Gerard E. Welch

Glenn Research Center, Cleveland, Ohio

Assessment of Aerodynamic Challenges of

a Variable-Speed Power Turbine for Large

Civil Tilt-Rotor Application

NASA/TM—2010-216758

August 2010
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Gerard E. Welch

Glenn Research Center, Cleveland, Ohio

Assessment of Aerodynamic Challenges of

a Variable-Speed Power Turbine for Large

Civil Tilt-Rotor Application

NASA/TM—2010-216758

August 2010

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

66th Annual Forum and Technology Display (AHS Forum 66)

sponsored by the American Helicopter Society

Phoenix, Arizona, May 11–13, 2010
Acknowledgments

The author is indebted to Mr. Robert J. Boyle (former NASA Glenn Research Center (GRC) Distinguished Research Associate) 

for innumerable conversations related to variable-speed power turbine, to Mr. Christopher A. Snyder (NASA GRC/RTM) for 

continued efforts in setting and refi ning the Large Civil Tilt-Rotor (LCTR) power-turbine requirements, and to Dr. Rodrick V. 

Chima for assistance with his Reynolds-Averaged Navier-Stokes (RANS) tools. The author is indebted to Dr. John P. Clark,

Air Force Research Laboratory (AFRL) for sharing his insights concerning computational modeling of transitional LPT

fl ows, for providing the L1-series blade sections, and for generously installing the AFRL Turbine Design and

Analysis System (TDAAS) at NASA.

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://gltrs.grc.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.
NASA/TM—2010-216758 1 

Assessment of Aerodynamic Challenges 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 (100% at 

take-off to 54% at cruise). The variable-speed power turbine, 

when coupled to a fixed-gear-ratio transmission, offers one 

approach to accomplish this speed variation. The key aerochallenges of the variable-speed power turbine are related to 

high work factors at cruise, where the power turbine operates 

at 54% of take-off speed, wide incidence variations into the 

vane, blade, and exit-guide-vane rows associated with the 

power-turbine speed change, and the impact of low aft-stage 

Reynolds number (transitional flow) at 28 kft cruise. Meanline 

and 2-D Reynolds-Averaged Navier-Stokes analyses are used 

to characterize the variable-speed power-turbine aerodynamic 

challenges and to outline a conceptual design approach that 

accounts for multi-point operation. Identified technical 

challenges associated with the aerodynamics of high work 

factor, incidence-tolerant blading, and low Reynolds numbers 

pose research needs outlined in the paper. 

Nomenclature 

AN2 product of annulus area and rpm-squared 

AR (rt-rh)/cx, blade aspect ratio 

cx axial chord 

f N/N100%, speed ratio factor 

h0, h total and static specific enthalpy 

i, is incidence, incidence at suction-side stall 

݉ሶ mass flow rate 

M, Mr absolute and relative Mach numbers 

N power-turbine shaft speed, rpm 

Nstg number of turbine stages (stator/rotor) 

p0, p total and static pressure 

rh, rt hub and tip radii 

Rstg (h1-h2)/(h0,0-h0,2), stage enthalpy reaction 

Recx Reynolds number based on axial chord 

s blade pitch 

u (ux, u), absolute velocity 

U rotor speed at pitchline 

w (ux, u - U), relative velocity 

ܹሶ shaft power 

VJ Speed of isentropic expansion through PRT-T

Z ௦

௖ೣ

ఘ௨ೣሺ୳θ,భି୳θ,మሻ

௣బ,ೝ,భି௣మ

, Zweifel loading parameter 

 absolute and relative flow angles 

stg stage efficiency (total-to-total) 

 density 

l turbulent, laminar viscosity 

ψ h0/U2

, work factor 

φ ux/U, flow coefficient 

Subscripts 

c corrected condition 

des design point 

0, 1, 2 Stations: nozzle inlet, rotor inlet, rotor exit 

4.5 power turbine inlet 

n nozzle (vane) 

r rotor (blade), or relative condition 

opt optimum 

Introduction 

A principal goal of the Subsonic Rotary Wing project of the 

NASA Fundamental Aeronautics program is to enhance the 

throughput capacity of airports by increased utilization of civil 

rotorcraft (see Johnson et al. (Ref. 1) and Wilkerson and 

Smith (Ref. 2)). The technical objectives of this project require 

development and maturation of technologies to enable a large 

vertical takeoff and landing (VTOL) transport, capable of 

Mach 0.5 forward cruise at 28 kft, with a range greater than 

1000 nm. Vehicle systems studies of large civil rotorcraft 

concepts have resulted in mission refinement and the 

definition of a notional Large Civil Tilt-Rotor (LCTR) vehicle 

that helps define the technical challenges and research 

requirements (Johnson et al. (Ref. 1) and Acree et al. 

(Ref. 3)). Fuel efficiency is of prime importance and must be 

maximized by balancing fuel-burn penalties associated with 

variable-speed engine/drive-train capability with gains 

achieved by slowing the main rotor speed substantially (to 

54% of take-off speed, cf. Acree (Ref. 4)) as required to 

maintain high propeller efficiencies at cruise flight speeds. 

The required main-rotor speed variation from 100% at takeoff (e.g., 650 ft/s tip speed) to near 54% (350 ft/s) at cruise can 

be achieved by use of a multi-speed transmission driven by a 

power turbine (PT) operating with minimal required speed 

change. Alternatively, the speed variation can be achieved by 

using a variable-speed power turbine (VSPT) driving a 

rotorcraft transmission with fixed gear ratio. The increase in 

fuel burn from the added weight of a multi-speed transmission 

can be traded against the capabilities and penalties of a VSPT; 
NASA/TM—2010-216758 2 

indeed, a combination of turbine speed change and variable 

transmission may prove optimal. The work reported here is 

focused on achieving main-rotor speed variation by powerturbine speed variation alone—i.e., assuming a fixed, singlegear ratio transmission. This speed variation approach is used 

in the V-22, albeit over a narrower range (0.82 < N/N100% < 1, 

Wilkerson and Smith2

) than considered in the present study 

(0.54 < N/N100% < 1). 

The results from an earlier tilt-rotor study (Figure 1 from 

D′Angelo (Ref. 5)) showed the trade-off between main-rotor 

prop efficiency and design-point power-turbine efficiency as a 

function of turbine operating speed. Although the particular 

Mach 0.7, 15 kft cruise point considered by D′Angelo (Ref. 5) 

is substantially different from the LCTR cruise conditions 

considered herein, the following relevant points are illustrated 

(Fig. 1). The strong increase in propulsive efficiency (e.g., 

15 pts.) achieved by slowing the main rotor motivates the 

variable-speed rotor requirements of the LCTR; however, as 

the main rotor and power turbine slow, the design-point 

efficiency of the power-turbine drops strongly (e.g., 5 to 

10 pts., see Fig. 1). Consideration of the product of the two 

efficiencies indicates that there is an optimum cruise speed in 

terms of fuel burn. 

The strong lapse in power-turbine design-point efficiency 

with decreasing speed can be offset somewhat by designing 

the power-turbine at, or near, its cruise speed (54% of take-off 

in this study) so that losses associated with positive incidence 

are mitigated; even so, as shown in the next section, the high 

work factors (flow turning) required at the lower PT speeds 

will inevitably result in lower efficiencies than can be 

achieved in a turbine optimized for near constant high-speed 

(100%) operation. 

Operation of a power turbine over a wide speed range (54% 

< N/N100% < 100%) represents a strong departure from 

traditional, nearly constant, power-turbine speed operation. 

The wide-speed operation poses formidable aerodynamic and 

mechanical challenges. The key aerodynamic challenges 

confronting the VSPT include a high work factor at cruise, a 

wide incidence variation between cruise and take-off, and low 

aft-stage Reynolds numbers at cruise altitudes. These 

challenges are discussed in the next section. A conceptualdesign approach for the VSPT is then outlined, and candidate 

designs that meet the LCTR engine requirements are provided. 

Findings from preliminary research related to incidence 

tolerant blading and low-Re flows are reported, with the intent 

to elucidate research needs. Finally, an overview of a VSPT 

research effort underway at NASA GRC is provided. 

Aerodynamic Challenges 

Relevant engine/VSPT requirements for key flight points of 

the LCTR mission are provided in Table 1 (Snyder and 

Thurman (Ref. 6)). The requirements reflect the load demand 

of the variable-pitch main rotor of the LCTR. The gas 

generator (LP and HP spools) operates with fixed geometry 

between sea-level take-off and 28 kft cruise, and the lapse in 

engine power and flow is associated with altitude changes 

alone. The fuel-throttle settings at the sea-level and cruise 

points are essentially constant, and hence, so is the corrected 

flow through the engine. The engine runs at essentially full 

power, when corrected for altitude, over the entire mission, 

although component temperatures at cruise are lower due to 

altitude-related temperature changes. 

Note that the power-turbine enthalpy extraction levels (i.e., 

specific power, Δ݄଴ ൌ ܹሶ /݉ሶ ൌ Δሺݑఏܷሻ ) at 2 kft take-off 

(100% speed) and 28 kft cruise (54, 62, 75, and 100% speed) 

are essentially constant. This leads to strong VSPT aeroperformance implications associated with high work factors at 

the 54%-speed cruise point and large incidence variation on 

the vanes and blades as the VSPT speed is changed. The low 

aft-stage Reynolds numbers (transitional flow) additionally 

burden the power turbine with higher design-point loss levels 

and reduced incidence-range capability. These challenges are 

discussed in this section. 

Efficiency at High Work Factors 

The mission requirement for near constant enthalpy 

extraction at take-off and cruise requires that the work factor, 

߰ ൌ Δ݄଴/ܷଶ, at cruise (54% speed) will be approximately 3.5 

times higher than at take-off (100% speed). To ensure that 

take-off work factors are unity or above for weight mitigation, 

cruise work factors are 3.5 to 4. Attainment of high efficiency 

blade rows at such high work factors constitutes a key 

technical challenge and objective for the variable-speed 

power-turbine aerodynamic design effort. The challenge is 

evident in the Smith charts of Figure 2, where stage efficiency 

is plotted as a function of work factor and flow coefficient for 

a family of low (0.2 to 0.3) reaction turbines. Figure 2(a) was 
NASA/TM—2010-216758 3 

TABLE 1.—VSPT REQUIREMENTS AT KEY FLIGHT POINTS OF LCTR MISSION (SNYDER AND THURMAN (REF. 6)). 

Flight point 

Altitude 

VSPT speed (N/N100%)

Main-rotor tip-speed 

Take-off 

2 kft 

100% 

650 ft/s 

Cruise 

28 kft 

54% 

350 ft/s 

Cruise 

28 kft 

61.5% 

400 ft/s 

Cruise 

28 kft 

75% 

500 ft/s 

Cruise 

28 kft 

100% 

650 ft/s 

Power, SHP 4593 2328 2330 2329 2330 

VSPT mass flow rate, lbm/s 22.03 12.22 11.71 11.63 11.55 

Specific power (SHP/lbm/s) 208.5 190.5 200.2 200.2 201.8 

PT inlet temp (T4.5), R 2204 1812 1798 1795 1818 

PT inlet pres. (p0,4.5), psia 58.0 26.76 26.3 26.1 26.6 

PT pressure ratio (total-to-total) 4.04 5.34 5.25 5.21 5.30 

Corrected flow, lbm/s 11.51 12.54 12.41 12.18 11.95 

Corrected speed (Nc/Nc100%) 102.3 60.8 69.7 85.1 112.7 

Aft-stage unit-Re (in.–1)

a

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

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

generated using the design-point methodology of Ainley and 

Mathieson (Ref. 7) with the modifications implemented by 

Dunham and Came (Ref. 8) and Kacker and Okapuu (Ref. 9), 

referred to as AMDCKO herein. The calculated efficiencies 

compare well with the experimental data (Fig. 2(b)) of Smith 

(Ref. 10) (as reported in Horlock (Ref. 11)). The strong 

decrease in maximum achievable stage efficiency with 

increasing work factor is evident in the figure. 

Considering Figure 2, the design-point flow coefficient can 

be selected to optimize efficiency for a given work factor 

level. Note however that the flow angle variation into 

embedded blade rows will generally decrease with increasing 

flow factor; therefore, as work factor is reduced, and the 

optimum design-point flow coefficient for maximum 

efficiency decreases, the associated incidence variations into 

embedded stages (and exit guide vane) would be expected to 

increase (cf. D′Angelo (Ref. 5)). The influence of stage 

reaction and flow coefficient on the stage efficiency of an 

example turbine with work factor of 3.6 is shown in 

Figure 2(c). 

In Figure 3, turbine design-point stage efficiency (total-tototal) is plotted as a function of average stage work factor for a 

number of turbine designs. The design-point stage efficiency 

decreases strongly with work factor. Relative to a PT 

operating at fixed (high) speed, as in a traditional helicopter 

engine or in an LCTR variant with a variable-speed 

transmission, there is a substantial efficiency debit associated 

with operation at high work factors. Viable VSPT designs 

must necessarily minimize this debit. The work factor 

(efficiency debit) can be minimized by adding turbine 

stages—weight—and by increasing pitchline speeds at cruise 

(high stress levels at take-off speeds). These options are 

investigated in the LCTR Power Turbine Conceptual Design 

section of this paper. 
NASA/TM—2010-216758 4 

Incidence-Tolerant Blade Rows 

As a result of the near 50% change in speed, the rotors and 

embedded stators (nozzles and exit guide vane row) of the 

variable-speed power turbine will be subject to large (e.g., 40 

to 80 degrees, see D′Angelo (Ref. 5)) incidence swings. The 

calculated incidence variations for LCTR VSPT conceptual 

designs are documented later in the paper; however, it is 

instructive to use rudimentary meanline analysis for a singlestage turbine (nozzle/rotor) to quantify the expected influence 

of the speed variation on the velocity triangles, and their 

implications regarding variable geometry and incidence levels 

into embedded blades and vanes. 

As described in the previous section, to maintain constant 

enthalpy extraction while reducing rotor speed from 100% to 

50% (for example), a 3.5 to 4-fold increase in work factor is 

required. There are a number of ways the turbine can achieve 

the required enthalpy extraction level at the high and low 

speeds. Using an incompressible analysis, two cases, 

considered relevant to the LCTR VSPT problem, are 

considered here: 

Case I—Variable geometry and fixed flow (ux) 

Case II—Fixed geometry and variable flow 

Case I represents an attempt to assess requirements for a 

turbine with variable geometry, while Case II represents a 

turbine with fixed geometry. The effect of speed factor, 

݂ ൌ N/Nଵ଴଴%, on work factors, flow coefficients, and flow 

angles for the two cases is summarized in Table 2 and rotor 

velocity triangles for the two cases are provided in Figure 4. 

The associated impact on blade row incidence levels are 

discussed in the following sub-sections. 

Case I—Variable Geometry and Constant Flow 

The use of variable geometry in turbines has traditionally 

been restricted to variable nozzles used to manage incidence 

so as to trim for efficiency (see recent study by Chen 

(Ref. 13)) and to throttle the gas generator (see Rogo and 

Benstein (Ref. 14) and Karstensen and Wiggins (Ref. 15)). 

This is accomplished using actuated vanes with variable 

setting angles, where their complexity and weight are 

warranted by the efficiency benefit derived. (Variable rotors 

were deemed technologically inadvisable and outside of the 

scope of the present effort.) For Case I, the vanes are reset to 

establish the work factor required to meet the constant h0

while maintaining constant axial velocity (mass flow rate). In 

an engine, the corresponding requirement would be to hold 

h0 while maintaining constant Mach number into the nozzle 

(in which case the flow coefficient will scale with inverse 

corrected, rather than physical, speed). To retain constant 

specific power at a constant mass flow rate, the nozzle needs 

to be relatively closed at the lower speed to impart increased 

pre-swirl into the rotor. The changes in 1, 1, and 2

associated with difference in VSPT speed at take-off and 

cruise are provided in Figure 5. 
NASA/TM—2010-216758 5 

TABLE 2.—EFFECT OF CRUISE-TO-TAKE-OFF SPEED RATIO (F) ON WORK FACTORS, 

FLOW COEFFICIENTS, AND FLOW ANGLES 

Cases ૐ

ૐ૚૙૙%

૖

૖૚૙૙%

૛ࢻ࢔ࢇ࢚ઢ઺૚ ࢔ࢇ࢚ઢ૚ ࢻ࢔ࢇ࢚ઢ

I. Variable geometry 

and fixed flow 

1

݂ଶ

1

݂

ψଵ଴଴% െ ݂

Ԅଵ଴଴%

1 െ ݂

݂ ൬

ψ

Ԅ൰

ଵ଴଴%

െ 1 െ ݂

Ԅଵ଴଴%

II. Variable flow and 

fixed geometry 

1

݂ଶ

1൅ψ

1൅ψଵ଴଴%

0

1

Ԅଵ଴଴%

൬

ψെψଵ଴଴%

1൅ψ ൰ െ1

Ԅଵ଴଴%

൬

ψെψଵ଴଴%

1൅ψ ൰

Blade row stations 1 = rotor inlet; 2 = rotor exit. 
NASA/TM—2010-216758 6 

The flow coefficient at cruise will be set in part by the 

optimization of overall turbine efficiency at the conceptual 

design level (see Figs. 2(a) and (b)). For cruise work factors 

from 3.5 to 4, the flow coefficient will be near unity or greater 

for optimum efficiency. Considering Figure 5 (and Table 2), 

for a design of a given stage reaction, the incidence variation 

for embedded rotors and stators (and exit guide vane) 

decreases with increasing cruise flow coefficient. In contrast, 

the nozzle/stator resets increase with increasing cruise flow 

coefficient. At a given flow coefficient, the nozzle/stator reset 

requirements and the rotor/stator incidence levels are 

minimized by setting low stage reactions at cruise. Influenced 

by this analysis, the stage reaction, Rstg = 0.3 was used in the 

conceptual designs herein. The choice for low stage reaction 

must be balanced against its deleterious impact on stage 

efficiency (Fig. 2(c)). 

An example Case I stage is shown in Table 3. As shown, to 

hold h0 and ux constant, the inlet nozzle would need to be 

opened by 11-degrees when changing from the cruise design 

point (54% speed) to take-off (100% speed). In practice, if a 

variable nozzle were employed, care would need to be taken to 

insure that reset (closing) of VSPT nozzles/vanes at cruise 

does reset engine flow (throttle the core, cf. Karstensen and 

Wiggins (Ref. 15), for example). The nozzle/vane profiles—

particularly on the pressure side—may need to be contoured 

so that sufficient margin on minimum flow area is maintained 

as vanes are reset. 

The change in rotor inlet flow angle is nearly 70 degrees 

between take-off and cruise (Table 3), representing a 

substantial incidence swing, and highlighting the need for 

incidence-tolerant rotors. The Ainley-Mathieson negative 

(i/is = –2.7) and positive (i/is = 1) stall incidence range 

(Ref. 16) is provided for reference. The change in the absolute 

flow angle out of the rotor (or into the downstream embedded 

stators or exit guide vane) is nearly 35-degrees, with lower 

swirl angles discharged at take-off speed. This large change in 

swirl discharged from the rotor highlights the need for 

incidence-tolerant stator rows in multistage machines, and the 

likely need for an incidence-tolerant exit-guide-vane (EGV), 

with associated added-weight, to be installed downstream of 

the aft-rotor (cf. D′Angelo (Ref. 5)). 

Case II—Fixed Geometry, Variable Flow 

Case II is considered an incompressible analog to the 

engine VSPT with fixed geometry (see LCTR Power Turbine 

Conceptual Design section). With no variability in the 

nozzle/stator settings, the axial velocity (flow) must change as 

shown in Tables 2 and 3 in order to maintain constant specificpower at the various PT speed settings. The flow coefficient is 

reduced from cruise (50% speed) to take-off (100% speed) by 

more than 50%. Relative to the variable geometry Case I at 

Rstg = 0.3 (see Table 3), the negative incidence in the rotor is 

reduced (23-degrees) at take-off (100% speed) while the 

negative incidence in the downstream stator (or EGV) is 

increased (23-degrees) at take-off. The rotor reaction for the 

corresponding 100% design-point (to achieve the same stator 

and rotor exit flow angles) is only slightly higher (0.42 vs. 0.3) 

than at the 50% design-point. As seen in Figure 6, the impact 

of increased stage reaction at a given flow coefficient is to 

increase rotor incidence variation and to decrease stator 

incidence variation. A balance is achieved at Rstg = 0.5. The 

higher stage reaction (relative to Rstg = 0.3 of Case I) enhances 

efficiency as well (see Fig. 2(c)). As found for Case I, the 

magnitude of incidence variations into the rotor and stator are 

increased as flow coefficient is reduced at a given work factor 

(Fig. 6). 

TABLE 3.—SINGLE-STAGE TURBINE VELOCITY TRIANGLE CHANGES TO OBTAIN CONSTANT ENTHALPY 

EXTRACTION WHILE UNDERGOING A 50%-SPEED CHANGE – DESIGNS AT Mr,2 = 0.7, Zr = Zn = 0.8 

Speed  φ stg Rstg A-M stall incidence, deg. 0, deg. 1, deg. 1, deg 2, deg. 2, deg. 

Case I—Constant h0 and ux, variable nozzle/stators/EGV

100% 1 0.6 b96.3 b0.65 b+27/–73 0 54.9 –14.0 –62.4 –14.0 a

50% 4 1.2 84.4 0.3 +14.1/–38.1 0 66.03 54.8 –62.4 –47.3 

Delta 400% 200% -- -- -- 0 +11.2 –68.7 0 –33.3 

Case II—Constant h0, fixed geometry, variable ux

100% 1 0.48 b

95.7 b0.42 b+28.7/–77.4 0 66.0 9.5 –62.4 +9.5 a

50% 4 1.2 84.4 0.3 +14.1/–38.1 0 66.0 54.8 –62.4 –47.3 

Delta 400% 250% -- -- -- 0 0 –45.8 0 –56.8 

 

100% 1 0.48 b

0.959 b0.5 b+28.7/–77.4 0 64.4 0. –64.4 0. a

50% 4 1.2 0.868 0.5 +16.5/–45 0 64.4 51.3 –64.4 –51.3 

Delta 400% 250% -- -- -- 0 0 –51.3 0 –51.3 

 

100% 1 0.4 b

95.7 b0.5 b+28.7/–77.4 0 68.2 0. –68.2 0. a

50% 4 1.0 0.857 0.5 +14.3/–38.6 0 68.2 56.3 –68.2 –56.3 

Delta 400% 250% -- -- -- 0 0 –56.3 0 –56.3 a

Design point 

b

Value if designed to match 1 and 2 of cruise design with take-off (100%) work and flow coefficients. 
NASA/TM—2010-216758 7 

Impact of Low Reynolds Number 

The 28 kft cruise requirement of the LCTR mission 

imposes a larger Reynolds number variation (ground to cruise) 

on the power turbine than encountered in conventional 

(< 15 kft) rotorcraft operation. The estimated aft-stage unitReynolds-numbers (see LCTR Power Turbine Conceptual 

Design section) are approximately 50,000/in. and 30,000/in. at 

take-off and cruise altitudes, respectively. The 7500 SHP-class 

blading is expected to have axial chords of 1 to 2 in., leading 

to chord Reynolds numbers associated with transitional 

suction-sides (Haselbach et al. (Ref. 17) and Praisner et al. 

(Ref. 18)). 

Design-Point Re Lapse 

The loss in design-point performance with altitude due to 

transitional flow is expected to be analogous to that 

experienced by larger low pressure turbines (LPT) of modern 

turbofans (e.g., see Hourmouziadis, (Ref. 19) Haselbach et al., 

(Ref. 17) and Gier et al. (Ref. 20)). The absolute change in 

Reynolds number will be lower—less variation in pressure 

from sea-level-static to 28 kft as compared to SLS to 40 kft—

but the variation will occur at lower aft-stage chord Reynolds 

numbers (60 k to 100 k). The need to run at all conditions 

above the point at which the airfoil stalls, after which loss 

coefficients rise precipitously, may ultimately set the axial 

chord of the VSPT blading (see Riegler and Bichlmaier 

(Ref. 21)). An increase in axial chord, though consistent with 

reduced blade count, leads to increased length-per-stage and 

ultimately increased engine length (weight and packaging). 

Gier et al. (Ref. 20) have argued convincingly, counter to 

recent trends toward ultra-high aerodynamic loading (Z > 1.3), 

to utilize moderate aerodynamic loading levels (0.8 < Z < 1). 

The optimum loading levels for the LCTR-class turbines are 

expected to emerge over time as industry, the labs, and 

academia apply component and engine-level preliminary 

design/optimization tools to the problem. 

The impact of low Reynolds number is firstly a designpoint problem, affecting all future turbines of this size class 

and mission—variable- or fixed-speed. Computed Reynolds 

number lapse for the Air Force Research Laboratory (AFRL) 

L1A and L1M high lift blades (Clark et al. (Ref. 22)) are 

provided in Figure 7. The L1-series has Zweifel coefficients at 

Z = 1.34 and 95-degrees of turning. The blades are considered 

to be relevant to embedded stages of the LCTR VSPT. The 

computations were performed using Chima’s 2-D ReynoldsAveraged Navier-Stokes (RANS) code (Ref. 23) and Wilcox’s 

low-Re variant of the - model (Ref. 24). The inlet 

turbulence intensity was set at 5% and the length scale of 

turbulence was set to achieve the desired freestream turbulent 

viscosity (l = 0.1). The length scale of turbulence selected 

strongly affected the location of transition on the suction-side. 

The C-grids utilized were generated using the GRAPE code 

(Sorenson (Ref. 25)). The grid spacing was set so that the y+

near the leading edge at high chord Recx,2 (620 k) was less 

than two. 

The computed loading diagrams and Reynolds number 

lapse for the L1A and L1M blade profiles are shown in 

Figure 7. The blades accomplish the same 95-degrees flow 

turning, at the same aerodynamic loading level, using midand aft-loaded sections (Fig. 7(a)). The loading distribution 

has an impact on the increase in loss with decreasing chord 

Reynolds number, though the power-law lapse rates in the 

fully turbulent (Recx,2 > 200 k) region are similar. 
NASA/TM—2010-216758 8 

Impact on Incidence Range 

The need for strong incidence-tolerance exacerbates the 

low-Re challenge. In addition to increased minimum loss, the 

loss buckets will generally narrow as Reynolds number is 

reduced. This impact was analyzed using the L1M high lift 

(Z = 1.34) blading. The reduction in incidence range with 

decreasing Recx,2 is evident in Figure 8(a). The minimum loss 

increases with decreasing Reynolds number (increasing 

altitude, see Fig. 7(b)) and the loss bucket narrows measurably 

(Fig. 8(a)). The canonical form of the loss bucket (Fig. 8(b)) is 

largely retained at the two Reynolds numbers, and is in good 

agreement with the off-design correlation of Ainley and 

Mathieson (Ref. 16). 

The AMDCKO meanline analysis shows that incidence 

range decreases, as expected, with increased loading (or 

reduced axial-chord to pitch ratio for a given turning). In 

addition to minimizing design-point loss due to Reynolds 

number lapse, there is a justifiable argument to restrict 

aerodynamic loading levels (Z) to obtain increased incidence 

range as well. 
NASA/TM—2010-216758 9 

LCTR Power Turbine Conceptual Design 

As outlined above, key aerodynamic challenges for the 

VSPT are associated with high work factors at cruise, the need 

for incident-tolerant blading that can accept rotor inlet flow 

changes from 40- to 80-degrees and stator/EGV inlet flow 

angle variations near 30- to 60-degrees, and the lapse in 

performance and incidence-range associated with the decrease 

in Reynolds number with altitude. In this section, the 

aerodynamic requirements are refined via conceptual design of 

candidate 3- and 4-stage turbines to meet the LCTR engine 

objectives. 

Design Approach 

The designs were carried out using the design- and offdesign meanline tools of F. Huber (see Clark et al. (Ref. 22)) 

which are consistent with AMDCKO methodology. The 

Huber tools are considered to be representative of industry 

state-of-the-practice in turbine meanline codes. They are used 

in the present study to set a realistic design space and to 

generate variables needed for design of detailed blade profiles 

vis-à-vis the AFRL design system (Clark et al. (Ref. 22)).I

As outlined in the previous sections, the following 

attributes influenced the design choices of the preliminary 

conceptual design: 

i.) The LCTR spends a majority of its mission in cruise. 

ii.) The VSPT work factors at cruise are substantially (3.5 to 

4 times) higher than at take-off and the associated loss 

buckets are narrower. 

iii.) The positive-incidence range is substantially (2 to 3 

times) narrower than negative-incidence range. 

iv.) The design-point loss increases and the incidence range 

decreases from take-off to cruise due to Reynolds number 

lapse. 

v.) The increase in design-point loss due to Re lapse is larger 

in high lift (Z) airfoils than in low lift designs. 

The confluence of these multiple factors means that the 

optimum design-point for the LCTR power turbine will be 

near the lowest-speed cruise condition (i.e., 54% of take-off 

speed). The corresponding flow coefficient will likely be near 

unity or greater, and will be reduced to about half (for 54% 

speed change) at take-off. The stage reaction at cruise is 

expected to vary little from that at take-off and should be 

optimized with consideration of efficiency at cruise and its 

lapse due to off-design (incidence at take-off). The optimum 

blade rows are expected to be achieved at moderate 

aerodynamic loading (0.8 < Z < 1). 

 

I

 The author is indebted to Dr. Lisa W. Griffin of NASA Marshall 

Space Flight Center for permission to use F. Huber’s meanline and 

blade generator codes, developed under earlier SBIR contract, and to 

Dr. J. P. Clark (AFRL) for use of the AFRL Turbine Design and 

Analysis System (Ref. 22). 

Setting Speed—AN2 Limited at Take-Off 

The specific power requirement is set by the engine 

analysis (see Table 1). In the present study, the cruise and 

take-off specific power levels are both approximately h0 = 

200 SHP/lbm/s, corresponding to the cruise and take-off 

pressure ratios shown in Table 1. An average enthalpy 

extraction per stage is used along with a specified work factor 

to set the pitchline velocity ( ܷଶ ൌ Δ݄଴/ሺܰ௦௧௚ψ )). The 

pitchline velocity sets the product of the pitchline radius and 

shaft speed. The pitchline radius must be consistent with a rim 

diameter and the flow area (near 200 to 220 in.2 in this study, 

as determined by scaling existing turbine geometries). 

The product of the flow area and the square of rpm, AN2

(rpm2

·in.2), is an indicator of acceptable mechanical stress 

levels (see Mattingly et al. (Ref. 27) and Mattingly (Ref. 28)) 

based on rim temperatures and material strength and life 

(creep) properties. The AN2

 mechanical limit is used herein to 

set the max acceptable VSPT shaft speed. The higher the 

speed, the lower the required average stage work factor, and 

generally the higher the design-point turbine efficiency 

(Figs. 9 and 3). AN2

 varies inversely with work factor as speed 

is changed (ܣܰଶ~1/ψ ~݂ଶ ); therefore, the max-allowable 

AN2

 must be set at the hotter 100% take-off speed (or 

contingency power) point, while at cruise the power-turbine 

operates with low AN2

. The present study limits take-off AN2

to the range 40 ≤ AN2 ≤ 50109

 rpm2 ·in.2. This high AN2

range implies that the power turbines operate with lighter 

weight turbine materials (e.g., Hastelloy) at low rim 

temperatures (e.g., 1000 F), predicated on high cooling air 

requirements, or at higher rim temperature (1300 F) with 

heavy and expensive Rene-80 type materials. Rotor taper (0.9 

is used for the present study) enables slightly higher AN2

limits (and see Riegler and Bichlmaier (Ref. 21)). 

Conceptual Design Results 

Attributes of (preliminary) three- and four-stage AN2

45109

 rpm2 ·in.2 designs are provided in Table 4. The turbines 

were designed at cruise (54%-speed, 28 kft) with fixed 

nozzle/stator geometry (Case II above). Corresponding 

pitchline flow angles are provided in Table 5. The turbine 

performance was evaluated at the off-design take-off (100% 

speed, 2 kft) and top-of-climb (100%, 28 kft) flight points, 

also shown in Table 4. The reported efficiencies predicted by 

Huber’s meanline code (Ref. 22) (see Fig. 3) do not include an 

exit guide vane, which will likely be required by the level of 

swirl discharged from the aft-stage rotor at cruise; indeed, 

D′Angelo (Ref. 5) concluded that a variable EGV might be 

required. 

The design-point efficiencies using the AFRL meanline tool 

(Ref. 22) were found to be substantially greater than those 

predicted by the in-house AMDCKO tool (see Fig. 3) and as 

reported by D′Angelo (Ref. 5) in his study (50109

 rpm2 ·in.2 

AN2 3- and 4-stage designs with EGV, Fig. 3). The 
NASA/TM—2010-216758 10 

TABLE 4.—THREE- AND FOUR-STAGE DESIGNS FOR PT REQUIREMENTS OF TABLE 1 (AN2

 = 45109, Zn = 0.8, Zr = 1) 

3-stage 4-stage 

Speed (N/N100%) 

Altitude 

100% 

2,000 ft 

54% 

28,000 ft 

100% 

2,000 ft 

100% 

28,000 ft 

54% 

28,000 ft 

VSPT efficiency 0.9212 0.8979 0.9245 0.9222 0.9081 

Total-pressure ratio 3.93 5.338 4.00 5.568 5.336 

N, rpm 15087 8146 14560 14560 7862 

Average ψ 1.07 3.67 1.04 1.04 3.57 

Average φ 0.49 1.15 0.48 0.48 0.985 

Average Rstg 0.36 0.39 0.41 0.43 0.34 

Spool U/VJ 1.203 0.347 0.781 0.753 0.414 

 

Rotor incidence, deg. (R1, 

R2, ..., RNstg) 

–35.2, –42.8, 

–54.1 

0 –35.5, –41.3, 

–50.5, –49.0 

–44.8, –50.1, 

–51.0, –39.4 

0 

 

Stator incidence, deg 

(S2, S3, ..., EGV) 

–39.0, –49.8, 

–38.6 

0 –43.6, –53.4, 

–53.8, –36.35 

–54.0, –59.1, 

–49.5, –23.65 

0 

 

Power, SHP 5070 2654 5151 2832 2683 

 

Blade count (S/R/Total) 274/304/578 309/340/649 

Design-point 

TABLE 5.—DESIGN-POINT FLOW ANGLES AND LOADING FOR 3-STAGE AND 4-STAGE ROTORS (AN2

 = 45109) 

AND ULTRA-HIGH LOADING L1-SERIES BLADING (CLARK et al. (Ref. 22)) 

3-stage 4-stage L1Ma

 L1Aa

Zweifel 1.0 1.0 1.34 1.34 

Rotor 1 2 Turn 1 2 Turn 1 2 Turn 1 2 Turn 

1 55 –65 120 53 –67 120 35 –60 95 35 –60 95 

2 50 –58 108 56 –66 122 

3 29 –42 70 46 –57 102 

4 -- -- -- 28 –39 66 

h/cx R1 2.54 2.36 

h/cx RNstg 3.77 4.01 a

AFRL ultra-high-load blade shapes provided by Dr. J. P. Clark (AFRL). 
NASA/TM—2010-216758 11 

performance values are in line with 1976 LPT designs 

documented by Oates (Ref. 12) (Fig. 3). Nonetheless, a degree 

of caution is deemed warranted by the calculated high 

efficiencies at work factors of 3.5 to 4, particularly given the 

low chord Reynolds numbers. The impact of low-Re 

efficiency lapse may not be captured fully by the meanline 

tool, an inference which is supported by the small difference 

in efficiencies (Table 4) of the 4-stage turbine operating at the 

two 100% speeds at the substantially different 2-kft and 28-kft 

Reynolds numbers. 

The off-design (100% speed) performance levels (Table 4 

and Fig. 3) are worthy of note. Firstly, as shown earlier, the 

average work factors are low (near unity) due to the increased 

rotor speed and substantially reduced work factor. The turbine 

is operating with substantial (30 to 60 degrees) of negative 

incidence in both rotor and stator rows (Table 4). Nonetheless, 

the performance levels at this off-design point are predicted to 

be higher than at the more highly loaded design point. While 

consistent with the efficiency potential at these low work 

factors (e.g., 95 to 96% stage efficiency), and with the 

D′Angelo’s (Ref. 5) off-design predictions (Fig. 3), a degree 

of caution is again warranted.II

For completeness, it is noted that it was difficult to achieve 

a 3-stage design at the 45109

 rpm2·in.2 AN2 limit. The design 

was achieved by pushing the engine out in radius (relative to 

the 4 stage) by a scale factor (1.1) and reducing the annulus 

flow area—that is, higher N and pitchline speed at the same 

AN2

. Three-stage designs at AN2 less than 45109 rpm2·in.2

were not achieved. Additionally, Huber’s off-design code did 

not converge on the 100% speed point at 28 kft with the 3-

stage. These two findings are taken to be indicative of a 

aerodynamically marginal 3-stage design. The 4-stage designs 

were substantially more robust in terms of attaining the design 

point at various AN2

 and running at the off-design points. 

VSPT Research Needs 

The variable-speed power turbine requirements evidently 

pose component and blade-row level aerodynamic challenges 

related to high work factor and loading, required incidence 

range, and efficiency and incidence-range degradation at lowRe conditions. These challenges lead to research objectives 

and needs identified in this section. 

High-Load Aerodynamics 

The design-approach taken in this effort was to set optimum 

incidence at the 54% speed, low-Re cruise point, and accept 

the high (35 to 60-degrees) negative incidence at 100% speed. 

The design-point challenge is then related to an optimization 

of performance and weight within mechanical constraints set 

at take-off (or contingency) power settings. This is a design-

 

II The details of the off-design tool were not available to the author; 

this cautionary note is not intended as commentary on the accuracy of 

the meanline tool. 

point optimization for which the industry is preeminently 

qualified. Attainment of maximum efficiencies is expected to 

require 3-D blading with lean and bow (see, for example, 

Hourmouziadis (Ref. 19) and Riegler and Bichlmaier 

(Ref. 21)) and endwall contouring (see, for example, Hartland 

et al., (Ref. 28) Praisner et al., (Ref. 29) Germain et al., 

(Ref. 30) and Knezevici et al. (Ref. 31)) in order to control 

secondary-flow and endwall loss production. Thus, there is an 

identified need to apply advanced design/optimization tools to 

achieve optimized cruise-point designs. In the context of the 

variable-speed power turbine, the aerodynamic design-point 

optimizations may need to be extended to include operation at 

multiple flight points; further, attainment of high design-point 

efficiency and incidence range will need to be traded for cost 

of weight and parts count. Setting the optimum aerodynamic 

loading level (Z) in the VSPT blade rows will involve 

consideration of both component and system level impacts. 

Aerodynamics of High Negative Incidence 

Arguably the hardest point for the turbine (designed at the 

54% speed low-Re cruise point) to achieve is 100% speed at 

28 kft altitude (see Table 1). The negative incidence levels at 

this operating point—as high as 60-degrees in some rows—

exceed levels at take-off (100% speed, 2 kft, see Table 4); 

unfortunately, this occurs at cruise altitude where reduction in 

range-of-acceptable-loss (Fig. 8) associated with Reynolds 

number lapse would be most severe. As mentioned, this was 

the point at which the 3-stage conceptual-design turbine could 

not operate. The negative 60-degree incidence is only 

marginally within the predicted pressure-side stall range of 

Ainley-Mathieson (Ref. 16) (i/is = –2.7) for a work factor 

unity stage. There is an identified need to develop blading that 

mitigates loss associated with strong negative incidence. 

A study by Brear et al. (Refs. 32 and 33) has showed a 0.6 

point efficiency decrement per 10-degrees negative incidence 

at exit Reynolds numbers of 130 k. The incidence loss was 

attributed to a separation occurring in the cove region of the 

blade due to the adverse pressure gradient. Brear et al. 

(Ref. 32) noted that the loss associated negative incidence 

could be controlled, to some extent, by tailoring the adverse 

pressure gradient through airfoil pressure-side profiling. 

Irrespective of profiling, the loss level at 60-degrees of 

negative incidence at Recx,2 = 62k (Fig. 8(a)) is likely 

unacceptably high. Considering Figure 8(a), 10-degrees of 

positive incidence could have been accepted at the design 

point with little impact on loss at cruise (54% speed). This 

would have reduced the negative incidence requirement at 

100% speed, 28 kft point to negative 50-degrees, a point with 

acceptable loss levels (Fig. 8(a)). This approach would lead to 

design at somewhat higher speed fraction than required at 

cruise, though still strongly biased toward minimum speed due 

to the asymmetry of positive and negative incidence losses 

(Fig. 8(b)), and the increase in 3-D losses with positive 

incidence at high aerodynamic loads. In this case, some 

efficiency at 54% speed (cruise) would be traded for a 
NASA/TM—2010-216758 12 

reduction in negative incidence (loss) at 100% speed. A key 

conceptual-design level decision—selection of the speed ratio 

(Ndes/N100%) at which to design the VSPT—will determine the 

balance between positive and negative incidence. To this end, 

there is an identified need to quantify accurately the 2-D and 

3-D loss mechanisms at both high negative incidence and 

moderate positive incidence. 

Aerodynamics of Low Reynolds Number Flows 

A key challenge for the 7500 SHP-class power turbine 

operation at 28 kft is the impact of low Reynolds number on 

design and off-design performance. Research needs in this 

area are outlined in this section. 

Reynolds Lapse in Meanline Tools 

The meanline tools used in the conceptual design phase 

need to capture the impact of low Reynolds number on profile 

and secondary flow loss levels, for both on- and off-design 

operation. There is an identified need to validate/calibrate the 

on- and off-design meanline tools to ensure correct prediction 

of lapse of efficiency and incidence range with altitude. 

Sub-Models for Transitional Flow 

Computational tools required for the turbine design, 

analysis, and optimization—including 2-D and 3-D RANS and 

unsteady RANS (URANS) solvers and associated turbulence 

models—require validated sub-models for transitional flow 

fields. The state of modeling transitional flow fields in 

turbines was documented by Praisner and Clark (Ref. 34) and 

Praisner et al. (Ref. 18). Their study highlighted the failure of 

a number of empirical models in the open literature to predict 

attached and separated-flow transition to the accuracy required 

for turbine design. Praisner and Clark (Ref. 34) developed 

transition sub-models and simulation approaches to be used 

within the - model (Ref. 24) that have delivered the 

required level of accuracy. Their approach represents the stateof-the-art for turbine RANS/URANS flow modeling, and its 

implementation is being pursued for use during future VSPT 

turbine blade design efforts. 

Impact of Unsteadiness 

Haselbach et al. (Ref. 17) and others have highlighted the 

impact of unsteadiness of wakes from upstream blade rows on 

the design-point loss levels. The interaction of a passing wake 

with a laminar/transitional-boundary-layer has been studied in 

great detail (see, for example, Halstead et al. (Ref. 35)). At a 

given aerodynamic loading level, the loss levels in steady 

flows were found to be substantially (e.g., 20%) higher than 

when subjected to wake passing; further, the loss increase with 

Reynolds number lapse (sensitivity) is mitigated to some 

degree (see Haselbach et al. (Ref. 17)). The aerodynamic 

loading levels (Z) will influence unsteady wake effects by 

setting effective inlet turbulence intensities, reduced 

frequencies, and length scales (cf. Haselbach et al. (Ref. 17) 

and Gier et al. (Ref. 20)). There is an identified need to 

simulate accurately the impact of unsteadiness on the 

transitional flow fields of the VSPT blade rows. 

Impact on Incidence 

The useful range of incidence decreases as Reynolds 

number lapses with increased altitude (see Fig. 8a). There is 

an identified need to quantify the effect of Reynolds number 

on the useful incidence range. 

Impact of Aerodynamic Loading Distribution 

The computational results shown earlier (Fig. 7(b)) indicate 

the potential role of loading distribution in setting loss level, 

and more subtly lapse rate, at a given Reynolds number. The 

loading distribution is also expected to play a strong role in 

setting the useful incidence range of the blade row. In addition 

to the chordwise loading distribution, the importance of 3-D 

aerodynamics in controlling secondary flow and endwall 

losses at off-design conditions (incidence) was reported by 

Gier et al. (Ref. 20) There is an identified need to understand 

the characteristics of loading schedules that mitigate lapse in 

efficiency and incidence-range as Reynolds number is 

reduced. 

Research Steps at NASA 

Under the NASA Fundamental Aeronautics Program, 

Subsonic Rotary Wing project, an effort is underway at Glenn 

Research Center (GRC) to conduct research to enable future 

variable-speed power turbines for LCTR-class engines. The 

stepwise approach adopted by the VSPT team is outlined 

below. 

VSPT Requirements and Conceptual Design 

A conceptual design of a VSPT that meets the LCTR 

mission/engine requirements is to be executed and refined to a 

level that establishes representative vane, blade, and EGV 

blade flow angle requirements. The performance levels 

predicted in on- and off-design meanline analyses (Ref. 22) 

will be used to refine the engine and VSPT requirements. 

Detailed Design of Incidence-Tolerant Blading 

Incidence-tolerant rotor, vane, and EGV blade shapes that 

meet the identified VSPT requirements are to be developed 

using flow angles from the meanline analyses. The envisaged 

approach utilizes the turbine airfoil design and optimization 

system developed by Clark et al. (Ref. 22) The process 

includes meanline analyses, through 2-D blade-profile 

design/optimization and 3-D blade generation (stacking), 

through 3-D RANS (with mixing-plane) and multi-blade-row 

URANS calculations (see Clark et al. (Ref. 22)). 
NASA/TM—2010-216758 13 

Transition Sub-Model Assessment/ 

Implementation 

Influenced by the work of Praisner and Clark (Ref. 34), 

there is an effort underway to assess, and to implement in 

internal research codes, transition sub-models which are 

compatible with Wilcox’s low-Re - turbulence model 

(Ref. 24). The intent is to develop a validated 3-D 

RANS/URANS-based computational methodology for 

simulation of the low-Re flow in multistage VSPT blade rows 

at on- and off-design (high incidence) conditions. The 

computational results will be used to refine engine and system 

level analyses. 

Transonic Cascade Testing of 2-D Sections 

Two-dimensional sections of the 3-D VSPT incidencetolerant rotor/stator/EGV blading are to be tested in NASA 

GRC transonic linear cascade (Fig. 10). LCTR-relevant exit 

relative Mach (0.6 to 1+) and unit exit isentropic Reynolds 

numbers (60 k/in. to 333 k/in.) can be established, and 

incidence can be varied by 45-degrees. The cascade, described 

in detail by Giel et al. (Ref. 36), is highly three-dimensional 

and has been used previously to assess heat transfer in blades 

with transitional flow (Ref. 36); indeed, data from previous 

entries are being used currently to assess the applicability of 

the existing turbulence/transition models available in in-house 

codes. (Note that the minimum Reynolds number attainable at 

M2 = 0.7 is just above sea-level take-off conditions, and nearly 

twice that of cruise conditions; thus, data obtained at flight 

Reynolds numbers will be at low M2.) 

Rotordynamics 

Assessment of the mechanical challenges associated with 

operation of a variable-speed power turbine, although beyond 

the scope of the present paper, is considered a key part of the 

VSPT research and technology development effort. Of 

particular interest are potential constraints imposed on the 

aerodynamic design by mechanical issues associated with 

variable speed—for example, torque capacity requirements 

and operational speeds relative to shaft critical speeds 

(rotordynamics). To this end, a preliminary design of the 

LCTR power-turbine shaft is underway, with the intent that 

any aero-relevant interactions between the shaft and turbineaero designs be identified. 

VSPT Component Experiment 

Initial aero-experiments with developed incidence-tolerant 

blading will be restricted to the cascade. The experiments will 

provide valuable data, over a range of Reynolds number and 

incidence, to be used to validate and calibrate in-house design 

and analysis tools. In order to include the effects of blade-row 

interaction, rotation, and leakage flows, plans are to conduct 

subsequent experiments at the multi-blade-row component 

level—minimum 1.5 stage (nozzle, rotor, EGV). An 

assessment of potential in-house and external vehicles for 

component level VSPT experimentation is currently 

underway. The assessment includes investigating the viability 

of utilizing an existing T700-700 test stand to conduct 

component level research. 

Conclusions 

The key aerodynamic challenges of the variable-speed 

power turbine are related to attainment of efficiency at high 

work factors (3.5 to 4 at cruise), the wide incidence variation 

associated with the speed change from take-off (100% speed) 

to cruise (54% speed), and operation at low chord Reynolds 

numbers encountered at 28 kft cruise. The efficiency at high 

work factor will require 3-D blading that manages 2-D (profile 

and shock losses) and 3-D secondary flow and endwall flow 

losses. Wake passing (unsteadiness) impacts blade row loss 

levels of the low-Re flow fields significantly and, therefore, 

must be accounted for in the design process. The high 

efficiency blading must also be incidence-tolerant, able to 

accept changes in incidence angle up to 60-degrees at the most 

challenging off-design point (100% speed, 28 kft), where 

particular attention to loss production at high negative 

incidence will be needed. 

The lapse in Reynolds number from sea-level to 28 kft has 

deleterious impact on both design-point and off-design 

efficiency levels, and incidence range. The design-point 

cruise-efficiency at low chord Reynolds number is a technical 

challenge shared by both fixed- or variable-speed power 

turbines for the LCTR missions. The high cruise-work-factors 

and incidence-range requirements of the VSPT exacerbate the 

Re-lapse issues. 

The design of low-loss, incidence-tolerant vane, blade, and 

EGV blading is considered a key technical challenge for the 

variable-speed power turbine. At the conceptual-design level, 

weight (AN2

, stage count, and blade count) will need to be 

traded against VSPT efficiency and incidence range. At the 

blade-row level, reduction of work factors and aerodynamic 

loading levels (Z), tailoring of blade loading schedules, and 

design/optimization of 3-D blade and endwall profiling, will 
NASA/TM—2010-216758 14 

aid in attainment of blade rows with required incidence range 

at satisfactory loss levels. The intent of the VSPT research 

effort underway at NASA GRC is to develop experimentally 

validated design methods and computational tools required for 

the design and optimization of incidence-tolerant blade rows 

for the variable-speed power turbines of the LCTR 

application. 

References 

1. Johnson, W., Yamauchi, G.K., and Watts, M.E., “NASA 

Heavy Lift Rotorcraft Systems Investigation,” NASA TP2005-213467, Sep., 2005. 

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. 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. 

4. Acree, C.W., Jr., “Integration of Rotor Aerodynamic 

Optimization With the Conceptual Design of a Large 

Civil Tiltrotor,” Proc. AHS Aeromechanics Conf., San 

Francisco, Jan. 2010. 

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

NASA CR-198380, August 1995. 

6. Snyder, C.A. and Thurman, D.R., “Gas Turbine 

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

Proc. AHS Int. 65th Ann. Forum, TX, May, 2009. 

7. 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. 

8. 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. 

9. 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. 

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

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

11. Horlock, J.H., Axial Flow Turbines, Krieger Publishing 

Co., USA, 1985, p. 127. 

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

Components, AIAA Education Series, 1985. 

13. Chen, S-C, S., “Preliminary Axial Flow Turbine Design 

and Off-design Performance Analysis Methods for Rotary 

Wing Aircraft Engines; II-Applications,” Proc. AHS 

Inter. 65th Ann. Forum, TX, May, 2009. 

14. Rogo, C. and Benstein, E.H., “Variable Cycle Turboshaft 

Technology for Rotorcraft of the ‘90s,” J. Propulsion, 2 

(1), Jan-Feb, 1986, pp. 73–80. 

15. Karstensen, K.W. and Wiggins, J.O., “A VariableGeometry Power Turbine for Marine Gas Turbines,” 

J. Turbomachinery, 112, Apr 1990, pp. 165–174. 

16. 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. 

17. Haselbach, F., Schiffer, H.-P., Horsman, M., Dressen, S., 

Harvey, N., and Read, S., “The Application of Ultra High 

Lift Blading in the BR715 LP Turbine,” J. 

Turbomachinery, 124, Jan 2002, pp. 45–51. 

18. Praisner, T.J., Grover, E.A., Rice, M.J., and Clark, J.P., 

“Predicting Transition in Turbomachinery – Part II: 

Model Validation and Benchmarking,” J. 

Turbomachinery, 129, Jan, 2007, pp. 14–22. 

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

Pressure Turbines,” in Blading Design for Axial 

Turbomachines, AGARD-LS-167, pp. 8-1 to 8-40, 1989. 

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

“Designing LP Turbines for Optimized Airfoil Lift,” 

ASME-GT2008-51101, 2008. 

21. Riegler, C. and Bichlmaier, C., “The Geared Turbofan 

Technology – Opportunities, Challenges and Readiness 

Status,” Proc. 1st CEAS European Air and Space Conf., 

Sept. 2007. 

22. 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, (Internal Report) Sept. 

2009. 

23. Chima, R.V., “Explicit Multigrid Algorithm for QuasiThree-Dimensional Viscous Flows in Turbo-machinery,” 

J. Propulsion and Power, 3 (5), Sept-Oct, 1987, pp. 397–

405. 

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

Industries, Inc. La Canada, CA, 1994. 

25. Sorenson, R.L., “A Computer Program to Generate TwoDimensional Grids About Airfoils and Other Shapes by 

Use of Poisson’s Equation,” NASA TM-81198, 1980. 

26. Mattingly, J.D., Heiser, W.H., and Daley, D.H., Aircraft 

Engine Design, American Institute of Aeronautics and 

Astronautics, Wash., D.C., 1987, pp. 562–574. 

27. Mattingly, J.D., Elements of Gas turbine Propulsion, 

McGraw-Hill, Inc., NY, 1996, pp. 926–929. 

28. Hartland, J.C., Gregory-Smith, D. G., Harvey, N. W., 

Rose, M.G., “Nonaxisymmetric Turbine End Wall 

Design: Part II – Experimental Validation,” J. 

Turbomachinery, 122, Apr, 2000, pp. 286–293. 

29. Praisner, T.J., Allen-Bradley, E., Grover, E.A., Knezevici, 

D.C., and Sjolander, S.A., “Application of NonAxisymmetric Endwall Contouring to Conventional and 

High-Lift Turbine Airfoils,” ASME GT2007-27579, 

2007. 

30. Germain, T., Nagel, M., Raab, M., Schüpbach, P., Abhari, 

R.S., Rose, M., “Improving Efficiency of a High Work 

Turbine Using Nonaxisymmetric Endwalls – Part I: 

Endall Design and Performance,” J. Turbomachinery, 

132, Apr, 2010, pp. 021007-1 to -9. 
NASA/TM—2010-216758 15 

31. 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. 

32. Brear, M.J., Hodson, H.P., and Harvey, N.W., “Pressure 

Surface Separations in Low-Pressure Turbines – Part I: 

Midspan Behavior,” J. Turbomachinery, 124, July, 2002, 

pp. 393–401. 

33. Brear, M.J., Hodson, H.P., Gonzalez, P., and Harvey, N. 

W., “Pressure Surface Separations in Low-Pressure 

Turbines – Part II: Interactions with Secondary Flow,” J. 

Turbomachinery, 124, July, 2002, pp. 402–409. 

34. Praisner, T.J. and Clark, J.P., “Predicting Transition in 

Turbomachinery – Part I: A Review and New Model 

Development,” J. Turbomachinery, 129, Jan 2007, pp. 1–

13. 

35. 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, 1997, pp. 225.

36. Giel, P.W., Boyle, R.J., and Bunker, R.S., “Measurements 

and Predictions of Heat Transfer on Rotor Blades in a 

Transonic Turbine Cascade,” J. Turbomachinery, 126, 

Jan, 2004, pp. 110–121. 
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4. TITLE AND SUBTITLE

Assessment of Aerodynamic Challenges of a Variable-Speed Power Turbine for Large Civil 

Tilt-Rotor Application 

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Welch, Gerard, E. 

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WBS 877868.02.07.03.01.02.01 

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John H. Glenn Research Center at Lewis Field 

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14. ABSTRACT

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

The variable-speed power turbine, when coupled to a fixed-gear-ratio transmission, offers one approach to accomplish this speed variation. 

The key aero-challenges of the variable-speed power turbine are related to high work factors at cruise, where the power turbine operates at 

54% of take-off speed, wide incidence variations into the vane, blade, and exit-guide-vane rows associated with the power-turbine speed 

change, and the impact of low aft-stage Reynolds number (transitional flow) at 28 kft cruise. Meanline and 2-D Reynolds-Averaged NavierStokes analyses are used to characterize the variable-speed power-turbine aerodynamic challenges and to outline a conceptual design 

approach that accounts for multi-point operation. Identified technical challenges associated with the aerodynamics of high work factor, 

incidence-tolerant blading, and low Reynolds numbers pose research needs outlined in the paper.

15. SUBJECT TERMS

Simulation; Jet mixing flow; Propellant tanks 

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