images and reconstruct the image using only the necessary component images. The difference between algorithms is how they filter, or truncate, the series of component images to reconstruct the ideal image. This study uses Wiener filtering, a widely used filter originating in the 1960s, which filters the component images based on the noise-to-signal ratio of the image [15]. The filter uses the noise-to-signal ratio of component images to determine the level they will contribute to the final recovered image. As the noise of the component image increases, the Wiener filter will decrease the importance of that component image [18]. Apart from the SVD methods, there are also iterative methods to deblurring. Iterative approaches are used when the PSF is not well known, when there are spatial or temporal changes in the PSF, or if it is possible to trade computational time for higher image quality [15,1921].

In this study, Wiener filtering is used because there is knowledge of the expected motion blur and the PSF can be assumed to be spatially invariant at the blade tip or the platform surface. The algorithm is fast compared to iterative methods, which is necessary to process the large number of images collected. Finally, Wiener filtering is readily available as a built-in matlab function, like a python function, or written in other coding languages.

Testing the image data processing was done using images from a benchtop test using a generic cooled turbine blade. Figure 7(a) shows an ideal infrared image of this stationary blade with the cooling flow. Artificial motion blur is added to the image along with white noise, as shown in Fig. 7(b). This distorted image is then processed through the deblurring steps described earlier to produce the image shown in Fig. 7(c). The difference between the deblurred image and the ideal image is shown in Fig. 7(d). Image deblurring is not perfect, but it does manage to recreate the tip cooling holes and shape of the blade with enough resolution to draw meaningful conclusions. The deblurring process introduces some undesirable artifacts including ringing, loss of intensity, and boundary artifacts that must be accounted for when analyzing the data.

Fig. 7
Fig. 7
Close modal

Ringing is an artifact that manifests as oscillations near sharp gradients in the deblurred image. It is most clearly visible at the top of the blade (top arrow) and the bottom edge of the view window in Fig. 7(d), where the temperature difference shifts from positive to negative. Ringing is commonly associated with Gibb’s effect, which is an incomplete reconstruction due to using a finite series rather than an infinite series of component images [20]. The filtering process necessarily eliminates some component images, so ringing will be present in the image. This is similar to a Fourier reconstruction of a square wave; when a finite number of frequencies are used, there is an oscillation at the sharp edge. Others have suggested that ringing at gradients is due to errors in the noise estimate and PSF near the sharp gradients [19]. To minimize ringing, iterative techniques are used to include the component images containing information about the sharp gradient or improve the estimate of the PSF.

In addition, the total intensity of the image is not conserved during the deblurring process without additional correction. Oswald-Tranta et al. demonstrated this by comparing the total intensity of the blurred image of a falling hot ball to the filtered (deblurred) image [22]. The total intensity of the deblurred image was less than the total intensity of the blurred image due to the filtering, resulting in the IR images reporting a temperature lower than the actual temperature of the ball. A scaling factor is added to the Wiener filtering to ensure that the total intensity of blurred and deblurred images matches. This correction is applied in the current study to match the intensities of the blurred and deblurred images.

The final deblurring artifacts of interest are the boundary effects alluded to in Fig. 5. Near the edges of the view window, an unknown portion of the image outside of the view window contributes to the signal calculated inside the view window. The effect of this unknown portion of the image manifests itself as oscillations at the boundary that damp out as the distance from the boundary increases [23]. The wavelength of this oscillation is approximately the distance the object moves during the image capture process. The boundary effects are the periodic high-temperature arcs that appear most visibly at the top and bottom cooling holes on the pressure surface of the blade, shown by the lower arrows in Fig. 7(d). The only way to reduce the impact of these boundary effects is to design the imaging view window, so that the data of interest are located as far as possible from the ringing edges and between peaks of the boundary condition oscillations.

Knowledge of these artifacts and the regions of the image that they disturb makes it possible to utilize large portions of the image where the deblurring is effective while masking out the regions where there is a significant error. The results presented in this article have been masked so that only valid deblurred data are included.

### 3.5 Three-Dimensional Projection.

After deblurring, the 2D image must be projected onto the 3D blade. To do this, the angular position of the blade must be determined by comparing the alignment of the discretized STL model with the 2D IR image at many small increments of blade rotation. The blade position that matches best with the details of the 2D images such as cooling holes or blade edges is selected as the correct position. This process is repeated for each individual run since changes in the rotor speed can shift the blade position by small fractions of a degree.

Once the blade position has been identified, the next task is to locate the position of each IR pixel on the 3D blade STL model. This entails two operations: finding which face of the STL model each pixel projects onto and then finding the 3D coordinates of the pixel on that face. First, all the triangular faces of the STL model are projected onto the 2D camera plane, creating a mesh of triangles overlapping the IR image. This is illustrated in Fig. 8, where the triangles, representing the mesh triangle of the STL model, is projected onto the camera plane. This projection is done by finding the intersection point between the camera plane and a line originating from the face vertices $(F¯n3D)$, represented as solid dots, and normal $(N¯)$ to the camera plane, the z-axis in the 2D coordinates. Mathematically this is equivalent to simultaneously solving the equation for the plane (Eq. (2)) and the equation for the line (Eq. (3)). The variables x, y, and z represent the intersection point between the line and the plane, and $O¯$ is the position vector of the origin of the camera plane. This is repeated for each of the three vertices in the triangular face. In Fig. 8, the projected face is represented as the dashed triangle.
$0=N¯⋅((x,y,z)−O¯)$
(2)
$x−Fnx3DNx=y−Fny3DNy=z−Fnz3DNz$
(3)
Fig. 8
Fig. 8
Close modal
Once the face has been projected onto the camera plane, the intersection point in 3D is converted into the 2D coordinate system of the camera plane by utilizing the dot product in Eqs. (4) and (5). In these equations, $x¯$ and $y¯$ are the unit vectors of the x and y axes, respectively, of the camera plane expressed in the 3D coordinate system. The intersection points $(F¯n2D)$ are the circles on the camera plane.
$Fnx2D=x¯⋅((x,y,z)−O¯)$
(4)
$Fny2D=y¯⋅((x,y,z)−O¯)$
(5)
Finding which triangle each pixel (circles) belongs to is done using a barycentric coordinate system. Barycentric, or mass centered, coordinates are a computationally inexpensive way to determine whether a point is contained within a simplex—in this case, the mesh triangle. This is done by calculating the three barycentric coordinates (Eqs. (6)(8)). With the coordinates calculated, there is a simple logical check to be performed. If all three of the coordinates s, t, and r are greater than zero, then, the point P lies within the triangle defined by the three vertices $F¯12D$, $F¯22D$, and $F¯32D$. If the point is not located in the face, then the process is repeated with a new face until a match is found.
$s=12A(F1y2DF3x2D−F1x2DF3y2D+Px2D(F3y2D−F1y2D)+Py2D(F1x2D−F3x2D))$
(6)
$t=12A(F1y2DF2x2D−F1x2DF2y2D+Px2D(F1y2D−F2y2D)+Py2D(F2x2D−F1x2D))$
(7)
where
$A=12(F1x2D(F2y2D−F3y2D)+F2x2D(F3y2D−F1y2D)+F3x2D(F1y2D−F2y2D))r=1−s−t$
(8)
Each IR pixel is now associated with a face, and multiple pixels can be associated with a single face. This means that there is no minimum or a maximum number of faces allowed. The STL model can be as fine as possible to minimize discretization errors in locating the IR pixels on the blade. Now the 2D position of the pixel is converted into 3D coordinates using Eq. (9).
$P3D=Px2Dx¯+Py2Dy¯+O¯$
(9)

Finally, the pixel is projected onto its corresponding face by finding the intersection point between the face and the camera plane normal line originating from the pixel location. This is represented as the four lines in Fig. 8. Similar to projecting the faces onto the camera plane, two equations are solved simultaneously: the equation for a plane, where the plane is the stl face, and the equation of a line. These two equations are similar to Eqs. (2) and (3). The normal vector in Eq. (2) would be the face normal vector, and the point would be any one of the face vertices. In Eq. (3), the face vertex coordinates are replaced with the pixel location in 3D coordinates. The intersection point between the face and line is the 3D location of the IR pixel on the turbine blade.

### 3.6 Correction.

Once the data are mapped to the blade, a final pixel-by-pixel correction can occur. In this correction step, the digital count values are converted into temperature values using the calibration developed by FLIR, which accounts for window transmissivity and surface emissivity among other factors. In this study, the transmissivity of the ZnSe window is set to a uniform value of 0.95 based on information from the manufacturer and a static calibration designed to verify the value. As mentioned earlier, a fixed emissivity of 0.92 was used for the blades, which limits the viable data to the tip and platform surfaces due to the view angle variation discussed in Sec. 2.1. Performing an in situ calibration would account for the variation of transmissivity and emissivity across the image assuming the calibrated image is isothermal. For this calibration, the camera would be installed in the TTF in the same configuration that it would be during experiments, and the entire facility would be heated to perform a calibration process like the one used to calibrate the heat-flux gauges described in the study by Celestina et al. [13]. This type of calibration will also enable fine-tuning of the integration time to tailor the camera sensitivity to a specific temperature range. Due to time constraints, this was not feasible, and the calibration developed by the camera manufacturer was used.

### 3.7 Final Images.

The result from this process is a point cloud of temperature data in space and time. A visualization of the data cloud for generic blade geometry is presented in Fig. 9. The 3D nature of the data can be seen from the rearview along with how the data points conform to the blade shape. It takes about 1 h to process the 800 IR images taken for one blade in one run. The longest step is the 3D projection phase, which only needs to be performed once but requires user input. The camera synchronization system ensures the image is taken at the same angular position every revolution, so once it is aligned for the first image of the run, all subsequent images are aligned as well. Deblurring the images is the second-longest operation and must be performed for each of the images collected.

Fig. 9
Fig. 9
Close modal

## 4 Uncertainty Identification

Several sources of uncertainty were identified in making the IR measurements. They are described here in terms of their contribution to the error in surface temperature measurements. First, the camera has an uncertainty of ±2 K. In addition, the transmissivity value of the ZnSe window is 0.95 with an uncertainty of ±0.04 based on the manufacturer’s specifications, which corresponds to an uncertainty in the measured temperature of ±0.6 K. As mentioned earlier, the surface emissivity is measured to be 0.92 ± 0.03. This causes a temperature uncertainty of ±0.3 K. Performing an in situ calibration would drastically reduce the uncertainty and at the same time account for variations in transmissivity and emissivity. Elfner et al. managed to reduce the uncertainty by a factor of four through their in situ calibration [24]. Surface RTDs were installed on the two cooled blades, with the hope of providing an in situ measurement source, but it was not possible to place them in a location with an acceptable view angle for accurate calibration. They do serve as a sanity check for the IR measurements.

Additional error is introduced because the camera housing moves slightly during the tests due to vibrations of the entire turbine rig caused by the start of the main flow. This is corrected for using a manual image stabilization process, but this does introduce an uncertainty of ±0.2 K. This value is determined by measuring the shift in the image due to vibration and then the spatial temperature variation within that region, typically a 3 × 3 pixel area. Finally, the deblurring process introduces error because there is an inherent lack of information from the image, as explained previously. Combined with the random noise, this complicates the deconvolution process and means that the deblurring results are an approximate reconstruction of what the blade temperature distribution could be. The uncertainty associated with deblurring is estimated to be ±3 K based on comparisons between raw and deblurred images like those shown in Fig. 7. Improvements to reduce the deblurring uncertainty could be made by using an iterative deblurring method to better approximate the PSF and noise within the image. The best way to improve deblurring and lower this uncertainty is to increase the information collected by increasing the size of the view window, but this is not possible in this study because of the geometric constraints imposed by the engine hardware.

The total uncertainty in the absolute temperature measurements is approximately ±5 K or 0.9% of the inlet total temperature. However, the uncertainty in the temperature changes (ΔT) during experiments will be closer to the uncertainty due to deblurring of ±3 K or 0.5% of the inlet total temperature. Reducing uncertainty could be done in a twofold approach of performing an in situ calibration and optimizing deblurring methods.

## 5 Results

Results will be presented from several areas of interest on the blade. These areas are shown in Fig. 10 and include a large averaging region to describe the mean tip temperature, a pitch line to show variation across the tip, and three cooling holes. The data presented are in the region of best data away from boundary oscillations.

Fig. 10
Fig. 10
Close modal

A simple time-accurate comparison between the IR measurements and the onboard instrumentation is generated by spatially averaging the IR data contained in the circular “Averaging Region” shown on the blade tip in Fig. 10. The variation of this average IR temperature in time is plotted with the front and backside temperature sensors of a double-sided heat-flux gauge (HFG) in Fig. 11. This heat-flux gauge is located at 90% blade span on the pressure surface of the airfoil. While the location does not exactly match the averaging region, it provides a reasonable check on the IR measurement response. All temperatures are represented as a percentage of the inlet total temperature at the quasi-steady design point, which occurs at 2.31 s and is shown by the middle two dashed lines. The same normalization temperature is presented as in Table 1. This normalization allows for the comparison between runs with different inlet temperatures.

Fig. 11
Fig. 11
Close modal

Both the IR camera and the two HFG sensors detect the start of the main flow at the same time, and the IR measurements closely track the back HFG sensor. This is expected because the time constant for the IR measurements will be related to the thermal capacity of the blade material. Similarly, the back HFG sensor is adhered to the metal surface by a thin layer of adhesive and insulated from the main flow by a layer of Kapton, producing a thermal time constant close to that of the blade surface. In contrast, the front sensor of the HFG is a thin film sensor exposed directly to the airflow and insulated from the surface; it tracks the local air film temperature more closely and therefore shows a much larger temperature increase with the start of the hot main flow. The IR temperatures increase throughout the period that the main flow is on, indicating that heat is flowing to the blade. The HFG temperatures reflect the different physics of a double-sided gauge and the influence of the small layer of adhesive between the back sensor and the blade material. They indicate a decrease in temperature after the initial flow startup period. However, the large temperature difference between the front and back sensors indicates that heat is always flowing to the blade, and the heat-flux derived from this sensor is positive and quite large. This indicates that the increasing IR temperature and slightly decreasing HFG temperatures are still consistent. There is an ongoing effort to deduce the time-accurate heat flux from the IR measurements for direct comparison to the HFG results, as described for a flat plate in the study by Chen and Mathison [25], but those results will be the topic of a future study.

To investigate the differences among the blade types, Fig. 12 plots the variation in time-averaged tip temperature along the “Pitch Line” that is illustrated in Fig. 10. To consolidate data from a variety of operating conditions and starting wall temperatures, Fig. 12 plots the relative to temperature at each point minus the relative temperature at 0% pitch where the pitch line reaches the pressure surface, and the definition is shown in Eq. (10).
$ΔTPS=(TIR−TIR@TipPitch=0%Tinlet)×100$
(10)
Fig. 12
Fig. 12
Close modal

As with the other time-averaged plots, they are averaged over the four consecutive frames in the design window. Parts a-c of the figure show data from the three blades (round cooling holes, advanced cooling holes, and solid blade), and Part d shows data from all three blade types taken from a single run without blade cooling flow.

Each line in these plots represents one of the main flow runs except in Fig. 12(d), where each line is one of the blades for a single run. The first and last vertical dashed lines represent the edges of the parapet wall, and the middle pair of dashed lines on Figs. 12(a) and 12(b) are the boundaries of the cooling hole on the pitch line. For both cooled blades, the temperature decreases across the pitch. This indicates that the tip cooling is reducing the heat transfer from any leakage flows over the tip. As noted earlier, the tip cooling scheme is identical for the round and advanced hole blades, so the difference between the two is likely caused by small differences in mass flow distribution between the two schemes. For the solid blade, the temperature increases over the tip pitch with a maximum near 50% pitch.

Finally, when there is no-cooling flow, all three of the tip-pitch distributions collapse onto the same shape similar to the solid blade with the maximum temperature again near 50% pitch. The change in shape when cooling is turned off is an important indication that the temperature reduction observed for the two cooled designs is in fact caused by the cooling flow and not some other change in the flow structure. The shape of the advanced holes and no-cooling scenario appear similar with the central peak, but there is a definite increase in the temperature across the blade pitch for the no-cooling scenario.

In addition, the average blade tip temperatures listed in Table 2 show that the solid blade and no-cooling scenarios are significantly hotter than the cooled blades. An ongoing computational fluid dynamics effort aims to investigate these behaviors in greater detail.

Table 2

Comparison of mean tip temperatures within tests, normalized by the main flow temperature

Cooling levelRunT (%)
HottestIntermediateColdest
Nominal357.756.055.7
2360.758.858.8
3858.957.557.5
Low1559.458.758.5
1658.957.757.7
3059.758.258.0
3158.357.257.1
High1858.057.056.9
1957.656.756.6
Very high1359.557.957.6
1459.857.857.6
2658.657.357.1
2759.057.657.4
None3965.264.863.9
Cooling levelRunT (%)
HottestIntermediateColdest
Nominal357.756.055.7
2360.758.858.8
3858.957.557.5
Low1559.458.758.5
1658.957.757.7
3059.758.258.0
3158.357.257.1
High1858.057.056.9
1957.656.756.6
Very high1359.557.957.6
1459.857.857.6
2658.657.357.1
2759.057.657.4
None3965.264.863.9

This table shows that within each run, the temperature order of the blades is consistent. The solid blade is always the hottest, which would be expected, followed by the round cooling hole blade and then the advanced cooling hole blade. The temperature difference between the solid and cooled blades is much larger (1% of the main flow temperature) than the temperature difference between the two cooled blades (closer to 0.1%). This narrow temperature difference accounts for run 23, where the two cooled blades are at the same temperature. Seeing consistency within the runs builds confidence in the reliability of the IR measurements at high speeds.

To gain a better understanding of the influence of cooling on blade tip temperature, two-dimensional contour plots of the time-averaged temperature at the design condition are presented. These plots are created by averaging over the four consecutive images captured during the experimental data window. The integration time, 47.6 µs, is the same for all experiments. Figure 13 plots the normalized temperature for the nominal cooling level for each of the three IR target blades as a percentage of the main flow temperature. The solid blade is hotter than the two cooled blades, and the impingement region, circled in Fig. 14(a), is cooler for the round blade. There is a hot spot that appears on the round hole blade near the pressure surface, but this is caused by the RTD appearing in the IR images. Apart from the impingement region, the two cooled blades perform similarly.

Fig. 13
Fig. 13
Close modal
Fig. 14
Fig. 14
Close modal
To better visualize the differences among the blade types, it is necessary to create a normalization to compare the two cooled blades to the uncooled solid blade. Many possible normalizing variables were considered including many of the standard film cooling parameters, and the temperature difference described in Eq. (11) does the best job showing consistent differences. It utilizes the temperature difference between a cooled blade and the solid blade normalized by the inlet temperature,
$ΔT=(Tcooled−TsolidTinlet)×100$
(11)

The purpose of this normalization is to make comparisons between different experiments more feasible. Numerous factors affect the measured experimental temperatures such as the initial temperature of the blade, inlet total temperature, coolant temperature, and others. By comparing results to a baseline scenario within an experiment, such as the solid blade, cooling trends that would have been masked by other effects can be elucidated. This has the added benefit of being able to compare the cooled and solid blades in the same plot.

Figure 14 presents contours of this variable for individual runs with low (run 15), nominal (run 38), high (run 18), and very high (run 13) cooling flowrates for the round hole blade. The geometry of the tip is indicated by black dots showing the vertices of the 3D model. The extent of the blade, the location of the cooling holes, and the position of the parapet walls surrounding the recessed tip cavity are all shown in this image. The exact shapes have been distorted to protect proprietary geometries.

In Fig. 14, the temperatures decrease with higher cooling levels as expected. The temperature contour at the front of the plotting area is dominated by a low-temperature region caused by flow from the internal serpentine passage impinging on this region of the tip surface, circled in Fig. 14(a). In this region, a channel flowing radially outward impinges on the tip cap and makes a 180 deg turn to proceed radially inward in the following passage. The adjacent cluster of five cooling holes marks the start of the radially inward flow. This produces a maximum temperature difference of −2.5% for the low cooling flow, which grows to almost −4% for the very high cooling scenario. As the amount of cooling increases, this spot appears to grow and get cooler. In the low cooling scenario, the spot is cooler but does not reach the two nearby cooling holes, but in the nominal scenario, it extends past hole 1. At high cooling flow, the coolest parts of the impingement region are near −4% cooler than the nominal scenario. For the very high cooling case, the entire measurable tip cap is strongly affected by the impingement flow. This is more clearly seen in Fig. 15, which plots the normalized temperature difference as a function of the relative cooling flowrate, where one is the nominal flowrate. There is a clear decrease in temperature difference as the cooling level increases except for the low cooling main flow run, Fig. 14(e).

Fig. 15
Fig. 15
Close modal

It should also be noted that the parapet walls surrounding the tip cavity can be observed. Not only do these walls produce an apparent temperature discontinuity but also they tend to be warmer than the floor of the tip cavity. This is because the walls are connected to the skin of the airfoil and do not have the cooling capability of the thin tip cap that makes up the floor of the cavity. The tip cap is cooled by internal convection, whereas the parapet wall is cooled by conduction from the blade tip, so the wall does not see benefits from effects such as internal impingement. This effect is most notable on the very high cooling run, Fig. 14(e), where the internal convection is strongest. The wall temperature difference is approximately 2.3% of the main flow temperature, and adjacent on the tip cap the temperature difference is near 2.9%. In addition, there is a discrepancy caused by a hotspot on the pressure surface of the cooled blades caused by the RTD appearing in the IR images.

Another observation is that the advanced hole blade and round hole blade perform slightly differently. Looking at Figs. 14(a) and 14(b), the round hole blade is consistently cooler than the advanced hole blade across the blade tip except for the parapet wall on the pressure side. The difference is small but present for the different runs at different cooling levels. This consistent observation indicates that there are slight differences in the cooling performance of the two blades. These could be differences in the cooling mass flow to the two blades or differences due to manufacturing. This result may seem to contradict the results presented in Table 2, but the averaging region also includes portions of the hotspot located on the pressure surface parapet wall of the round hole blades. Differences in the overall blade temperatures are small, but the round hole blade is consistently cooler than the advanced hole blade. It is possible to further isolate the influence of the internal cooling channels by performing experiments with no main flow and only internal cooling flows. Because the cooling jets are venting into a vacuum, it is likely that they are completely separated from the surface, so any heat transfer taking place is due to the internal flows. In addition, the lack of main flow precludes matching the corrected speed, so cooling-only runs are available for a variety of different speeds of rotation.

Figure 16(a) shows the normalized temperature history for a location immediately adjacent to cooling hole 1 on the advanced hole blade tip, as indicated in Fig. 10. As expected, higher cooling levels cause the temperature of the blade to drop more quickly, indicating greater heat transfer from the blade. The amplification of heat transfer would be due to changes in the flow structures within the blade. Since the vented jets are separated from the blade, they will have little effect on the tip temperatures compared to the internal cooling. The internal heat transfer will be determined by the fluid flow, blade temperature, and coolant temperature. Between the runs, the coolant temperature is constant, and the initial blade temperature would not stray far from the ambient leaving the fluid flow driving the differences in heat transfer.

Fig. 16
Fig. 16
Close modal

During the cooling period, the slope of the temperature curve is relatively constant. In Fig. 16(b), the average value of the slope is plotted against the cooling flowrate normalized by the nominal cooling flowrate. Here, the variation in the cooling flowrate becomes more apparent, and a linear relationship between temperature slope and cooling flow rate can be seen. In addition, the low noise and constant slope will make these data useful in a transient heat transfer model. A lumped capacitance heat transfer model, like the one used in the study by Christensen and Mathison, can be used to determine the heat transfer on a pixel-by-pixel basis across the blade tip [26]. This type of information further illuminates where the cooling is most efficiently removing heat from the blade.

Contour plots of the tip for reduced speed cooling-only runs are shown in Fig. 17. As in the main flow tests, the blade with an advanced cooling hole has warmer tip temperatures compared to the round hole blade. This is most noticeable around cooling hole 2 and cooling hole 3, where the colder blue region is darker on the round hole blade. Not only does this show a difference in the two blades but it also shows that even at speeds in excess of 5000 rpm, the effects of individual cooling holes can still be identified. As with the main flow runs, the effect of the impingement region strengthens as the cooling flow is increased, but at the very high cooling level, the decrease in the temperature compared to the high cooling level is minimal. This is more clearly shown in Fig. 15.

Fig. 17
Fig. 17
Close modal

Apart from identifying individual cooling holes, the parapet walls surrounding the tip cavity are visible. They are visible for the same reasons discussed for the main flow runs, but they are more distinct due to the absence of any external flow.

Rotational effects on the tip cooling are detectable in the IR data. As with the previous plots, the difference between the cooled and solid blade temperatures is shown in Fig. 18, but for these three tests, the rotation speed of the rotor is varied from 2400 to 8800 rpm. The most striking difference between the three plots is the effect of rotation on the overall tip temperatures. With higher rotational speeds, the tip cooling is enhanced. The impingement region sees the largest change, increasing from −0.75% at 2400 rpm to −1.5% at 8800 rpm. The cooling-only tests demonstrate that operating at the proper corrected speed is essential to capture the design condition cooling performance.

Fig. 18
Fig. 18
Close modal

## 6 Conclusions

This first set of high-speed experiments involving infrared data from a fully cooled turbine operating at corrected conditions provides significant amounts of valuable data in ways that are impossible for traditional instrumentation. Tip temperature data are presented at a variety of cooling flow levels and rotation speeds with the core main flow on and off. These data show the impact different cooling levels, blade types, and rotational speeds have on the temperature distribution. In addition, the effects of internal and external heat transfer can be separated through experiments utilizing only the cooling flow. On top of this, the IR data provide fully 2D measurements across the blade tip, which is not possible with instrumentation. These experiments with high rotational speeds, relatively low surface temperatures, and short duration provide a challenging environment for any type of instrumentation. However, the IR camera has proven itself capable of making reliable measurements and producing valuable data even in this environment. This work lays the foundation for further experimentation with infrared cameras in high-speed environments and the postprocessing of the data to maximize its value.

As disruptive technologies such as additive manufacturing mature, there is a need for more experimentation with novel cooling arrangements, such as fluidic oscillators, microcooling, or complex hole shapes. Infrared measurements are essential to the future of turbine research because they are quick to setup and provide reliable 2D measurements, factors that will be crucial in the development of these next-generation turbine cooling technologies.

## Acknowledgment

The authors would like to thank Honeywell Aerospace and the Ohio Federal Research Network for funding this work. In addition, this work would not be possible without the assistance of the GTL staff and students: Jeff Barton, Kyle Ruff, Rick Scheiderer, Ken Fout, Gabe Torres, Igor Ilyin, Aditya Kulkarni, Anjali Gupta, and Ryan Howard. Finally, the guidance of Professor Michael Dunn has been continually helpful.

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

The authors attest that all data for this study are included in the paper.

## Nomenclature

• $x¯$ =

X axis unit vector of the camera plane in 3D coordinates

•
• $y¯$ =

Y axis unit vector of the camera plane in 3D coordinates

•
• $N¯$ =

normal unit vector of the camera plane in 3D coordinates

•
• P2D =

pixel position in 2D coordinates

•
• $P¯3D$ =

pixel position in 3D coordinates

•
• $F¯n3D$ =

position of the face vertex n in 3D coordinates

•
• $F¯n2D$ =

position of the face vertex n in 2D coordinates

## References

1.
Bunker
,
R. S.
,
2007
, “
Gas Turbine Heat Transfer: Ten Remaining Hot Gas Path Challenges
,”
ASME J. Turbomach.
,
129
(
2
), pp.
193
201
.
2.
Uguccini
,
O. W.
, and
Pollack
,
F. G.
,
1976
,
High-Resolution Surface Temperature Measurements on Rotating Turbine Blades With an Infrared Pyrometer
,
NASA
,
Cleveland, OH
.
3.
Astarita
,
T.
,
Cardone
,
G.
,
Carlomagno
,
G. M.
, and
Tecchio
,
P.
,
2002
, “
Spiral Vortices Detection on a Rotating Disk
,”
ICAS 2002 Congr.
,
Toronto, ON
,
Sept. 8–13
, pp.
1
8
.
4.
Mori
,
M.
,
Novak
,
L.
, and
Sekavčnik
,
M.
,
2007
, “
Measurements on Rotating Blades Using IR Thermography
,”
Exp. Therm. Fluid Sci.
,
32
(
2
), pp.
387
396
.
5.
Wang
,
W.
,
Gao
,
J.
,
Xu
,
L.
, and
Shi
,
X.
,
2012
, “
Flow and Heat Transfer Characteristics in Rotating Two-Pass Channels Cooled by Superheated Steam
,”
Chin. J. Aeronaut.
,
25
(
4
), pp.
524
532
.
6.
Lang
,
W.
,
Gardner
,
A. D.
,
Mariappan
,
S.
,
Klein
,
C.
, and
Raffel
,
M.
,
2015
, “
Boundary-Layer Transition on a Rotor Blade Measured by Temperature-Sensitive Paint, Thermal Imaging and Image Derotation
,”
Exp. Fluids
,
56
(
6
), pp.
1
14
.
7.
Raffel
,
M.
, and
Heineck
,
J. T.
,
2014
, “
Mirror-Based Image Derotation for Aerodynamic Rotor Measurements
,”
AIAA J.
,
52
(
6
), pp.
1337
1341
.
8.
Lazzi-Gazzini
,
S.
,
Schädler
,
R.
,
Kalfas
,
A. I.
, and
Abhari
,
R. S.
,
2017
, “
Infrared Thermography With Non-Uniform Heat Flux Boundary Conditions on the Rotor Endwall of an Axial Turbine
,”
Meas. Sci. Technol.
,
28
(
2
), p.
15
.
9.
Nickol
,
J. B.
,
Mathison
,
R. M.
,
Dunn
,
M. G.
,
Liu
,
J. S.
, and
Malak
,
M. F.
,
2017
, “
Unsteady Heat Transfer and Pressure Measurements on the Airfoils of a Rotating Transonic Turbine With Multiple Cooling Configurations
,”
ASME J. Eng. Gas Turbines Power
,
139
(
9
), p.
092601
.
10.
Nickol
,
J.
,
Mathison
,
R.
,
Dunn
,
M.
,
Liu
,
J.
, and
Malak
,
M.
,
2017
, “
An Investigation of Coolant Within Serpentine Passages of a High-Pressure Axial Gas Turbine Blade
,”
ASME J. Turbomach.
,
139
(
9
), p.
091006
.
11.
Nickol
,
J. B.
,
Mathison
,
R. M.
,
Malak
,
M. F.
,
Rana
,
R.
, and
Liu
,
J. S.
,
2015
, “
Time-Resolved Heat Transfer and Surface Pressure Measurements for a Fully Cooled Transonic Turbine Stage
,”
ASME J. Turbomach.
,
137
(
9
), p.
091009
.
12.
Dunn
,
M.
, and
Mathison
,
R.
,
2014
, “
History of Short-Duration Measurement Programs Related to Gas Turbine Heat Transfer, Aerodynamics, and Aeroperformance at Calspan and the Ohio State University
,”
ASME J. Turbomach.
,
136
(
4
), p.
041004
.
13.
Celestina
,
R.
,
Christensen
,
L.
,
Sperling
,
S.
,
Mathison
,
R.
,
Aksoy
,
H.
, and
Liu
,
J.
,
2020
, “
Unsteady Heat Transfer Measurements From Single and High-Density Double-Sided Heat-Flux Gauges on the Airfoils of a Rotating Transonic Turbine
,”
ASME Turbo Expo 2020
,
Virtual
,
Sept. 21–25
, pp.
1
14
.
14.
Elfner
,
M.
,
Schulz
,
A.
,
Bauer
,
H.-J.
, and
Lehmann
,
K.
,
2017
, “
A Novel Test Rig for Assessing Advanced Rotor Blade Cooling Concepts, Measurement Technique and First Results
,”
ASME Turbo Expo 2017
,
Charlotte, NC
, Paper No. GT2017-64539.
15.
Hansen
,
P. C.
,
Nagy
,
J. G.
, and
O’Leary
,
D. P.
,
2006
,
Deblurring Images Matrices, Spectra, and Filtering
,
Society for Industrial and Applied Mathematics
,
.
16.
Thielicke
,
W.
, and
Stamhuis
,
E. J.
,
2014
, “
PIVlab—Towards User-Friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB
,”
J. Open Res. Softw.
,
2
(
1
).
17.
Björck
,
A.
,
1991
, “
Algorithms for Linear Least Squares Problems
,”
NATO ASI Ser.
,
77
, pp.
1
38
.
18.
Wiener
,
N.
,
1964
,
Extrapolation, Interpolation, and Smoothing of Stationary Time Series: With Engineering Applications
,
MIT Press
,
Cambridge, MA
.
19.
Shan
,
Q.
,
Jia
,
J.
,
Agarwala
,
A.
, and
Systems
,
A.
,
2008
, “
High-Quality Motion Deblurring From a Single Image
,”
ACM Transactions Graphics
,
1
(
212
), pp.
1
10
.
20.
Pandey
,
A.
, and
Gregory
,
J. W.
,
2018
, “
Iterative Blind Deconvolution Algorithm for Deblurring a Single PSP/TSP Image of Rotating Surfaces
,”
Sensors
,
18
(
9
), pp.
1
22
.
21.
Zhang
,
X.
,
Burger
,
M.
,
Bresson
,
X.
, and
Osher
,
S.
,
2010
, “
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
,”
SIAM J. Imaging Sci.
,
3
(
3
), pp.
253
276
.
22.
Oswald-Tranta
,
B.
,
Sorger
,
M.
, and
O’Leary
,
P.
,
2010
, “
Motion Deblurring of Infrared Images From a Microbolometer Camera
,”
Infrared Phys. Technol.
,
53
(
4
), pp.
274
279
.
23.
Fan
,
Y. W.
, and
Nagy
,
J. G.
,
2011
, “
Synthetic Boundary Conditions for Image Deblurring
,”
Linear Algebra Appl.
,
434
(
11
), pp.
2244
2268
.
24.
Elfner
,
M.
,
Glasenapp
,
T.
,
Schulz
,
A.
, and
Bauer
,
H. J.
,
2019
, “
A Spatially Resolved In Situ Calibration Applied to Infrared Thermography
,”
Meas. Sci. Technol.
,
30
(
8
), pp.
1
9
.
25.
Chen
,
L.
, and
Mathison
,
R. M.
,
2016
, “
Determination of Transient Heat Transfer Rates for a Film Cooled Metal Plate in a Blowdown Facility Using Infrared Thermography
,”
52nd AIAA/SAE/ASEE Jt. Propulsion Conference 2016
,
Salt Lake City, UT
,
July 25–27
.
26.
Christensen
,
L.
, and
Mathison
,
R.
,
2018
, “
Measurement of Heat Transfer Inside a Channel Using External Infrared Thermography
,”
AIAA Propulsion and Energy Forum
,
Cincinnati, OH
,
July 9–11
.