Ashlie B. Flegel

Glenn Research Center, Cleveland, Ohio

Aerodynamic Measurements of a Variable-Speed 

Power-Turbine Blade Section in a 

Transonic Turbine Cascade

NASA/TM—2014-218133

August 2014
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Ashlie B. Flegel

Glenn Research Center, Cleveland, Ohio

Aerodynamic Measurements of a Variable-Speed 

Power-Turbine Blade Section in a 

Transonic Turbine Cascade

NASA/TM—2014-218133

August 2014

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

I would first like to thank my thesis advisor, Dr. Mounir Ibrahim, for his support and encouragement. I also wish to thank my 

research group members Dr. Paul Giel of Vantage Partners, LLC and Dr. Gerard Welch of NASA Glenn Research Center for their 

support and guidance throughout this research effort. This thesis would not be possible without them. This work is supported 

under the NASA Fundamental Aeronautics Program, Rotary Wing Project. I’d like to thank my family members for all of their 

support and motivation. 

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 

This report contains preliminary findings, 

subject to revision as analysis proceeds.
NASA/TM—2014-218133 iii

Contents

Abstract.........................................................................................................................................................1

1.0 Introduction.........................................................................................................................................1

1.1 Motivation .................................................................................................................................1

1.2 Literature Review......................................................................................................................2

1.3 Scope of Work...........................................................................................................................3

2.0 Experimental Facility..........................................................................................................................4

2.1 Facility Description ...................................................................................................................4

2.2 Instrumentation Description ......................................................................................................6

3.0 Description of Experiment ..................................................................................................................9

3.1 Blade Description......................................................................................................................9

3.2 Test Configuration...................................................................................................................10

3.3 Boundary Conditions...............................................................................................................11

3.4 Exit Periodicity........................................................................................................................12

4.0 Results...............................................................................................................................................14

4.1 Three-Dimensional Flowfield Results.....................................................................................14

4.1.1 Survey Data ................................................................................................................14

4.1.2 Blade Loading ............................................................................................................20

4.2 Two-Dimensional Midspan Results........................................................................................23

4.2.1 Exit Survey Data ........................................................................................................23

4.2.2 Midspan Loss Coefficients.........................................................................................27

4.2.3 Midspan Turning........................................................................................................30

5.0 Conclusions.......................................................................................................................................31

Appendix—Symbols List............................................................................................................................33

References...................................................................................................................................................35

List of Tables

Table I.—Blade Description .........................................................................................................................9

Table II.—Angles Settings and Zweifel Coefficients.................................................................................10

Table III.—Nominal Flow Conditions........................................................................................................11

Table IV.—Passage Average Integrations..................................................................................................19

List of Figures

Figure 1.—Cascade Test Section with Blade Geometry...............................................................................4

Figure 2.—Operating Envelope of NASA Transonic Turbine Cascade. ......................................................5

Figure 3.—Original facility configuration....................................................................................................5

Figure 4.—Facility after modifications. Arrows indicate flow boards. ........................................................5

Figure 5.—Three-hole B-L probe (left) and five-hole probe details.............................................................6

Figure 6.—Blade geometry and survey plane locations. ..............................................................................7

Figure 7.—Blade static pressure tap locations..............................................................................................8

Figure 8.—Endwall instrumentation configuration. .....................................................................................9

Figure 9.—Design intent and experimental data at high and low Reynolds numbers and design 

exit Mach number at i = +5.8°. .........................................................................................................10

Figure 10.—B-L measurements for i = +5.8°, 1.0⋅Reb, M2,i = 0.72.............................................................11

Figure 11.—B-L measurements for i = +5.8°, 0.4⋅Reb, M2,i = 0.35.............................................................11

Figure 12.—B-L measurements for i = –36.7°, 1.0⋅Reb, M2,i = 0.72. ..........................................................12

Figure 13.—B-L Measurements for i = –36.7°, 0.4⋅Reb, M2,i = 0.35...........................................................12
NASA/TM—2014-218133 iv

Figure 14.—Endwall static pressure at ReCx,2 = 4⋅Reb, M2,i = 0.72. .............................................................13

Figure 15.—Station 2 endwall and midspan blade base pressures at ReCx = 1.0⋅Reb and M2,i = 0.72. ........14

Figure 16.—Total pressure coefficient contours over three passages.........................................................15

Figure 17.—Detailed view of flow at i = +5.8°, ReCx,2 = 5.30×105 (Reb), M2,i = 0.72.................................15

Figure 18.—Detailed view of flow at i = –36.7°, ReCx,2 = 5.30×105 (Reb), M2,i = 0.67. ..............................16

Figure 19.—Pitchwise integrations for i = +5.8° at Reb and M2,i = 0.72. ....................................................17

Figure 20.—Pitchwise integrations for i = –36.7° at Reb and M2,i = 0.72....................................................18

Figure 21.—Pitchwise integrations for i = –36.7° at 0.4·Reb and M2,i = 0.35. ............................................19

Figure 22.—Blade loading (Cps versus x/Cx) for five incidence angles at five flow conditions. ...............21

Figure 23.—Blade loading—Effects of exit Mach number at ReCx,2= 5.30×105 (Reb). ..............................22

Figure 24.—Net loading versus incidence..................................................................................................22

Figure 25.—Effects of Reynolds number and exit Mach number at i = +10.8°. ........................................23

Figure 26.—Effects of Reynolds number and exit Mach number at i = 0.0°. ............................................24

Figure 27.—Effects of Reynolds number and exit Mach number at i = –16.1°. ........................................24

Figure 28.—Effects of Reynolds number and exit Mach number at i = –36.7°. ........................................25

Figure 29.—Effects of Reynolds number and exit Mach number at i = –51.0°. ........................................25

Figure 30.—Effects of incidence angle at ReCx,2 = 2.12×106 (4·Reb) and M2,i = 0.72. ................................26

Figure 31.—Effects of incidence angle at ReCx,2 = 2.12×105 (0.4·Reb) and M2,i = 0.35. .............................27

Figure 32.—Midspan loss versus incidence. ..............................................................................................28

Figure 33.—Re-0.5 scaled midspan loss versus incidence............................................................................28

Figure 34.—Midspan loss bucket on Ainley-Mathieson scaling................................................................29

Figure 35.—Midspan Loss versus Net blade Loading................................................................................29

Figure 36.—Midspan deviation angle from exit metal angle as function of incidence and 

Reynolds number. .............................................................................................................................30
NASA/TM—2014-218133 1

Aerodynamic Measurements of a Variable-Speed Power-Turbine 

Blade Section in a Transonic Turbine Cascade

Ashlie B. Flegel

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

The purpose of this thesis is to document the impact of incidence angle and Reynolds number 

variations on the three-dimensional flow field and midspan loss and turning of a two-dimensional section 

of a variable-speed power-turbine (VSPT) rotor blade. Aerodynamic measurements were obtained in a 

transonic linear cascade at NASA Glenn Research Center in Cleveland, Ohio. Steady-state data were 

obtained for 10 incidence angles ranging from +15.8° to –51.0°. At each angle, data were acquired at five 

flow conditions with the exit Reynolds number (based on axial chord) varying over an order-ofmagnitude from 2.12×105 to 2.12×106

. Data were obtained at the design exit Mach number of 0.72 and at 

a reduced exit Mach number of 0.35 as required to achieve the lowest Reynolds number. Midspan totalpressure and exit flow angle data were acquired using a five-hole pitch/yaw probe surveyed on a plane 

located 7.0 percent axial-chord downstream of the blade trailing edge plane. The survey spanned three 

blade passages. Additionally, three-dimensional half-span flow fields were examined with additional 

probe survey data acquired at 26 span locations for two key incidence angles of +5.8° and –36.7°. Survey 

data near the endwall were acquired with a three-hole boundary-layer probe. The data were integrated to 

determine average exit total-pressure and flow angle as functions of incidence and flow conditions. The 

data set also includes blade static pressures measured on four spanwise planes and endwall static 

pressures. 

1.0 Introduction

The aerodynamic effects of large incidence and Reynolds number variations on a two-dimensional

midspan section of a variable speed power turbine (VSPT) blade are investigated in this study. 

Downstream midspan total-pressure, exit flow angles, and blade loading measurements were acquired for 

10 incidence angles and at five flow conditions each. This dataset is important for understanding the 

aerodynamic challenges of a VSPT application for a Large-Civil Tilt-Rotor (LCTR). Detailed threedimensional half-span flowfield measurements were acquired for two incidence angles corresponding to 

the LCTR points of cruise and takeoff. Because admitting transitional flow on the blade surface was of 

importance for this study, all the tests were conducted with low inlet turbulence.

In this section, the motivation behind a VSPT will be discussed. The VSPT is a key driver in allowing 

efficient operation of a LCTR. The VSPT will allow the main rotor speeds to vary from 100 percent at 

takeoff to 54 percent at cruise. At these large speed variations, incidence angle and Reynolds number 

effects are important. In a review of the literature it will be discovered that little experimental data exists 

that covers a large applicable range of incidence angles at engine relevant Reynolds and Mach numbers. 

The section will conclude with discussion of the scope of this thesis.

1.1 Motivation

The Rotary Wing Project of the NASA Fundamental Aeronautics Program is investing in technology 

to enable civil rotor craft use to help relieve airport congestion and enhance airspace throughput capacity. 

One concept vehicle of interest is the Large Civil Tilt-Rotor (LCTR). The LCTR is an economically 

competitive rotary-wing vehicle with both VTOL and Mach 0.5 cruise capability (Johnson et al. (Ref. 1)
NASA/TM—2014-218133 2

and Acree et al. (Ref. 2)). In order to minimize mission fuel burn, it has been found that the main rotor 

speeds must vary from 100 percent N* at takeoff to 54 percent N* at cruise in order to optimize the 

propulsive efficiency at cruise. In order to accommodate this large speed variation, a variable gear-ratio 

(two-speed) transmission can be used (Stevens et al. (Ref. 3)), which introduces complexities such as gear 

shifting during flight and additional weight of the transmission. Another approach is to use a variable 

speed power turbine (VSPT) (D’Angelo (Ref. 4) and Welch (Ref. 5)). 

There are several challenges associated with the VSPT technology which include attainment of high 

turbine efficiency at high work factors, management of loss levels over a large (40° to 60°) incidence 

variation in all blade rows, and operation at low Reynolds numbers (transitional flow) (Welch (Ref. 5)). 

Understanding the loss levels due to incidence and effects of transitional flow are the two challenges 

which are the focus of this thesis. These challenges stem from the consideration of two key LCTR 

mission points: 2,000 ft takeoff/hover and 28,000 ft Mach 0.5 cruise. At takeoff, the main rotor and VSPT 

operate at 100 percent N*, while at cruise the rotors and VSPT are slowed to 54 percent N*. The engine 

requirements for an LCTR were established in a previous study (Ref. 6). In that study, it was found that as 

the main rotor shaft is reduced by nearly 54 percent from take-off to cruise speed the corrected flows do 

not change significantly and the flow coefficient essentially doubles. The nearly constant corrected flow 

rates and 40 percent corrected speed change lead to incidence angle swings of 40° and 60° in all turbine 

blade and vane rows downstream of the first vane, including any required exit guide vane row. The study 

also indicated that the unit Reynolds numbers (in-1

) at the aft-stage rotor exit of the VSPT for the LCTR 

application varies between 0.45×105

<Re/Cx [in–1] < 0.75×105 from takeoff to cruise. This is a range in 

which transitional flow may impact performance. 

1.2 Literature Review

Several studies have been reported in the literature that address challenges relevant to variable-speed 

power turbines. With respect to the Reynolds number effects on the blade losses, this has been well 

documented in the open literature for Low Pressure Turbine (LPT) applications. Hourmouziadis (Ref. 7), 

Haselbach (Ref. 8), and Gier et al. (Ref. 9) considered the impact of Reynolds number lapse on LPT blade 

row performance. Halstead et al. (Ref. 10) and Coull et al. (Ref. 11) addressed the sensitivity of the 

transitional flow fields to deterministic unsteadiness associated with upstream wakes. This thesis does not 

explore the impact of wake passing on blade row performance. All tests were carried out in a steady-state 

cascade.

The effects of a wide range incidence on blade loading and downstream wakes for a wide range of 

engine relevant flow conditions are scarce in the open literature. Some studies addressing incidence 

effects will now be discussed. Yamamoto and Nousse (Ref. 12) conducted exhaustive tests in a low speed 

cascade looking at the impact of incidence on the three-dimensional flow field and losses over a 60.5° 

incidence range (–53.3° < i < +7.2°)for five discrete angle settings. Five-hole pressure probe surveys were 

conducted on 15-16 axial planes downstream and upstream of the blade row and between blade passages 

from hub to midspan. This study only examined the incidence effects at one Reynolds number condition. 

The authors noted that Reynolds number will influence the boundary layer thicknesses at the inlet endwall 

and blade surface. There will also be changes in the turbulence level as the velocity is varied. In 

Yamamoto and Nousse’s (Ref. 12) study, the chordwise development of the secondary flows and totalpressure fields were provided for the five incidence angles tested. The authors noted that the front part of 

the blade is very sensitive to incidence and that the front loading decreases with decreasing incidence. 

The total pressure contours indicate two loss regions, one located on the suction surface where it is 

insensitive to incidence and on the pressure surface near the leading edge which increases with increasing

negative incidence. The authors observed the endwall effects related to incidence and found that as 

incidence increases; the flow migrates towards the suction surface. This is consistent with Hodson and 

Dominy’s (Ref. 13) findings which show the low momentum endwall flow accumulating on the blade 

suction surface. The losses due to the suction side and pressure side leg of the horseshoe vortex and 

passage vortex was observed. The intersection of the horseshoe and passage vortex moves from suction to 
NASA/TM—2014-218133 3

pressure side as the incidence increases. The cascade incidence influences the passage vortex and 

horseshoe vortex intersection which rotates in the same direction.

Moustapha et al. (Ref. 14) have summarized previous work related to profile and secondary flow 

losses at design and off-design incidence conditions. In addition to Moustapha et al.’s (Ref. 14) valuable 

review of available cascade data with wide ranges of incidence angle testing, they noted that blade rows 

with high inlet Mach numbers would likely be more sensitive to inlet gas angle changes. They also noted 

the lack of data in the open literature related to the impact of compressibility, leading edge geometry, and 

axial loading schedule on incidence losses. 

Joinini et al. (Ref. 15) examined the impact of leading edge geometry—in particular, metal angle 

selection—on midspan incidence loss. They noted that detailed experimental data for off-design 

incidence, particularly in transonic flow conditions, were sparse in the open literature, and highlighted the 

importance of such data for CFD validation. 

Turbulence effects play a role in the losses of a turbine cascade as examined in Hoheisel et al. 

(Ref. 16). Measurements were made on three blade geometries; one was front-loaded and two were aftloaded blading. Tests were conducted in a seven blade linear cascade. The authors noted that it is the 

boundary layer transition that determines the losses on turbine cascades. It is essential to have velocity 

distributions with the laminar-turbulence transition point as far downstream as possible. The two factors 

affecting transition behavior are the pressure gradient on the blade surface and the free stream turbulence

levels. The laminar separation bubble influenced the boundary layer transition; its size was reduced with 

increasing Reynolds number and turbulence. The aft-loaded blading performed better in terms of loss at 

the different incidence levels at Tu = 5 percent. The most front-loaded blade performed more poorly at 

positive incidence but retained lower loss levels at negative incidence.

Corriveau and Sjolander (Ref. 17) provided midspan profile losses, loading distributions, and base 

pressure measurements for a series of HPT airfoils with front-, mid-, and aft-loading. The linear cascade 

tests were conducted over a wide range of LPT-relevant Mach numbers and at Reynolds numbers from 

0.4 to 1.0×106

. While the results illustrated superior loss performance for aft-loaded blades, lower loss 

levels were achieved at off-design incidence with the mid-loaded blading.

1.3 Scope of Work

The objective of this thesis is to advance the understanding of the aerodynamic effects of large 

incidence angle and Reynolds number variations with the development of an extensive cascade dataset 

that addresses the key VSPT challenges. The NASA Transonic Linear Cascade Facility was used to assess 

the performance of a VSPT blade section at design and off-design inlet flow angles over an enginerelevant range of Mach and Reynolds numbers. 

Section 2.0 contains descriptions of the experimental facility and of the instrumentation used during 

this study. While the facility boasts many capabilities that made it desirable to test the VSPT blade

geometry, modifications had to be made in order to span the desired incidence range. After discussing the 

facility, a description of the instrumentation will be given. This will highlight the features of obtaining 

measurements of the inlet boundary layer, inlet turbulence, and exit flow features. 

In Section 3.0 a description of the current experiment will be given. The two-dimensional extruded 

midspan section of the VSPT blade geometry will be described. This section will also discuss the test 

configuration and the test matrix. 

Section 4.0 will present the results of the aerodynamic measurements acquired for 10 incidence 

angles at five flow conditions. The section will begin with looking at the three-dimensional flowfield 

measurements for the take-off (i = –36.7°) and cruise (i = +5.8°) angles. These data, along with the blade 

loadings, will show the influence of secondary flows on the blade loading. Pitchwise integrated averages 

of the half-span data are shown as well. The two-dimensional midspan total-pressure and exit pitch angle 

measurements for all 10 incidence angles varying from i = +15.8° to i = –51.0° will then be presented.

Averaged midspan total pressures were used to establish profile loss buckets. 
NASA/TM—2014-218133 4

Section 5.0 will conclude with a summary of the major findings and recommendations for future 

research. 

2.0 Experimental Facility

The experimental study was conducted at NASA Glenn Research Center’s (GRC) Transonic Turbine 

Blade Cascade Facility. This large-scale linear cascade facility was desirable for this test because of its

adjustable inlet flow angle test section (77° range), wide range of flow (Mach and Reynolds number)

capabilities, the large-scale blades which enable detailed flow field measurements, and the large number 

of blades which would promote better periodicity. Testing in the steady-state, nonrotating cascade 

inherently neglects the rotational effects associated with Coriolis and centrifugal acceleration fields, the 

relative motion of endwalls, and the impact of unsteadiness of upstream and downstream blade rows. 

However, a transonic cascade test of a VSPT blade section will allow for the examination of the 

fundamental physics occurring and will serve as an important step towards VSPT technology level 

advancement.

2.1 Facility Description

The NASA GRC Transonic Turbine Blade Cascade Facility is shown in Figure 1. A detailed facility 

description is given in Verhoff et al. (Ref. 18). Since then, the inlet flow boards were modified to improve 

the inlet flow uniformity as described in Giel et al. (Ref. 19). The cascade’s large scale and continuous 

run capability at engine relevant Mach numbers and Reynolds numbers have allowed for detailed 

aerodynamic (Refs. 20 and 21) and heat transfer studies (Refs. 22 and 23) on a wide range of turbine 

blades. 

The tunnel operates by utilizing inlet air that is supplied by GRC’s 40 psig Combustion Air system. 

Clean, dry, ambient temperature air enters the facility and is throttled to a maximum inlet pressure of 

14.7 psia under current safety restrictions. This restriction is shown as the red dashed line in Figure 2. The 

air passes through flow conditioning and contraction sections and is directed to the cascade test section by 

upper and lower inlet flow boards. The air is then exhausted through an altitude exhaust system that is 

maintained at 2 psia. Independent control of the inlet and exhaust valves allows for a wide range of 

engine relevant Mach and Reynolds numbers to be achieved, as shown in the facility operating envelope 

of Figure 2. 

Figure 1.—Cascade Test Section with Blade Geometry.
NASA/TM—2014-218133 5

Figure 2.—Operating Envelope of NASA Transonic Turbine Cascade.

Figure 3.—Original facility configuration. Figure 4.—Facility after modifications. Arrows indicate 

flow boards. 

For this study, the cascade was made up of nominally 10 blade passages. The blades are attached to a 

disk that can be rotated to set inlet flow angles (from axial) in the range –17° ≤ β1 ≤ +78.8°. This allows 

for a wide range (96°) of incidence angles to be studied. Prior to this test the original facility 

configuration (see Figure 3) allowed a 45° range in inlet angles from +33.8° ≤ β1 ≤ +78.6°. These angles 

are typical of HPT (high pressure turbine) applications. In the previous section it was noted that the VSPT 

may see incidence swings of 40° to 60°. The blade designs also require lower inlet flow turning for more 

negative incidence. This VSPT requirement resulted in modifications to cascade’s exhaust and inlet board 

configurations as described by McVetta et al. (Ref. 20). The modifications, shown in Figure 4, include a 

new exhaust which extends the length of the top of the tunnel and structural supports in the test section in 

order to accommodate the range of the exit angles required for the current tests. As part of the facility 

modifications, unique upper flow board extensions with respective blade suction-side profiling were 

fabricated for five discrete incidence angles in the range of –16.1° ≤ i ≤ –51.0°. For these five angles, the 

upper-most blade was removed and replaced with a flow board extension that connected at the blade bolt 

hole and to the end of the original upper flow board. These extensions ensured that the flow was properly 

directed into the first blade passage, the upper and lower flow boards were horizontal, and the flow board

hinged leading edges were maintained in the same plane normal to the inlet flow. The other incidence 

angles tested outside of this range did not require an upper extension board and utilized the original flow 

board configuration. 

−

−

−

−

−

−

−

−

−

−

−

current study

Ma2,i,des=0.72

Ma2,i

=0.35

Ref. [21]

Ref. [22]

Ref. [23]

Isentropic exit unit Reynolds number,

0.0

0.5

1.0

1.5

2.0

0.1 0.2 0.3 0.5 0.7 1.0 2 3 5 7 10

Re2,i × 10

−6 [1/ft]

Isentropic

exit Mach number,

Ma2,i

minimum

exhaust pressure ≈13.8 kPa (2.0 psia)

max mass flow

≈ 26 kg/s

(58 lbm/s)

maximum

inlet pressure

= 159 kPa (23.0 psia)

7.0

6.0

5.0

4.0

3.0

2.0

1.5

1.3

1.2

1.1

1.0

Pressure Ratio,

Pt,1

P2

Pt = 14.7 psia
NASA/TM—2014-218133 6

2.2 Instrumentation Description

Detailed data documenting the inlet characteristics and downstream flowfield along three blade 

passages were acquired by using pneumatic pressure probes, static taps, and a hotwire anemometer probe. 

Details of the instrumentation are discussed below.

Pressure Probes: Inlet boundary layer measurements and downstream total-pressure and exit flow 

angle data were acquired using a three-hole boundary layer probe and a five-hole pitch-yaw probe. The 

probes are shown in Figure 5. Both are 45° forward-facing pyramid probes with the measurement ports

located on the shaft centerline. For the downstream aerodynamic measurements both probes were 

installed in a survey plane located 7.0 percent axial-chord downstream of the blade trailing edge in 

Station 2. The survey station locations are shown in Figure 6 and cover three blade passages. Inlet 

boundary layers measurements were measured using the three-hole probe at Station 0, which is 0.415

axial-chords upstream of the blade leading edge. The boundary layer probe has a flattened probe end and 

can be traversed to touch the endwall and acquire measurements as close as 0.005 in. (0.13 mm) from the 

endwall surface. 

The five-hole probe was used to measure total-pressure, pitch angle (x-y plane), and yaw angle (x-z

plane). For each inlet angle, the five-hole probe was used for midspan surveys consisting of 123 pitchwise 

points spaced nonuniformly over the three passages noted in Figure 6. Pitchwise/spanwise surveys were 

also taken at the takeoff (i = –36.7°) and cruise (i= +5.8°) angles. The surveys at each immersion 

consisted of 62 pitchwise points spaced uniformly over three passages. The three-hole boundary-layer 

probe was used to measure total pressure and pitch angle only. The half-span three-dimensional flowfield 

was resolved by using the three-hole probe near the endwall for 0.0 < z/H ≤ 0.043 with 14 spanwise 

points spaced logarithmically. The five-hole probe was used above this region for 0.042 ≤ z/H ≤ 0.50 with 

12 spanwise points spaced uniformly.

Inlet boundary-layer measurements were acquired using the three-hole probe installed in Station 0, 

located 0.415 axial-chords upstream of the blades. The surveys were acquired at two to three pitch 

locations and consisted of 29 spanwise points. 

Figure 5.—Three-hole B-L probe (left) and five-hole probe details.
NASA/TM—2014-218133 7

Figure 6.—Blade geometry and survey plane locations.

Both pressure probes were calibrated using the same method as described in Giel et al. (Ref. 21). The 

probes were calibrated in NASA GRC’s Free Jet Calibration Rig (CE-12). The pitch and yaw angles of 

the five-hole probe were calibrated over a Mach number range from 0.1 to 0.9. The pitch angle was 

traversed from ± 35° and the yaw ranged from ± 40°. Similarly, the three-hole probe was calibrated over 

the same Mach number and pitch angle range. During the cascade test, the probe pitch angle coefficient 

was monitored to ensure that it remained well within the angular calibration range corresponding to 

approximately ±40°. When needed, the probe survey was stopped and the probe was approximately 

nulled before resuming. The overall estimated uncertainty in flow angle was ±1.5° and the overall 

estimated local uncertainty in total-pressure coefficient was ±1.7 percent, as reported in Giel et al. 

(Ref. 21) and scaled for the current definition of total-pressure coefficient. 

The time responses for each probe were measured to be: τ5-hole = 0.42 s and τ3-hole = 0.82 s. To ensure a 

95 percent time recovery, a three second delay was imposed between the time the probe reaches the 

desired survey location and the initiation of data recording. Five readings, taken one second apart, were 

averaged at each measurement point. 

Static Pressure Measurements: The primary measurement Blades 4, 5, and 6, shown in Figure 6, 

were instrumented with static pressure taps along four spanwise locations. Blade 5 was fully instrumented 

with 44 taps along 10, 15, 30, and 50 percent of span. A pre-test RANS prediction of the blade surface 

pressure distribution, shown in Figure 7, was used to establish the placement of the Blade 5 static taps. To 

verify periodicity, 20 redundant taps were installed on the suction side of Blade 4 and 16 taps were 

installed on the pressure side of Blade 6.
NASA/TM—2014-218133 8

z (in.)

Figure 7.—Blade static pressure tap locations.

The endwall was fully instrumented with approximately 550 static pressure taps located both 

upstream and downstream of the blade row and within each passage (see Figure 8). Data from these 

pressure measurements were used for periodicity checks which will be discussed in further detail in 

Section 3.0.

Twelve exit static-pressure taps, located approximately three axial-chords downstream of the blades 

and spanning almost nine blade pitches, were used to set the exit Mach number condition. The inlet static 

pressure was measured by five to six inlet static pressure taps, depending on inlet flow angle, located 

96.77 mm (3.81 in.) upstream of the blade row at Station 0. These inlet taps can be seen in Figure 8, 

represented by the orange dots at x = –5 in.

Additional inlet measurements: Inlet total pressure and temperature were measured with two 

combination Kiel/total-temperature probes located at midspan approximately 96.77 mm (3.81 in.) 

upstream of the blades, just outside the passages of interest. These Kiel probes, shown in Figure 8 as the 

blue dots, were used to set the tunnel inlet conditions. A third Kiel probe was also used for some of the 

inlet flow angle measurements.

Hotwire Anemometer: A constant temperature single-wire hotwire anemometer probe (TSI 1210-

T1.5) was used to acquire inlet turbulence intensity measurements. The hotwire was installed in Station 0, 

located approximately 0.415 axial chord upstream of the blades (see Figure 8). The data were acquired at 

a rate of 92 kHz for 7 s. The uncertainties in the measurements were calculated to be less than 4 percent

for the mean velocities and 5 percent for the fluctuations using the methodology found in (Ref. 24). The 

turbulence intensities, calculated as the normalized root-mean square of the velocity fluctuations, ranged 

from 0.25 to 0.40 percent (Ref. 20). The integral length scale was calculated though an autocorrelation 

technique (e.g., see Coull et al. (Ref. 25)) and was found to be between 1.0 to 1.5 in.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.0

1.0

2.0

3.0

4.0

5.0

6.0

Ps

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.55

0.50

s [inches]

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.5

0.6

0.7

0.8

0.9

1.0

k=26, z=3.000, 50.0%

k=25, z=2.540, 42.3%

k=24, z=2.101, 35.0%

k=23, z=1.700, 28.3%

k=22, z=1.349, 22.5%

k=21, z=1.053, 17.6%

k=19, z=0.617, 10.3%

k=16, z=0.259, 4.3%

taps; 10% span

taps; 15% span

taps; 30% span

taps; 50% span

s [inches]

Ps / Pt,in Ps/Pt,in.

s (in.)

s (in.)
NASA/TM—2014-218133 9

Figure 8.—Endwall instrumentation configuration.

TABLE I.—BLADE DESCRIPTION

Geometry Value

Axial chord, Cx ..........................................180.57 mm (7.109 in.)

True chord .................................................194.44 mm (7.655 in.)

Pitch, S ......................................................130.00 mm (5.119 in.)

Span, H......................................................152.40 mm (6.000 in.)

Throat diameter ...........................................72.85 mm (2.868 in.)

Leading edge diameter ................................15.16 mm (0.597 in.)

Trailing edge diameter...................................3.30 mm (0.130 in.)

Stagger angle ......................................................................20.35°

Inlet metal angle .................................................................34.20°

Uncovered turning..............................................................19.47°

Exit metal angle................................................................–55.54°

3.0 Description of Experiment

3.1 Blade Description

The blade geometry is a scaled two-dimensional midspan section of the VSPT second stage rotor 

designed by Rolls-Royce. Details of the blade design are documented in (Ref. 26). In that effort, meanline

analyses were used to analyze three and four-stage variable-speed power turbines (VSPT) to meet 

specified engine requirements. A four-stage turbine was selected for additional optimization and a

detailed three-dimensional blade aero design/optimization was concentrated on the second rotor of the 

selected four-stage meanline design. Rotor 2 was selected as a representative embedded blade row, both 

in terms of turning (96° at cruise and 53° at takeoff) and incidence-range (42°) requirements between 

cruise and takeoff (Ref. 26). The midspan section, which was optimized to minimize loss at the cruise 

condition (i = +5.8°, M2,i = 0.72) and achieve the required incidence range at acceptable loss levels, was 

chosen for this cascade test. The blade has an inlet metal angle of 34.2° relative to the axial direction and 

a scaled axial chord of 180.6 mm (7.109 in). Details of the scaled (test) blade are listed in Table I. The 

cascade of the current test comprised 10 blade passages (nominally).

10 9 8 7 6 5 4 3 2 1

Ps Ps Pt Ps Ps Ps , Tt Pt

, Tt Pt Ps

9 8 7 6 5 4 3 2 1

11

y - tangential coordinate [inches]

x - axial coordinate [inches]

35 30 25 20 15 10 5 0 -5 -10 -15 -20 -25 -30

-5

0

5

10

15

20

cw22/rr1/aero/psend/endwall_taps_v6.lay

VSPT-RR1 Blades and

endwall taps

exit static pressure taps

Station 0

Station 2

x

– axial coordinate (in.)

y – tangential coordinate (in.)
NASA/TM—2014-218133 10

Figure 9.—Design intent and experimental data at 

high and low Reynolds numbers and design exit 

Mach number at i = +5.8°.

The design intent blade loading (Ref. 26) compared to the experimental midspan data at two 

Reynolds number conditions is shown in Figure 9. As described in (Ref. 26), the design calculation was 

carried out in two-dimensional on a code assuming fully turbulent flow whereas the midspan of the 

experiment is influenced by the strong three-dimensionality and secondary flow fields in the low aspect 

ratio cascade (see Figure 6) and transitional flow effects. The optimum profile from the design is 

considered to be aft-loaded and has notably high uncovered turning (19.5°) with respect to the suctionsurface curvature.

3.2 Test Configuration

Measurements were acquired for 10 incidence angles ranging from –46.0° to +15.8°. Details of the 

incidence angles and corresponding Zweifel coefficients are listed in Table II. As previously discussed, 

there are three mission design point angles: takeoff (i= –36.7°), cruise (i = +5.8°), and maximum mission 

incidence (i = –46.0°). Additional detailed flowfield data and inlet boundary layer measurements were 

acquired at the cruise and takeoff points. 

At each incidence angle setting, data were acquired at the five nominal flow conditions listed in Table 

III. The design pressure ratio was 1.412 which corresponds to an exit isentropic Mach number of 0.72. A 

baseline flow condition was established by finding the lowest Reynolds number at which the tunnel could 

consistently maintain an exit Mach number of 0.72. The baseline Reynolds number, Reb, was found to be 

0.53×106

. Higher Reynolds number cases were run at 1.06×106 and 2.12×106. An order-of-magnitude 

variation in Reynolds number could be achieved by reducing the exit Mach number to 0.35. The lowest 

Reynolds number point of 2.12×105

(0.4⋅Reb) could not be achieved at the design exit Mach number due to 

the limitations of the tunnel operating envelope (see Figure 2). 

TABLE II.—ANGLES SETTINGS AND ZWEIFEL COEFFICIENTS

Inlet angle,

β1

Incidence angle, 

i

Zw

50.0°

45.0°

40.0° (Cruise)

34.2°

28.0°

18.1°

8.2°

–2.5° (Takeoff)

–11.8° (Mission Max-i)

–16.8°

15.8°

10.8°

5.8°

0.0°

–6.2°

–16.1°

–26.0°

–36.7°

–46.0°

–51.0°

1.22

1.13

1.06

0.99

0.92

0.82

0.74

0.65

0.58

0.53

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

expr, Re = 1⋅ Reb

expr, Re = 4⋅ Reb

design intent

Cps
NASA/TM—2014-218133 11

3.3 Boundary Conditions

Inlet Boundary Layer: The estimated inlet boundary-layer thickness range is documented for each flow 

condition in Table III. The boundary-layer heights were calculated by inlet Reynolds number scaling 

(turbulent flow) of detailed inlet boundary-layer measurements acquired in Giel et al. (Ref. 21). The range in 

Table III indicates the variation in the boundary-layer thickness for the 10 incidence angles and 

corresponding inlet Reynolds number variations. This Reynolds number scaling was verified during this 

study by acquiring inlet boundary layer measurements at the take-off and cruise incidence angle for three 

flow conditions. Figure 10 to Figure 13 compare the estimated boundary layer thickness (orange) to the 

directly calculated thickness from the data (blue) and using two additional scalings. These data confirmed that 

the use of the Reynolds number scaling for turbulent flow is adequate for the remainder of the inlet 

conditions. 

TABLE III.—NOMINAL FLOW CONDITIONS

Exit ReCx Pressure

ratio

Exit Mis a

δ99,1,

in.

a

2δ99,1/H

2.12×106

1.06×106

5.30×105

5.30×105

2.12×105

1.412

1.412

1.412

1.087

1.087

0.72

0.72

0.72

0.35

0.35

1.16 to 1.23

1.28 to 1.36

1.42 to 1.50

1.40 to 1.49

1.60 to 1.69

0.39 to 0.41

0.43 to 0.45

0.47 to 0.50

0.47 to 0.50

0.53 to 0.56 a Reynolds-scaling estimated range of boundary-layer thickness over 10 incidence angle settings.

Figure 10.—B-L measurements for i = +5.8°, 1.0⋅Reb, M2,i = 0.72.

Figure 11.—B-L measurements for i = +5.8°, 0.4⋅Reb, M2,i = 0.35.

y/pitch -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

δ 99 directly

δ 99=8×δ 1

δ 99=(72/7)×δ 2

δ 99 scaled from previous

δ 99

[in.]

y/pitch -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

δ 99 directly

δ 99=8×δ 1

δ 99=(72/7)×δ 2

δ 99 scaled from previous

δ 99

[in.]

δ99 (in.)

δ99 (in.)

y/pitch

y/pitch
NASA/TM—2014-218133 12

Figure 12.—B-L measurements for i = –36.7°, 1.0⋅Reb, M2,i = 0.72.

Figure 13.—B-L Measurements for i = –36.7°, 0.4⋅Reb, M2,i = 0.35.

Inlet Turbulence: The facility has an optional upstream blowing turbulence grid located roughly five 

axial-chords upstream of the blade row. Hoheisel et al. (Ref. 16) described the influence of turbulence 

intensity on the location of two-dimensional transition and on trailing edge suction-side momentum 

thickness for the suction surface of front- and aft-loaded blading. The transition point moved upstream 

with increasing turbulence and appeared always to be associated with a laminar separation bubble. At low 

turbulence intensities (Tu = 0.8 percent), the trailing edge momentum thickness increased with diffusion 

level. Since the minimum accessible tunnel exit Reynolds number (0.53×106

) at M2,i = 0.72 of the present 

effort was significantly higher than that anticipated for engine cruise (e.g., 0.045×106 to 0.15×106

) it was 

decided to test without the turbulence grid (i.e., at low turbulence) in order to admit transitional flow 

appropriate to altitude cruise conditions. Outside of this thesis, data have been taken at higher turbulence 

intensities (Tu = 7 to 8 percent) to examine the effects of turbulence. As previously mentioned, the inlet 

turbulence intensity without the grid was documented to range from 0.25 to 0.40 percent. The integral 

length scale was found to be 25 mm (1.0 in.) to 38 mm (1.5 in.) which is largely independent of Reynolds 

number and immersion in the boundary layer. 

3.4 Exit Periodicity

The endwall static pressure contours are shown in Figure 14 for all 10 incidence angles. The location 

of the downstream measurements plane (Station 2) is at roughly x= +5.5 in. and covers the pitch distance 

–11.5 ≤ y ≤ +4.0. In Figure 14, the positive incidence angle data show the upper-board and exhaust (near 

Blade 1) creates a low pressure field. At i = +15.8° this difference is almost negligible. Between the blade 

passages the static pressure appears periodic as will be shown in the downstream survey data. As the 

incidence is reduced in the negative direction the static pressure nonuniformity increases and influences 

the downstream pressure field between Blades 1 to 3. This causes the blade-to-blade passage 

nonuniformity. At i = –46.0° and i = –51.0° the lower flow board induces a negative pressure field 

affecting Blades 9 to 11.

y/pitch -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

δ 99 directly

δ 99=8×δ 1

δ 99=(72/7)×δ 2

δ 99 scaled from previous

δ 99

[in.]

y/pitch -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

δ 99 directly

δ 99=8×δ 1

δ 99=(72/7)×δ 2

δ 99 scaled from previous

δ 99

[in.]

δ99 (in.)

δ99 (in.)

y/pitch

y/pitch
NASA/TM—2014-218133 13

i = +15.8° i = –16.1°

 i = +10.8° i = –26.0°

 i = +5.8° i = –36.7°

 i = 0.0° i = –46.0°

i = –6.2° i = –51.0 °

Figure 14.—Endwall static pressure at ReCx,2 = 4⋅Reb, M2,i = 0.72.
NASA/TM—2014-218133 14

Figure 15.—Station 2 endwall and midspan blade base 

pressures at ReCx = 1.0⋅Reb and M2,i = 0.72.

Focusing on the region of interest (Blades 3, 4, and 5) for this test in Figure 15, the data from the 

endwall pressure taps located near the Station 2 survey plane (x/Cx = 1.070) are shown for two inlet 

angles for the baseline Reynolds number and design exit Mach number condition. These data are also 

compared to the blade base pressures measured on Blades 4, 5, and 6. For both incidence angles the static 

pressure increases in the positive pitch direction. From the contours it can be seen that the pressures are 

influenced by the downstream exhaust configuration which induces a pitchwise static pressure 

nonuniformity. The aperiodicity is negligible at positive incidence angles, but increases at the negative 

incidence angle settings. This aperiodicity will be observable in the flowfield data discussed later.

4.0 Results

The effects of incidence, Reynolds number, and Mach number variations on the exit flowfield are 

explored in this section. First, the detailed exit flowfield measurements at the take-off and cruise angles 

will be discussed which will give a good initial comparison of the flowfield for negative and positive 

incidence conditions. The impact of incidence change on secondary flowfield effects and blade loading 

will be very noticeable. This will be supported by the blade loading data for the 10 incidence angles. Once 

the flowfield and blade loading trends are established, the midspan total-pressures and exit flow angles 

will be discussed. 

4.1 Three-Dimensional Flowfield Results

4.1.1 Survey Data

Detailed exit flowfield measurements were obtained for the cruise (i = +5.8°) and takeoff (i = –36.7°)

incidence angles at the baseline Reynolds number (Reb = 530,000) and design exit Mach number

(M2,i = 0.72). To look at the effects of Reynolds number and Mach number, detailed measurements were 

also obtained at a low flow condition (ReCx,2 = 212,000 and M2,i = 0.35) and the takeoff incidence setting. 

Data were taken at 26 spanwise locations over 62 pitchwise points. 

The total-pressure contours in Figure 16 show that at the positive incidence angle (Figure 16(a)) the 

blade is highly loaded, producing strong secondary flows which drive the endwall flow to and along the 

suction side of the blade. The blade loading is reduced and the flow becomes very two-dimensional at the 

negative incidence angle (Figure 16(b)). The contours of total-pressure coefficient remain largely 

unchanged as the Reynolds number and Mach number are reduced as shown in Figure 16(c). 

A detailed single-passage view of the secondary flow vectors and pitch and yaw angles are shown for the 

baseline flow conditions at the positive (Figure 17) and negative (Figure 18) incidence angles. The impact of 

secondary flows is evident for i = +5.8°. The flow vectors and pitch angles show strong overturning near the 

hub (z = 0). At y/S = –0.45 and z/H = 0.33 in Figure 17(a) the flow vectors show the core of the horseshoe 

vortex. This is also evident in the pitch and yaw angle data. For i = –36.7°, the secondary flow vectors, and the 

pitch and yaw angle show little variation due to the two-dimensionality of the flowfield. 

y / S -2.0 -1.5 -1.0 -0.5 0.0 0.5 -0.4

-0.2

0.0

0.2

0.4

β1=−2.5°, endwall

β1=−2.5°, base

β1=40.0°, endwall

β1=40.0°, base Cps

passage 4 passage 5
NASA/TM—2014-218133 15

The total pressure data of the three- and five-hole probe measurements were in good agreement for 

both incidence angles as seen at z/H = 0.042. Figure 16 also shows reasonable periodicity between 

passages 4 and 5. Consistent with the downstream endwall static pressure contours in Figure 14, there is a 

slight aperiodicity observed in Passage 6. 

(a) i = +5.8°, M2,i = 0.72, ReCx,2 = Reb.

(b) i = –36.7°, M2,i = 0.67, ReCx,2 = Reb.

(c) i = –36.7°, M2,i = 0.35, ReCx,2 = 0.4⋅Reb.

Figure 16.—Total pressure coefficient contours over three passages.

Figure 17.—Detailed view of flow at i = +5.8°, ReCx,2 = 5.30×105 (Reb), M2,i = 0.72.

-2.0 -1.5 -1.0 y / S -0.5 0.0 0.5

0.0

0.1

0.2

0.3

0.4

z 0.5 H

PS SS PS SS PS SS

Passage 4 Passage 5

-2.0 -1.5 -1.0 -0.5 0.0 0.5

0.0

0.1

0.2

0.3

0.4

0.5

-2.0 -1.5 -1.0 y / S -0.5 0.0 0.5

0.0

0.1

0.2

0.3

0.4

0.5 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

z

H

PS SS PS SS PS SS

Cpt :

-2.0 -1.5 -1.0 -0.5 0.0 0.5

0.0

0.1

0.2

0.3

0.4

0.5
NASA/TM—2014-218133 16

Figure 18.—Detailed view of flow at i = –36.7°, ReCx,2 = 5.30×105 (Reb), M2,i = 0.67.

Pitchwise integrations of the total-pressure coefficient, pitch angle, and yaw angle were calculated at 

each spanwise immersion for i = +5.8° (Figure 19) and i = –36.7° (Figure 20 and Figure 21). Areaaveraging of the total pressure was performed so that calculated loss coefficients would account for loss 

production both within the blade passage and in downstream mixing. The area-averaged total-pressure 

coefficient (Figure 19(a) and (b)) reflects strong spanwise variation in the secondary-flow field; the thick 

inlet boundary-layer fluid is thinned out near the hub and transported to a higher span section on the blade 

suction side. The estimated inlet boundary layer, noted in Table IV, for this flow condition is 1.44 in., 

which accounts for roughly 24 percent of the blade span. As seen in the flowfield contours (Figure 17), 

the horseshoe vortex and its core location can be seen in Figure 19(c) and (d) at z/H = 0.33. The pitch 

angle in Figure 19(c) show the flow is always overturned near the hub. The point of minimum turning 

is located at z/H = 0.33. This is the same spanwise location of the maximum yaw angle shown in 

Figure 19(d). 

The integrations at i = –36.7° are shown in Figure 20 at the baseline flow conditions. The inlet 

boundary-layer thickness was 1.50 in., roughly 50 percent of the half-span; due to the two-dimensionality 

of the flow at this incidence angle, the boundary-layer thickness at the exit remains nearly consistent 

through the blades. The pitch angle in Figure 20(c) reflects overturning at the endwall; further up the 

span, the flow tends towards the exit metal angle and remains constant spanwise. The integrations at the 

same incidence angle but at a reduced Reynolds and Mach number are shown in Figure 21. The trends are 

the same for both flow conditions. Only five-hole probe data were obtained due to tunnel test-time 

constraints. 

The total-pressure integrations for both angles show good agreement between each passage and 

between the three-hole and five-hole probes. The yaw angle data could only be acquired with the fivehole probe. Passage-to-passage differences in yaw angles and the average offset from 0° are within the 

measurement uncertainty.
NASA/TM—2014-218133 17

(a) Cpt (area averaged) (b) Cpt (area averaged)

(c) β, deg (mass averaged) (c) γ, deg (mass averaged)

Figure 19.—Pitchwise integrations for i = +5.8° at Reb and M2,i = 0.72.

0.0 0.2 0.4 0.6 0.8

0.0

0.1

0.2

0.3

0.4

0.5

4 5-hole

4 3-hole

5 5-hole

5 3-hole

z

H

passage probe  

0.00 0.05 0.10 0.15 0.20 0.25

0.0

0.1

0.2

0.3

0.4

0.5

z

H

(detailed view)

-65 -60 -55 -50 -45

0.0

0.1

0.2

0.3

0.4

0.5

z

H avg. exit metal angle

-1.0 0.0 1.0 2.0

0.0

0.1

0.2

0.3

0.4

0.5

z

H
NASA/TM—2014-218133 18

(a) Cpt (area averaged) (b) Cpt (area averaged)

(c) β, deg (mass averaged) (c) γ, deg (mass averaged)

Figure 20.—Pitchwise integrations for i = –36.7° at Reb and M2,i = 0.72.

0.0 0.2 0.4 0.6 0.8

0.0

0.1

0.2

0.3

0.4

0.5

4 5-hole

4 3-hole

5 5-hole

5 3-hole

z

H

passage probe  

0.00 0.05 0.10 0.15 0.20 0.25

0.0

0.1

0.2

0.3

0.4

0.5

z

H

(detailed view)

-65 -60 -55 -50 -45

0.0

0.1

0.2

0.3

0.4

0.5

z

H

avg. exit

metal angle

-1.0 0.0 1.0 2.0

0.0

0.1

0.2

0.3

0.4

0.5

z

H
NASA/TM—2014-218133 19

(a) Cpt (area averaged) (b) Cpt (area averaged)

(c) β, deg (mass averaged) (c) γ, deg (mass averaged)

Figure 21.—Pitchwise integrations for i = –36.7° at 0.4·Reb and M2,i = 0.35.

TABLE IV.—PASSAGE AVERAGE INTEGRATIONS

i Passage Exit Mis ReCx,2 ω

+5.8°

+5.8°

–36.7° 

–36.7° 

–36.7° 

–36.7° 

4

5

4

5

4

5

0.72

0.72

0.72

0.72

0.35

0.35

530,000

530,000

530,000

530,000

212,000

212,000

0.00044

0.00287

0.02319

0.02109

0.02481

0.02610
NASA/TM—2014-218133 20

4.1.2 Blade Loading

The effects of incidence and Reynolds number on blade loading are shown in Figure 22 for five 

selected incidence cases. The nominal flow conditions are listed above the plots. The loading plots are 

arranged with the highest Reynolds number (4⋅Reb) on the left column decreasing to the minimum tested 

Reynolds number on the right most column (0.4⋅Reb). The incidence angle begins with the highest 

positive incidence in the top row and decreases to the lowest negative incidence at the bottom row. 

There are several notable observations from these data. The blade loading data for i = +15.8°

confirms the three-dimensional characteristics observed in the total-pressure contours for the positive 

incidence in Figure 16. The three dimensionality of the flow can be observed by the spanwise variation in 

the static pressures represented by the colored symbols. A majority of the blade surface had mid-span 

static taps which are shown as the black symbols. This extreme positive incidence is clearly noted to have 

the highest loading of the other incidence angles, which increases with decreasing Reynolds and Mach 

number. For all five flow conditions, the suction surface exhibits a neutral pressure gradient region, 

followed by an abrupt diffusion near x/Cx = 0.45. This jump is indicative of a reattachment following a 

laminar separation bubble (see Hoheisel et al. (Ref. 14)). For this incidence and all subsequent incidence 

angles, the data show excellent blade-to-blade periodicity. 

As incidence decreases, the front portions of the blades unload and the secondary flow effects 

diminish. At zero incidence the blade still exhibits a suction side separation that has moved farther aft on

the blade at x/Cx = 0.8. This separation becomes more prominent at the lowest flow condition. With 

decreasing incidence, negative loading is measured at the front portions of the blade. At i = –16.1°, a 

suction side separation is again observed at the lowest flow condition. When the incidence decreases to i

= –36.7°, a pressure-side separation is observed at the lowest flow condition and is reflected in the 

midspan exit surveys shown later. At the extreme negative incidence of i = –51.0° the pressure side is 

separated for all Reynolds and Mach numbers. This is consistent with Yamamoto and Nouse (Ref. 12)

and Brear et al. (Ref. 25). A suction surface separation/reattachment is still observed which occurs near 

x/Cx = 0.59. 

The effects of exit Mach number on blade loading are shown in Figure 23. All data in this figure were 

acquired at the baseline Reynolds number. The loading increases and the location of minimum Cps moves 

forward with decreasing M2,i. The increased diffusion causes the suction-surface reattachment points to 

move forward.

The net blade loading was calculated for the five incidence angles and plotted in Figure 24. It is 

clearly shown that as the incidence decreases to a large negative values, the overall loading decreases. 

The loading levels are higher for the reduced Mach number conditions at incidence angles between 

+15.8° ≥ i ≥ –16.1°. The net loading converges at –36.7° for all Mach number conditions. At negative 

incidence angles larger than –36.7° the net loading is lower for the low Mach number conditions. How 

this relates to losses will be discussed in the following section. 
4⋅Reb 2⋅Reb 1⋅Reb 1⋅Reb 0.4⋅Reb

Mi,2 = 0.72 Mi,2 = 0.72 Mi,2 = 0.72 Mi,2 = 0.35 Mi,2 = 0.35

Figure 22.—Blade loading (Cps versus x/Cx) for five incidence angles at five flow conditions.

x / Cx 0.0 0.2 0.4 0.6 0.8 

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=+15.8°

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=+15.8°

x / Cx 0.0 0.2 0.4 0 6. 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=+15.8°

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=+15.8°

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=+15.8°

x / Cx 0.0 0.2 0.4 0.6 0.8 

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=+0.0°

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=+0.0°

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=+0.0°

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=+0.0°

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0 0.

0.2

0.4

0.6

0.8

1.0

Cps

i=+0.0°

x / Cx 0.0 0.2 0.4 0.6 0.8 

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=−16.

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=−16.1°

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=−16.1°

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=−16.1°

x / Cx 0.0 0.2 0 4. 0.6 0.8 1.0 -1 2.

-1.0

-0.8

-0.6

-0 4.

-0.2

0 0.

0.2

0.4

0 6.

0.8

1.0

Cps

i=−16.1°

x / Cx 0.0 0.2 0.4 0.6 0.8 

-1.2

-1.0

-0 8.

-0 6.

-0 4.

-0.2

0.0

0.2

0.4

0 6.

0.8

1.0

Cps

i=−36.7

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0 2.

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=−36.7°

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=−36.7°

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=−36.7°

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=−36.7°

x / Cx 0.0 0.2 0.4 0.6 0.8 

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=−51.0

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=−51.0°

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=−51.0°

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

i=−51.0°

x / Cx 0.0 0.2 0.4 0 6. 0.8 1 0. -1.2

-1.0

-0 8.

-0.6

-0.4

-0.2

0.0

0.2

0 4.

0.6

0 8.

1.0

Cps

i=−51.0°

NASA/TM

—2014-218133 21
NASA/TM—2014-218133 22

Figure 23.—Blade loading—Effects of exit Mach number at ReCx,2= 5.30×105 (Reb).

Figure 24.—Net loading versus incidence.

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

c) i=+5.8°, M2,i

=0.35

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

a) i=+5.8°, M2,i

=0.72

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

d) i=−36.7°, M2,i

=0.35

x / Cx 0.0 0.2 0.4 0.6 0.8 1.0 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cps

b) i=−36.7°, M2,i

=0.67

0

0.2

0.4

0.6

0.8

1

1.2

-60 -50 -40 -30 -20 -10 0 10 20

Net Loading

i

4 Re 0.72

2 Re 0.72

Re 0.72

Re 0.35

0.4 Re 0.35
NASA/TM—2014-218133 23

4.2 Two-Dimensional Midspan Results

4.2.1 Exit Survey Data

Midspan total-pressure and exit flow angle (pitch angle) surveys were measured for all 10 incidence 

angles at five flow conditions. Figure 25 to Figure 29show the effects of Reynolds number and Mach 

number variations for a sample of five incidence angles. At the positive incidence angle in Figure 25, the 

influence of the high blade loading and secondary flows on the mid-span total-pressure wake profile is 

observed. As the Reynolds number is reduced, the suction-side wake width increases. This is due to the 

suction-side separation observed in the blade loading. At the baseline Reynolds number, 1.0·Reb, the 

wake width remains constant as the exit Mach number is varied from 0.72 (design) to 0.35. The Mach 

number influences the exit angle as seen in the bottom plot shown in Figure 25 but the exit flow angle is 

relatively independent of Reynolds number. As the Reynolds and Mach numbers decrease, the exit flow 

angle decreases and stays at or above the pressure-side exit metal angle. 

As the incidence decreases, it is noted that the blade becomes unloaded and the flow becomes more 

two-dimensional. The influence of the suction side separation decreases, which results in a narrower wake 

profile as incidence decreases (Figure 26 to Figure 28). For these incidence angles, the trends are still the 

same; as the Reynolds number decreases, the wake width and depth increases. The exit angles begin to 

increase in the negative direction and generally remain between the pressure surface exit metal angle and 

the average exit metal angle. 

Figure 25.—Effects of Reynolds number and exit Mach number at i = +10.8°.

Passage 4 Passage 5

PS exit metal angle

avg exit metal angle

SS exit metal angle

-2.0 -1.5 -1.0 y / pitch -0.5 0.0 0.5 -65

-60

-55

-50

-45

-40

-35 β2

[deg]

PS SS PS SS PS SS

-2.0 -1.5 -1.0 y / pitch -0.5 0.0 0.5

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

4.0×des 0.72

2.0×des 0.72

1.0×des 0.72

1.0×des 0.35

0.4×des 0.35

Pt,1 − Pt

Pt,1 − P2

Cpt

Cpt =

4.0⋅Reb 0.72

2.0⋅Reb 0.72

1.0⋅Reb 0.72

1.0⋅Reb 0.35

0.4⋅Reb 0.35

ReCx,2 Ma2,i
NASA/TM—2014-218133 24

Figure 26.—Effects of Reynolds number and exit Mach number at i = 0.0°.

Figure 27.—Effects of Reynolds number and exit Mach number at i = –16.1°.

PS SS PS SS PS SS

-2.0 -1.5 -1.0 y / S -0.5 0.0 0.5

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

4.0×des 0.72

2.0×des 0.72

1.0×des 0.72

1.0×des 0.35

0.4×des 0.35

Pt,1 − Pt

Pt,1 − P2

Cpt

Cpt =

ReCx,2 Ma2,i

PS exit metal angle

avg exit metal angle

SS exit metal angle

-2.0 -1.5 -1.0 y / S -0.5 0.0 0.5 -65

-60

-55

-50

-45

-40

-35 β2

[deg]

PS SS PS SS PS SS

-2.0 -1.5 -1.0 y / S -0.5 0.0 0.5

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

4.0×des 0.72

2.0×des 0.72

1.0×des 0.72

1.0×des 0.35

0.4×des 0.35

Pt,1 − Pt

Pt,1 − P2

Cpt

Cpt =

ReCx,2 Ma2,i

PS exit metal angle

avg exit metal angle

SS exit metal angle

-2.0 -1.5 -1.0 y / S -0.5 0.0 0.5 -65

-60

-55

-50

-45

-40

-35 β2

[deg]
NASA/TM—2014-218133 25

Figure 28.—Effects of Reynolds number and exit Mach number at i = –36.7°.

Figure 29.—Effects of Reynolds number and exit Mach number at i = –51.0°.

At an incidence of –36.7° (Figure 28), there is little variation in the wake profile due to changes in the 

Reynolds and Mach number. The overall levels of Cpt have decreased at this incidence. At the lowest 

Reynolds number (0.4⋅Reb) there is a small wake width increase on the pressure side. This becomes 

greatly exacerbated at the largest negative incidence tested (i = –51.0°, Figure 29) where the pressure-side 

separation is evident. This separation covers most of the blade passage and its influence increases with 

Passage 4 Passage 5

PS SS PS SS PS SS

-2.0 -1.5 -1.0 y / pitch -0.5 0.0 0.5

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

4.0×des 0.73

2.0×des 0.72

1.0×des 0.72

1.0×des 0.35

0.4×des 0.35

Pt,1 − Pt

Pt,1 − P2

Cpt

Cpt =

ReCx,2 Ma2,i

4.0⋅Reb 0.73

2.0⋅Reb 0.72

1.0⋅Reb 0.72

1.0⋅Reb 0.35

0.4⋅Reb 0.35

PS exit metal angle

avg exit metal angle

SS exit metal angle

-2.0 -1.5 -1.0 y / pitch -0.5 0.0 0.5 -65

-60

-55

-50

-45

-40

-35 β2

[deg]

Passage 4 Passage 5

PS exit metal angle

avg exit metal angle

SS exit metal angle

-2.0 -1.5 -1.0 y / pitch -0.5 0.0 0.5 -65

-60

-55

-50

-45

-40

-35 β2

[deg]

PS SS

PS SS PS SS

-2.0 -1.5 -1.0 y / pitch -0.5 0.0 0.5

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

4.0×des 0.72

2.0×des 0.72

1.0×des 0.62

1.0×des 0.35

0.4×des 0.35

Pt,1 − Pt

Pt,1 − P2

Cpt

Cpt =

ReCx,2 Ma2,i

4.0⋅Reb 0.72

2.0⋅Reb 0.72

1.0⋅Reb 0.62

1.0⋅Reb 0.35

0.4⋅Reb 0.35
NASA/TM—2014-218133 26

decreasing Reynolds number. There is also a small variation on the suction side as well with decreasing 

Reynolds number. At this angle, it is also noted that the wake profile remains unchanged at the fixed 

Mach number (M2,i = 0.35) condition as Reynolds number is varied from 1.0⋅Reb to 0.4⋅Reb. The exit flow 

angle varies little with Reynolds number and remains near the average exit metal angle, except for the 

highest Reynolds number (4.0⋅Reb) where the exit metal angle is lower and is consistent with the exit 

angles measured in Figure 28. The exit angles and loss profiles indicate that at the extreme negative 

incidence conditions, as Reynolds number is decreased, the pressure side separation-induced wake 

thickens substantially. The increased aerodynamic blockage on the pressure-side resets the aerodynamic 

throat upstream and effects increased turning and a more negative discharge angle. 

The effects of incidence-angle variation at the highest and lowest Mach number conditions are 

summarized in Figure 30 and Figure 31, respectively. An order of magnitude variation in Reynolds 

number is reflected between these two figures. The three incidence angles shown represent the cruise 

(i = +5.8°), takeoff (i = –36.7°), and maximum mission incidence (i = –46.0°) angles. At the highest 

Reynolds number (4.0⋅Reb) in Figure 30, the positive incidence produces an overall higher loss and 

decreases with decreasing incidence and loading. In Figure 31, at the lowest Reynolds number (0.4⋅Reb) 

and Mach number of 0.35, large incidence variations are observed. The positive incidence shows a large 

suction side wake which is consistent with the suction-side separation observed in the blade loading. As 

the incidence decreases, the blade is unloaded and the losses decrease. At the takeoff incidence the 

suction-side is attached and a slight increase in pressure-side losses is observed. As the negative incidence 

increases further, an extensive pressure-side separation is evident. 

Figure 30.—Effects of incidence angle at ReCx,2 = 2.12×106 (4·Reb) and M2,i = 0.72.

PS SS PS SS PS SS

y / pitch -2.0 -1.5 -1.0 -0.5 0.0 0.5

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

i = +5.8°

i = −36.7°

i = −46.0°

Pt,1 − Pt

Pt,1 − P2

Cpt

Cpt =

Passage 4 Passage 5
NASA/TM—2014-218133 27

Figure 31.—Effects of incidence angle at ReCx,2 = 2.12×105 (0.4·Reb) and M2,i = 0.35.

4.2.2 Midspan Loss Coefficients

Area-averaged integrations of the total-pressure data were used to calculate midspan profile loss 

coefficients, ω, for each incidence angle and flow condition. Midspan loss coefficients are plotted as a 

function of incidence in Figure 32. The integrations were calculated separately over two complete 

passages, 4 and 5. Passage-to-passage variations are noted at the extreme negative incidence angles. As 

expected, as the Reynolds number decreases, loss levels increase and the loss bucket narrows. For the two 

conditions where the baseline Reynolds number (Reb) is held constant and the Mach number is varied 

from M2,i = 0.72 to M2,i = 0.35, the loss levels are independent of Mach number except at the extreme 

positive (i = +15.8°) and negative (i = –46.0°, and –51.0°) incidence angles. 

The midspan profile loss coefficients were plotted as a function of Reynolds number. The power-law 

functionality was examined and found to be indicative of regions of transitional flow, with the higher 

Reynolds numbers scaling with a –0.1 to –0.2 exponent (turbulent) and the lower Reynolds number 

scaling with –0.5 exponent (laminar); however, the power-law exponent was found to vary with incidence 

angle. Nonetheless, it is interesting that the strongest collapse of the overall bucket on Reynolds number, 

shown in Figure 33, was obtained with a ω ∝ Re-0.5 scaling, indicative of a significant influence of laminar 

flow on the midspan loss levels.

The same loss coefficient data (Figure 32) were plotted in terms of reduced loss and incidence 

according to the Ainley-Mathieson (A-M) scaling (ω/ωi versus i/is) (Ref. 27), shown in Figure 34. For 

each loss curve, ωs = 2×ωi=0 and the stalling incidence, is, is the incidence corresponding to ωs. The A-M 

scaling strongly collapses the data down to i/is = –5°. Thus a canonical shape can be used to represent the 

data, with the following caveat: the narrowing of the loss bucket is found to be a function of Reynolds 

number to an extent beyond that tared out by the scaling on the stalling incidence. That is, the lack of 

collapse at the extreme negative incidence range, though consistent in Reynolds number, reflects a rate of 

change that is not tared out by a change in stalling incidence with Reynolds number.

PS SS PS SS PS SS

y / pitch -2.0 -1.5 -1.0 -0.5 0.0 0.5

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

i = +5.8°

i = −36.7°

i = −46.0°

Pt,1 − Pt

Pt,1 − P2

Cpt

Cpt =

Passage 4 Passage 5

,
NASA/TM—2014-218133 28

Figure 32.—Midspan loss versus incidence.

Figure 33.—Re-0.5 scaled midspan loss versus incidence.

0

0.05

0.1

0.15

0.2

0.25

0.3

-60 -50 -40 -30 -20 -10 0 10 20

ω (Area Averaged)

i, Incidence [deg]

4 0.72 4

4 0.72 5

2 0.72 4

2 0.72 5

1 0.72 4

1 0.72 5

1 0.35 4

1 0.35 5

1 0.35 4

1 0.35 5

(Recx,2)/〖Re〗_b

0

0.05

0.1

0.15

0.2

0.25

0.3

-60 -50 -40 -30 -20 -10 0 10 20

ωcorrected (Area Averaged)

i, Incidence [deg]

4 0.72 4

4 0.72 5

2 0.72 4

2 0.72 5

1 0.72 4

1 0.72 5

1 0.35 4

1 0.35 5

1 0.35 4

1 0.35 5

(Recx,2)/〖Re〗_b M2,i

ωcorrected (area averaged)

i, Incidence (deg)

i, Incidence (deg)

ω (area averaged)
NASA/TM—2014-218133 29

Figure 34.—Midspan loss bucket on Ainley-Mathieson scaling.

Figure 35.—Midspan Loss versus Net blade Loading.

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.2 0.4 0.6 0.8 1 1.2

ω (Area Averaged)

Net Loading

ω/ωi ω (area averaged)
NASA/TM—2014-218133 30

To account for blade loading, the midspan losses were plotted as a function of the net blade loading as 

shown in Figure 35. Overall, the losses increase with decreasing Reynolds number as expected. There is a 

region of net loading (0.53 to 0.74) where there is little variation in loss level and the loss is at the 

minimum. From the loading data in Figure 22 it is noted in this region that the flow over the blade 

becomes two-dimensional and a loss-generating suction surface separation occurs at the lower flow 

conditions. There are high losses at the minimum net blade loading which is due to the gross separation 

on the blade pressure surface. As the net loading increases, secondary flows begin to develop, as seen in 

the flow field data, and a suction side separation causes the loss levels to increase. 

4.2.3 Midspan Turning

The deviation angle, or the difference between the exit flow angle and the mean exit metal angle 

(Δβ2 = β2 + 55.54°), is plotted as a function of incidence in Figure 36. Deviation angles asymptotically 

(see i ≥ –26.0°) approach Δβ2 = 2° as the blade unloads at the design Mach numbers (M2,i= 0.72) and 

Δβ2 = 4° at the lower M2,i= 0.35 conditions. Deviation angles at cruise, i = +5.8°, are between Δβ2 = 5°

(M2,i = 0.72) and Δβ2 = 9° (M2,i= 0.35). At the lower Reynolds number and extreme negative incidence 

angles, the exit flow angles shifts to the exit metal angle. The increased aerodynamic blockage on the 

pressure side of the airfoil at reduced Reynolds numbers is thought to affect the more negative discharge 

angle. 

Figure 36.—Midspan deviation angle from exit metal angle as function of incidence 

and Reynolds number.

-2

0

2

4

6

8

10

12

14

16

-60 -50 -40 -30 -20 -10 0 10 20

Δβ2 [deg]

i, Incidence [deg]

4 0.72 4

4 0.72 5

2 0.72 4

2 0.72 5

1 0.72 4

1 0.72 5

1 0.35 4

1 0.35 5

1 0.35 4

1 0.35 5

(Recx,2)/〖Re〗_b M2,i

∆

β2 (deg)

i, Incidence (deg)
NASA/TM—2014-218133 31

5.0 Conclusions

This thesis was intended to advance the understanding of aerodynamic effect of large incidence angle 

and Reynolds number variations by documenting and explaining measurements on a variable-speed 

power-turbine blade. This work expands on previous work in the open literature by documenting inlet and 

exit characteristics, exit total pressure, flow angles, and blade loading at relevant Reynolds number and 

Mach number conditions.

Detailed survey data at the blade exit showed the influence of secondary flows at positive incidence. 

The low momentum endwall flow was transported by the secondary flows to the suction side. As the 

incidence decreased, the blade row became unloaded and the secondary flows reduced. The flow field 

became largely two dimensional at this unloaded condition. 

The blade loadings at different spanwise locations corroborated the two-dimensionality of the 

flowfield at the negative incidence condition. This test was run at low inlet turbulence levels in order to 

admit transitional flow on the blade surface. The measured loading reflected transitional flow on the blade 

suction surface. With the exception of the maximum Reynolds number condition, the loading diagrams 

were consistent with a laminar separation, transition, and reattachment as a turbulent boundary layer. At 

the negative incidence angles, reverse loading was observed. Pressure surface separation was also noted at 

the extreme negative incidence angles. 

The midspan surveys for all 10 incidence angles were documented. The corresponding integrated 

losses showed that the loss levels decreased with increasing negative incidence until the pressure-side 

cove separation or reattachment occurred. Loss levels increased with decreasing Reynolds number as 

expected, and the range of acceptable loss levels decreased.

The results of this thesis show the effects of incidence and Reynolds number at a low inlet turbulence

level. An additional test looking at the effects in a more engine-realistic high turbulence environment is 

warranted. 

NASA/TM—2014-218133 33

Appendix—Symbols List

Cps static pressure coefficient, (P − P2 ) (Pt,1 − P2 )

Cpt total-pressure coefficient, (Pt,1 − Pt) (Pt,1 − P2 )

Cx blade axial chord, in.

H blade span, in.

M Mach number

N power-turbine shaft speed, rpm

N* N/N100%, fraction of 100 percent speed

PR pressure ratio, PR = Pt,1 P2

PS pressure surface

P area-averaged static-pressure

Ps static pressure

Pt total pressure

Pt area-averaged total-pressure

Re Reynolds number, Re = ρ2U2Cx/μ

Reb baseline exit Reynolds number, Reb = 5.30×105

S blade pitch, in.

SS suction surface

Tu turbulence intensity, us

2 U

U total mean velocity, ft/s

U mean velocity, ft/s, (Ux, Uy, Uz)

Zw Zweifel coefficient, 2 ( 1 2 ) 2 cos tan tan

2 β β − β Cx

S

i incidence angle, β1 – inlet metal angle (34.2°)

u fluctuating velocity, (ux, uy, uz)

x chordwise (axial) coordinate, in.

y pitchwise (tangential) coordinate, in.

z spanwise coordinate, in.

Δβ2 departure angle from trailing edge mean camber line

β relative flow angle, pitch angle, deg., tan–1

(Uy / Ux)

β2 angle of mass-averaged velocity components

γ yaw angle, deg., tan–1

(Uz / Ux)

δ1 boundary-layer displacement thickness, in.

δ2 momentum thickness, in.

δ99 boundary layer thickness, in.

μ dynamic viscosity
NASA/TM—2014-218133 34

ρ density

τ probe time constant, s

ω loss coefficient, (Pt,1 − Pt) (Pt,1 − P2 )

ωc loss coefficient, ω (Re/Reb)

1/2

Subscripts

1 cascade inlet value

2 cascade exit value

i isentropic value

s streamwise component

t total condition
NASA/TM—2014-218133 35

References

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Concepts,” NASA/TM–2009–215456; also ARL-TR-4728, Mar., 2009.

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Large Civil Tilt-Rotor Application,” Proc. of the AHS Int. 66th Annual Forum, Arizona, May 2010; 

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(LCTR),” Proc. AHS Int. 65th Ann. Forum, May, 2009.

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Application of Ultra High Lift Blading in the BR715 LP Turbine,” J. Turbomachinery, 124, Jan 

2002, pp. 45-51.

9. Gier, J., Franke, M., Hübner, N. and Shröder, T., “Designing LP Turbines for Optimized Airfoil 

Lift,” ASME-GT2008-51101, 2008.

10. Halstead, D.E., Wisler, D.C., Okishii, T.H., Walker, G.J., Hodson, H.P, Shin, H-W., “Boundary 

Layer Development in Axial Compressors and Turbines: Part 3 of 4—LP Turbines,” J. 

Turbomachinery, 119 (2), pp.225-237, April 1997.

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Cascade,” J. Turbomachinery, 109, pp.201-209. 

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method for turbine airfoils,” J. Turbomachinery, 112, Apr., pp. 267-276.

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2012. NASA/TM—2013-218070.
NASA/TM—2014-218133 36

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J. Turbomachinery, 132, Oct, pp. 041006-1 – 13.

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Turbines,” Aeronautical Research Council (ARC), R&M 2974, 1957.

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4. TITLE AND SUBTITLE

Aerodynamic Measurements of a Variable-Speed Power-Turbine Blade Section in a

Transonic Turbine Cascade

5a. CONTRACT NUMBER

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6. AUTHOR(S)

Flegel, Ashlie, B.

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WBS 877868.02.07.03.01.02.01

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135-3191

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E-18929

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14. ABSTRACT

The purpose of this thesis is to document the impact of incidence angle and Reynolds number variations on the three-dimensional flow field

and midspan loss and turning of a two-dimensional section of a variable-speed power-turbine (VSPT) rotor blade. Aerodynamic

measurements were obtained in a transonic linear cascade at NASA Glenn Research Center in Cleveland, Ohio. Steady-state data were

obtained for 10 incidence angles ranging from +15.8° to -51.0°. At each angle, data were acquired at five flow conditions with the exit

Reynolds number (based on axial chord) varying over an order-of-magnitude from 2.12×105

 to 2.12×106. Data were obtained at the design

exit Mach number of 0.72 and at a reduced exit Mach number of 0.35 as required to achieve the lowest Reynolds number. Midspan totalpressure and exit flow angle data were acquired using a five-hole pitch/yaw probe surveyed on a plane located 7.0 percent axial-chord

downstream of the blade trailing edge plane. The survey spanned three blade passages. Additionally, three-dimensional half-span flow fields

were examined with additional probe survey data acquired at 26 span locations for two key incidence angles of +5.8° and -36.7°. Survey

data near the endwall were acquired with a three-hole boundary-layer probe. The data were integrated to determine average exit totalpressure and flow angle as functions of incidence and flow conditions. The data set also includes blade static pressures measured on four

spanwise planes and endwall static pressures.

15. SUBJECT TERMS

Turbines; Turbomachinery; Axial flow turbines; Tilt rotor aircraft; Aerodynamics

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