Measurements are presented for a high-pressure transonic turbine stage operating at design-corrected conditions with forward and aft purge flow and blade film cooling in a short-duration blowdown facility. Four different film-cooling configurations are investigated: simple cylindrical-shaped holes, diffusing fan-shaped holes, an advanced-shaped hole, and uncooled blades. A rainbow turbine approach is used so each of the four blade types comprises a wedge of the overall bladed disk and is investigated simultaneously at identical speed and vane exit conditions. Double-sided Kapton heat-flux gauges are installed at midspan on all three film-cooled blade types, and single-sided Pyrex heat-flux gauges are installed on the uncooled blades. Kulite pressure transducers are installed at midspan on cooled blades with round and fan-shaped cooling holes. Experimental results are presented both as time-averaged values and as time-accurate ensemble-averages. In addition, the results of a steady Reynolds-averaged Navier–Stokes computational fluid dynamics (RANS CFD) computation are compared to the time-averaged data. The computational and experimental results show that the cooled blades reduce heat transfer into the blade significantly from the uncooled case, but the overall differences in heat transfer among the three cooling configurations are small. This challenges previous conclusions for simplified geometries that show shaped cooling holes outperforming cylindrical holes by a great margin. It suggests that the more complicated flow physics associated with an airfoil operating in an engine-representative environment reduces the effectiveness of the shaped cooling holes. Time-accurate comparisons provide some insight into the complicated interactions that are driving these flows and make it difficult to characterize cooling benefits.

## Introduction

The effort to better understand hot-section cooling technologies in axial gas turbines is critical to improve the efficiency and reliability of these engines. There are many active technologies utilized, including internal cooling within each airfoil, purge cooling between rotating and stationary components, and film cooling. Additionally, many passive approaches such as improved materials and coatings that can handle higher temperatures are being investigated. The experiment described herein utilizes engine hardware and so features all of these technologies; however, rotor airfoil film cooling is the primary technology under investigation, with a focus on cooling hole shape.

Film cooling was originally performed with simple cylindrical holes protruding at sharp angles into the airfoil surface. Improvements in both manufacturing ability, and understanding of the complicated flow physics produced by film cooling, have led to compound-angled holes and more complicated hole shapes. Beginning with Goldstein et al. [1], hundreds of papers have investigated different hole configurations and shapes. For the most part, these more advanced cooling hole shapes reduce coolant liftoff from the surface. Haven et al. [2] showed how cooling jets are prone to liftoff the surface due to a pair of counter-rotating kidney vortices generated by the interaction of the jet with the freestream flow. The vortices are oriented such that each will lift the other off the surface by mutual induction and proceed to pull hot gas in under the cooling jet. They continue to explain how properly designed diffusing holes can reduce this effect both by increasing the distance between the two vortices, which will weaken their mutual effect on each other, and by creating a vortex pair of opposite direction within the jet, reducing overall liftoff. Brittingham and Leylek [3] performed an early investigation that coupled experimental data with computational prediction, providing significant detail into the flow physics of the counter-rotating vortices produced at each cooling hole exit. There are several dozen different variations of diffuser-shaped cooling holes; a summary of their geometry and performance can be found in a review by Bunker [4].

Noncylindrical holes can incur a penalty in manufacturing cost and time. A different approach to the diffuser-shaped holes has been to combine cylindrical holes into more complicated forms, in order to simplify manufacturing. Heidmann and Ekkad [5] performed a computational study on a scheme that used two small holes to complement each main cooling hole, with an experimental study on the same pattern following by Dhungel et al. [6]. The complementary holes were designed to produce antivortices to help reduce the liftoff, and it was seen to improve the effectiveness over just cylindrical holes, but not as much as diffuser-shaped holes can. Another approach reported by Lu et al. is to have cylindrical holes eject into craters [7] or trenches [8], which also improves the cooling effectiveness without requiring the manufacturing of diffuser-shaped holes.

The other end of the spectrum is to utilize very complicated cooling hole shapes, accepting the increased manufacturing costs as a tradeoff to their enhanced performance. A number of complicated shapes have been suggested, including an arrowhead shape by Okita and Nishiura [9], dumbbell and bean-shaped holes presented by Liu et al. [10], and crescent and converging slot holes presented by Lu [11]. These holes all perform better than diffuser-shaped holes for at least some range of blowing ratio. Unfortunately, all of the work investigating these shaped holes thus far has either been on a simplified geometry or purely computational in nature. The primary goal of this work is to extend this to a rotating environment and see if the improved effectiveness still persists.

## Experimental Setup

The experiment was performed using The Ohio State University Gas Turbine Laboratory's Turbine Test Facility (TTF). The turbine stage utilizes engine hardware supplied by Honeywell Engines for the bladed rotor disk assembly, vane row, shroud, onboard injection system, and seal components.

### Facility.

The TTF is a 100 ft (30 m) long shock-tunnel facility with a tube inner diameter of 1.5 ft (0.46 m). The facility can operate in shock mode, but for this experiment it operates in blowdown mode. A schematic of the overall rig is provided in Fig. 1. At the outlet of the shock tube is a fast-acting valve (FAV), choke, and supersonic expansion nozzle leading to an evacuated dump tank. The inlet piece to the rig protrudes into the expansion nozzle. The inlet feeds into a combustor emulator, which is a 2 ft (0.61 m) long mesh of Inconel that is heated prior to the experiment. The combustor emulator heats the inlet flow to the desired temperature (about 550 K) prior to entering the nozzle guide vane. It can also produce radial and hot-streak temperature profiles (see Refs. [1219]), but the inlet temperature profile was kept constant for this experiment. Downstream of the emulator, the flow enters a nozzle guide vane, and rotor, which is spun up to about 98% design-speed prior to the experiment, and freely accelerates up to about 102% before the FAV is closed.

Fig. 1
Fig. 1
Close modal

Cooling flow is provided by a separate large cooling facility (LCF). For the current experiment, the LCF consists of a large supply tank of dry air, massflow instrumentation, heat exchangers to chill the air, and a manifold of adjustable chokes that are used to meter the flow appropriately.

### Turbine.

The turbine that is investigated is the first stage of a high-pressure transonic turbine manufactured by Honeywell Engines. A schematic of the stage is provided in Fig. 2, showing the core flow path, stator vane, rotor blade and disk, and purge cavities both forward and aft of the rotor. There are two cooling supply circuits, each controlled separately and shown in Fig. 2. The first is the tangential on-board injector (TOBI) cooling circuit, which provides both the forward purge (between the vane and blade rows) and the blade film cooling. In addition to these coolant flows, some of the TOBI flow also leaks out of the stage through numerous leakage paths through bearings and other seals. The second circuit supplies the aft purge, which is injected in the gap between the blades and stationary components downstream of the rotor. The aft purge is not thought to directly cool any of the instrumented geometry; however, its ejection does form a blockage to the main flow, and therefore it may have an impact on the flow physics in the rotor platform region. Nominal cooling flow rates are set to match coolant-to-freestream massflow ratios representative of the engine, and runs are performed with each circuit above and below these levels as well.

Fig. 2
Fig. 2
Close modal

Each blade features seven rows of cooling holes, labeled A–G as shown in a photo of the blade in Fig. 3. Row A is near midchord on the pressure-side, B–F are near the leading edge (E cannot be seen in the image, but is between D and F), and G is near midchord on the suction side. The two shaped-hole cooling configurations still have cylindrical holes in rows B, C, D, and E. Only rows A, F, and G are composed of shaped holes.

Fig. 3
Fig. 3
Close modal

The surface geometry of each blade is identical; however, the cooling configurations follow a “rainbow” format whereby three different cooling hole shapes can all run simultaneously, along with solid uncooled blades. Several blades of each style are placed sequentially in the rotor such that they make up a wedge of the complete rotor, as shown in Fig. 4.

Fig. 4
Fig. 4
Close modal

Photographs of the three hole shapes are provided in Fig. 5. The first shape (Fig. 5(a)) is a standard circular-cross-sectioned cylindrical hole. The second is a diffusing “fan” shaped hole (Fig. 5(b)) that is designed to reduce blowoff and coolant separation. The third is an advanced-shape hole (Fig. 5(c)) that directs the coolant in three directions in an effort to modify the counter-rotating vortices to keep the coolant on the blade. The advanced-shape hole is a patented Honeywell proprietary design [20,21]. A more detailed schematic of each hole is also provided in Fig. 6. Note that the 30 deg angle of injection is approximate, and not the same for all holes due to the curvature of the airfoil. While the different shapes should create different flow profiles on the airfoil, they are designed to flow the same overall magnitude of coolant. Likewise, all designs have the same number of holes, and the hole centers are placed in the same locations.

Fig. 5
Fig. 5
Close modal
Fig. 6
Fig. 6
Close modal

The high-pressure vane is composed of 12 vane doublets, for 24 total vanes, and the rotor is composed of 38 blades. The vane cooling holes are blocked for this experiment, but can be reopened for future experiments.

### Instrumentation.

Heat-flux is measured on the blade airfoil using two-sided Kapton heat-flux gauges that are constructed at the Gas Turbine Laboratory. The gauges consist of two high-frequency response (in excess of 100 kHz) temperature measurements above and below a 2-mil (51-μm) strip of Kapton. Time-accurate heat-flux is calculated numerically for each gauge using a 1D transient heat transfer model as described by Weaver et al. [22], and then nondimensionalized to Stanton number by Eq. (1), where Ach is the choke area or the effective throat area of the entire stage. More detail on the operation of these gauges is presented by Murphy [23]
$St≡q″(m˙Ach)([cpT]inlet−[cpT]metal)$
(1)

Airfoil surface pressure measurements are measured using Kulite XCQ-062-100 A pressure transducers embedded into the surface of the blade. These transducers are able to provide time-accurate data with their high-frequency response rate in excess of 50-kHz. These transducers are also placed, along with miniature butt-welded thermocouples, inside four different serpentine cooling passages within the blade on one cooled blade of each cooling hole shape to help determine cooling parameters.

All signals are sampled by the data acquisition system at 500-kHz, which is oversampling relative to the frequency response time of the instrumentation. This allows for running averaging of the signals to help reduce random noise without losing any unsteady information. The vane-passing frequency is approximately 5.25-kHz, allowing for capturing unsteady content over 15 times the vane-passing frequency, even after the running averaging, although frequency content above three times the vane-passing frequency is generally found to be negligible.

Signals taken on rotating hardware are transferred to the stationary frame of reference through one of two 300-channel slip rings, which are located on both the forward and aft ends of the drive shaft, as indicated in Fig. 1.

### Operating Conditions.

The turbine is operated at engine-representative corrected conditions, matching the corrected speed, stage pressure ratio, and flow function. Coolant-to-core massflow ratios are provided (the core flow is defined as the massflow at the turbine inlet) for each circuit. The experiment also featured a run at a lower turbine inlet temperature (TIT), reducing the freestream-to-metal temperature ratio. Table 1 provides these nominal operating conditions, as well as a range (defined as twice the standard-deviation of run-to-run variation).

Table 1

Summary of turbine operating conditions

ParameterValue
Corrected speed (rpm)9640 ± 660
Total-to-total pressure ratio3.457 ± 0.093
TOBI coolant/core (%)8.64 ± 0.40
Aft purge/core (%)0.516 ± 0.027
TIT/Tmetal1.836 ± 0.012
ParameterValue
Corrected speed (rpm)9640 ± 660
Total-to-total pressure ratio3.457 ± 0.093
TOBI coolant/core (%)8.64 ± 0.40
Aft purge/core (%)0.516 ± 0.027
TIT/Tmetal1.836 ± 0.012

The static temperature and pressure measurements that are taken at midspan of several of the serpentine passages are used as boundary conditions in a model that calculates coolant temperature, pressure, massflow, and other parameters as a function of span by accounting for frictional losses, centrifugal pressure loading, heat transfer, and other effects. The modeled pressure and density at the span of each cooling hole is combined with the static pressure on the airfoil at that hole's exit (as predicted by the accompanying computational prediction) to determine massflow out of each of 101 cooling holes. More details on the setup of the model and a detailed analysis of its results are the subject of a separate paper by Nickol et al. [24].

Cooling flows are quantified using the coolant-to-freestream massflux ratio, typically referred to as the blowing ratio; however, both massfluxes can be defined in different ways. Because the fan and advanced-shape holes increase in cross-sectional area, the massflux at hole exit is less than that at the hole inlet. Using the hole-exit massflux would result in a lower blowing ratio for those holes, despite ejecting the same magnitude of coolant (this is actually one of the reasons commonly attributed to the increased performance of diffuser-shaped holes, as originally suggested by Goldstein et al. [1]). For this paper, the massflux at hole inlet will be used in the definition of blowing ratio, as is typical in the literature, and to keep blowing ratio from being a function of cooling hole geometry.

The freestream massflux also varies greatly across the airfoil. Thus, blowing ratios are provided in two forms. The first is a “global” average freestream massflux (Eq. (2)), defined as the core massflow divided by the choke area. The second is a “local” freestream massflux (Eq. (3)), as predicted directly above the boundary layer for each hole by the computational prediction. The local blowing ratio is the physically relevant parameter for the cooling flow physics, but obscures the respective ejection rates. For example, row F ejects a significantly higher massflux than any other row (as evidenced by its greater global blowing ratio), but it has far from the greatest local (physical) blowing ratio due to the high freestream massflux where it ejects. Table 2 presents the average local and global blowing ratios for all holes in each row, as well as the minimum and maximum local blowing ratio for any given hole in each row to show the variation in ejection rates for each row. This variation within one row is large near the leading edge (rows B–D), mainly due to high variation in freestream massflux. At low span, the stagnation point is near row D, resulting in a very low freestream massflux and thus very high blowing ratio. At higher spans, the stagnation point moves toward rows C and B, causing their blowing ratios to increase due to lower freestream massflux, while the opposite occurs for row D. This results in blowing ratios varying within a single row by a factor of three in some cases. A detailed analysis of these cooling results, as well as the effect of varying the total supplied coolant flow, is provided by Nickol et al. [24]

Table 2

Summary of coolant blowing information for each cooling row

Cooling rowMinimum BRLocalAverage BRLocalMaximum BRLocalAverage BRGlobal
A1.071.351.461.93
B1.602.884.142.22
C1.513.095.292.37
D1.462.624.742.36
E1.011.151.242.29
F1.171.201.222.71
G1.231.281.382.31
Cooling rowMinimum BRLocalAverage BRLocalMaximum BRLocalAverage BRGlobal
A1.071.351.461.93
B1.602.884.142.22
C1.513.095.292.37
D1.462.624.742.36
E1.011.151.242.29
F1.171.201.222.71
G1.231.281.382.31
$BRGlobal=ρu|hole inletρu|avg=m˙holeAhole,inletm˙coreAchoke$
(2)
$BRLocal=ρu|hole inletρu|local=m˙holeAhole,inletρu|local$
(3)

### Experimental Uncertainty.

The pressure transducers are all calibrated in situ against a high-accuracy Heise digital pressure transducer by pressurizing the facility dump tank at various times throughout the experimental matrix. Their calibration accuracies were found to be within ±0.7 kPa (±0.1 psi) for each calibration and within ±1.4 kPa (±0.2 psi) for repeatability throughout the matrix, corresponding to an experimental uncertainty of 0.40% of the rig total inlet pressure.

The exact locations of the pressure transducers are also subject to some uncertainty, equal to about ±0.55% wetted-distance. While this does not increase the uncertainty in the pressure value, it is important when comparing the data to CFD to confirm good agreement. Its approximate contribution to uncertainty is shown in Eq. (4). The greatest value of pressure gradient on the blade is used (excluding the leading edge, which is subject to very high pressure gradients, but no pressure instrumentation) to be conservative, and this comes to another 0.24% of total inlet pressure, resulting in a final uncertainty value of 0.47% of inlet total pressure
(4)

The data reduction process for the two-sided Kapton heat-flux gauges is much more complicated, and consequentially the uncertainty propagation is as well. Additionally, the uncertainty depends on the context. If one is focused on determining the shape of the unsteady wave form (or amplitude of variation), one only needs to consider the relative error due to changes from a known starting point. This is significantly smaller than the absolute error that governs comparisons between gauges that is commonly used for time-averaged plots. A detailed explanation of the data reduction process and its corresponding uncertainty analyses for both average and time-accurate heat-flux is described for a similar experiment by Nickol et al. [18] and will not be repeated here, but the final values are shown in Table 3.

Table 3

Summary of experimental uncertainty values

Type of measurementUncertainty
Pressures±0.47% inlet pressure
Time-average Stanton number±0.43 × 10−3
Time-accurate Stanton number±0.053 × 10−3
Type of measurementUncertainty
Pressures±0.47% inlet pressure
Time-average Stanton number±0.43 × 10−3
Time-accurate Stanton number±0.053 × 10−3

## Computational Setup

A steady 3D RANS prediction of the stage is performed to compliment the data. A picture of the computational domain is provided in Fig. 7. The domain begins approximately one vane-chord upstream of the stator and includes the stator, rotor, an outlet section (about one blade-chord long), and both the aft purge and rotor cooling passages. The tip gap region between the rotating blade tip and stationary shroud is also included. The rotor cooling passage (see Fig. 7) splits early into two directions: either up a labyrinth seal and to become forward purge flow or into a plenum that feeds the rotor film cooling at the hub of the blade. The entire serpentine passage system is also fully meshed, complete with turbulators and every film-cooling hole. The full domain consists of 5.7 × 106 polyhedral cells, in addition to six layers of prism cells around all solid boundaries to resolve the boundary layer. A mesh sensitivity study was performed before the experiment using approximate boundary conditions.

Fig. 7
Fig. 7
Close modal

The mesh and solver used are both star-ccm+. The computation utilized a k–ε turbulence model and uses a mixing plane approach at the interface midway between the stator and the rotor. Maximum y+ values throughout the domain are approximately 3, with the majority of the domain lower than 2. One vane and one blade are each meshed and solved, with a periodic boundary condition on their pitchwise boundaries. Total inlet pressure and temperature, as well as flow angle, are defined at the stator inlet according to the experimental measurements, with both of the coolant inlet boundary conditions being defined based on the experimentally measured massflow rates. Inlet turbulence conditions are taken from prior experiments using the same facility. The exit boundary condition is static pressure, also based on experimental measurements.

The final simulations presented here were run for 200,000 iterations to reach full convergence. This is an unusually high number of iterations, however, it was found to be necessary for convergence within the serpentine passages. Originally, the simulation was set for 5000 iterations, based on previously determined best practices from Honeywell for uncooled turbines, and this was falsely validated by observing that each overall domain-totaled residual (mass, momentum, energy, etc.) stopped dropping at around 4000 iterations. However, a small minority of cells in the domain (all within the serpentine cooling passages) continued to change in a consistent manner as more iterations were performed. After extensive trials, it was found that 200,000 iterations were required for the serpentine passage cells to converge; however, these cells made up a sufficiently small minority of total cells that the random fluctuation in residuals due to machine accuracy in the rest of the domain dominated the domain-totaled residual.

It should be noted that the computational methodology used for this simulation has some limitations (for example, it neglects time-resolved and unsteady phenomenon), but it is typical of a simulation used in an industry design-phase of actual turbomachinery.

To compare CFD results to the data, the CFD cells are put into “boxes,” each from 40% to 60% span, and extending 2% WD long. All cells falling within each box are grouped, and their area-weighted average, minimum, and maximum values are plotted. The minimum and maximum values are presented to give a range for the comparison to data for two reasons. First, the exact span value for the gauges varies from about 40% to 60%. Second, the heat-flux gauge sensing elements are a square with length about 0.040-in. (1.0 mm, or about 2% span), and they provide the average value across that square. The cooling hole pitch (spanwise gap between adjacent holes) is about twice that size, meaning that exact location of said gauge with respect to the upstream cooling jet can have a significant effect on the film coverage, and therefore the heat-flux at that location. Figure 8 shows a contour plot of the CFD heat-flux, with sample boxes shown in white dotted lines (boxes not to scale). The figure also shows the strong spanwise gradients in surface heat-flux downstream of each coolant jet that form as a result of nonuniform coolant coverage.

Fig. 8
Fig. 8
Close modal

## Time-Averaged Results

Figure 9 provides the midspan static pressure CFD and data for the airfoil, with all pressures normalized by the turbine inlet total pressure. Data come from two blades, one with round holes, and one with fan-shaped, although the cooling hole shape has no consistent trend on the static pressure. Nonetheless, both measurements are presented where possible. The CFD is presented with the average, maximum, and minimum value for each wetted-distance as was described by the boxing method, although there is not a large spanwise variation in pressure between 40% and 60% span. The CFD presents good agreement on the pressure-side until the trailing edge, where it over-predicts the data. A large disagreement comes on the suction side near the leading edge. As the turbine is transonic, this area is likely seeing an unsteady shock, and the steady computation puts the shock upstream of this location. The remaining data on the suction side are over-predicted, getting worse moving toward the trailing edge, likely a consequence of the prediction placing the shock upstream of where its true average location is.

Fig. 9
Fig. 9
Close modal

Figure 10 presents the time-averaged Stanton number for each gauge with different symbols for each film-cooling hole shape and the uncooled blade along with corresponding CFD results for the four cooling schemes. Data from all available gauges are plotted together regardless of the spanwise position. The locations of the film-cooling rows are indicated by vertical lines, with dotted lines representing holes that are cylindrical for all blades, and solid lines corresponding to rows featuring the shaped holes.

Fig. 10
Fig. 10
Close modal

The data show significant spread at any given location, even among gauges seeing the same shaped cooling hole. This is due both to experimental uncertainty, and the spanwise variation in heat transfer caused by the discreet nature of the film-cooling jets. The cooled gauges at about −25% WD are upstream of any shaped hole, so the results here will not show any variation due to hole shape and can be used as a sort of control to show spread due to the other phenomenon. With few exceptions, the cooled experimental Stanton numbers fall between the uncooled and cooled Stanton numbers predicted by the CFD, suggesting that the computation over-predicts the effectiveness of the coolant in reducing heat transfer into the airfoil.

The higher Stanton number observed for the uncooled blade appears to agree well with the uncooled prediction over much of the pressure and suction surface, with the biggest excursions occurring near the trailing edge on the suction side, consistent with the biggest region of concern observed for the pressure distribution in Fig. 9.

Shortly downstream of the shaped row on the pressure-side, the data seem to show the round hole outperforming the advanced-shape, but this may be a misleading pattern because the advanced gauge is slightly further downstream of the round gauges, and the Stanton number is increasing moving toward the trailing edge at this location. Further downstream, the advanced-shape Stanton number drops quickly and is seen to outperform the fan shape, but the difference is fairly small. The CFD on the pressure-side shows relatively little variation among the three cooling hole shapes. There is a small trend showing the advanced-shape to have superior performance immediately following the cooling holes, with the fan-shaped holes performing better further downstream, and the round holes performing the best at a further distance, but the difference in their average performance is small, especially when compared to the significant difference between the uncooled prediction and any of the cooled computations.

On the suction side downstream of the final row of cooling holes, the advanced-hole blade has two gauges with a very low Stanton number, and two more gauges showing a much higher Stanton number a short distance further downstream. This is consistent with the computation for the advanced-shaped row, which also shows a very low Stanton number followed by a quick spike up in heat transfer after this row of holes, although the exact location and magnitude of this spike are not predicted well. The fan-shaped rows demonstrate a slow climb in Stanton number downstream of this row, which is seen both in the data and CFD. The round-hole data appear relatively flat in this region, and the round-hole prediction is also flatter than the other two.

At the furthest downstream measurement location on the suction side, the data show the advanced-shape producing the lowest Stanton number, with the cylindrical and fan-shaped performing similar to each-other, but with a greater heat transfer than the advanced-shape. The computation predicts different results, with the advanced-shape clearly resulting in the greatest Stanton number, although as with all of the locations on the blade, the difference between cooling hole shapes is relatively minor and difficult to distinguish from uncertainty. The computation predicts a relatively small difference in average surface heat transfer between the different cooling hole shapes, but the spanwise extremes in Stanton number produce more noticeable differences.

Figure 11 shows the minimum, average, and maximum predicted Stanton number for spans between 40% and 60% for each cooling hole type. It also presents the experimental data from every spanwise location at a given wetted-distance.

Fig. 11
Fig. 11
Close modal

There are some very large jumps in maximum and minimum Stanton number immediately at each row of cooling holes. For the most part, these are extremely local phenomenon (within one hole-diameter of the hole), which is why the axes are not expanded to show their peaks. The minima are usually located within a cooling hole and are negative (heat transfer out of the metal). The maxima are usually just to the side of a cooling hole.

Further away from a cooling hole, the Stanton number becomes more uniform and the minimum and maximum Stanton number curves get closer, but the hole shape plays some role in how quickly this occurs. The cylindrical and fan-shaped holes behave fairly similarly, but the advanced-shape hole maximum Stanton number is significantly greater than the other two hole shapes after the shaped row on the pressure and suction sides.

## Time-Accurate Results

Time-accurate results are presented in the form of ensemble-averages. An encoder fixed to the rotor shaft precisely measures the position of the rotor in time, and this information is locked to the simultaneously sampled heat-flux and pressure data. The encoder measurements are used to select data from exactly four rotor revolutions, and each revolution is broken into 24 periods corresponding to a rotor blade passing one of the 24 vanes. This produces a total of 96 vane-passing periods for the selected data window. The data from these 96 vane passes are then collapsed into a single passage and ensemble averaged into a single representative signal. For the purpose of visualization, this ensemble average is repeated and shown twice in succession when plotted. The phase alignments of these ensemble-averages have been corrected to account for the position of the blade in the rotor. More detail on the ensemble averaging process is provided by Nickol et al. [18].

In order to develop a basic understanding of these plots, it is helpful to first review the ensemble-averages of heat-flux gauges located at midspan on the pressure and suction surfaces of the uncooled blades, as shown in Fig. 12. Each of these plots presents the ensemble averaged Stanton Number for multiple gauge locations multiplied by a factor of 1000. The horizontal axis represents the movement of the gauge across two full vane passages. Figure 12(a) shows the ensemble-averages for heat-flux gauges on the suction side of the blade. The plot colors start with red at the leading edge gauge (7% wetted-distance) and transition through the spectrum moving toward the trailing edge gauge (91% wetted-distance). It is clear that as the high-temperature air between the vane wakes impinges on the blade, it causes a large increase in Stanton number at the leading edge. This peak quickly propagates downstream with the movement of the blade and creates a smaller peak at 20% wetted-distance, followed by peaks at 30% and 55% wetted-distance. Less fluctuation is observed at 91% wetted-distance because the wake-cutting behavior of the rotor interrupts this stream of higher-enthalpy fluid, allowing it to be carried away downstream without attaching to the aft portion of the suction surface.

Fig. 12
Fig. 12
Close modal

Instead, this slug of high-temperature fluid tends to impinge on the pressure surface, causing generally higher levels of unsteady fluctuation over most of the pressure surface, as shown in Fig. 12(b). As in part (a), this plot shows the ensemble averaged heat-flux propagating down the blade from the leading edge gauge at −13% (in red) through the spectrum to the trailing edge gauge at −80% wetted-distance (in blue). Again, the peak in Stanton number is first observed by the gauge at −13% wetted-distance. However, as the peak sweeps downstream, it grows in magnitude at −35% and −58% wetted-distance before dissipating slightly at −80% wetted-distance. This shows that the hotter gas from the vane midpitch is able to impinge on the blade pressure surface as the blade cuts through the stream.

To gain a broader perspective on these sweeps of high-temperature fluid and to compare their impact on different cooling configurations, it is necessary to create a plot that focuses on the phase shift between maximum values from one gauge to the next. Figure 13 presents the vane-passing position of the maximum value of the ensemble average observed for each gauge location plotted against wetted-distance. As an example, it is helpful to consider the ensemble average plotted in Fig. 12(b) for the gauge at −35% wetted-distance (represented by orange squares). Here, the maximum value occurs at a vane passing of 0.35, as indicated by the arrows. Thus, the data point for this gauge is plotted in Fig. 13 at −35% wetted-distance with an offset value of 0.35 (again indicated by arrows).

Fig. 13
Fig. 13
Close modal

This plot clearly shows that the first peak values are observed at the leading edge and then sweep backward over the airfoil surface, regardless of the cooling configuration. The peak moves consistently across the pressure surface within a single vane passing, but the aft gauges on the suction side with offset values greater than one will still be experiencing the Stanton number peak when a new sweep begins again at the leading edge. The suction side also shows a less consistent progression, as the Stanton number peak is delayed in reaching the first gauge but then sweeps rapidly over the aft portion of the blade where the flow is accelerated.

Figure 13 also highlights a few regions where the sweep behavior is less consistent or produces unexpected results, such as the wide range of offset values observed for gauges at −25% wetted-distance and 55% wetted-distance. A more detailed investigation of the ensemble-averages for these two locations shows that there are two primary causes for these deviations: radial migration on the pressure surface and variation in blade incidence angle. As it turns out, these instrumentation locations are installed on common blades; the grouping of gauges at −25% wetted-distance on the pressure surface is installed on the same blade as the 55% wetted-distance gauges on the suction surface for each blade type. These locations are illustrated by the inset pictures contained in Fig. 14.

Fig. 14
Fig. 14
Close modal

As in Sec. 4, the plots in Fig. 14 and the rest of the paper use a color scheme to represent the type of blade cooling scheme, with blue representing the advanced-shape hole, green representing fan-shaped holes, red representing cylindrical holes, and black representing uncooled blades. Additional colors may be utilized to distinguish between two blades of the same cooling geometry. At the same time, the shapes used for each line indicate the radial position of the gauge, with circles used for the innermost gauges, squares used for the middle gauges, and diamonds used for the outermost gauges.

The effect of radial migration is clearly evident in Fig. 14(a). This gauge location is downstream of the showerhead cooling holes, which have cylindrical hole shapes on every blade type. Temporarily ignoring the round holes in red, the first peak value is detected by the innermost gauge on the fan-shaped hole (represented by green circles) at a vane passing of just 0.1. It appears that the advanced-hole blade lags this peak, but it is important to recognize that the innermost gauge is missing from the advanced-hole blade and that the first blue line is actually for the middle gauge location. This actually aligns well with the middle gauge from the fan-shaped blade with peaks at a vane passing near 0.2. The final trace from the advanced-hole blade comes from the outermost gauge (represented by the blue diamonds). This is a consistent trend observed at all midspan locations on the pressure surface, with disturbances appearing first on the gauges closer to the hub then moving outward. This is consistent with the flow directions indicated by the CFD prediction in Fig. 8, which shows significant radial migration from approximately 20% span to near 75% span.

The case of the round cooling hole blade in Fig. 14(a) requires more detailed consideration. The only data for the pressure surface come from the outermost gauge location, but the maximum value still lags the outermost gauge on the advanced-hole blade by a considerable amount. Fortunately, there are also data from the suction surface of the blade to complete this picture.

Figure 14(b) shows measurements from heat-flux gauges at 55% wetted-distance on the suction surface of the same blades used in part (a), with the addition of two more gauges from a duplicate location on a second round-hole blade (blade #5, represented in pink). This plot shows that on the suction surface, there is not much radial migration near midspan, so the maximum value of Stanton number occurs at nearly the same vane-passing position for every blade type and all three radial gauge locations. The exception to this is the data from the round-hole blade plotted in red (blade #4), which is on the same blade as the round-hole pressure surface gauge plotted in part (a).

Considering Figs. 14(a) and 14(b) together, it is clear that the red trace lags the other blades on the pressure surface and leads them on the suction surface. This indicates that the incidence angle for this blade is slightly different, and the stagnation point has shifted toward the pressure surface. Because of this shift, disturbances have a shorter distance to travel on the pressure surface and a longer distance to travel on the suction surface. This does not appear to be caused by the cooling hole shape, since the other round-hole blade did not experience a similar shift. The data also indicate that a similar change of incidence angle likely occurred for the suction side gauges on the fan-shaped hole blade at 75% wetted-distance, but there is not enough data on the pressure-side of those blades to prove it.

Based on this information, it seems most likely that these changes in incidence angle are due to manufacturing variation or slight shifts in the assembled position of the rotor. It would not take much of a geometry change to alter the incidence angle and cause more significant effects downstream.

There is actually still more going on at the 55% wetted-distance location. In order to avoid having too many lines on the graph, the previous analysis did not include data from a second advanced-hole shape blade that has two more gauges at the same wetted-distance location. Figure 15 presents data from both of the advanced-hole shape blades (represented by different shades of blue) along with data from the fan and cylindrical hole blades (blade #5 only) and the uncooled blade. Once again, it is clear that all of the blade hole types agree relatively well except for the middle gauge of the advanced hole (blade #18). The trace for this gauge is shifted 0.3 vane passages from the other blades and from its neighboring gauge on the same blade. This rules out radial migration and changes in the blade incidence angle. Instead, it points to a local disturbance causing this phase shift for a single gauge.

Fig. 15
Fig. 15
Close modal

Because the gauges are downstream of a row of shaped cooling holes, it is possible that this is the effect of a higher level of cooling coverage than is reaching the other gauges. The prediction shown in Fig. 8 shows that cooling coverage is expected to be very streaky. This is also true on the suction surface, making it possible for cooling to impact one gauge but not its neighbor. While there is not enough information to definitively identify this as the effect of cooling, this theory is supported by the lower average Stanton number of the shifted gauge. It could also be possible that rather than leading the other gauges by 0.3 vane passages, this gauge is trailing by 0.7 passages. This could be caused by the lower momentum cooling flow and the thicker boundary layer delaying hot fluid from affecting the gauge.

Figure 15 also provides an interesting comparison of the difference between the cooled and uncooled blades. Based on the reduction in time-averaged Stanton number observed with the introduction of cooling in Fig. 10, one might expect that the ensemble average would simply show a DC offset between similar waveform shapes. However, Fig. 15 shows that the maximum values for every blade type are relatively consistent, but changes in the minimum value are actually responsible for the reduction in average value. This indicates that the cooling does not provide a uniform benefit over an entire vane period and that it is critical to understand the significance of unsteady interactions for new cooling designs.

## Conclusions

The static pressure and heat transfer into the airfoil at midspan of a cooled rotating transonic turbine blade have been measured experimentally and compared to a steady 3D RANS CFD prediction. Both experiment and prediction investigated three different cooling hole shapes at identical engine-representative conditions. The computation predicts the external pressure field of the turbine on the pressure-side but struggles to capture the pressure field on the suction side, likely due to the steady computation being unable to capture the effect of the unsteady shock.

Likewise, the experiment and computation both show a significant decrease in heat transfer on the cooled blades. In comparing the different hole shapes, the fan-shaped hole appears to perform about the same as the cylindrical cooling hole, and the advanced-shaped hole offers a small performance advantage. The time-accurate Stanton number results show that these results are strongly impacted by radial migration on the pressure surface, and that even small variations in blade geometry can have a significant impact on flow behavior. They also show that the time-averaged reductions in Stanton number due to cooling are not achieved universally throughout the vane passage. These findings demonstrate the importance of investigating cooling designs in realistic environments that include the complexity of unsteady interactions and heavily skewed inlet flows.

## Acknowledgment

The authors would like to thank Honeywell Aerospace for providing the engine hardware and much of the funding for this experiment. Further funding was provided by the U.S. Army through the AGGT program, and the U.S. Federal Aviation Administration (FAA) through the CLEEN program. In addition, the Gas Turbine Lab technical staff including Jeff Barton, Ken Fout, Igor Ilyin, and Jonathan Lutz were essential in the design, building, and instrumenting of the rig. Finally, we would like to thank students Hannah Lawson, Tim Lawler, Chris Cosher, Matt Tomko, Miles Reagans, Eric Barbe, and Kevin McManus for their help in setting up of the experiment.

## Nomenclature

• $Ach$ =

turbine choke area

•
• $BR$ =

blowing ratio

•
• $e$ =

uncertainty

•
• $m˙$ =

turbine core (inlet) massflow

•
• $St$ =

Stanton number

•
• $u$ =

fluid velocity

•
• $ρ$ =

fluid density

•
• $%WD$ =

percent wetted-distance

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