Development of a Lifetime Pressure Sensitive Paint Procedure for High-Pressure Vane Testing

Modern turbine-based systems evolve toward smaller cores with applications in aviation, nuclear small core reactors, or supercritical CO₂ cycles, for example. Traditionally turbine test facilities have used intrusive and discrete sensing technology, such as pneumatic lines, to assess the airfoil loading. However, the small airfoil geometry constrains the practical implementation of the tubulation. Moreover, these diverse implementations share common concerns regarding the increasing relevance of unsteady flow detachment, which is unfortunately difficult to predict using unsteady Reynolds-averaged Navier–Stokes (URANS) solvers. Advanced optical measurements such as fast response pressure-sensitive paint (PSP) can provide improved spatial resolution, i.e., the pixel and temporal resolution of the 2D surface pressure field.

Since the pioneering work of Peterson and Fitzgerald [1], PSP has been applied extensively for aerodynamic testing. Two main PSP methods are used in the literature (intensity and lifetime). The intensity method requires a continuous illumination source and a wind-off reference image at no-flow conditions. It is thus more susceptible to illumination intensity, temperature, and model movement errors. The lifetime approach correlates pressure to the luminescent lifetime decay of the excited luminophores. This method requires a time-varying light source and is less sensitive to illumination intensity. The lifetime method is well suited to non-stationary test articles such as turbomachinery or rotorcraft airfoils, where the test article moves, and luminophore concentration may vary along the surface.

Several researchers have used conventional PSP on turbomachinery to measure steady pressures in the stationary or rotating frame of references [2–4]; fewer studies have focused on unsteady lifetime PSP implementation in high-pressure turbine testing conditions. Gregory et al. [5] applied intensity-based unsteady PSP to the inlet wall of a turbocharger compressor inlet. The pressure fluctuations on the blades and periodic variations in blade loading were resolved using a polymer ceramic (PC) binder with platinum tetra (pentafluoro phenyl) porphyrin (PtTFPP) luminophore molecules (PC-PSP). Pastuhoff et al. [6] used lifetime PSP to measure pressure on the airfoils of a radial compressor. A diode laser with a scanning-mirror system illuminated the paint, and the luminescent lifetime was measured with a photomultiplier tube. The time-resolved measurements were able to detect the frequency of flow at surge conditions. Several researchers have also used unsteady PSP with the lifetime method applied to rotorcraft airfoils [7–9].

Some experimental studies demonstrate that lifetime PSP has several advantages compared to the intensity method. Schreivogel et al. [10] tested both intensity and lifetime techniques with the flow around isolated surface roughness in supersonic flow. The lifetime technique did not show a significant sensitivity to paint thickness or temperature. Klein et al. [11] showed that LED modulated lifetime had an error of 200 Pa while the laser single-shot lifetime had an error of 250 Pa. The measurement error was calculated from the difference between pressure tap and PSP data. The unsteady flow was resolved with the laser-based lifetime measurement system. Sugioka et al. [12] used PC-PSP to measure pressure distribution on a pitching airfoil in transonic flow. The results indicated that the measurement error for lifetime PSP was 50% less compared to the intensity method. Nevertheless, higher spatial-temporal accuracy is required for high-fidelity analysis of the performance of high-pressure turbine airfoils.

This work demonstrates unsteady lifetime PSP at 20 kHz in an annular vane cascade at engine representative conditions. First, the development of the quasi-continuous burst-mode laser lifetime PSP method is evaluated in a low Technology Readiness Level (TRL) linear wind tunnel. A data processing routine with pixel binning is performed to reduce the uncertainty of the PSP calibration. Following the evaluation of the technique in the linear wind tunnel, the optical setup and experimental conditions in the annular wind tunnel are described, and the laser lifetime PSP is applied to the suction surface of a high-pressure turbine vane. A 10 × 10 binning is applied to the PSP calibration, and the surface pressure results are compared with local pneumatic pressure taps, and Reynolds-averaged Navier–Stokes (RANS) computation results. The frequency spectrum from the time series PSP data is investigated at mid-span and 30% span.

The three major types of luminophores (porphyrin-, Pyrene-, and ruthenium-based complexes have short luminescent lifetimes (∼10⁻⁶ s). Therefore, the PSP’s dynamic response constraint is the diffusion time scale typically more extended than the luminescent lifetime. The diffusion time scale is improved by decreasing the paint thickness; however, coating thickness affects both dynamic response and signal-to-noise ratio (SNR). Porous binders in fast responding PSP increase the mass diffusivity of oxygen and provide a larger air-polymer surface area.

A PtTFPP luminophore with a porous PC binder from Innovative Scientific Solutions, Inc. was used for the experiments. The absorptive spectrum has peak efficiencies at the Soret band (395 nm) and Q-band (541 nm). The PSP emission spectrum was measured with a spectrometer after excitation with a Neodymium-doped yttrium aluminum garnet (Nd: YAG) laser (532 nm) at ambient pressure and temperature. The results showed that the PC-PSP emission spectrum has a peak at 650 nm. Therefore, both a 610 nm long-pass filter and a 532 nm notch filter were mounted on the camera lens to block any incident light reflections.

The paint formula has three components (Parts A, B, and C). Parts A and B make the binder, and Part C is the luminophore solution. Part A’s volume is determined based on the interrogation region and paint thickness required for the experiment. Using a graduated cylinder and pipette, 4% of Part A is measured from Part B and mixed with Part A. The mixture is poured into a lid with a tight jar and shaken thoroughly. The mixture is then poured into an Iwata precision airbrush spray gun that is adjustable for fine and coarse brush painting. After coating the binder in-situ, the surface is dried at room temperature for an hour. Afterward, part C is poured into a thoroughly cleaned spray gun and sprayed unto the binder until uniformly pale pink.

A state-of-the-art quasi-continuous burst-mode Nd: YAG laser following the design of Slipchenko et al. [13] was used as a light source to excite the paint at 532 nm (second harmonic output of the laser). The laser has a linewidth of < 2 GHz at 1064.3 nm with 215 mJ/pulse at 20 kHz. The laser has already been tested with high-speed surface imaging applications [14]. The pulse-burst duration of the laser is 10.8 ms with nominal repetition rates at 10 kHz and 20 kHz. A repetition rate of 20 kHz provides a window of 50 µs to capture the total decay (5τ ∼ 99%) of the excited luminophores at ambient pressure between laser pulses. At vacuum conditions, the PC-PSP has a longer decay lifetime, with a time between each laser pulse of 100 µs.

The steady characteristics of PC-PSP were evaluated at wind-off and wind-on conditions in a low TRL (1–2) wind tunnel at the Purdue Experimental Turbine Aerothermal lab (PETAL). The Linear Experimental Aero-thermal Facility (LEAF) was designed to be entirely optically accessible with removable quartz windows and maximum modularity to evaluate and test advanced optical techniques. The optical path for the laser beam and the mounting of the camera is shown in Fig. 1(a).

The test case consists of a converging-diverging nozzle, accelerating the flow to Mach 2, followed by a wavy surface to study shock-separation phenomena, as depicted in Fig. 1(b). Due to high spatial gradients, the test article is suitable to precisely evaluate new optical diagnostics for high-speed applications [15]. The laser beam was guided through a series of Nd: YAG mirrors and finally through a 1500 grit diffuser lens to provide uniform illumination on the wavy surface. A SAZ Photron complementary metal-oxide-semiconductor (CMOS) camera was used at a frame rate of 200 kHz with a 160 × 384 spatial resolution. A 532 nm notch filter and 610 nm long-pass optical filter were used to damp out the incident laser reflections.

A vacuum pump was used to reduce the pressure in the linear wind tunnel test section from 101.15 kPa to 16.34 kPa for the PC-PSP calibration. At each of the 14 calibration points within the pressure range, a transistor-transistor logic (TTL) pulse from a Quantum Composer 9530 pulse generator was used to trigger the timing signals of the experiment. After each laser pulse, the camera is triggered to acquire 20 images at 200 kHz for a total acquisition time window of 100 µs. A summary of the timing chart and raw images of the PC-PSP fluorescence decay is shown in Fig. 2. An offset of 10 ns was added to delay the camera to account for the nominal laser pulse width. The burst duration for the laser is 10.8 ms, which yields 108 datasets. During the wind-on experiments, the TTL pulse from the pulse generator was triggered once the flow conditions were established.

The following PSP data processing routine was applied to remove images with low SNR, reduce uncertainty, and select the optimal binning selection for analysis of the flow field. The flowchart for the data post-processing is shown in Fig. 3. All the raw images are cropped to a 64 × 372 region of interest (ROI) for the pre-analysis steps and averaged across all pixels into a single averaged value. In total, there are 108 datasets, each containing 20 images. The points in the intensity decay are normalized by the first point, which is the maximum intensity. For each dataset, an upper threshold is applied for the first point (101.15 kPa—ambient) of 0.9, and a minimum threshold for the last point (16.34 kPa—vacuum) is set to 0.01, described in Figs. 4(a) and 4(b), respectively. Any datasets not within the upper and lower threshold are discarded. After this checkpoint in the routine, 99 out of 108 datasets are resolved, as shown in Fig. 4(c). The normalized intensity decay at 101.15 kPa dissipates energy faster (shorter time constant) than at 16.34 kPa due to less O₂ quenching at lower pressures.

The second step in the pre-analysis was to select the start and endpoints as inputs for the single exponential decay curve fitting. The optimal start and endpoint maximize the correlation fit coefficient while minimizing the number of points for curve fitting. Of the 20 points in each dataset, the first 18 data points are used for this evaluation. The results shown are averaged across 99 datasets. Figures 5(a) and 5(b) show the calculated lifetime constant for starting points (1 to 5) and up to 20 points used the curve fit. Compared to the ambient results, the coefficient of determination (R²) is above 0.99 at vacuum, as shown in Figs. 5(c) and 5(d). The differences in the trend of time constants between ambient Figs. 5(a) and vacuum 5(b) are related to the luminescence decay slope in Fig. 4(c). Following the fifth frame, the decay curve is at zero intensity at ambient. As a result, there is no change in the time constant when more than five points are used for the exponential decay fitting. Finally, the fourth image was selected as the starting point with four points used for the curve fit. The time constant cut-off frequency at ambient pressure was 19 kHz and 6.4 kHz at vacuum from the final selection of curve fit points.

After the pre-analysis, a trade-off study with binning sizes was performed to reduce the uncertainty of using a single-averaged value across all pixels. The binning approach is shown in Fig. 6. Six binning bundles are evaluated from a single-pixel (1 × 1) to all of the image’s pixels (64 × 372). For each bundle of pixels, the block average is computed, which creates a new image with dimensions of the applied binning. The Kron function in matlab is applied to reconstruct the image back to a 64 × 372 pixel resolution.

For each of the binning bundles, the spatially averaged exponential time constant is computed and shown in Fig. 7(a). The standard deviation of the exponential time constant is also calculated for each binning bundle as shown in Fig. 7(b). Although there is no difference for the averaged time constant for different binning bundles, an overall decrease in standard deviation is observed as the binning block size increases from 1 × 1 to 50 × 100. Across all binning bundles, there is a common trend of reduced time constant variation with increasing pressure. However, for pressures larger than 70 kPa, the decay time constants do not vary.

From the a priori calibration, a relation between luminescent lifetime and pressure is expressed by a second-order polynomial in Eq. (4). The experimentally determined coefficients C₁, C_2, and C_3, are unique for each binning bundle of pixels. The polynomial coefficients are then applied to the single exponential time constants calculated from the calibration data to retrieve the pressure. Similar to the exponential time constant results, there is no difference between each binning bundle when the pressure data is spatially averaged, as shown in Fig. 8(a). Figure 8(b) shows that with a 1 × 1 binning bundle, the pressure variation can be as high as 1.6 kPa compared to 400 Pa with a 10 × 10 binning. Additionally, it shows that the advantage of pixel binning is reduced for lower pressures.

The calibration coefficients for each binning bundle of pixels are applied to wind-on data from a wind tunnel test. The selected test case consists of a set of wavy surfaces in a Mach 2 environment. The 2D averaged pressure distribution from a total of 90 datasets is shown in Fig. 9. The pressure distribution for the binning bundles up to 10 × 10 shows favorable agreement in streamwise and spanwise directions. The spanwise-averaged pressure for each binning shown in Fig. 10(a) follows the expected pressure trend of compression, expansion, and separation shock. A first compression wave provides a pressure increase (at a location of x = 0 to 0.1 [−]), followed by a first expansion region. A first separation shock appears at a location of x = 0.25 [−] followed by a separation region (x = 0.25–0.5 [−]) due to the onset of the second wavy surface downstream. A second compression region with pressure rise is shown in the PSP data, followed by an expansion fan and a second separation shock. The results from a Shadowgraph experiment of the same test case show good agreement with the PSP results shown in Fig. 10(b). Although all the binning bundles show the expected trend in Fig. 10(a), the 10 × 10 binning data results had the best agreement with the test case with no binning applied. Therefore, the 10 × 10 binning dataset was selected for future investigation.

The data processing routine’s final steps include mapping the surface pressure data to the surface geometry [15], followed by uncertainty analysis. The camera calibration was performed via the photogrammetry method developed by Liu et al. [16], and the dot target is shown in Fig. 11(a). The optimization method, combined with an initial guess from the Direct Linear Transformation (DLT) process, allows rapid semi-automatic camera calibration. Based on the camera focus, perspective, and region of interest, an array of dots is selected from the dot target and used in the calibration procedure. Next, any rotation or translational shifts needed for the system are applied based on the camera’s mounting. After these steps, the dots’ centroids are selected and used in the calibration technique to build the image space. Finally, the collinearity equations are applied to directly map the image space to the object or model space. The calibration is demonstrated in Fig. 11(b) for a wind-on image of the wavy geometry in which the compression, expansion, and separation shock appear.

Uncertainty analysis of the laser lifetime PSP methodology is performed considering the parameters that affect the conversion of the exponential time constant to pressure in Eq. (4). The uncertainty in the calibration coefficients, lifetime ratio, and reference pressure is evaluated with a 95% confidence interval. To estimate the effect of each parameter’s uncertainty on the final result, the pressure variation is calculated with uncertainty values added for each parameter. Each individual error source is combined to give the total pressure variation.

The uncertainty results for a single calibration test point at 22.5 kPa are shown in Table 1. As observed in Table 1, the largest contribution to the uncertainty is from calculating the lifetime ratio and the calibration coefficients retrieved from the polynomial fitting. The reference pressure has a sensitivity equal to unity, which means that any variation in that pressure is directly transmitted to the final uncertainty without amplification. The final uncertainty is 4.26% relative to a calibration pressure of 22.5 kPa.

CFD simulations of the annular vane cascade were performed for comparison to the measured PSP and static pressure data. The simulations were performed using the Rolls-Royce proprietary meshing package PADRAM and the CFD package HYDRA [17]. A half annulus simulation was modeled using a structured H-O-H mesh with ∼ 17M cells. The k-omega SST turbulence model was used. A close-up view of the mesh in the region of the PSP measurements is provided in Fig. 12.

The simulation boundary conditions were based on test data. The inlet boundary was defined using a specified total pressure, total temperature, k-omega turbulence quantities, and radial and pitch angles. The exit boundary condition was set using an outflow condition with a specified hub static pressure and a radial equilibrium assumption. Periodic surfaces were assumed on the circumferential boundaries, and the solid surfaces were defined as viscous walls.

The experimental application consists of measuring the static pressure on a high-pressure turbine vane’s suction surface via laser lifetime PSP. The experiments were performed in the annular cascade (TRL 3–4) at PETAL [18]. This annular vane cascade is a large capacity test section with a shroud diameter of 840 mm, able to handle mass flows up to 18 kg/s at a wide range of temperatures. The test section’s large size maximizes the spatial resolution of optical techniques such as PSP and high-frequency particle imaging velocimetry (PIV) [19].

During facility operation, compressed dry air at 15 MPa is stored in a 56 m³ pressure tank. From the high-pressure reservoir, one pipeline guides flow into the test cell and discharges in a mixer. The other pipeline diverts air through a natural gas heat exchanger. For uniform flow temperature, pipe elbows are placed in the pipeline downstream to enhance mixing between hot and cold lines. The mass flow ratio between both pipelines determines the flow temperature of the experiment.

While the heat exchanger heats the fluid, the air is vented through a purge line outside the test cell. Once the flow temperature is stable, a fast-actuating valve upstream of the annular cascade is opened, and another fast-actuating valve in the bypass line is closed. The air is radially discharged into a settling chamber before it passes through a series of honeycombs and flow straighteners. The flow is then accelerated through the inlet contraction area and discharged into the test section with uniform spatial and temporal flow conditions. The flow exits to a vacuum tank through a sonic valve. The sonic valve isolates the test article from the downstream conditions once it is choked and provides an independent adjustment of Reynolds and Mach numbers. The annular cascade operating conditions for this experiment are shown in Table 2. The vane has an outer radius of 420 mm, a radial span of 63 mm, and a flow turning of ∼76 deg. The vane aspect ratio is low, reflective of the small core turbine design space.

The annular test section shown in Fig. 13 is equipped with instrumentation for performance characterization, including static pressure tappings to compare with PC-PSP pressure data and thermocouples mounted on the adjacent vane’s suction side (SS) to monitor the surface temperature. The laser beam is guided into the laser delivery probe installed in one of the 32 optical ports in the test section. A rigid borescope is mounted in a different optical port downstream of the vane trailing edge and is connected to a high-speed intensifier and high-speed camera. The optics are mounted on optical tables furnished with leveling isolation dampers. These isolators are necessary to mitigate misalignment from the vibrations of the test rig.

The laser delivery probe shown in Fig. 14 can be adjusted radially into and out of the flow path and rotated 360 deg around the probe shaft. A prism at the bottom can be rotated 45 deg pitch-wise. Just upstream of the prism, a window is installed to seal the probe. This permanent window has a visible anti-reflection coating to maximize light throughput to the reflector prism. A plano-convex positive lens with a 120 mm focal length and a 1500 grit ground glass diffuser is spaced out 20 mm in the lens tube. The laser beam is first spread by the diffuser and then refocused by the positive lens adjacent to the permanent window. The laser is aligned with a laser level aid to ensure that the delivery path is concentric and parallel to the delivery probe axis. Figure 15(a) shows the laser alignment process. The laser probe yaw and pitch are first determined by centering the unexpanded beam in the region of interest. Afterward, the 12.7 mm optics are carefully installed to capture a homogeneous portion of the expanded beam precisely within the interest region. After the final check for a uniform, diffused beam on the vane surface area, the final laser probe position is fixed and marked. The rectangular large window opening, shown in Fig. 15(b), provides access to mount the 3D-printed calibration dot target used for camera calibration and applying the PC binder and PtTFPP luminophore on the vane in-situ with the airbrush spray gun.

A close-up view of the optical layout inside of the test section is shown in Fig. 16. Before installing the laser delivery probe in the test section, the spacing between the diffuser and focusing lens was precisely measured to produce a uniformly diffused beam with a 63 mm spot size. The 304.8 mm long rigid Hawkeye borescope has a 50 deg field-of-view (FOV) and provides the interrogation region near aft SS of the turbine vane. The borescope was aligned with an angle of view fixed at 90 deg. The maximum lens outer diameter is 7.95 mm, and a focusing lens is used to adjust and optimize the sharpness of the image for different distances. A SAZ Photron camera with a frame rate of 200 kHz and pixel resolution of 160 × 384 pixels is synchronized with a HiCATT (high-speed intensified camera attachment) and the quasi-continuous burst mode laser. TTL pulses from a Quantum Composer 9530 pulse generator are used to trigger the experiment timing signals shown in Fig. 17. After every laser pulse, the camera acquires a series of 10 images, of which the first three useful images are used to model the pressure-sensitive luminescent lifetime.

The PC-PSP thickness was measured with a Fischer Dual scope FMP40 system. The Eddy current probe has a tip diameter of 2.4 mm and a maximum outer diameter of 18 mm. The probe is first calibrated on the unpainted aluminum base material. Thereafter, standard thin foils are measured on the base material to complete the calibration. The thickness is measured at seven sectors on the painted surface, as summarized in Table 3. The largest minimum to maximum variation was 27.1 µm at a location near the edge of the vane. The binder’s non-uniform concentration is controlled by the thickness measurements and can be applied to uncertainty analysis.

To calibrate the PC-PSP in-situ, a vacuum pump connected to the wind tunnel is used to lower the test section’s pressure from ambient pressure to 80 kPa in several steps. At each pressure level within the calibration range, the laser is triggered, and a feedback signal from the intensifier exposure is synchronized with the pressure tap data on an adjacent vane.

The 10 × 10 binning data processing routine described in Sec. 2 is applied to each image of cropped 88 × 128 pixels to calculate the exponential time constant. Equation (2) is used to model the relationship between pressure and lifetime. The comparison between the pressure taps and the PSP calibration pressure retrieved from the regression coefficients averaged over 88 × 128 pixels is shown in Fig. 18. The maximum difference is 5100 Pa. The uncertainty bars in the ordinate represent 95% of the readings among all the pixels for each calibration pressure calculated from PSP. The abscissa’s uncertainty bars represent ±0.05% of the full-scale range of the reference Scanivalve DSA 3217 unit.

The CFD results show a good agreement with the static pressure taps data at 50% span, depicted in Fig. 19(a). The pressure taps on the pressure surface of the vane were not included since the pressure surface was not used for PSP measurements. The calibration coefficients from the PSP calibration are applied to the wind-on experiment with test conditions from Table 2. The normalized 2D pressure distribution from the CFD simulations is compared to the 2D normalized pressure from the PSP, as shown in Fig. 19(b). The PSP results are time-averaged over a duration of 3.4 ms or 69 pressure fields.

The CFD results match well with the PSP results qualitatively. In the aft section of the vane suction surface, both CFD and PSP pressure distributions show a gradual increase in pressure along the streamwise direction with higher pressures near the trailing edge. Additionally, there is a gradual increase of pressure along the spanwise direction from the hub. The PSP results along the streamwise direction at 15% and 50% span are also compared with static pressure taps shown in Fig. 20. The uncertainty bars from PSP represent the single standard deviation range on either side of the mean. The difference between the static pressure taps and the PSP at 50% span is 3160 Pa.

The time history of pressure data from two 5 × 5 bundles of pixels at 50% and 30% span is processed to evaluate the unsteady PSP results. The average pressure of 25 pixels is monitored in a time window of 2.3 ms. To improve the frequency resolution, the pressure signal is repeated 100 times resulting in a duration of 0.23 s. The discrete Fourier transform (DFT) of the pressure signal is applied to two datasets (wind-off and wind-on conditions). At 50% span, the difference between wind-on and wind-off results is insignificant, as shown in Fig. 21. Closer to the hub at 30% span, there is an increase in frequencies and pressure amplitude in the wind-on results compared to wind-off, as shown in Fig. 22. The flow conditions near 50% span are less dominated by secondary flow structures and are therefore steady. Several researchers [20–22] have studied the horseshoe vortex system formation in low-speed flows. Wang et al. [20] identified a horseshoe vortex frequency of 2.5 Hz with an inlet velocity of 0.8 m/s in a linear cascade. If we consider the same Strouhal number scaled to the high-speed test conditions in Table 2, we can anticipate several hundred Hz frequencies.

In this work, the procedure for laser lifetime PSP measurements at 20 kHz is successfully demonstrated in an annular test section at engine representative conditions. The initial evaluation of the technique in a low TRL linear test section evidenced that the 10 × 10 binning calibration resulted in the optimal binning size with reduced uncertainty. Compared to the 1 × 1 binning bundle, the 10 × 10 binning results showed comparable spatial resolution in the wind-on 2-D pressure distribution, and the spanwise-averaged pressure. Additionally, a minimum of four points used to compute the decay time constant resulted in the maximum correlation fit determination using a single exponential decay curve fit. The precise calibration procedure and mapping of the wind-on pressure image to the test geometry captured the compression, expansion, and separation shock features along the wavy surface in supersonic flow. The uncertainty analysis showed that the most significant contribution to the uncertainty was the lifetime ratio and the polynomial coefficients. The total uncertainty was 4.26% relative to the mean.

In the annular experiment, a 10 × 10 binning calibration was applied to the calibration and wind-on PSP data on a high-pressure turbine vane's suction surface. The PSP thickness measurements showed that the largest minimum to maximum variation was 27.1 µm with a difference of 5100 Pa between the PSP and pressure taps from the PSP calibration. The results from the two-dimensional normalized static pressure in the interrogation region showed a gradual increase of pressure from the hub in the spanwise direction. Additionally, along the flow direction, the pressure increased toward the trailing edge, and the difference between the PSP and pressure taps at mid-span was 3160 Pa. The DFT of the unsteady pressure signal showed increased frequency content in wind-on conditions compared to wind-off at both 30% and 50% span. At a 30% span, an increase in frequencies and pressure amplitude was identified compared to the mid-span region.

The authors would like to acknowledge Dr. Jordan Fisher and second Lt. Daniel Inman for their support with the experimental setup and Rolls-Royce Corporation for their technical and financial support during this work. Special thanks to Dr. Valeria Andreoli, Dr. Jorge Saavedra, and Mr. Francisco Lozano for Big Rig for Annular Stationary Turbine Analysis (BRASTA) initial shakedown tests.

There are no conflicts of interest.

t =

time

A =

constant

C =

second-order polynomial coefficients

I =

fluorescence intensity with quenching

K =

quenching characteristic of molecules

P =

pressure

T =

temperature

M, m =

number of matrix rows

N, n =

number of matrix columns

Re/m =

Reynolds number per unit length

τ =

lifetime decay constant

σ =

standard deviation

avg =

average

max =

maximum

o =

no quenching mechanism

q =

quenching

r =

ratio of lifetime decay constant

ref =

reference pressure

s =

static

std =

standard deviation

t =

total

1,2,3 =

second-order polynomial coefficients