## Abstract

The betterment of turbine performance plays a prime role in all future transportation and energy production systems. Precise uncertainty quantification of experimental measurement of any performance differential is therefore essential for turbine development programs. In this paper, the uncertainty analysis of loss measurements in a high-pressure turbine vane is presented. Tests were performed on a stator geometry at engine representative conditions in a new annular turbine module called BRASTA (big rig for annular stationary turbine analysis) located within the Purdue Experimental Turbine Aerothermal Lab. The aerodynamic probes are described, with emphasis on their calibration and uncertainty analysis, first considering single point measurement, followed by the spatial averaging implications. The change of operating conditions and flow blockage due to measurement probes are analyzed using computational fluid dynamics, and corrections are recommended on the measurement data. The test section and its characterization are presented, including calibration of the sonic valve. The sonic valve calibration is necessary to ensure a wide range of operation in Mach and Reynolds. Finally, the vane data are discussed, emphasizing their systematic and stochastic uncertainty.

## 1 Introduction

Current trends toward compact turbomachinery for high-speed propulsion and power generation lead to low aspect ratio airfoils, causing large secondary flow structures. Understanding the behavior of these secondary flow structures and their interaction becomes pivotal for predicting turbine performance. Detached flows remain a challenge for commercial computational fluid dynamics (CFD) solvers employed during the design phase; therefore, experimental data are required to anchor the turbulence models in Reynolds-averaged Navier–Stokes (RANS) and unsteady Reynolds averaged Navier–Stokes simulations. The need for extensive high-fidelity experimental data has motivated efforts over the past years to enhance accuracy in exploratory testing at engine-representative Reynolds and Mach, while respecting engine temperature ratios.

Hardware limitations often constrain the range of testing conditions, duration of the experiments, and measurement techniques development. Continuously operating facilities are often considered the gold-standard for performance measurements [13]. However, they are ill-suited to replicate the heat transfer of the engine, which justifies the development of short-duration facilities [46]. The Purdue Experimental Turbine Aerothermal Laboratory [7] allows continuous or long-duration testing for efficiency measurements and short transient testing for heat transfer measurements, together with multiple access locations for optical measurement techniques. Numerical simulations have been proposed to define experiment requirements to characterize the flow field within a designated time and spatial resolution [8]. Previous research has documented which measurement resolution is sufficient to reconstruct the turbine loss mechanism [9,10]. This process is used to assess a given geometry's performance and perform a back-to-back comparison of geometries. Furthermore, experiments are still needed to evaluate numerical tools [11].

In this paper, the experimental methodology to characterize the flow field in a vane row of a high-pressure turbine is presented, along with the sources of uncertainty and their propagation in the calculation of derived quantities. The results include static pressure, total pressure, and flow angle measurements of a state-of-the-art gas turbine. The vane row was tested in a modular test section within big rig for annular stationary turbine analysis (BRASTA). The sources of uncertainty are budgeted, and the experimental data are presented. The paper presents the annular cascade design, and the contribution of the facility operation to reduce measurement uncertainty is highlighted. A combination of numerical tools and good experimental practice is presented to provide a comprehensive quantification of the measurement uncertainty.

## 2 Measurement System

### 2.1 Probe Design.

Probe geometry design is heavily influenced by the conditions at the measurement plane. Kiel head rakes and five-hole rakes were used downstream of the vane for spatial traverses of total pressure and flow angle, respectively. A 12-head total temperature rake, Kiel rakes, reference Kiel probe and a hot wire probe were used at the annular cascade inlet. Pictures of these probes are shown in Figs. 1(a)1(c). The reference probe was used to account for test to test variability and variability during an individual test. The 12-head facility inlet probes and the nine-head probes just upstream of the vanes give a spatial resolution of 6.1% and 11.5% of span.

Fig. 1
Fig. 1
Close modal

The traverse rakes were designed and built in-house to provide sufficiently high spatial resolution. They were designed using the practices outlined in Ref. [12] and proven experience [10,13]. The shields for the rakes maximize total pressure recovery and reduce the angular sensitivity. Probe calibrations showed angular insensitivity of −20 deg to 20 deg in the lateral and radial directions.

Pressure recovery is also corrected through calibration at different Mach numbers against a reference through-shield Kiel probe. For the exit plane, three, nine-head Kiel rakes were used, as shown in Fig. 1(a), with the heads 5.4 mm apart. The probes were moved with a traverse system, with a radial step of 2.7 mm. The hot wire probe data are conditioned using the test conditioning system from AA Lab Systems Ltd., which provides high accuracy and high signal-to-noise ratio [14]. The temperature rakes are designed with side-vented shields. K-type thermocouple sensors are used along with a VTI thermocouple measurement system.

Five-hole probes were used for flow angle measurements with the design shown in Fig. 1(d). The heads have a hemispherical shape with the lateral holes located at 60 deg, relative to the axis. Three heads per rake were selected to minimize the probe blockage while still providing adequate space for 0.305 mm pressure lines. Pressures lines of this diameter were selected for rapid probe response.

### 2.2 Probe Calibration.

The Kiel probes were calibrated to characterize the total pressure recovery and yaw angle sensitivity. The five-hole probes were calibrated to relate the pressure readings to the flow angles using the pressure coefficient approach described in Ref. [15]. Calibrations were carried out at the Purdue Experimental Turbine Aerothermal Laboratory (PETAL) using the LEAF facility (Linear Experimental Aerothermal Facility), shown in Fig. 2(a). The LEAF facility consists of a settling chamber, the linear test section, and a sonic valve to set the Mach number inside the test section. The details are documented in Ref. [7].

Fig. 2
Fig. 2
Close modal

The probe to be calibrated is compared against two reference Kiel probes. Moreover, two reference thermocouples are used to compute the flow conditions. The probes are calibrated at engine-representative Mach and Reynolds. The sonic valve position is adjusted to achieve the selected Mach during the test, while the valves upstream of the tunnel set the Reynolds.

A radial and yaw traverse system is mounted on top of the test section for the angular sensitivity characterization. The system uses stepper motors to rotate the probe in yaw at a fixed axial and radial location. A robotic arm is used to turn the traverse system along with the probe in the pitch-wise direction. Figure 2(b) shows the experimental setup for the five-hole probe's calibration at 0 deg yaw and 0 deg pitch angle. During the calibration process, the probe angle is measured relative to the probe frame of reference, eliminating the need to correct the calibration angles to the test rig angles [16].

### 2.3 Pressure Probe Performance.

The robotic arm rotated the Kiel probes ±40 deg in yaw during the calibration. The shield desensitizes the flow angle influence on the pressure, yielding negligible effects within ±15 deg. This range is within the angle variations predicted during the current test campaign. The measurement probes dynamic performance is also assessed to determine the dwell (waiting) time at each traverse location. A pressure step is generated for each head of the rake using a balloon [17]. The balloon is pressurized and then popped, causing a step change in pressure. The response is recorded as the measurement returns to ambient pressure. The time to reach 99% of the steady value is on average 0.42 s, inferring a minimum dwell time of at least 0.6 s. The experiment was done with a dwell time of 7 s, and the last 2 s are averaged.

The five-hole probes were calibrated between −15 deg and 15 deg in yaw and pitch. The following coefficients were extracted from the calibration and were used for the computation of the measured angles, as described in Ref. [16]:
$Pavg=mean(P1,P2,P3,P4)$
(1)
$Cpv=P2−P4P5−Pavg,Cpw=P1−P3P5−Pavg$
(2)
$Cp0=P5−PsP0−Ps,Cpavg=Pavg−PsP0−Ps$
(3)

### 2.4 Hot Wire Calibration.

The hot wire was also calibrated in the LEAF facility. The methodology is outlined in Ref. [14]. From the calibration, the uncertainty in the velocity measurement is 4.23%. The overheat ratio was set to 1.3.

### 2.5 Pressure Sensor Performance.

Pressure scanners from Scanivalve Corp. (Liberty Lake, Washington, DC) were used to measure pressures in the test rig. Validation of the calibration was done at different pressure points. The reference pressure was measured with a Druck DPI 612 Pressure calibrator with an accuracy level of ±3.5 Pa. The errors were under the quoted rating, as shown in Fig. 3(a). The scanners have an error band of 26 Pa. All pressure scanners are zeroed to a reference reading of the rig ambient pressure with a 0.015% accuracy sensor. Figure 3(b) shows the drift of the mean pressure signal over the test flow duration, which is also incorporated in the bias uncertainty. The standard deviation changes depending on the pressure scanner channel, with an average value across all channels of 29.6 Pa. The total uncertainty on a pressure measurement on average is around ±63 Pa, computed from Eq. (4)
$ΔP=+−t95(B2)2+σ2$
(4)
Fig. 3
Fig. 3
Close modal

### 2.6 Uncertainty in Flow Direction Algorithm.

The angle from the five-hole probe is computed using interpolating functions that are dependent on the coefficients discussed in Eqs. (1)(3). These calculated angles suffer from uncertainty in the interpolation functions and uncertainty in the measured pressure used to calculate the coefficient map. First, the variation in the coefficients is assessed due to the uncertainty in pressure. The pressure signals are treated as Gaussian distributed signals with the mean value used for the calibration, and the uncertainty equals the standard deviation, as shown in Eq. (5). A Latin hypercube sampling (LHS) algorithm is used to uniformly sample the distribution and compute the mean and variance of the interpolation function coefficients. Convergence with variation of size of sampling for the LHS is shown in Figs. 4(a) and 4(c) for one calibration point
$P∼N(Pmeasured,ΔP)$
(5)
$Cp∼N(Cpmeasured,σcp)$
(6)
Fig. 4
Fig. 4
Close modal

The sampling of pressure values gives a mean value of the coefficients for that calibration point and the coefficient variance. The pressure is sampled assuming a normal distribution around the mean with the computed variance, as shown in Eq. (6) and then passed into the interpolation function. The mean and variance of the computed angle are determined, as shown in Figs. 4(b) and 4(d), respectively. The coefficient values mean and variance stabilize after ∼2000 samples, and the yaw angle stabilizes after ∼1200 samples. The advantage of this approach is that variation in the uncertainty in the pressure measurement can be propagated in the angle calculation. The interpolation functions were validated against the measured calibration angles by removing the validation point from the coefficient map and calculating the flow angles from the pressure measurements. The error between the computed and the measured angles are shown in Fig. 5(a) for both yaw and pitch. The maximum error is near 1 deg at the ends of the calibration map. The average error over the entire calibration range displayed in Fig. 5(a) is 0.2 deg. The variance in the angle prediction is shown in Fig. 5(b). It reaches a maximum value of 0.08 deg, with a standard deviation of 0.28 deg. Figure 5(c) shows the difference between the error in the prediction of the angle using LHS sampling and the error in prediction of the angle without using LHS sampling. In that case, the maximum error is 0.2 deg, with the average error less than 0.01 deg. For pressure uncertainty of the order of ± 60 Pa, the error in not assuming any uncertainty is less than 0.01 deg, which scales up with increasing pressure uncertainty.

Fig. 5
Fig. 5
Close modal

### 2.7 Probe Turbine Coupling Effect—Uncertainty.

In the test rig, both the measurement probes and the flow path geometry affect the flow field. The effect on the vane pressure profile by the placement of the measurement probes downstream is assessed using RANS simulations. Figure 6 depicts the numerical domain. The probe geometry is simplified as cylinders, and they are placed according to the traverse system geometry. The upstream convergent section and the downstream section are modeled together with four vane passages. The unstructured grid is built using Numeca HEXPRESS and solved with ansysfluent. Inlet boundary condition of one value of total pressure and temperature are imposed at zero pitch and yaw angles. The kω shear stress transport model is used for turbulence closure, and the turbulence is set at the inlet in terms of length scale and turbulent intensity, both measured in the test rig. The static pressure is imposed at the hub at the outlet section, and the distribution is calculated via radial equilibrium.

Fig. 6
Fig. 6
Close modal

Figure 7(a) shows the effect that probe blockage has on the pressure profile of the vanes. In this example, there is a notable deceleration near the trailing end, which results in a change in Cp of up to 0.05. To avoid this, the test article is designed to perform vane endwall measurements in a different sector, away from the traversing probes. The probe blockage effect on the Cp distribution also diminishes as the probes are moved farther from the trailing edge.

Fig. 7
Fig. 7
Close modal

Introduction of the probes into the flowpath also distorts the pressure field upstream of the probe. This effect is exacerbated in a transonic flow, in the vicinity of the endwall, leading to artificial pitch angle indication in the flow measurement, as shown in Fig. 7(b). To better understand this flow distortion, a series of RANS simulations were performed with the numerical domain shown in Fig. 8(a). A full five-hole probe geometry adjacent to the shroud is simulated in a passage downstream of the vane at three radial locations, near the shroud, midspan and near hub.

Fig. 8
Fig. 8
Close modal

Fig. 9
Fig. 9
Close modal

### 2.8 The Uncertainty Associated With Spatial Averaging Due to Tip Size.

The effect of discrete measurements on assessing the overall uncertainty in the averaged quantities was estimated using a methodology developed for a previous turbine program [8]. RANS CFD simulations were performed on the vane geometry experimentally evaluated in the annular facility (BRASTA). The CFD vane exit total pressure data were used to investigate the error between the total pressure contour that could be reconstructed from discrete experimental measurements versus the CFD result. The actual contour was assumed to be equal the RANS data. The CFD was sampled at the discrete experimental measurement locations and a contour was reconstructed based on information only from those points. Finally, the spatial discretization uncertainty was evaluated as the L2 error. The expression for this error is given in Eq. (7), where p0 true corresponds to total pressure values from the CFD contour and p0calc represents total pressure values from the contour reconstructed based on data at the experimental measurement locations. p0calc was obtained by averaging over the projected area of the Keil probe tube, at the discrete experimental measurement locations. This analysis for the five hole probe was not carried out
$L2= 100(p0 true− p0 calc)2p0 true$
(7)

When reconstructing the total pressure contour at the experimental locations, two effects were considered. These are the grid size and the Kiel tube diameter. Figure 10(a) represents two different grids superimposed. The blue one is coarser than the red one. It can be observed that the fine grid employs the points already present in the coarse grid and adds more in between those both in the radial and tangential directions. Figure 10(b) shows the effect of the probe diameter on its reading. When a probe is immersed in a flow, it averages over the area that it covers. Therefore, the larger the probe s diameter, the larger the area over which it averages the data. The sketch in Fig. 10(b) sketches the probe area (shaded) over a total pressure contour.

Fig. 10
Fig. 10
Close modal

Figure 11(a) represents the mean value of the total pressure discretization error downstream of the vane for the experimental grid size. Curves are presented for four different possible probe diameters. It can be observed that the error rapidly decays toward an asymptotic behavior when increasing the number of points in the experimental measurement grid. No major differences can be observed between the three lower probe diameters. However, the larger one features lower error values. Note that this is a mean value, taken over the complete contour under evaluation. Figure 11(b) shows the standard deviation of this discretization error, also taken over the complete domain. This value shows a similar behavior to that observed in the mean one. Although not directly represented here, larger probe diameters feature larger maximum values at the areas of large gradients as they average over a larger region.

Fig. 11
Fig. 11
Close modal

For the experiments performed in the present study, the experimental grid size had 270 points (18 radial and 15 tangential positions) and the Kiel probe of tube diameter 0.8 mm was employed. Figure 12(b) depicts the $L2$ error contour obtained. It features values of the order of 1% throughout most of the domain. The exception is found in the wake and near the shroud, for a pitchwise position near 1. The exception is found in the wake and the hub and shroud boundary layers. Looking at the normalized total pressure signature from CFD represented in Fig. 12(a), one can find that the higher spatial discretization error values found there are due to the higher total pressure gradients they feature.

Fig. 12
Fig. 12
Close modal

## 3 Annular Test-Section Characterization

The experiments were conducted in the annular wind tunnel BRASTA at PETAL. Figure 13 shows a schematic view of the facility. High pressure, dry air from 56 m3 storage tanks can be passed through the heater, diverted around the heater, or a mixture of the two streams can be used. When both streams are used, the streams are combined in a mixer, designed to deliver a uniform temperature flow.

Fig. 13
Fig. 13
Close modal

The flow is then passed through a calibrated critical flow venturi for accurate mass flow measurements. Further downstream, the flow can be diverted to the linear (LEAF) or annular (BRASTA) wind tunnel test section. The flow is straightened upstream of either test section using settling chambers that remove the large turbulent structures created by upstream components. Downstream of both test sections, a sonic valve is used to decouple the Mach and Reynolds inside the test section [18].

The BRASTA test section is designed with multiple plugs and windows located along the flow path. These allow access for optical and conventional instrumentation, as shown in Fig. 14(a). The test section has space claim for a single-stage turbine, allowing testing of stators and/or rotors in a stationary frame. Rotors can be mounted to a disk connected to a shaft with a mounted load cell to measure the torque. BRASTA is modular, allowing for multiple test configurations and convenient, rapid changing of the test articles. The rig includes four windows spaced across four sectors. These windows are used to route instrumentation and allow optical access for flow visualization, PIV, PSP, and IR thermography [19]. The test section also has three traverse slots at different axial locations downstream of the stator and/or rotor geometries test article. The traversing carriage is moved in the azimuthal direction with an industrial robotic arm, while two stepper motors control radial and yaw positions.

Fig. 14
Fig. 14
Close modal

Figure 14(b) shows a schematic of the inside of the test section and the instrumentation locations. Plane 0 is the inlet plane upstream of the struts, plane 1 is 35% Cx upstream of the vane inlet, and plane 1.5 is located 50% Cx downstream of the vane leading edge. Vane passages are machined with static pressure taps at the end walls. Plane 2 is downstream of the vanes and has end wall pressure taps and slots for downstream traversing. Plane 3 is upstream of the flow path dump, the downstream struts, and the sonic throat. The shroud endwall static pressures are positioned on the four instrumentation windows. The sonic throat also contains equally spaced circumferential pressure taps. The test section has RTDs embedded at the hub and the casing in planes 1, 1.5, 2, and 3 along with the outer casing. The test section is instrumented with a total of 311 sensors for performance measurements. For facility control, the sonic throat allows regulation of the Mach inside the test section, and the Reynolds is matched by the inlet mass flow to the facility.

The traverse system of BRASTA allows probes to move in the yaw, radial, and circumferential directions, as seen in Fig. 15. An aluminum carriage is mounted to BRASTA over the traverse slots. A brass carriage is then mounted to tracks on the aluminum carriage.

Fig. 15
Fig. 15
Close modal

The tracks allow the brass carriage to slide relative to the aluminum carriage in the circumferential direction. Dynamic O-rings provide sealing at the interfaces. The brass carriage has three azimuthal probe access locations at each of three axial planes. The stepper motors give a resolution of 0.003 mm in the radial direction and 0.015 deg in yaw. Potentiometers on the traverse system provide an incremental position feedback signal to a Wheatstone bridge. The design of the traverse system simplifies the calculation of the flow angle. Figure 16(a) shows the mounting of the five-hole probes inside the rig and Fig. 16(b) shows a two-dimensional projection of the angle measured by the probe with respect to the rig axis. To convert the probe readings to the actual flow angle, the correct reference frame must be used, as described in the methodology of Ref. [20]. The traverse design ensures that the probe is reading in the local flow radial frame of reference. The calibration performed in the absolute reference frame can be transferred to the measurement without any correction, as shown in Fig. 16(c).

Fig. 16
Fig. 16
Close modal

The annular test section performance was characterized with the vanes removed. The instrumentation planes were the same as those shown in Fig. 14(b).

### 3.1 Temporal Stability and Repeatability.

There are three modes of operation of the facility, first flowing through the heater (Hot), second bypassing the heater (Cold), and the third mixing the two streams (Mixed). Both flow lines have independent control valves, and all three modes of operation were characterized. Figure 17(a) shows the mass flow stability in all three modes of operation for 5 min of testing.

Fig. 17
Fig. 17
Close modal

Figure 17(b) shows the mass flow repeatability of the test section for the same target flow condition for three different tests executed over several days. The maximum variation between the tests is 0.2 kg/s. Figure 17(c) shows the temperature stability and repeatability for multiple test periods. In these cases, the target temperature was 505 K. A maximum deviation between tests of 3 K was achieved.

### 3.2 Tangential Uniformity.

Uniformity of the flow is assessed in the test rig to ensure that measurements from different sectors can be compared.

The test section was designed with circumferentially distributed pressure taps at different axial locations. The uniformity of the pressure at the hub at various axial locations is shown in Figs. 18(a) and 18(b) for two operation modes. The shaded region corresponds to the uncertainty computed as twice the standard deviation of the measurements, giving a 95% confidence value.

Fig. 18
Fig. 18
Close modal

### 3.3 Turbulence Characterization.

Turbine inlet turbulence levels were estimated using a hot wire following the methodology presented in Refs. [21] and [22]. Multiple inlet velocities were tested to obtain the variation in turbulence properties with inlet Reynolds, shown in Table 1. The turbulence intensity increases with Reynolds and then stabilizes around 6%. The dissipative length scale is computed to be around 3 × 10−3 m. The integral length scale is around 5x10−2 m, attributed to the dimensions of the flow straighteners and honeycomb within the settling chamber. The uncertainty in the calculation is 0.029%, 4.27% and 4.22%, respectively.

Table 1

Turbulence characteristics of BRASTA

Re/m (105)4.257.028.118.6711.413.1
$u¯$(m/s)4.569.4811.512.615.617.7
Tu (%)4.165.215.825.616.136.02
L int (10−2 m)3.404.983.714.815.055.87
Ldis (10−3 m)2.63.23.33.53.43.6
Re/m (105)4.257.028.118.6711.413.1
$u¯$(m/s)4.569.4811.512.615.617.7
Tu (%)4.165.215.825.616.136.02
L int (10−2 m)3.404.983.714.815.055.87
Ldis (10−3 m)2.63.23.33.53.43.6

### 3.4 Sonic Valve Calibration.

The sonic valve located immediately downstream of the test section was designed to cover an extensive range of mass flows, swirl angles, and pressures. The sonic valve enables the decoupling of Mach and Reynolds in the upstream test section. The area sensitivity of the valve is shown in Figure 19(a). The Mach sensitivity, based on the isentropic relations and assuming axial flow, is shown in Fig. 19(b). A 1-mm axial translation of the sonic valve yields a 0.01 variation in the Mach number when the valve is choked (below a position of 90%). Once the valve is opened enough to unchoke, the slope changes dramatically. The peak of valve sensitivity is at the end of its stroke, when the sonic valve area is equal to the test section area. At this point, the test section is at transonic conditions based on the isentropic calculations of area ratio.

Fig. 19
Fig. 19
Close modal

The sonic valve calibration is unique for each tested configuration since the swirling flow from the tested stator or rotor modifies the choking area. The calibration was performed in the first phases of the measurement campaign, targeting a given Mach number at the stator exit. The calibration was performed at three different mass flows and temperature conditions

Figure 20(a) depicts the variation of the Mach number at the exit plane with different sonic valve throat openings. By varying the opening area, variations from subsonic to Mach 1.0 can be achieved at nearly constant mass flow. Based on isentropic flow theory, the sonic valve has two positions that lead to the same Mach number value at the exit plane, as confirmed by the nonlinear behavior of the sonic valve. The swirl angle at the throat was found to oscillate between 55 deg and 65 deg, depending on the pressure conditions at the sonic throat. Increase of pressure in the test section leads to smaller swirl angles. Hence, the results observed in Fig. 20(a) are nonlinear. When the area in the valve is reduced, the flow chokes in the valve, and the Mach number upstream is defined by the area ratio between the test section outlet and valve critical area. In contrast, when the valve area is larger than the test section minimum area for a given mass flow, the Mach number in the test section is exclusively determined by the mass flow and the upstream pressure.

Fig. 20
Fig. 20
Close modal

All of the test results shown in the following section correspond to a fixed sonic valve position calibrated to achieve a target mass flow. The mass flow was selected to provide a specific Mach at the stator row exit.

## 4 Vane Performance Results

### 4.1 Vane Pressure Profile.

The vane geometry has static pressure taps at three different span locations. Figure 21 shows the scaled pressure profiles for the vane at each span for two different tests (labeled test 1 and test 2), as well as the locations of the static pressure taps at each span. The experimental pressure measurements are compared with RANS CFD results evaluated with boundary conditions based on the experiments. The CFD setup was described earlier in this paper. The maximum difference in P/P0 within the measurements from test 1 and test 2 is 0.0051, and the contrast with the CFD has a maximum value of 0.13. The previously estimated pressure uncertainty of 63 Pa leads to a relative uncertainty in calculating the Cp value of ±0.07%.

Fig. 21
Fig. 21
Close modal

### 4.2 Pressure Traverse.

Vane exit area traverses at plane 2 were performed using two nine head Kiel pressure probes. Measurements at twenty-seven radial positions and eleven different circumferential positions were gathered with two probes. This yielded 594 measurements with a grid of 418 locations since some measurement points overlapped between heads. The overlap acts as a check on the performance of every head. Figure 22 shows the radial distribution of the scaled pressure ratio at two different circumferential locations, one in the main passage and one in the wake. The uncertainty band is computed through calibration in the LEAF facility to obtain the pressure recovery.

Fig. 22
Fig. 22
Close modal

After correction for the total pressure recovery and the angle sensitivity, the total uncertainty is 0.002.

Figure 23 shows a contour plot of the scaled pressure ratio of the measurements taken. Lower pressures are observed in the vane wake region and in the endwall regions. The main passage is characterized by small pressure variations, with a maximum variation of 0.01 scaled pressure ratio. Measurements were also taken by another nine head total pressure probe in the mainstream of an adjacent passage to confirm passage-passage uniformity. The contour uncertainty, uncertainty in the contour due to spatial averaging, is shown in Fig. 23, with a maximum uncertainty of 1% of the pressure ratio from the contour interpolation. This error was calculated using an approach as the one shown in Eq. (7), however not taking into account the probe diameter, simply interpolating at the experimental locations. This interpolation was a cubic one, using the matlab built-in method “pchip.”

Fig. 23
Fig. 23
Close modal

### 4.3 Angle Traverse.

Two 5-hole probes were used to characterize one passage, with the third probe in the next passage. A measurement grid of 330 points was selected, using 15 radial and 22 circumferential positions. The variation of the static pressure is shown in Figs. 24(a) and 24(b) shows the total pressure from the Kiel probe and from the five hole probe at one circumferential location.

Fig. 24
Fig. 24
Close modal

As can be seen, due to the pressure distortion near the shroud, the static pressure is much lower. Accounting for the distortion gives a prediction of the static pressure that is in line with the trend of radial equilibrium. Figure 24(c) shows the yaw angle at one circumferential location from the five-hole probes compared to the throughflow solution. The measurements show significant under turning near the shroud that does not match the predicted trends. This is in line with what is observed for the radial Mach distribution. Accounting for the pressure distortion for the top head, the corrected angles show the same trend as the numerical predictions. The uncertainty on the angles has increased from an average of 0.1 deg to almost 4 deg. Quantification of this pressure correction with distance from the wall and flow conditions is an active research area among turbine laboratories focused on high-speed turbine testing. The angles extracted by blocking the holes for which pressure is distorted are also plotted, which shows a trend comparable to the throughflow.

### 4.4 Uncertainty.

From the five-hole probe traverse, the loss coefficient is computed as shown in Eq. (8)
$Yv=P01−P02P02−P2$
(8)

Here,$Yv$ is the total pressure loss coefficient, $P01$ is the inlet total pressure, $P02$ is the exit plane area-averaged total pressure, and $P2$ is the area averaged static pressure. The pressures for $Yv$ are area averaged for experimental simplicity [23]. Figure 25 shows the flow of uncertainty propagation for the computation of both the flow angle and the loss coefficients. The calibration and the experiment both involve pressure measurements, which are both independent with their own sources of uncertainty. The uncertainties are classified into bias and stochastic and each step has some sources of uncertainty that is added into the overall calculation. The uncertainty is propagated into the calculation through LHS sampling as discussed in Sec. 2.6.

Fig. 25
Fig. 25
Close modal
The uncertainty in the pressure measurement during the calibration is propagated into the calculation of the calibration coefficients along with the uncertainty in the measurement of the pitch and yaw angles. This gives an uncertainty in the coefficient, which is then used in the validation step, discussed in Sec. 2.6, to obtain the bias in the calculated angles and pressures from the measured value and the variance of the calculated values. The coefficients and the uncertainty from the validation are then propagated to the experimental processing where it is combined with the uncertainty from the pressure measurement into the calculation of the flow angles and pressure through the use of the calibration coefficients, see Eqs. (1)(3). This gives the spatial distribution of angles and pressures. To obtain the loss coefficient, the pressures need to be integrated using trapezoidal approximation (Eq. (9)) which has a bias uncertainty associated with it (Eq. (10)). The integration step also takes the uncertainty from spatial discretization, discussed in section 2.8, for 330 measurement points in one pitch. The total uncertainty and the mean uncertainty at each step are tabulated in Table 2. $Δ$ is the total uncertainty for a parameter computed as Eq. (4), $B$ is the bias uncertainty for the parameter, and $σ$ is the stochastic uncertainty. The uncertainty is propagated upwards to the uncertainty in $Yv$in Table 2
$I=(b−a)(f(b)−f(a))2$
(9)
$Et=−(b−a)312n3Σi=1nf″(ξi)$
(10)
Table 2

Uncertainty in derived coefficient

Parameter valueUncertainty
$ΔYv, %$5.9
$ΔP02 area averaged,%$2.57
$ΔP2 area averaged,%$2.58
$ΔP01 area averaged,%$0.008
$B(numerical integration),%$0.013
$B(spatial averaging),%$1.86
$ΔP2 total,%$3.57
$B(P2 bias calibration),%$2.41
$σ(P2 stochastic ),%$0.694
$σ(P2 stochastic calibration),%$0.692
$σ(P2 stochastic experiment),%$0.044
$ΔP02 total,%$0.11
$B(P02 bias calibration),%$0.081
$σ(P02 stochastic),%$0.0033
$σ(P02 stochastic from calibration),%$0.0030
$σ(P02 stochastic from experiment),%$0.0033
$ΔYawpressure correction, deg$4.2
$ΔYaw, deg$0.2034
$B(Yawbias calibration), deg$0.0869
$σ(Yawstochastic calibration), deg$0.0275
$σ(Yawstochastic experiment), deg$$3.7×10−7$
$ΔPmeasurement, Pa$63
$B(Pmeasurement bias), Pa$26
$σ(Pmeasurement stochastic), Pa$29.6
Total uncertainty$Yv, %$5.9
Parameter valueUncertainty
$ΔYv, %$5.9
$ΔP02 area averaged,%$2.57
$ΔP2 area averaged,%$2.58
$ΔP01 area averaged,%$0.008
$B(numerical integration),%$0.013
$B(spatial averaging),%$1.86
$ΔP2 total,%$3.57
$B(P2 bias calibration),%$2.41
$σ(P2 stochastic ),%$0.694
$σ(P2 stochastic calibration),%$0.692
$σ(P2 stochastic experiment),%$0.044
$ΔP02 total,%$0.11
$B(P02 bias calibration),%$0.081
$σ(P02 stochastic),%$0.0033
$σ(P02 stochastic from calibration),%$0.0030
$σ(P02 stochastic from experiment),%$0.0033
$ΔYawpressure correction, deg$4.2
$ΔYaw, deg$0.2034
$B(Yawbias calibration), deg$0.0869
$σ(Yawstochastic calibration), deg$0.0275
$σ(Yawstochastic experiment), deg$$3.7×10−7$
$ΔPmeasurement, Pa$63
$B(Pmeasurement bias), Pa$26
$σ(Pmeasurement stochastic), Pa$29.6
Total uncertainty$Yv, %$5.9

Tables 2 shows for this work, the uncertainty in $Yv$ is 5.9% of the computed value and the average uncertainty for the yaw angle without correction applied is 0.2 deg. When pressure correction is applied, the uncertainty with measurements close to the shroud can be as high as 4 deg. From the calibration, it is seen that the prediction of static pressure has greater uncertainty than the prediction of the total pressure. Static pressure at the probe location is not measured during calibration, and it is compared to a wall tapings, which leads to a more difficult validation. The current interpolation function needs to be improved to have better prediction of static pressure. The largest uncertainty source for the prediction of pressure, both static and total, at the measurement location is the accuracy of the interpolation function. For the given radial and circumferential increments, the numerical approximation is very close to the analytical solution, the largest source of uncertainty is that associated with spatial averaging. For further improvement in uncertainty, more measurement locations are needed or larger probe diameter though at the expense of lower fidelity for spatial gradients. The integration step also averages out the spatial variation of uncertainty and hence decreases the effect of the pressure correction uncertainty in the uncertainty of $Yv$, since the correction is only applied to points close to the shroud.

## Conclusions

A methodology was presented for evaluating uncertainty in vane performance measurements. The design of the measurement probes and its impact on the spatial and temporal resolution of the measurement was discussed. The pressure scanner performance and sources of uncertainty were discussed, as well as how that uncertainty is propagated in the calculation of derived quantities, like flow angle. For the scanners and probes used, a total 95% uncertainty of ±63 Pa was obtained. The corresponding difference in angle prediction from the calibration was less than 1 deg, with a maximum variance of 0.08 deg. The measurement discretization effect on the interpolation of data is computed from CFD results and is shown to be less than 2% for the measurement grid used. The flow distortion due to the probe–vane coupling is studied through RANS simulations, and the distortion on the readings for both the vane pressure profile and downstream traverse is quantified. The BRASTA facility design is presented and flow stability and uniformity were validated through test section characterization. The sonic valve design and behavior are presented. The valve is used to achieve engine representative conditions inside the test rig. Finally, vane performance measurements and uncertainty quantification methodology are discussed. The uncertainty on the vane Cp is 0.07%, and on the total pressure loss coefficient is 5.9%. The sources of uncertainty are budgeted at each step of calculation. The largest source of uncertainty is for the calculation of static pressure and the effect of the discrete measurement locations. The angle prediction is corrected, and the uncertainty on the angle increases from 0.1 deg to 4 deg. Future work is needed to understand the flow distortion better and reduce this uncertainty.

## Acknowledgment

The authors would like to acknowledge the efforts of Dr. Valeria Andreoli for the design and analysis of the test section and test article, Mr. Paul Clark for the manufacturing of the measurement probes and Dr. Jorge Saavedra and Mr. Swapnil Ingale for help with the turbulent characterization of the annular wind tunnel and second Lt Daniel Inman, Mr. Udit Vyas, and Mr. Hunter Novak for helping with the experimental setup.

## Nomenclature

### Abbreviations

Abbreviations

• B =

bias error

•
• Cp =

pressure coefficient $P−PrefP0−Pref$

•
• N =

normal distribution

•
• Mis =

isentropic Mach number

•
• P =

pressure

•
• P0 =

total pressure

•
• Pref =

reference pressure

•
• Ps =

static pressure

•
• t95 =

95% percentile student t distribution constant

•
• Tu =

turbulence intensity

•
• $u¯$ =

mean velocity

•
• X =

random variable

•
• Δ =

difference

•
• Σ =

standard deviation

### Acronyms

Acronyms

• BRASTA =

big rig for annular stationary turbine analysis

•
• CFD =

computational fluid dynamics

•
• LEAF =

linear experimental aerothermal facility

•
• PETAL =

Purdue experimental turbine aerothermal laboratory

•
• PIV =

particle image velocimetry

•
• PSP =

pressure-sensitive paint

•
• RANS =

Reynolds-averaged Navier–Stokes

•
• RTD =

resistance temperature detector

## References

1.
Tiedemann
,
M.
, and
Kost
,
F.
,
2001
, “
Some Aspects of Wake-Wake Interactions Regarding Turbine Stator Clocking
,”
ASME. J. Turbomach.
,
123
(
3
), pp.
526
533
.10.1115/1.1370158
2.
Göttlich
,
E.
,
Woisetschläger
,
J.
,
Pieringer
,
P.
,
Hampel
,
B.
, and
Heitmeir
,
F.
,
2006
, “
Investigation of Vortex Shedding and Wake-Wake Interaction in a Transonic Turbine Stage Using Laser-Doppler-Velocimetry and Particle-Image-Velocimetry
,”
ASME. J. Turbomach.
,
128
(
1
), pp.
178
187
.10.1115/1.2103092
3.
Barringer
,
M.
,
Coward
,
A.
,
Clark
,
K.
,
Thole
,
K. A.
,
Schmitz
,
J.
,
Wagner
,
J.
,
Alvin
,
M. A.
,
Burke
,
P.
, and
Dennis
,
R.
,
2014
, “
The Design of a Steady Aero Thermal Research Turbine (START) for Studying Secondary Flow Leakages and Airfoil Heat Transfer
,”
ASME
Paper No. GT2014-25570.10.1115/GT2014-25570
4.
Chana
,
K.
,
Cardwell
,
D.
, and
Jones
,
T.
,
2013
, “
A Review of the Oxford Turbine Research Facility
,”
ASME
Paper No. GT2013-95687.10.1115/GT2013-95687
5.
Anthony
,
R. J.
, and
Clark
,
J. P.
,
2013
, “
A Review of the AFRL Turbine Research Facility
,”
ASME
Paper No. GT2013-94741.10.1115/GT2013-94741
6.
Paniagua
,
G.
,
Sieverding
,
C. H.
, and
Arts
,
T.
,
2013
, “
Review of the Von Karman Institute Compression Tube Facility for Turbine Research
,”
ASME
Paper No. GT2013-95984.10.1115/GT2013-95984
7.
Paniagua
,
G.
,
,
D.
,
Saavedra
,
J.
,
Andreoli
,
V.
,
Meyer
,
T.
,
Solano
,
J. P.
,
Herrero
,
R.
,
Meyer
,
S.
, and
Lawrence
,
D.
,
2018
, “
Design of the Purdue Experimental Turbine Aerothermal Laboratory for Optical and Surface Aerothermal Measurements
,”
ASME. J. Eng. Gas Turbines Power
,
141
(
1
), p.
012601
.10.1115/1.4040683
8.
De Maesschalck
,
C.
,
Lavagnoli
,
S.
, and
Paniagua
,
G.
,
2017
, “
Integration of CFD to Design Experiments for Enhanced Spatial and Temporal Discretization
,”
ASME
Paper No. GT2017-64863.10.1115/GT2017-64863
9.
Yasa
,
T.
,
Paniagua
,
G.
, and
Bussolin
,
A.
,
2007
, “
Performance Analysis of a Transonic High-Pressure Turbine
,”
Proc. Inst. Mech. Eng. Part A: J. Power Energy
,
221
(
6
), pp.
769
778
.10.1243/09576509JPE467
10.
Denos
,
R.
,
Paniagua
,
G.
,
Yasa
,
T.
, and
Fortugno
,
E.
,
2006
, “
Determination of the Efficiency of a Cooled HP Turbine in a Compression Tube Facility
,”
ASME
Paper No. GT2006-90460.10.1115/GT2006-90460
11.
Andreoli
,
V.
,
Lavagnoli
,
S.
,
Paniagua
,
G.
, and
Fernandez Villace
,
V.
,
2016
, “
Robust Model of a Transient Wind Tunnel for Off-Design Aerothermal Testing of Turbomachinery
,”
Measurement
,
82
, pp.
323
333
.10.1016/j.measurement.2015.12.032
12.
Saravanamuttoo
,
H. I.
,
1990
,
Recommended Practices for Measurement of Gas Path Pressures and Temperatures for Performance Assessment of Aircraft Turbine Engines and Components
, Advisory Group for Aerospace Research and Development,
Neuilly-Sur-Seine
,
France
.
13.
Liu
,
Z.
, and
Paniagua
,
G.
,
2018
, “
Design of Directional Probes for High-Frequency Turbine Measurements
,”
ASME. J. Eng. Gas Turbines Power
,
140
(
1
), p.
011601
.10.1115/1.4037640
14.
Saavedra
,
J.
, and
Paniagua
,
G.
,
2019
, “
Transient Performance of Separated Flows: Experimental Characterization of Flow Detachment Dynamics
,”
ASME
Paper No. GT2019-91020.10.1115/GT2019-91020
15.
Dudzinski
,
T. J.
, and
Krause
,
L. N.
,
1969
, “
Flow-Direction Measurement With Fixed-Position Probes in Subsonic Flow Over a Range of Reynolds Numbers
,” NASA, Glenn Research Centre, Cleveland, OH, Report No.
NASA TMX-52576
16.
Yasa
,
T.
, and
Paniagua
,
G.
,
2012
, “
Robust Procedure for Multi-Hole Probe Data Processing
,”
J. Flow Meas. Instrum.
,
26
, pp.
46
54
.10.1016/j.flowmeasinst.2012.03.004
17.
Paniagua
,
G.
, and
Dénos
,
R.
,
2002
, “
Digital Compensation of Pressure Sensors in the Time Domain
,”
Exp. Fluids
,
32
(
4
), pp.
417
424
.10.1007/s003480100355
18.
,
D. G.
,
,
N.
,
Andreoli
,
V.
,
Bhatnagar
,
L.
,
Lozano
,
F.
,
Fisher
,
J. M.
,
Paniagua
,
G.
et al.,
2019
, “
Purdue Small Turbine Aerothermal Rotating Rig (STARR)
,”
AIAA
Paper No. 2019-4004.10.2514/6.2019-4004
19.
,
N.
,
Andreoli
,
V.
,
Long
,
N.
, and
Paniagua
,
G.
,
2019
, “
CFD-Based Design of Optical Diagnostic Techniques for Turbine Vane Testing
,”
AIAA
Paper No. 2019-4086.10.2514/6.2019-4086
20.
Roca
,
L. V.
,
2013
, “
Experimental Aerothermal Performance of Turbofan Bypass Flow Heat Exchangers
,” Ph.D. dissertation,
Universitat Politècnica de València
, Valencia, Spain.
21.
Yasa
,
T.
,
Paniagua
,
G.
, and
Denos
,
R.
,
2007
, “
Application of Hot-Wire Anemometry in a Blow-Down Turbine Facility
,”
ASME. J. Eng. Gas Turbines Power
,
129
(
2
), pp.
420
427
.10.1115/1.2364191
22.
El-Gabry
,
L.
,
Thurman
,
D.
, and
Poinsatte
,
P.
,
2014
, “Procedure for Determining Turbulence Length Scales Using Hotwire Anemometry,”
Glenn Resarch Centre, NASA
, Glenn Research Centre, Cleveland, OH, Report No.
NASA/TM—2014-218403
23.
Cumpsty
,
N. A.
, and
Horlock
,
J. H.
,
2006
, “
Averaging Nonuniform Flow for a Purpose
,”
ASME. J. Turbomach.
,
128
(
1
), pp.
120
129
.10.1115/1.2098807