Gerard E. Welch

Glenn Research Center, Cleveland, Ohio

Computational Assessment of the Aerodynamic 

Performance of a Variable-Speed Power Turbine 

for Large Civil Tilt-Rotor Application

NASA/TM—2011-217124

November 2011
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Gerard E. Welch

Glenn Research Center, Cleveland, Ohio

Computational Assessment of the Aerodynamic 

Performance of a Variable-Speed Power Turbine 

for Large Civil Tilt-Rotor Application

NASA/TM—2011-217124

November 2011

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

67th Annual Forum and Technology Display (Forum 67)

sponsored by the American Helicopter Society

Virginia Beach, Virginia, May 3–5, 2011
Acknowledgments

The author is grateful to Dr. Rodrick V. Chima for his expert assistance with his RANS tools and to Dr. John P. Clark (AFRL) 

for facilitating use of the AFRL Turbine Design and Analysis System (TDAAS) at NASA. This work was funded by the NASA 

Fundamental Aeronautics program, Subsonic Rotary Wing project.

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

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

This report contains preliminary fi ndings, 

subject to revision as analysis proceeds.

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.
NASA/TM—2011-217124 1 

Computational Assessment of the Aerodynamic Performance of a 

Variable-Speed Power Turbine for Large Civil Tilt-Rotor Application 

Gerard E. Welch 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

The main rotors of the NASA Large Civil Tilt-Rotor notional 

vehicle operate over a wide speed-range, from 100% at take-off 

to 54% at cruise. The variable-speed power turbine offers one 

approach by which to effect this speed variation. Key aerochallenges include high work factors at cruise and wide (40 to 

60°) incidence variations in blade and vane rows over the speed 

range. The turbine design approach must optimize cruise 

efficiency and minimize off-design penalties at take-off. The 

accuracy of the off-design incidence loss model is therefore 

critical to the turbine design. In this effort, 3-D computational 

analyses are used to assess the variation of turbine efficiency 

with speed change. The conceptual design of a 4-stage variablespeed power turbine for the Large Civil Tilt-Rotor application is 

first established at the meanline level. The design of 2-D airfoil 

sections and resulting 3-D blade and vane rows is documented. 

Three-dimensional Reynolds Averaged Navier-Stokes 

computations are used to assess the design and off-design 

performance of an embedded 1.5-stage portion—Rotor 1, 

Stator 2, and Rotor 2—of the turbine. The 3-D computational 

results yield the same efficiency versus speed trends predicted 

by meanline analyses, supporting the design choice to execute 

the turbine design at the cruise operating speed. 

Nomenclature 

AN2 product of annulus area and shaft-speed squared 

cx axial chord 

h0, h total and static specific enthalpy 

i, iopt incidence, incidence at minimum loss 

N power-turbine shaft speed 

N*

 N/N100%, fraction of 100% speed 

PRTT overall total-pressure ratio 

p0, p total and static pressure 

Recx Reynolds number based on axial chord 

s blade pitch, or specific entropy 

T0 total temperature 

TRTT overall total-temperature ratio 

Tu turbulence intensity 

u (ux, u, ur), absolute velocity 

U rotor speed at pitchline 

Y ௣బ,భି௣బ,మ

௣బ,భି௣మ

, loss coefficient 

Z ௦

௖ೣ

ఘ௨ೣሺ୳θ,భି୳θ,మሻ

௣బ,ೝ,భି௣మ

, Zweifel loading parameter 

W weight flow 

 absolute and relative flow angles 

TT adiabatic efficiency (total-to-total) 

 turbulent kinetic energy 

 density 

ψ h0/U2

, work factor 

φ ux/U, flow coefficient 

 vorticity 

Subscripts 

c corrected to standard day 

1, 2 Blade-row inlet, blade-row exit 

4.5 power turbine inlet 

r rotor (blade), or relative condition 

Introduction 

A key challenge of the NASA Large Civil Tilt-Rotor (LCTR) 

mission is the required variation of main rotor tip-speed from 

650 ft/s (100%) at take-off to 350 ft/s (54%) at cruise (Ref. 1). 

The wide speed variation can be accomplished by using a multispeed transmission with a fixed-speed power turbine. 

Alternatively, the speed change can be effected by varying the 

speed of the power turbine rather than the transmission gearratio. The variable-speed power-turbine (VSPT) approach is used 

in the V-22, in which the output speed of the AE1107 engine 

varies speed in the range 80% < N/N100% < 100% (Ref. 2). The 

present study was focused on the VSPT approach to meeting the 

speed range requirement of the LCTR mission. 

Results from NASA engine cycle studies (Ref. 3) were used 

to determine that LCTR power-turbine enthalpy extraction 

levels at take-off and cruise are nearly equal; therefore, the 

work factor, h0/U2

, at cruise (54% N*) is about 3.5 times that 

at take-off (100% N*

). The high work factors at cruise, speedchange requirement, and 28-kft altitude operation lead to 

significant aero-challenges (Ref. 4): (1) attainment of high 

efficiency at high work factor; (2) management of large (40 to 
NASA/TM—2011-217124 2 

60°) incidence swings in all embedded vane/blade rows, and 

(3) operation at low (60 to 100 k) Reynolds number. The 

present study is focused on performance levels at design-point 

(28 kft cruise, 54% N*

) and off-design (2 kft take-off, 

100% N*

), and in particular the variation in VSPT performance 

with shaft-speed change. 

A conceptual aero-design approach for the VSPT of the 

LCTR application was outlined earlier (Ref. 4). The design airangles of a 4-stage VSPT were set at the cruise operating 

condition (54% N*

) where Reynolds numbers were lowest and 

work factors (h0/U2

) were highest. The impact of design point 

work factor on efficiency is documented in Figure 1. In 

addition to illustrating the decrease in design-point efficiency 

with work factor, the impact of operation at high (40 to 60°) 

negative incidence at the 100% speed take-off condition is 

shown as well. The meanline results—for example, compare the 

two green triangles of the present study—indicate that efficiency 

at the off-design take-off point is higher than at the cruise designpoint. At off-design, although the air-angles are far from 

design, the turbine is lightly loaded (aerodynamically) and 

blade-row turning is low. The stage efficiency potential at the 

low work factor is high enough that, even with high incidenceinduced loss production, the off-design efficiency exceeds that at 

design. The accuracy of this predicted trend depends strongly on 

the incidence correlation of the meanline system. 

In an earlier study (Ref. 4), 2-D CFD analyses (Fig. 2(a)) 

were used to assess the range of useful incidence as a function 

of Reynolds number for the relevant LPT mid-span section of 

Clark et al. (Ref. 11). The 100% N*

 operating condition had 

50° of negative incidence, leading to a separated region in the 

cove on the blade pressure-side (Fig. 2(a)). In spite of the 

pressure-side separation, the profile loss at –50°. incidence was 

quite acceptable. In the same study (Ref. 4), the loss buckets in 

Figure 2(a) were shown to collapse on the standard AinleyMathieson incidence-loss correlation (Ref. 12). Thus, the 

efficiency versus operating speed trend of the meanline was 

substantiated by the loss buckets of the 2-D analysis. The 2-D 

and meanline analyses omit loss mechanisms and flow 

structures associated with 3-D aerodynamics and acceleration 

fields due to rotation. Considering Figure 2(b), for example, it 

is clear that the benign cove separation of the 2-D analysis is 

associated with a tornado like structure which transports low 

momentum flow radially outward toward the casing. The reset 

of the spanwise flow by secondary flows and radial transport is 

of particular concern in blade rows with high aerodynamic 

loading levels and turning. The present work was motivated by 

the need to verify, at the 3-D level, the loss versus incidence 

correlation of vane and blade (rotating) rows. 

The key objective of the present effort was to conduct 3-D 

aero-design and analysis of a relevant stage of the VSPT 

turbine at a level sufficient to verify that the design (54% N*

) 

and off-design (100% N*

) performance of 3-D computational 

results is consistent with the meanline design/analysis used in 

the conceptual design of the VSPT for the LCTR. The paper is 

organized as follows: The aerodynamic design methodology, 

including meanline analysis used to design the 4-stage VSPT 

and 3-D design used to design incidence-tolerant blading, is 

first provided. Computational analysis of a selected three 

blade-row embedded 1.5-stage at design and off-design 

conditions is then provided to gauge performance potential and 

variation with shaft speed. Finally, conclusions from the 

present study are provided. 

Figure 1.—Modified Smith chart showing design-point efficiency as a function 

of work factors for 3- and 4-stage VSPT meanline designs by Welch (Ref. 4) 

and D’Angelo (Ref. 5), compared with open literature (AMDCKO) (Refs. 6 to 8) 

meanline performance, Smith data (Ref. 9) and LPT turbine data (Ref. 10). 

Efficiencies of 

1965

Smith Chart

3-stage

(D′Angelo)

AMDCKO

4-stage

(D′Angelo)

3-stage

(D′Angelo)

Work factor, ψ

1 2 3 4 5

80

85

95

90

Stage efficiency, η

45E9 AN2

7862 rpm

4-stage 1976 LPTs

(Oates)

Improved

Aero

At take-off

(off-design

100% speed)

40 to 60-deg.

negative

incidence

45E9 AN2

8147 rpm

3-stage

47.7E9 AN2

8100 rpm

4-stage
NASA/TM—2011-217124 3 

 (a) (b)

Figure 2.—Loss bucket for high-lift rotor blading of Clark (Ref. 11), showing cruise (design air angles) and take-off (–50° 

incidence) operation. (a) 2-D mid-span loss bucket. (b) Flow in representative LCTR VSPT rotor at –50° incidence. 

Aerodynamic Design Methodology 

The conceptual design of the VSPT and the detailed aero 

design/optimization of airfoil sections and blade rows are 

documented in this section. The intent of the conceptual 

design at the meanline level was to obtain flow path 

geometry, air angles and boundary conditions for subsequent 

airfoil and 3-D blade row design, and to gauge expected 

design and off-design performance levels. The intent of the 

3-D design was to create a representative embedded 1.5 

stage (R1/S2/R2) with design-point stage efficiencies 

consistent with the meanline, in which the impact of offdesign operation of a rotor impacts the off-design 

performance of a stator (R1/S2), and vice-versa (S2/R2). 

Stator 1 (S1) was not included in the simulations because the 

S1 inlet and exit flow angles will not change appreciably 

with speed change; therefore, the S1 design was assumed 

achievable, and the S1 exit conditions at design and offdesign exit flow conditions were set to those of the meanline 

analyses. 

Conceptual Design/Meanline Analysis 

The operational requirements of the VSPT were obtained 

from NASA engine cycle studies (Ref. 3). Key VSPT 

requirements were provided in Table 1 for the 2 kft take-off 

power point (100% N*

) and a 28 kft cruise point (54% N*). 

Design-Point Selection 

The VSPT of this study was designed at the 54% N*

, 

28 kft cruise condition. As documented earlier (Ref. 4), the 

following considerations impacted this decision: mission 

fuel burn is dominated by the 28 kft cruise leg; work factors 

at cruise are 3 to 3.5 times higher than at take-off, and the 

TABLE 1.—VSPT REQUIREMENTS AT KEY FLIGHT 

POINTS OF LCTR MISSION (REF. 3) 

Flight point Take-off Cruise 

Altitude 2kft 28 kft 

VSPT speed (N/N100%) 100% 54% 

Main-rotor tip-speed 650 ft/s 350 ft/s 

Power, SHP 4593 2328 

VSPT mass flow rate, lbm/s 22.03 12.22 

Specific power (BTU/lbm) 147 135 

PT inlet temp (T4.5), R 2204 1812 

PT inlet pres. (p0,4.5), psia 58.0 26.76 

PRTT 4.04 5.34 

Corrected flow, lbm/s 11.51 12.54 

Corrected speed (Nc/Nc100%), % 102.3 60.8 

Aft-stage unit-Re (in–1)

a

 50,000/in. 30,000/in. a

Based on static conditions at last stage rotor exit with Mr,2 = 0.7. 

associated loss buckets are narrower; the positive-incidence 

range of the turbine blade rows is 2 to 3 times narrower than 

the negative-incidence range (see Fig. 2(a)); and, designpoint loss-levels increase and the incidence range decrease 

from take-off to cruise, due to Reynolds number lapse. 

These factors support the choice to design at cruise, so as to 

obtain maximum possible efficiency at cruise turbine-speed 

(54% N*

). The turbine then runs with negative incidence at 

the higher shaft-speed conditions. As noted, results of 

meanline and 2-D CFD analyses indicate that the efficiency 

at the higher shaft-speed points, characterized by lower 

turning and extreme negative incidence, is predicted to be 

higher than at the design point. 

Four-Stage Turbine Design at Meanline Level 

The turbine flow path, number of stages, and design air 

angles were determined using F. Huber’s meanline design 

and off-design codes, which are constituents of the AFRL 

 

a. Loss as a function of incidence.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-80 -60 -40 -20 0 20 40

Profile loss coefficient

i - iopt

L1M, Re_cx,2 = 620k, Tu = 2%

L1M, Re_cx,2 = 62k, Tu = 3%
NASA/TM—2011-217124 4 

Turbine Design and Analysis System (TDAAS) (Ref. 11). 

The meanline codes are consistent with the open-literature 

methodology of Ainley-Mathieson (Ref. 6), Dunham and 

Came (Ref. 7), and Kacker and Okapuu (Ref. 8), referred to 

herein as AMDCKO (see Fig. 1). As in previous work 

(Ref. 4), the aerodynamic loading levels of the vanes (Z = 1) 

and blades (Z = 1.1) are set near unity so as to be consistent 

with operation with transitional flow (Ref. 13) and required 

incidence-tolerance. The stage reaction levels were set near 

0.45. The stage work splits were based on trades between 

optimum efficiency and management of maximum turning 

per stage. The rotors were tip-shrouded and leakage flows 

were neglected. Huber’s off-design code (meanline) was 

used to assess off-design operation. Example design- and 

off-design point performance levels from the Huber code 

were provided in Figure 1. 

A mechanical design constraint of maximum AN2

 based 

on temperatures and anticipated material properties was 

imposed at take-off (100% N*

) hot condition (Ref. 4). In 

the 4-stage design of the previous study (Ref. 4), the 

mechanical limit was set at AN2

 = 45 ∙109 rpm2∙in.2, 

corresponding to an aft blade-row exit annulus area of 

Aex = 212 in.2

 and 100% speed of 14,560 rpm. In the 4-stage 

design considered here, the exit area was maintained at 

Aex = 212 in.2

 and 100% shaft speed was increased to 

15,000 rpm (AN2

 = 47.7 ∙109 rpm2∙in.2). 

The VSPT flow path is provided in Figure 3. Key turbine 

parameters, including blade row incidence levels at offdesign, are provided in Table 2, and the design flow angles 

are provided in Table 3. Note that design-point blade-row 

turning levels are as high as 110°. 

High negative incidence levels (–40 to –60°) are 

experienced by all blade rows (blade, vane, and EGV) at offdesign operation (see Table 2 and Ref. 4). In spite of the 

Figure 3.—Four-stage VSPT flow path from 

Huber’s meanline, showing embedded 1.5-stage 

of computational analysis. No exit guide vane 

(EGV) shown. 

 incidence levels at 100% N*, the VSPT operating map 

(Fig. 4) reflects the increase in efficiency as speed is 

changed from the 8,100 rpm (54% N*

) at the cruise design 

point to the 15,000 rpm (100% N*

) at take-off. Note that the 

corrected flow in the turbine drops slightly as speed is 

increased. 

TABLE 2.—FOUR-STAGE DESIGN FOR LCTR VSPT 

REQUIREMENTS OF TABLE 1 

Take-off Cruise 

Speed (N/N100%) 

Altitude, ft 

100% 

2,000 

54% 

28,000 

VSPT efficiency 0.9294 0.9154 

Total-pressure ratio 4.04 5.34 

N, rpm 15,000 8,100 

Average ψ 0.75 2.36 

Average φ 0.493 0.957 

Average h0, BTU/lbm 41.8 39.1 

Max. AN2, rpm2∙in.2 47.7109

 13.9109

 

Stage efficiency 0.9371, 0.9219, 

0.9229, 0.9068 

0.9105, 0.8887, 

0.9050, 0.9251 

 

Rotor incidence, deg 

(R1, R2, R3, R4) 

–38, –42, 

–50, –54 0 

 

Stator incidence, deg 

(S2, S3, S4, EGV) 

–34, –40, 

–48, –35 

0 

 

Power, SHP 5287 2701 

TABLE 3.—DESIGN-POINT FLOW ANGLES AND LOADING 

FOR 4-STAGE ROTORS (AN2 = 47.7109 rpm2·in.2) 

Stage Vane Rotor 

1 2 Turn 1 2 Turn 

1 0 62 62 42 –56 99 

2 –39 64 104 50 –60 110 

3 –42 62 104 42 –56 98 

4 –31 54 85 27 –47 74 

Figure 4.—VSPT performance map in terms of PRTT as 

a function of corrected flow and rpm of output shaft. 

 

5 10

5

10

R1/S2/R2

X, in.

r, in.

R1 S1

S2 R2

S3

R3 S4 R4

0

0

Wc, lb

m/s
NASA/TM—2011-217124 5 

Two-Dimensional Air Foil Design and Stacking 

With air angles set in the meanline design (assuming free 

vortex flow), the TDAAS (Ref. 11) system was used to 

design and optimize 2-D airfoil sections at hub, mid-span, 

and tip, and to stack the 2-D sections to construct the 3-D 

blade geometry. The 2-D sections were generated by 

Huber’s blade profile generator, a 19-parameter description 

of the turbine blade section, including 5 arbitrary NURBS 

control points. Within TDAAS, the blade generator is driven 

by a MATLAB script, and contains options for Design-ofExperiments (DOE) and gradient search optimization. Effort 

was expended in selecting chordwise loading distributions 

with minimum pressure placed toward the front to midchord regions, consistent with lower-loss operation at low 

Reynolds numbers (Ref. 13). The 2-D analysis of blade 

sections was conducted using the commercial software of 

AeroDynamic Solutions, Inc. (ADS). H-O-H grids were 

generated about blade sections using the ADS WAND code 

and fully turbulent  RANS solutions were obtained 

using the ADS LEO solver. Design-intent for each blade 

section included matching meanline geometry, flow angles, 

gauge angles, and Mach numbers while minimizing totalpressure loss coefficient. The key parameters of the DOE 

optimization were the blade setting angle, the leading edge 

wedge angle, and NURBS control points controlling areaand blade-thickness distributions. The hub, mid-span, and tip 

blade-sections for the R1, S2, and R2 blade rows are shown 

in Figures 5, 6, and 7. 

The hub, mid, and tip sections of a given blade row were 

stacked on their center of gravity along a radial stacking 

axis. No dihedral was considered in the present study, 

although the benefits of using 3-D aerodynamic design—

including bow and lean—are well documented for turbines 

(see, for example, Hourmouziadis (Ref. 14). 

Figure 5.—Hub, mid-, and tip-sections of Rotor 1. 

Figure 6.—Hub, mid-, and tip-sections of Stator 2. 

Figure 7.—Hub, mid-, and tip-sections of Rotor 2. 

Three-Dimensional CFD Analysis Method 

The 3-D blading was analyzed at design and off-design 

conditions using 3-D RANS turbomachinery flow solver, 

SWIFT (Ref. 15). The finite-difference form of the thinlayer Navier-Stokes equations in Cartesian coordinates are 

marched in pseudo-time using a multi-stage explicit RungeKutta integration with implicit residual smoothing. Inviscid 

flux vector differences are calculated using centraldifference with artificial viscosity, or with the H-CUSP 

(used herein) or AUSM+

 upwind schemes. The viscous 

terms are central differenced. Three-dimensional C-grids 

without clearance blocks were used in all blade rows and 

were generated using the TCGRID code (Ref. 16). A suite of 

turbulence sub-models are available, including the BaldwinLomax (Ref. 17) (B-L) and low-Re  turbulence model 

for transitional flows (Ref. 18) used in this study. The 

SWIFT code has been validated against a number of 

turbomachinery data sets. 

 

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

-0.4 -0.2 0 0.2 0.4 0.6

y, in.

x, in.

Hub

Mid

Tip

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

x, in.

x, in.

Hub

Mid

Tip

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

y, in.

x, in.

Hub

Mid

Tip
NASA/TM—2011-217124 6 

Boundary conditions were obtained from the design and 

off-design meanline analyses. Inlet total conditions and swirl 

angles at the mid-span were prescribed along with an 

assumption of free-vortex flow. The free vortex flow is 

consistent with the spanwise flow distributions of the 

meanline code and the 2-D airfoil design. Radial equilibrium 

and a specified hub static pressure were prescribed at the 

exit. 

The mixing-plane interface condition was used between 

blade rows. In addition to neglecting unsteady blade-row 

interaction, the mixing-plane approach does not conserve 

streamwise vorticity between blade rows. While these 

limiting assumptions will impact accuracy, particularly at 

off-design and high-load conditions, the accuracy was 

deemed sufficient to address the principal question of the 

study concerning the trend of VSPT efficiency trend with 

speed change. 

Computational Results 

Computational results for the design (54% N*, 28 kft 

cruise) and off-design (100% N*

, 2 kft take-off) performance 

of the embedded 1.5-stage turbine comprising R1, S2, and 

R2 are considered in this section. First computed design and 

off-design spanwise profiles are compared to meanline 

predictions. At both design (54% N*

) and off-design (100% 

N*

), the 3-D structures associated with secondary flow 

transport and rotor acceleration fields are discussed. Finally, 

the blade row, stage, and overall 1.5-stage performance 

levels at design and off-design are compared. 

Design Point (Cruise at 28 kft, 54% N*) 

Spanwise Profiles 

Spanwise profiles of passage-averaged (mixed-out) 

normalized total-temperature and total-pressure (referenced 

to S1 inlet) and absolute flow angles are provided below 

(Figs. 8 to 10). The computed R1 inlet total-temperature is 

unity (not plotted in Fig. 8), as specified by the meanline 

analysis. The computed inlet boundary-layer thickness is 

evident in the R1 inlet total-pressure profile (black) in 

Figure 9. The computed R1 inlet absolute flow angle (black) 

of Figure 10 matches the free-vortex profile of the meanline. 

In general, the agreement between the 3-D CFD and 

meanline for total-temperature (Fig. 8), an indication of 

work, and total-pressure (Fig. 9) is acceptable, although 

lower enthalpy extraction is achieved by R2 for the 

prescribed total-to-static pressure ratio. A large deficit in 

passage-averaged total-pressure is evident from 60 to 95% 

of span at the exit of S2; similarly, the hub of the R2 

discharge is weak from hub to 20% of span. These low totalpressure sections are consistent with the cross-passage 

contours of entropy shown Figure 11. In addition to low 

enthalpy extraction (and associated turning) in R2 for the 

prescribed total-to-static pressure ratio, the axial rating 

planes for the CFD and meanline are not coincident, and this 

may contribute to the disparity in flow angles in Fig. 10. 

Figure 8.—Spanwise profiles of normalized totaltemperature, T0, at R1 and R2 exits, showing 

comparison with meanline at design point 

(54% N*, 2 kft cruise). 

Figure 9.—Spanwise profiles of normalized totalpressure, p0, at R1 inlet and R1, S2, and R2 exits, 

showing comparison with meanline at design point 

(54% N*

, 2 kft cruise). 

Figure 10.—Spanwise profiles of absolute flow angle at 

R1 inlet and R1, S2, and R2 exits, showing comparison 

with meanline at design point (54% N*

, 2 kft cruise). 

0

10

20

30

40

50

60

70

80

90

100

0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98

Percent span from hub, %

Normalized absolute T0

R1 exit

R2 exit

R1 exit meanline

R2 exit meanline

0

10

20

30

40

50

60

70

80

90

100

0.4 0.5 0.6 0.7 0.8 0.9 1

Percent span from hub, %

Normalized absolute p0

R1 inlet

R1 exit

S2 exit

R2 exit

R1 inlet meanline

R1 exit meanline

S2 exit meanline

R2 exit meanline

0

10

20

30

40

50

60

70

80

90

100

-60 -40 -20 0 20 40 60 80

Percent span from hub, %

Absolute flow angle, deg.

R1 inlet

R1 exit

S2 exit

R2 exit

R1 exit meanline

S2 exit meanline

R2 exit meanline
NASA/TM—2011-217124 7 

Figure 11.—Computed contours of entropy at the 

blade-row exit planes at design point. 

Three-Dimensional Flow Field 

Entropy contours at the exit plane of blade rows R1, S2, 

and R2 are provided in Figure 11. The low momentum flow, 

transported by the secondary flow field, accumulates 

preferentially at the hub/suction-side corners of the rotors 

and at the case/suction-suction side corner of the stator. In 

the present study, these regions of low relative total-pressure 

are mixed-out between blade rows, and are manifested as 

axisymmetric bands (not shown) of high entropy flow 

downstream of each mixing plane; in practice the regions of 

high aero-blockage would be strong sources of spanwise 

mixing and unsteadiness in the downstream blade row. An 

unsteady multistage simulation capability would facilitate 

accurate account of such mechanisms. Three-dimensional 

blade and endwall features, including bow and lean (Ref. 14) 

and nonaxisymmetric endwall contouring (Ref. 19), have 

been demonstrated to be effective in minimizing the 

secondary-flow-field transport and associated loss and 

aerodynamic blockage production. This level of 

aerodynamic design was not pursued in this study. 

Off-Design Point (Take-Off at 2 kft, 100% N*) 

Spanwise Profiles 

Spanwise profiles of normalized total-temperature and 

total-pressure (referenced to S1 inlet conditions), and 

absolute flow angle are provided below. R1 inlet plane 

values of the meanline are plotted where appropriate. As 

with the design-point, the agreement between the 3-D CFD 

and meanline for total-temperature (Fig. 12), total-pressure 

(Fig. 13), and absolute flow angle (Fig. 14) were found 

acceptable; indeed, the agreement at off-design was perhaps 

better than at the design point. The computed R2 enthalpy 

extraction was again low, as at the design point. The 

aerodynamic loading levels in the blade rows are lower at 

the higher shaft-speed condition. The total-pressure profiles 

are more uniform (spanwise) in all sections (Fig. 13). The 

computed flow turning (Fig. 14) is again found to be low 

relative to the meanline. This is consistent with lower 

enthalpy extraction in R2, and may be attributable in part to 

axial offset of the computational and meanline rating planes. 

Figure 12.—Spanwise profiles of normalized total-temperature, 

T0, at R1 and R2 exits, showing comparison with meanline 

at off-design (100% N*

, 2 kft take-off). 

Figure 13.—Spanwise profiles of normalized total-pressure, 

p0, at R1 inlet at R1, S2, and R2 exits, showing comparison with meanline at off-design (100% N*

, 2 kft take-off). 

Figure 14.—Spanwise profiles of absolute flow angle at R1 

inlet and R1, S2, and R2 exits, showing comparison with 

meanline at design point (100% N*, 2 kft take-off).

R1

exit

R2

exit

S2

exit

0

10

20

30

40

50

60

70

80

90

100

0.8 0.85 0.9 0.95 1

Percent span from hub, %

Normalized absolute T0

R1 exit

R2 exit

R1 exit meanline

R2 exit meanline

0

10

20

30

40

50

60

70

80

90

100

0.4 0.5 0.6 0.7 0.8 0.9 1

Percent span from hub, %

Normalized absolute p0

R1 inlet

R1 exit

S2 exit

R2 exit

R1 inlet meanline

R1 exit meanline

S2 exit meanline

R2 exit meanline

0

10

20

30

40

50

60

70

80

90

100

-20 0 20 40 60 80

Percent span from hub, %

Absolute flow angle, deg.

R1 inlet

R1 exit

S2 exit

R2 exit

R1 exit meanline

S2 exit meanline

R2 exit meanline
NASA/TM—2011-217124 8 

Three-Dimensional Flow Field 

Entropy contours at the exit plane of blade rows R1, S2, 

and R2 are provided in Figure 15. As at the design point 

(Fig. 11), the secondary flow fields transport flow to the 

rotor hub/suction-side corners and stator case/suction-side 

corner. In general, the regions of lower total-pressure are 

more diffuse, particularly in the high-turning second rotor, 

R2, due to radial transport induced by acceleration fields of 

rotation and associated redistribution of low momentum 

flow from the hub regions to the casing via the pressure-side 

cove separation/vortex (Figs. 2(b) and 16). 

It was noted that the lower-turning rotor, R1, was not 

impacted as strongly as the higher turning blade rows (S2 

and R2). Indeed a blade-to-blade view of the 1.5-stage 

(Fig. 16) reflected little reverse flow in the cove region of 

R1. In R2, a strong vortical structure (tornado) was induced 

by the radial acceleration fields associated with rotor 

rotation and the substantial region of reversed flow in the 

pressure-side cove. Low momentum flow is transported 

outward, through the cove separation, toward the case. S2 

had significant regions of reverse flow in the pressure-side 

cove as well; however, without the strong radial acceleration 

fields, no comparable 3-D structure was formed. 

Figure 15.—Computed contours of entropy at the blade-row 

exit planes at the 100% N*

 off-design take-off point. 

Design and Off-Design Performance 

The performance of the individual blade rows and overall 

1.5-stage were provided in Table 4. The meanline 

efficiencies reported in Table 4 were re-calculated for this 

comparison using the temperatures from the meanline and 

the constant ratio of specific heats of the corresponding 3-D 

computation. Note, for example, that the S2/R2 efficiency is 

0.9005 with this approach rather than 0.8887 (see Table 3) 

of the meanline output. The CFD parameters are based on 

mixed-out properties, accounting for loss production in the 

blade rows and in downstream-mixing. 

The computed (B-L and ) R1 rotor-alone efficiencies 

at design and off-design are consistently about 1 point lower 

than meanline. The R1 efficiency increases from design to 

off-design, as in the meanline analysis. The computed stator 

S2 design-point loss is twice that of the meanline calculation 

at both design and off-design, and strongly shifts all stage 

efficiencies to lower levels. The S2 loss decreases from 

design to off-design in agreement with the meanline. The 

design- and off-design efficiencies of the high-turning R2 

are essentially equal. Relative to the meanline results, R2 

efficiency is 2 points low at design and 4.5 points low at offdesign. The efficiency variation with speed of the meanline 

Figure 16.—Computed contours of axial velocity and 

streamlines in R1 and R2 at the 100% N*

 off-design 

take-off point. 

TABLE 4.—COMPARISON OF 3-D COMPUTATIONAL RESULTS WITH MEANLINE PREDICTIONS 

Design (54% N*,  = 1.33) Off-design (100% N*,  = 1.315) 

Model B-L a Meanline B-L a Meanline 

R1 tt 0.9108 0.9152 0.9275 0.9439 0.9481 0.9530 

R2 tt 0.9254 0.9329 0.9453 0.9251 0.9258 0.9692 

R1/S2tt 0.8083 0.8100 0.8682 0.8695 0.8679 0.9080 

S2/R2 tt 0.8398 0.8444 0.9005 0.8334 0.8269 0.9042 

R1/S2/R2 tt 0.8749 0.8792 0.9152 0.9023 0.9013 0.9448 

S2 Y 0.1387 0.1414 0.0718 0.1214 0.1326 0.0666 

S2 dp0/p0 0.0426 0.0436 0.0222 0.0297 0.0329 0.0165 

PRTT R1/S2/R2 2.1438 2.1375 2.1454 2.1303 2.1307 2.1555 

TRTT R1/S2/R2 1.1776 1.1779 1.1875 1.1758 1.1756 1.1887 

Wc, lbm/s 12.865 12.942 12.868 12.306 12.423 12.060 a

Low Reynolds number model.

 

R1

exit

R2

exit

S2

exit

R1

R2

S2
NASA/TM—2011-217124 9 

Figure 17.—Variation of embedded 1.5 stage (R1/S2/R2) 

adiabatic efficiency with speed from cruise (54% N*

) to 

take-off (100% N*

). 

is not supported by the CFD, potentially due to the 

deleterious impact on performance of the cove vortex 

(tornado) at the extreme negative incidence of take-off, 

which is not accounted for in the secondary-flow loss model 

of the meanline solver. 

Embedded Stage Efficiency Trend With Speed 

Change 

The principal objective of the present study was to 

determine the variation of embedded 1.5-stage (R1/S2/R2) 

efficiency with speed. As shown in Table 4, the embedded 

stage efficiency increases from cruise to take-off operation. 

The variation is plotted in Figure 17. The CFD results were 

found to follow the meanline. This is the key finding of this 

study, emphasizing that the design-point shaft-speed should 

be set near the cruise shaft-speed (54% N*

), as done in the 

present study. 

At both cruise (54% N*

) and take-off (100% N*), the 

overall R1/S2/R2 efficiencies predicted by CFD are 

consistently about four points lower than the meanline 

values (Fig. 17). The slight change in slope of the low-Re 

 model relative to the fully turbulent B-L and meanline 

models can be attributed to regions of low-loss laminar flow, 

on the accelerating portions of the suction-side, admitted by 

the low-Re  transition sub-model at cruise Reynolds 

number. Highly loaded aft stages may well trend differently. 

Conclusions 

The performance of representative blade rows of a 

variable-speed power turbine for the NASA LCTR 

application, in particular the variation of efficiency with 

shaft-speed change, was the subject herein. A conceptual 

design of the LCTR VSPT led to a 4-stage turbine designed 

for an altitude (28 kft) cruise point. The turbine performance 

map and key turbine parameters were provided. The design 

approach led to a turbine with 91.5% cruise-point (54% N*

, 

28 kft) efficiency and 92.9% efficiency at take-off 

(100% N*

, 2 kft) at the meanline level. 

A key objective of the study was to verify, using 3-D 

RANS analyses, the efficiency versus speed trend of the 

meanline analyses. The concern was that 3-D flow features 

associated with transport due to radial acceleration fields and 

cross-passage gradients would lead to higher losses at the 

extreme negative incidence operation of the 100% N*

 takeoff condition than predicted by the meanline loss 

correlations and 2-D CFD analyses. To this end, a 3-D 

design of a representative embedded 1.5-stage was designed 

and analyzed. The design- and off-design performance were 

found to be sufficiently close to the design intent to be 

considered relevant for use in assessing the variation of 

efficiency with shaft-speed. 

Two significant 3-D aero effects were noted in the 3-D 

RANS analyses. Firstly, as normative in highly loaded blade 

rows, the secondary flow fields transported low momentum 

fluid to the rotor hub/suction-side corners and stator 

case/suction-side corners. This occurred at both design and 

off-design conditions. Secondly, at the 100% N*

 off-design 

condition, the separation in the cove region of the pressureside of R2 and the radial acceleration fields combined to 

form a tornado-like structure which transported flow radially 

outward along the cove to the case. No such structure existed 

in the first rotor, R1, as the negative incidence levels in the 

first rotor did not cause a cove separation. Although a strong 

cove separation was found in S2 at off-design, the absence 

of the acceleration fields of rotation precluded formation of 

the tornado-like cove vortex found in R2. 

Consistent with meanline analyses, the blade-row loss 

levels were generally found to be lower at the off-design 

conditions where, though operating with 40 to 60-deg. of 

negative incidence, the blade rows are unloaded. An 

exception to this general trend of higher efficiency at offdesign was found in R2, attributable to the impact of the 3-D 

cove vortex. This finding may push future rotor airfoil 

designs toward thicker sections that admit less of a pressureside cove. Enhancement of the meanline secondary loss 

model for rotors at extreme negative incidence, to account 

for increased loss due to such 3-D structures, appears to be 

warranted as well. 

Although the regions of loss associated with the 3-D flow 

structures detailed here reset the spanwise profiles, as shown 

in the CFD and meanline comparisons, the variation of 

embedded 1.5-stage efficiency with shaft-speed was found 

to match that predicted by the meanline. This agreement 

between 3-D RANS computations and the meanline both 

corroborates the incidence correlation of the meanline 

code—with the exception of R2 deficiency noted above—

and supports the conceptual design approach that establishes 

the design speed at the lowest operating shaft speed 

(54% N*

, cruise). In practice, the specific VSPT design 

speed is expected to be strongly biased toward the cruise 

shaft-speed, and selected so as to minimize mission fuel 

burn. 

0.87

0.88

0.89

0.9

0.91

0.92

0.93

0.94

0.95

0 0.2 0.4 0.6 0.8 1 1.2

Adiabatic efficiency of R1/S2/R2

N / N100%

CFD B-L

CFD k-w

Meanline

Cruise

Take-off
NASA/TM—2011-217124 10 

References 

1. Acree, C.W., Hyeonsoo, Y., and Sinsay, J.D., 

“Performance Optimization of the NASA Large Civil 

Tiltrotor,” Proc. Int. Powered Lift Conf., London, UK, 

July 22–24, 2008. 

2. Wilkerson, J.B. and Smith, R.L., “Aircraft System 

Analysis of Technology Benefits to Civil Transport 

Rotorcraft,” NASA/CR—2009-214594, June, 2009. 

3. Snyder, C.A. and Thurman, D.R., "Gas Turbine 

Characteristics for a Large Civil Tilt-Rotor (LCTR)," 

Proc. AHS Int. 65th Ann. Forum, Grapevine, TX, May, 

2009; also NASA/TM—2010–216089, Feb. 2010. 

4. Welch, G. E., “Assessment of Aerodynamic Challenges 

of a Variable-Speed Power Turbine for Large Civil TiltRotor Application,” Proc. AHS Int. 66th Ann. Forum, 

Phoenix, AZ, May, 2010; also NASA/TM—2010-

216758, Aug. 2010. 

5. D′Angelo, M., “Wide Speed Range Turboshaft Study,” 

NASA/CR—1995–198380, Aug. 1995. 

6. Ainley, D.G. and Mathieson, G.C.R., “A Method of 

Performance Estimation for Axial-Flow Turbines,” 

Aeronautical Research Council (ARC), R&M 2974, 

1957. 

7. Dunham, J. and Came, P.M., “Improvements to the 

Ainley-Mathieson Method of Turbine Performance 

Prediction,” J. Eng. for Power, July, 1970, pp. 252–256. 

8. Kacker S.C., and Okapuu. U., “A Mean Line Prediction 

Method for Axial Flow Turbine Efficiency,” J. Eng. 

Power, 104, Jan, 1982, pp. 111–119. 

9. Smith, S.F., “A Simple Correlation of Turbine 

Efficiency,” J. Royal Aero. Soc., 69, 1965, p. 467–470. 

10. Oates, G.C, Aerothermodynamics of Aircraft Engine 

Components, AIAA Education Series, 1985. 

11. Clark, J.P., Koch, P.J., Ooten, M.K., Johnson, J.J., 

Dagg, J., McQuilling, M.W., Huber, F., and Johnson, 

P.D., “Design of Turbine Components to Answer 

Research Questions in Unsteady Aerodynamics and 

Heat Transfer,” AFRL-RZ-WP-TR-2009-2180, Sept, 

2009. 

12. Ainley, D.G. and Mathieson, G.C.R., “An Examination 

of Flow and Pressure Losses in Blade Rows of Axial 

Turbines, British Aeronautical Research Council 

(ARC), R&M 2891, 1955. 

13. Gier, J., Franke, M., Hübner, N. and Shröder, T., 

“Designing LP Turbines for Optimized Airfoil Lift,” J. 

Turbomachinery, 132, Jul, 2010, pp. 031008-1 to -12. 

14. Hourmouziadis, J., “Aerodynamic Design of Low 

Pressure Turbines,” in Blading Design for Axial Turbomachines, AGARD-LS-167, pp. 8–1 to 8–40, 1989. 

15. Chima, R.V., "Calculation of Multistage 

Turbomachinery Using Steady Characteristic Boundary 

Conditions," AIAA-98-0968, Jan. 1998; also 

NASA/TM—1998-206613. 

16. Chima, R.V., “TCGRID 3-D Grid Generator for 

Turbomachinery—User’s Manual and Documentation,” 

Dec. 1999. 

17. Baldwin, B.S. and Lomax, H., “Thin-Layer 

Approximation and Algebraic Model for Separated 

Turbulent Flows,” AIAA 78–257, Jan. 1978. 

18. Wilcox, D.C., Turbulence Modeling for CFD, DCW 

Industries, Inc., La Canada, CA, 1994. 

19. Knezevici, D.C., Sjolander, S.A., Praisner, T.J., 

AllenBradley, E., Grover, E.A., “Measurements of 

Secondary Losses in a Turbine Cascade With the 

Implementation of Nonaxisymmetric Endwall 

Contouring,” J. Turbomachinery, 132, Jan, 2010, pp. 

011013-1 to -10. 
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Computational Assessment of the Aerodynamic Performance of a Variable-Speed Power 

Turbine for Large Civil Tilt-Rotor Application 

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14. ABSTRACT

The main rotors of the NASA Large Civil Tilt-Rotor notional vehicle operate over a wide speed-range, from 100% at take-off to 54% at 

cruise. The variable-speed power turbine offers one approach by which to effect this speed variation. Key aero-challenges include high work 

factors at cruise and wide (40 to 60°) incidence variations in blade and vane rows over the speed range. The turbine design approach must 

optimize cruise efficiency and minimize off-design penalties at take-off. The accuracy of the off-design incidence loss model is therefore 

critical to the turbine design. In this effort, 3-D computational analyses are used to assess the variation of turbine efficiency with speed 

change. The conceptual design of a 4-stage variable-speed power turbine for the Large Civil Tilt-Rotor application is first established at the 

meanline level. The design of 2-D airfoil sections and resulting 3-D blade and vane rows is documented. Three-dimensional Reynolds 

Averaged Navier-Stokes computations are used to assess the design and off-design performance of an embedded 1.5-stage portion-Rotor 1, 

Stator 2, and Rotor 2-of the turbine. The 3-D computational results yield the same efficiency versus speed trends predicted by meanline 

analyses, supporting the design choice to execute the turbine design at the cruise operating speed. 

15. SUBJECT TERMS

Low pressure turbine; Rotary wing; Aerodynamics 

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