Mark Suchezky and G. Scott Cruzen

Williams International Co. LLC

Variable-Speed Power-Turbine 

for the Large Civil Tilt Rotor

NASA/CR—2012-217424

February 2012

TR2011-02-28-0724
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Mark Suchezky and G. Scott Cruzen

Williams International Co. LLC

Variable-Speed Power-Turbine 

for the Large Civil Tilt Rotor

NASA/CR—2012-217424

February 2012

TR2011-02-28-0724

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

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subject to revision as analysis proceeds.
NASA/CR—2012-217424 iii

Contents

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

Nomenclature ................................................................................................................................................ 2 

2.0 VSPT Concept Development ............................................................................................................... 2 

2.1 Figure of Merit ............................................................................................................................ 2 

2.2 Efficiency Prediction Technique ................................................................................................. 4 

2.3 Structural Constraints .................................................................................................................. 5 

2.4 Exhaust Constraint ....................................................................................................................... 5 

2.5 List of Analytical Studies ............................................................................................................ 6 

2.6 Flow Path Selection: Cx/U .......................................................................................................... 6 

2.7 Work Coefficient ....................................................................................................................... 11 

2.8 3–D Design Execution ............................................................................................................... 17 

2.9 Loss System Validation via CFD .............................................................................................. 19 

2.10 Turbine Blade Incidence Study ................................................................................................. 19 

2.11 Thin Turbine Blade Incidence Study ......................................................................................... 21 

2.12 Third Stage Combined Incidence Study .................................................................................... 24 

2.13 Airfoil Leading Edge Geometry ................................................................................................ 27 

3.0 VSPT LCTR Mission Performance Modeling ................................................................................... 32 

4.0 Development of a Cost-Effective Approach to an LCTR-Relevant VSPT Component 

Experiment ......................................................................................................................................... 34 

4.1 Experimental Test Plan and Instrumentation List ..................................................................... 36 

4.2 VSPT Component Experiment Program Plan, Schedule, and ROM Cost ................................. 38 

5.0 Conclusions ........................................................................................................................................ 40 

Appendix A.—NPSS Outputs ..................................................................................................................... 43 

Appendix B.—Definitions .......................................................................................................................... 51 

Appendix C.—FlowPath Details................................................................................................................. 53 

Appendix D.—Four Stage CFD Analysis ................................................................................................... 63 

D.1 Stage 1 ....................................................................................................................................... 64 

D.2 Stage 2 ....................................................................................................................................... 65 

D.3 Stage 3 ....................................................................................................................................... 67 

D.4 Stage 4 ....................................................................................................................................... 68 

Appendix E.—Meanline Results for Four Stage: High Loading 1 ............................................................. 73 

Appendix F.—Disk Sizing .......................................................................................................................... 75 

Appendix G.—Efficiency and Reaction Definitions .................................................................................. 77 

Appendix H.—NPSS Output for Critical Mission Point ............................................................................ 79 

References ................................................................................................................................................... 89 

List of Tables

Table 2.1—LCTR Mission Segments ........................................................................................................... 3 

Table 2.2.—Fuel Burn Comparison for High and Low CX/U Designs ...................................................... 10 

Table 2.3.—Three-Stage Turbine Results ................................................................................................... 14 

Table 2.4.—Four-Stage Turbine Segment Fuel Burn ................................................................................. 16 

Table 3.1.—Critical Mission Points ............................................................................................................ 32 

Table 4.1.—NASA GRC Single-Spool Turbine Test Facility Capabilities ............................................... 34 

Table 4.2.—Proposed Map/Test Plan ......................................................................................................... 37 

Table 4.3.—Proposed Instrumentation List for VSPT Component Experiment ......................................... 38 

Table A.1.—Sea level static (MRP) 100 percent NPT ............................................................................... 43 

Table A.2.—2,000 altitude, +45 °F day, hover (not at maximum power) 100 percent NPR ...................... 45 
NASA/CR—2012-217424 iv

Table A.3.—Cruise mission 1, 303.4 kn, 28,000 altitude, +0 °F day, Initial cruise power level, 

100 percent NPR rpm/650 rotor tip speed .......................................................................................... 47 

Table A.4.—Cruise mission 1, 303.4 kn, 28,000 altitude, +0 °F day, Initial cruise power level, 54 

percent NPR rpm/350 rotor tip speed—NO multispeed gearbox ....................................................... 49 

Table H.1.—65 Percent Design Speed Take Off ....................................................................................... 80 

Table H.2.—65 Percent Design Speed Climb ............................................................................................. 81 

Table H.3.—65 Percent Design Speed Cruise ............................................................................................ 82 

Table H.4.—75 Percent Design Speed Take Off ........................................................................................ 83 

Table H.5.—75 Percent Design Speed Climb ............................................................................................. 84 

Table H.6.—75 Percent Design Speed Cruise ............................................................................................ 85 

Table H.7.—85 Percent Design Speed Take Off ........................................................................................ 86 

Table H.8.—85 Percent Design Speed Climb ............................................................................................. 87 

Table H.9.—85 Percent Design Speed Cruise ............................................................................................ 88 

List of Figures

Figure 1.1—NASA LCTR Concept .............................................................................................................. 1 

Figure 2.1.—LCTR Mission Profile ............................................................................................................. 3 

Figure 2.2—Falcon Meanline Code Interface ............................................................................................... 4 

Figure 2.3.—Airfoil Shapes .......................................................................................................................... 7 

Figure 2.4.—Low CX/U Design Velocity Triangles .................................................................................... 8 

Figure 2.5—High CX/U Design Velocity Triangles..................................................................................... 8 

Figure 2.6.—Comparison of High and Low CX/U Flowpaths ..................................................................... 9 

Figure 2.7.—Design Speed Selection for High and Low CX/U Designs ................................................... 11 

Figure 2.8.—Work Coefficient Versus Flow Coefficient ........................................................................... 12 

Figure 2.9.—Work Coefficient Versus Flow Coefficient ........................................................................... 12 

Figure 2.10.—Comparison of Three Stage and Four Stage Turbine Flowpaths ......................................... 13 

Figure 2.11.—Turbine Design Speed Selection .......................................................................................... 14 

Figure 2.12.—Smith Correlation for Three Turbines ................................................................................. 15 

Figure 2.13.—Four-Stage Turbine Flowpath .............................................................................................. 15 

Figure 2.14.—Design Speed Versus Segment Fuel Burn ........................................................................... 16 

Figure 2.15.—Smith Correlation for Four Study Turbines ......................................................................... 16 

Figure 2.16.—Airfoil Stacking ................................................................................................................... 18 

Figure 2.17.—FoilGen Output .................................................................................................................... 18 

Figure 2.18.—Third Stage extracted from full simulation to investigate off-design performance ............. 19 

Figure 2.19.—Efficiency Comparisons for Four Turbine Designs ............................................................. 20 

Figure 2.20.—A Simple Turbine Blade Cascade ........................................................................................ 22 

Figure 2.21.—A sample thin blade cascade ................................................................................................ 22 

Figure 2.22.—Blade Profile Modifications ................................................................................................. 23 

Figure 2.23.—Thin turbine blade geometry compared to nominal ............................................................. 24 

Figure 2.24.—Third Stage Speed Study composed of Three airfoils ......................................................... 25 

Figure 2.25.—Third Stage Performance ..................................................................................................... 25 

Figure 2.26.—Third Vane Pressure Loss .................................................................................................... 26 

Figure 2.27.—Vane Velocity Vectors ......................................................................................................... 26 

Figure 2.28.—Fixed geometry LE slats. Used with permission from Zenith Aircraft Company, 

Mexico, Missouri, 65265-0650. ......................................................................................................... 28 

Figure 2.29.—Typical Turbine Airfoil Leading Edge Profile .................................................................... 28 

Figure 2.30.—Third Blade Mean, surface curvature smoothed .................................................................. 29 

Figure 2.31.—Third Blade mid span static pressure distribution ............................................................... 30 

Figure 2.32.—Smoothed third Blade Efficiency Trend with Speed ........................................................... 31 
NASA/CR—2012-217424 v 

Figure 2.33.—Separation bubble visualization ........................................................................................... 32 

Figure 3.1.—VSPT Total Mission Fuel Burn for Three Williams International Designs .......................... 33 

Figure 4.1.—Schematic of Recommended Engine Configuration for LCTR ............................................. 35 

Figure 4.2.—VSPT Test Article Mated to NASA-GC Single Spool Turbine Test Facility ....................... 36 

Figure 4.3.—Proposed Schedule for VSPT Experiment ............................................................................. 39 

Figure B.1.—Turbine AN2 and Rim Speed Definitions ............................................................................. 51 

Figure C.1.—High Cx/U Four Stage .......................................................................................................... 53 

Figure C.2.—Low Cx/U Four Stage ........................................................................................................... 54 

Figure C.3.—Three Stage ........................................................................................................................... 55 

Figure C.4.—Four Stage High Loading (1) ................................................................................................ 56 

Figure C.5.—Four Stage High Loading (2) ................................................................................................ 57 

Figure C.6.—SixStage High Cx/U .............................................................................................................. 58 

Figure C.7.—Three Stage B ........................................................................................................................ 59 

Figure C.8.—Four Stage C ......................................................................................................................... 60 

Figure C.9.—Smith Curve of All Turbines ................................................................................................. 61 

Figure C.10.—Design Speed Comparison: All Turbines............................................................................ 61 

Figure F.1.—Approximate Disk Size ......................................................................................................... 75 

NASA/CR—2012-217424 1 

1.0 Introduction

The Large Civil Tilt-Rotor (LCTR) is part of NASA’s Heavy Lift Systems Investigation. This 

proposed 90 passenger aircraft would offload short to medium range air traffic from large airports and/or 

runways. Due to its vertical takeoff and landing capability, only a helipad would be needed within 

existing airport infrastructure (Figure 1.1).

The proposed vehicle has four turbo-shaft engines powering two rotors. Each engine is to develop 

7,500 hp for a total 30,000 hp. The mission would require high rotor rpm at sea level take off (650 ft/s tip 

speed) and significantly lower rpm at cruise (350 ft/s tip speed) (Ref. 1).That is, the cruise rpm of the 

main rotors is 54 percent of the SLTO rpm. This requirement comes from the fact that the main rotors are 

more efficient at low rpm during the altitude cruise but require high rpm during sea level take-off 

(SLTO). The turboshaft engines will drive the main rotors through a gearbox enabling the high rpm 

power turbines (PT) to spin the low rpm (103 to 191 rpm) main rotors. Each main rotor is driven by two

engines. There are two possible methods for achieving the required rpm sweep.

1. Two (or higher) gear-ratio transmission: with the power turbine operating at near constant rpm. 

2. Fixed gear-ratio transmission: with the power turbine experiencing the full 54 to 100 percent

speed range.

For method 1, the complexity of designing a flight weight, 15,000 hp transmission (two engines X 

7,500 hp each), while obtaining high life and reliability is a formidable task. The method for changing 

gears (ex. torque converter, clutch, etc.) would also need to be addressed. This method is not within the 

scope of this study and will not be further considered. 

Figure 1.1—NASA LCTR Concept
NASA/CR—2012-217424 2 

Nomenclature

AN2 See Appendix B 

Cm/U Flow Coefficient 

Cx/U Flow Coefficient 

Δh0/U2

 Work Coefficient 

FOM Figure of Merit

h0 Total Enthalpy 

LCTR Large Civil Tilt-Rotor 

LE Leading Edge 

η Efficiency (see Appendix G) 

NPSS Numerical Propulsion System Simulator 

PT Power Turbine

SLTO Sea Level Take Off

TE Trailing Edge

U Wheel Speed (usually associated with midspan) 

VSPT Variable Speed Power Turbine 

2.0 VSPT Concept Development

2.1 Figure of Merit

In this study various techniques are investigated to improve efficiency and off-design characteristics 

of a power turbine operating in the LCTR mission. The relative performance of each design modification 

needs to be assessed using some form of figure of merit (FOM). The FOM chosen for this study is overall 

fuel burn during the mission. The overall mission profile is not well established at this time so a fictitious 

but representative mission needs to be assumed. Based on the work of Snyder and Thurman (Ref. 1), a 

study engine simulation was generated using the Numerical Propulsion System Simulator (NPSS). This 

simulation software has the ability to predict engine performance throughout the flight envelope based on 

performance maps of the individual engine components. Four output points were generated from this 

model and made available for this study. These four flight conditions are: 

Point 1

SLTO; 100% PT Speed, 100ft, 0.0 Mach, Std. Day 

Point 2 

Climb; 100% PT Speed, 2,000ft 0.0 Mach +45 °F

Point 3

Start Cruise; 100% PT Speed 28,000ft 0.51 Mach Std. Day 

Point 4

Cruise; 54% PT Speed 28,000ft 0.51 Mach Std. Day 

A detailed output from the NPSS cycle model is included in Appendix A. These four points are the 

only points currently available from the model and therefore a mission made up of only these four points 

was assumed. The actual mission will deviate significantly from this mission, but this mission is used as a 

starting point (Table 2.1). 

This mission was made to mimic the mission shown in Figure 2.1, provided by C. Sndyer of NASA at 

contract start. 
NASA/CR—2012-217424 3 

TABLE 2.1—LCTR MISSION SEGMENTS 

Figure 2.1.—LCTR Mission Profile

Unfortunately, cycle points such as idle and taxi were not available to use in this cycle so there is 

some error introduced. The mission used in this study (Table 2.1) includes a long cruise segment of 3 hr 

with 1⁄2 hr of climb condition before and after. There is also some high power SLTO time at the beginning 

and end of the mission to simulate vertical takeoff and landing. 

Given the cycle predicted fuel burns at each condition and the assumed duration of each segment, the 

fuel burned can be integrated. (Eq. (1)) 

∑=

∆×=

nseg

seg 1

Wfuel Wfuel Time  (1) 

Point Description Δtime Cycle PT Power Wf PT Fuel Burned

Minutes ETA hp lbm/hr Speed lbm

1 SLTO;100% PT Speed,100ft,0.0 Mach, Std. Day 2 0.85 7500 2581.28 100.0% 86.0

2 Climb;100% PT Speed,2,000ft0.0 Mach+45°F 2 0.8266 4639.6 1761.6 100.0% 58.7

3 Start Cruise;100% PT Speed 28,000ft 0.51Mach Std. Day 30 0.8485 2651.5 836.01 100.0% 418.0

4 Cruise;54% PT Speed 28,000ft 0.51 Mach Std. Day 180 0.7859 2345.4 805.23 54.0% 2415.7

3 Start Cruise;100% PT Speed 28,000ft 0.51Mach Std. Day 30 0.8485 2651.5 836.01 100.0% 418.0

2 Climb;100% PT Speed,2,000ft0.0 Mach+45°F 2 0.8266 4639.6 1761.6 100.0% 58.7

TOTALS 246 Minutes 3455.2 lbm

 -or4 hours

6 minutes
NASA/CR—2012-217424 4 

Table 2.1 shows that the predicted fuel burn would be 3455.2 lbm of fuel per engine over the 4 hr and 

6 min flight. Because all of the power to drive the main rotors comes from the power turbine, the fuel 

burn at any condition will be proportional to PT efficiency. Therefore we can evaluate the impact of 

predicted PT efficiencies (ηPT) throughout the mission by scaling the fuel flows by the ratio of predicted 

ηPT to cycle ηPT. 

∑=

∆×

η

η =

nseg

seg 1

fuel

cycle

predicted Wfuel W Time  (2) 

Using this technique, a prediction for ηPT can be input into Equation (2) for each of the four cycle points 

and an overall mission fuel burn can be calculated. Comparing the new predicted fuel burn back to the 

cycle prediction (3455.2 lbm) yields the FOM used in this study. 

2.2 Efficiency Prediction Technique

Efficiency predictions are made by the use of a ‘meanline’ analysis. The meanline used is proprietary 

to Williams International and is referred to as ‘MeanTurb’. MeanTurb is a row by row analysis tool that 

tracks the mean particle through each airfoil row. All three components of velocity are modeled which 

makes the tool very general and can be used for axial, mixed flow, or radial turbines. The velocity 

triangles are solved with the loss system, cooling flows (if applicable), gas properties, and seal leakages 

all converged simultaneously. The solution technique is to solve each blade row independently and then 

use small-change effects (Jacobian matrix) and Newton’s Method to close on continuity, angular 

momentum, and energy. The loss system used in this study is a combination of various public domain loss 

systems (Kacker and Okapuu (Ref. 4) and Moustapha, Kacker and Tremblay (Ref. 5)) with modifications 

based on Williams International experience. 

The technique used to predict turbine efficiency is two parts. The first part is referred to as ‘design 

mode’. In this phase a simpler design-mode meanline called “Falcon” is used. This meanline is different 

from MeanTurb in that you specify mass-flow, power, pressure reaction and airfoil loading coefficient 

(Zweifel). The velocity triangles are calculated using nearly the same loss system as MeanTurb with 

several simplifying assumptions. Falcon is wrapped with a graphical user interface which allows for 

intuitive design as well as optimization functionality. Figure 2.2 is a screen shot of the interface.

Figure 2.2—Falcon Meanline Code Interface
NASA/CR—2012-217424 5 

The second part of the efficiency prediction process begins after a satisfactory design has been 

produced in Falcon. Falcon writes out an off-design input file for MeanTurb. At this point the geometry is 

assumed fixed and parameters such as power, work split, reaction, mass-flow and efficiency are outputs 

of MeanTurb. One important point in this study is that the LE metal angles are assumed fixed so the 

impact of off-incidence design is captured in the MeanTurb calculations.

2.3 Structural Constraints

The 100 percent speed condition must be structurally viable. This study used aggressive AN2 and Rim 

Speed limits of 60. E9 in2

∙rpm2 and 1200 ft/s respectively as upper limits. (See Appendix B for 

definitions.) The most challenging structural design will be the last stage blade which will have the largest 

span and highest pull stress. Fortunately it is also the coolest airfoil which aids in creep rupture life. 

Although challenging, these limits should be achievable for a long life application. After designing 

several flowpaths to this criterion, a sanity check calculation was performed. A meanline analysis was run 

for Point 1 (the hottest and fastest of the four performance conditions used) with the inlet temperature 

raised by 100 °F to simulate deterioration and hot day operation. The average blade pull-stress was 

estimated at 68 ksi and metal temperature at 1190 °F. Based on proprietary material databases, there are 

several commercially available alloys capable of >20,000 hr of useful life at these conditions. Over-speed 

protection in the event of a gearbox or coupling failure has not been addressed. It is possible that failure 

analysis may require more structural conservatism. 

2.4 Exhaust Constraint 

Choosing the exit annulus area determines the exit Mach number from the turbine (last blade, 

absolute frame of reference). The four cycle points given have nozzle (tail pipe) exit Mach numbers of 

about 0.27. This very low exit Mach number corresponds to a design philosophy of extracting as much 

energy out of the power turbine as possible and achieving nearly no thrust from the nozzle. Achieving 

such low exit Mach numbers at the exit of a gas turbine is difficult and results in large, heavy turbines 

operating at low rpm. It is more advantageous to design to an exit Mach number of .4 to .55 and diffuse 

through the exhaust system. For the purposes of this study, Mach numbers in this range will be used. In a 

more formal detailed design, a trade study between nozzle exit Mach number, turbine weight, exhaust 

system weight and fuel burn should be performed to find the best overall system trade. 

It can be shown that the combination of the structural and exhaust constraints sets the turbine rpm and 

the last stage flowpath. That is: picking a Mach number exiting the turbine sets the turbine exit annulus 

area because of continuity (although swirl angle and boundary layer blockage play a role). Then, with 

AN2 already chosen, the rpm falls out. (See Appendix B for more information)

A = function(PT, TT, Mdot, Mach, Swirl) (3) 

A

AN

rpm

2

= (4) 

The Rim Speed can be used to calculate the last blade trailing edge hub radius:

Rim Speed(ft/s) = Radius Hub (in.)/12. * rpm *π / 30. (5) 

Then the trailing edge tip radius can be determined by the annulus area. 

2

Tip RadiusHub

A Radius +

π = (6) 

From the above relations it is clear that selecting structural criteria and an exit Mach number uniquely 

defines the exit of the turbine and the rpm. In a more detailed engine design exercise, the front of the 

power turbine would need to mate to the exit of the previous turbine which would further define the 
NASA/CR—2012-217424 6 

flowpath. In this work, no special attention is given to the proceeding turbine. Detailed design of the 

overall turbine section is out of scope. 

2.5 List of Analytical Studies

Several analytical studies have been performed to gain confidence and reduce risk in designing a 

power turbine capable of nearly a 2X speed variation while maintaining acceptable efficiency levels.

1. Flow Path Selection 

a. CX/U

b. Work Coefficient

c. Number of Stages

2. Loss System Validation via CFD

3. Incidence Tolerant Design

a. LE Shape

b. Airfoil Thickness

2.6 Flow Path Selection: Cx/U 

Turbine Flow Coefficient, commonly referred to as Cx/U, is the ratio of through-flow velocity to 

mean wheel speed. Often Cx/U is referred to as axial velocity over wheel speed but in this study the radial 

velocity is taken into account. The meridional velocity is used instead and defined as:

2

radial

2 Vmeridional axial +≡ VV (7) 

For the purposes of this study, Cx/U and Cm/U will be used synonymously and is defined as:

r

VV

Cm U/ Cx U/

2

radial

2

axial

ω

+ ≡= (8) 

where: 

all values are calculated at the TE plane of the turbine blade 

r equals the average of the hub and tip radius of the blade TE

The Flow Coefficient, Cx/U is a good indicator of the velocity triangles. Low Cx/U designs are 

characterized by high turning and relatively low velocity whereas high Cx/U designs tend towards low 

turning (camber) and higher velocities. The airfoil shapes can be dramatically different as shown in Figure 

2.3. 

The off-incidence loss generated at the LE of an airfoil is a function of two factors: 1) Loss 

Coefficient and 2) Inlet dynamic head. Low CX/U designs have lower LE Mach number but higher 

swings in incidence. High CX/U designs have lower excursions in incidence but always operate at higher 

inlet Mach number. Therefore it is reasonable to assume that there is an optimum CX/U for off incidence 

performance. Figure 2.4 and Figure 2.5 show a simplified example of velocity triangle for Low versus

High CX/U designs. 

For the VSPT, the corrected speed variation is from 54 to 100 percent. This implies that the wheel 

speed (U) varies from 54 to 100 percent but velocity triangle analysis shows that the Cx is nearly 

constant. Therefore, CX/U is approximately inversely proportional to speed. 

Two flowpaths were generated to look at the impact of CX/U on mission fuel burn. The design 

philosophy was to follow the structural and exhaust constraints as given in the previous section and build 

turbine flowpaths that have good cruise velocity triangles and airfoil loadings. Once the flowpaths are 

established, MeanTurb is run to investigate the off design characteristics. Very good cruise performance 

(>90 percent) is achieved with four stage turbines. See Figure 2.6. 
NASA/CR—2012-217424 7 

Figure 2.3.—Airfoil Shapes
NASA/CR—2012-217424 8 

Figure 2.4.—Low CX/U Design Velocity Triangles

Figure 2.5—High CX/U Design Velocity Triangles

Stator

Rotor

Absolute tangential 

velocity (Ct)

Through-flow 

Velocity (Cx)

Wheel speed (U)

Figure 6:

High Cx/U turbine

Characterized by low turning, 

high inlet velocity airfoils.

Low swings in incidence with 

speed variation

Stator

Rotor Absolute tangential 

velocity (Ct)

Through-flow 

Velocity (Cx)

Wheel speed (U)

Figure 5:

Low Cx/U turbine

Characterized by high 

turning, low inlet velocity 

airfoils.

Large swings in incidence 

with speed variation
NASA/CR—2012-217424 9 

Figure 2.6.—Comparison of High and Low CX/U Flowpaths
NASA/CR—2012-217424 10

If the turbines in Figure 2.6 were designed for the low speed cruise condition (54 percent speed), they 

would have predicted efficiencies of 91.4 and 90.2 percent respectively when operating at that design 

point. Unfortunately, each of these turbines is predicted to have an efficiency of 69.3 percent when 

operating at the high speed cruise condition (100 percent speed). Likewise, if the two turbines were 

designed for the 100 percent speed condition, the efficiencies would be 92.8 and 91.4 percent

respectively. These turbines both would have very low efficiencies (<58 percent) when operating at the 

54 percent speed conditions. Of course, these off-design efficiency predictions are highly dependent on 

the empirical loss system used in the meanline prediction system. Nonetheless, a compromised design 

point somewhere between 54 and 100 percent would most likely be a good compromise. A method for 

determining the optimal design point was developed. Four design speeds were chosen: 54, 69, 85 and

100 percent speed. A preliminary design was produced for each of these turbines at each of these speeds.

This preliminary design process sets the LE metal angles and blade counts for the velocity triangles 

corresponding to that speed. Each of these designs was then run off-design using MeanTurb to the four 

different mission points in order to predict the efficiency. The resulting efficiencies are available in Table 

2.2. For each of these designs, the resulting efficiencies for points 1, 2, 3, and 4 were used in Equation (2) 

(via spread sheet) and the overall impact to mission fuel burn was calculated, the results of which are also 

included in Table 2.2. 

The results of Table 2.2 are plotted in Figure 2.7. From this plot, the best design practice is to pick a 

design point that is compromised between the low speed and high speed cruise but favoring the low speed 

cruise condition. An unexpected outcome of this study is the fact that both the High CX/U design and the 

Low CX/U design optimize at about the same speed and result in about the same overall fuel burn.

Neither design philosophy appears to have an advantage. There is no compelling evidence from this study 

that CX/U (in of itself) is a determining factor in the design of this type of turbine.

TABLE 2.2.—FUEL BURN COMPARISON FOR HIGH AND LOW CX/U DESIGNS

High CX/U

% Speed Design RPM Fuel Burn% ETA 1 ETA 2 ETA 3 ETA 4

53.8 8045 -3.29 73.34 68.62 69.34 91.39

69.2 10343 -7.88 88.33 84.71 84.12 88.62

84.6 12642 1.41 92.95 90.84 90.63 74.87

100.0 14941 23.20 91.25 91.58 92.80 57.42

Low CX/U

% Speed Design RPM Fuel Burn% ETA 1 ETA 2 ETA 3 ETA 4

53.8 8045 -2.22 69.98 66.62 69.30 90.20

69.2 10343 -7.80 87.58 83.60 82.85 89.14

84.6 12642 -1.84 92.00 89.60 89.44 78.75

100.0 14941 24.30 89.29 89.78 91.43 57.00
NASA/CR—2012-217424 11

Figure 2.7.—Design Speed Selection for High and Low CX/U Designs

2.7 Work Coefficient

The Work Coefficient (Δh0/U2) is a dimensionless parameter relating the turbine work to the mean 

wheel speed of the turbine. The use of Work Coefficient (Wcoeff) combined with Flow Coefficient 

(Cx/U) was popularized by Smith (Ref. 6) with his correlation of turbine efficiency using both 

parameters. Smith showed that there was an optimum relationship between the two parameters. There is 

no indication that Smith’s 1965 correlation considered turbines operating far off-design so it is not 

obvious whether his correlation is helpful in determining optimum velocity triangles for the LCTR power 

turbine application when operating at its full range of speeds. The Smith correlation was presented 

(Ref. 6) as a plot and Figure 2.8 is a reproduction produced by digitizing the figure in his paper. 

Assuming the LCTR power turbine is designed at the 54 percent cruise condition, then as the turbine 

transitions from 54 to 100 percent speed, the Flow Coefficient (Cx/U) and Work Coefficient (Δh0/U2

) 

change considerably. MeanLine and cycle analysis confirm that Δh0/U2

 is nearly proportional to 1/rpm2

and Cx/U is nearly proportional to 1/rpm. Therefore the Wcoeff increases by 1/.542 or 3.4 times when the 

rotor speed drops from 100 to 54 percent rpm. Likewise the Cx/U increases by a corresponding factor of 

1/.54 or 1.85. If Smith’s correlation indicates optimum relationships between these two parameters, it is 

reasonable to assume that it may provide some guidance in designing a turbine that transitions over a 

large swing in these parameters. The two turbines in the Cx/U study were placed on the Smith correlation 

in Figure 2.9. 

 

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25.00

30.00

35.00

40.00

6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000

Design RPM

Mission Fuel Burn Impact %

High CX/U

Low CX/U

Cruise RPM

Max(SLTO) 

Best Compromise 

Design Space
NASA/CR—2012-217424 12

Figure 2.8.—Work Coefficient Versus Flow Coefficient

Figure 2.9.—Work Coefficient Versus Flow Coefficient

Smith Correlation

0.5

1

1.5

2

2.5

3

3.5

0.2 0.4 0.6 0.8 1 1.2 1.4

Flow Coefficient

Work Coefficient

94% Efficiency

93% Efficiency

92% Efficiency

91% Efficiency

90% Efficiency

89% Efficiency

88% Efficiency

87% Efficiency

86% Efficiency

0

0.5

1

1.5

2

2.5

3

3.5

0.2 0.4 0.6 0.8 1 1.2 1.4

Flow Coefficient

Work Coefficient

94% Efficiency

93% Efficiency

92% Efficiency

91% Efficiency

90% Efficiency

89% Efficiency

88% Efficiency

87% Efficiency

86% Efficiency

4 stg Hi Cx/U

4 stg Low Cx/U
NASA/CR—2012-217424 13

Figure 2.10.—Comparison of Three Stage and Four Stage Turbine Flowpaths

From this plot, the high Cx/U flowpath is shown to transition through the heart of the efficiency 

islands while the low Cx/U is in a non-optimum part of the correlation. 

Both flowpaths developed in the Cx/U study have similar Work Coefficients which drop to very low 

levels when the rotor rpm is at 100 percent. These low levels are outside of normal gas turbine design 

experience. Another study was conducted to investigate the impact of running to higher Work coefficients 

in order to assure operation within the traditional design space. A new flowpath was generated by 

removing the first stage but holding the same rpm and about the same overall radius of the last three 

stages. This Three Stage turbine has the same power and speed as the two four stage turbines already 

analyzed but the average work per stage is higher (by the ratio of 4/3). Figure 2.10 compares the Three 

Stage turbine with the High Cx/U four stage design from the previous study. 

The same process of picking four design speeds, calculating efficiency at each of the four mission 

points, and integrating the fuel burn across the mission was performed with the Three Stage design. Table 

2.3 documents the results and Figure 2.11 plots the Three Stage turbine results against the results of the

Four Stage Cx/U study. 

The Three Stage does not show a predicted improvement in overall fuel burn relative to the lower 

work four stage designs, but it does show a significantly different trend. Figure 2.11 shows that the Three 

stage turbine is more forgiving than any of the Four Stage designs in choosing the design speed. It also 

indicates that the optimal design speed is closer to the SLTO rpm which is different than the previous two 

designs and is not the expected result. In Figure 2.12, the Three Stage turbine is shown on the Smith 

Correlation compared to the two Four Stage designs. The Three Stage falls between the two Four Stage 

designs. If the Smith Correlation were a good indicator of off-design capability, then it could be expected 

that the Three Stage design would have off-design performance characteristics between the two Four 

Stage designs: which it clearly does not. 

The large difference in character between the Three Stage and Four Stage designs begs the question 

as to what makes the Three Stage so different. The difference in Work Coefficient appears to have played 
NASA/CR—2012-217424 14

a significant role. At 54 percent speed, the Work coefficient of the Three Stage turbine is about 2.1 which 

is well within design experience. Designing to higher Work Coefficient may further improve 

performance. Higher Work Coefficients are generally more challenging to design because they result in 

higher airfoil turnings and Mach numbers. The practical limit is approximately 3.0, above which the 

design becomes very challenging. To assess whether higher Work Coefficient is better for overall mission 

fuel burn, a High Work Four Stage turbine was designed (Figure 2.13). The Work Coefficient at the 54 

percent cruise speed was set at 2.83 and the Flow Coefficient was set to 1.0 in an attempt to stay in the 

center of the Smith Correlation. After the same process of picking four design speeds, calculating 

efficiencies, and integrating mission fuel burn, this design proved to be the best out of a total of 8 

flowpaths that were examined (Table 2.4). The flowpath is reduced in radius relative to the designs 

presented so far, making it smaller and lighter, which is an added benefit. (Figure 2.14) 

The fuel burn calculation versus speed plot for this turbine is shown in Figure 2.14. 

The corresponding Smith Curve correlation is shown in Figure 2.15. 

TABLE 2.3.—Three-STAGE TURBINE RESULTS 

Figure 2.11.—Turbine Design Speed Selection

3 Stage

% Speed Design RPM Fuel Burn% ETA 1 ETA 2 ETA 3 ETA 4

53.8 8045 -1.11 70.57 66.14 67.52 89.72

69.2 10343 -4.51 78.24 74.89 74.04 89.63

84.6 12642 -7.19 93.53 91.76 91.60 84.44

100.0 14941 -6.36 92.35 92.49 93.53 66.26

 

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25.00

30.00

35.00

40.00

6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000

Design RPM

Mission Fuel Burn Impact %

High CX/U

Low CX/U

3 Stage

Cruise RPM

Max(SLTO) 
NASA/CR—2012-217424 15

Figure 2.12.—Smith Correlation for Three Turbines

Figure 2.13.—Four-Stage Turbine Flowpath 

0

0.5

1

1.5

2

2.5

3

3.5

0.2 0.4 0.6 0.8 1 1.2 1.4

Flow Coefficient

Work Coefficient

94% Efficiency

93% Efficiency

92% Efficiency

91% Efficiency

90% Efficiency

89% Efficiency

88% Efficiency

87% Efficiency

86% Efficiency

4 stg Hi Cx/U

4 stg Low Cx/U

3 Stage
NASA/CR—2012-217424 16

Figure 2.14.—Design Speed Versus Segment Fuel Burn

TABLE 2.4.—FOUR-STAGE TURBINE SEGMENT FUEL BURN

4 Stg Hi Loading (1)

% Speed Design RPM Fuel Burn% ETA 1 ETA 2 ETA 3 ETA 4

53.8 8045 -0.84 78.77 71.42 69.10 87.45

69.2 10343 -7.98 90.15 87.28 87.13 87.37

84.6 12642 -8.31 93.67 92.32 92.37 85.64

100.0 14941 -3.68 93.96 93.59 94.26 79.31

Figure 2.15.—Smith Correlation for Four Study Turbines

 

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6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000

Design RPM

Mission Fuel Burn Impact %

High CX/U

Low CX/U

3 Stg

4 Stg Hi

Loading

Cruise RPM

Max(SLTO) 

0

0.5

1

1.5

2

2.5

3

3.5

0.2 0.4 0.6 0.8 1 1.2 1.4

Flow Coefficient

Work Coefficient

94% Efficiency

93% Efficiency

92% Efficiency

91% Efficiency

90% Efficiency

89% Efficiency

88% Efficiency

87% Efficiency

86% Efficiency

4 stg Hi Cx/U

4 stg Low Cx/U

3 Stage

4 Stage Hi Loading (1)
NASA/CR—2012-217424 17

A complete description of the 8 flowpaths examined in this study is provided in Appendix C. 

This flowpath (Four Stage: High Loading 1) emerges from the flowpath study as having the best 

potential to minimize mission fuel burn. This conclusion is based on the assumption that the meanline

loss model and, more specifically, the off-design loss model adequately predict the efficiency 

characteristics through a significant range in incidence and loading. Presumably, the design is centered in 

the design space such that the turbine will not rapidly lose performance as speed and loading change 

throughout the flight envelope. In order to gain confidence in this conclusion, a 3–D design was executed 

at 75 percent speed (11174 rpm) and investigated in various CFD simulations. Appendix D contains both 

the 3–D and 1–D analysis summaries for the design conditions. An additional summary of the meanline 

predictions for 54 and 100 percent design speed is presented in Appendix E. This is provided to illustrate 

the large impact of the full speed variation and its implication to the design velocity triangles.

2.8 3–D Design Execution

Airfoils were designed consistent with the chosen flowpath (Four Stage: High Loading 1). The design 

was executed at 75 percent speed, i.e., 11174 rpm. The basic methodology for executing the 3–D design 

was as follows:

• Each of the 8 airfoils is designed by stacking three 2–D design sections, i.e., a hub section, a 

mean section and a tip section. (Figure 2.16) 

• Each 2–D section is manually designed in an interactive design tool called “FoilGen”. (Figure 

2.17) FoilGen has a variety of tools that allow for simple structural analysis, 2–D aerodynamics, 

3–D stacking and airfoil internal core validation if applicable.

• Design iterations are passed through an in-house 3–D solver called VORTEX. VORTEX has an 

inviscid mode with an empirical loss model which aids in establishing the correct velocity 

triangles in the absence of viscous effect. This solver runs fast enough to execute several design 

iterations per day. 

• Designs are validated via viscous simulation. VORTEX can be run with the full Navier Stokes 

equations turned on. The turbulence model is the κ-ω model with integration to the walls (no wall 

functions). A steady state mixing plane assumption was used at the interface between stators and 

rotors.

The full Four Stage design was executed at 75 percent speed which is consistent with Figure 2.14. 

This places the design point approximately half way between the cruise (54 percent speed) and the SLTO 

(100 percent speed) conditions. The airfoil geometry was not refined to a final status for all 8 airfoils, but 

only to a satisfactory level for further study. The third Stage was chosen as a representative stage for more 

in-depth analysis. The third Stage design was pulled out and further refined (Figure 2.18). Calculations 

were performed using boundary conditions from the full Four stage calculation. A detailed review of the 

full four stage 3–D CFD run is documented in Appendix D. 
NASA/CR—2012-217424 18

Figure 2.16.—Airfoil Stacking

Figure 2.17.—FoilGen Output
NASA/CR—2012-217424 19

Figure 2.18.—Third Stage extracted from full simulation to investigate off-design performance

2.9 Loss System Validation via CFD 

The optimum flowpath selected for this turbine and the choice of design speed relies on the off-design 

predictive capability of the meanline analysis. In order to assess the validity of this model, various CFD 

models were exercised. The third stage vane and blade were chosen as a representative set of airfoils.

Two separate studies were performed. The first study addresses the incidence tolerance of the third blade 

and the other adds the vane and assesses the third stage together. The blade study was performed with two 

different blade thicknesses.

2.10 Turbine Blade Incidence Study

The third stage vane and blade were run together through a series of CFD runs. All CFD runs are 

based on steady state assumptions using mixing planes to account for time averaging between stationary 

and rotating frames. The inlet conditions (Total Pressure, Total Temperature, and gas angles) to the third

vane were held fixed and the exit static pressure from the third blade was also fixed. The CFD was then 

run over a sweep of rpm. This analysis will simulate the incidence and loading sweeps that the blade 

would undergo throughout the operating envelope while the vane remains fixed at design point. The 

meanline was run exactly the same way to predict the efficiency changes as the speed changes. Both the 

meanline and the CFD assume no leakage flows, cooling flows or tip clearance. The meanline has a real 

gas model while the CFD runs assume ideal gas. The CFD confirms the large incidence swing and 

loading changes that are expected as the rpm is varied. Four different CFD simulations were performed; 

each one was swept through the speed range. All four simulations predict better incidence tolerance than 

the meanline correlation. This result is particularly satisfying because the meanline prediction was better 

Mid-Span slice 

through 3–D 

simulation
NASA/CR—2012-217424 20

than the cycle simulation. If actual incidence tolerance is better than the meanline characteristic, than 

overall engine performance should surpass the NPSS simulation. 

The four CFD simulations used are:

1. VORTEX (Williams International proprietary solver). κ-ω turbulence model, integrated through 

boundary layers to the wall. 

2. FLUENT (ANSYS, Inc.) κ-ε realizable, using wall functions 

3. FLUENT κ-ω turbulence model, transitional flow model 

4. FLUENT κ-ω turbulence model, SST

All FLUENT calculations used a density based, implicit solver while VORTEX used a density based 

explicit solver. FLUENT version 6.3 was used. 

Figure 2.19 compares the meanline prediction and the four CFD runs. Inside of the design speed 

range, all four CFD simulations predict flatter efficiency trends than the meanline. There is considerable 

variability in the predicted level of efficiency among the FLUENT turbulence models. VORTEX and the 

Std, κ-ω SST model are very similar and close to the meanline level. The transitional flow model for κ-ω

predicts unrealistically low efficiency even at the design point. VORTEX was run to a more broad speed 

range to search for an incidence cliff. It did reveal a very rapid fall off in efficiency at 40 percent speed 

when the loading was high enough to cause suction side separations. At that condition, the efficiency fall 

off was more rapid than predicted by the meanline. 

Figure 2.19.—Efficiency Comparisons for Four Turbine Designs

80

82

84

86

88

90

92

94

30 40 50 60 70 80 90 100 110 120

%Speed

3rd Stage Efficiency

MeanLine

CFD-VORTEX

Std, K-Epsilon Realizable

Std, K-Omega, Standard, Transitional Flows

Std, K-Omega, SST

Speed Range
NASA/CR—2012-217424 21

Figure 2.19 is good testimony to the fact that CFD is still paced by the lack of fidelity in turbulence 

modeling. The level of efficiency predicted by various turbulence models is significant. However, all four 

models predict a very similar efficiency trend with speed. The results give some confidence that the 

design may meet its incidence tolerance goals but is not adequate to completely mitigate risk. If it were 

necessary to chose between a fixed speed turbine and a variable speed turbine, a turbine rig test would 

still be recommended to determine if this design can truly meet the incidence tolerance goals. Another 

observation from Figure 2.19 is that the turbine blade is more tolerant to negative incidence than positive. 

This would lead us to move the design speed lower (higher camber airfoils) and allow the turbine to run 

off-design further on the negative side than the positive. 

2.11 Thin Turbine Blade Incidence Study

Traditional airfoil design philosophy would indicate that larger leading edge diameters are more 

incidence tolerant than smaller diameters. While this is well established for airfoils in a free-stream, it is 

not nearly so obvious for airfoil cascades where the internal flow between the airfoils is more like channel 

flow than external flow. When a cascade airfoil has a larger LE diameter, the entire airfoil must be 

thicker. Thicker airfoils have higher through flow velocities and therefore (by intuition) generate more 

viscous scrubbing losses. Although this statement seems straight forward and logical, the high camber 

inherent in gas turbine blades complicates the situation.

Consider the airfoil shown in Figure 2.20. The throat of the airfoil cascade spans from the TE of one 

airfoil to the suction side of an adjacent airfoil. The passage between the two airfoils is bounded by the 

suction side of one airfoil and the pressure side of the adjacent. This passage controls the through-flow 

Mach numbers of the gas as it passes through the airfoils. It is desirous for this passage to be separation 

free and as low loss as possible. In this figure, the design philosophy is to produce a smooth, converging 

passage through the airfoil to the throat. To illustrate this passage convergence, a line of the same 

dimension as the throat is shown in orange. It is swept forward in the direction of the green line 

perpendicular to the suction side resulting in the orange trace. This gives a visual cue to the convergence 

through the passage as well as how the airfoil pressure side can impact the channel convergence. 

Now consider the airfoil shown in Figure 2.21. This cascade has the same suction side as Figure 2.22 

but a pressure side that results in a thinner airfoil. The airfoil passage now has a non-smooth area 

distribution through the channel. After the leading edge of the airfoil, the pressure side diffuses and then 

converges to the airfoil throat. Experience with this type of cascade would predict pressure side separation 

and reattachment as sketched in light grey. If the resulting separation bubble is large enough, the resulting 

blockage may result in through-flow Mach numbers similar to the airfoil in Figure 2.20. Separation 

bubbles that occur at relatively low velocities and are followed by strong acceleration generally do not 

generate high pressure loss. However, in the case of a rotating blade, the low momentum fluid trapped in 

a separation bubble can be centrifugally pumped outward due to the high rotational acceleration field. 

This can cause much higher loss than in the case of a stationary airfoil.

A study was executed to determine if a thin blade could potentially improve overall fuel burn by 

lowering through-flow velocity or would a separation bubble out-weigh any perceived benefit. Again the 

third stage was used as a representative stage. The blade was redesigned to be thinner but still maintain 

the same suction side as the nominal blade. 

Figure 2.22 shows visually the change made to the blade. The brown line in the background indicates 

the nominal blade pressure side. 
NASA/CR—2012-217424 22

Figure 2.20.—A Simple Turbine Blade Cascade

Figure 2.21.—A sample thin blade cascade

Throat

Throat

Suction Side

Pressure Side

Throat Trace
NASA/CR—2012-217424 23

Figure 2.22.—Blade Profile Modifications
NASA/CR—2012-217424 24

Figure 2.23.—Thin turbine blade geometry compared to nominal

The thin blade should be more susceptible to pressure side separation at high negative incidence (high 

speed). At positive incidence (low speed), the air impinges on the airfoil in a more favorable way for the 

pressure side and may not separate. We would therefore expect a thin blade to be similar or better at low 

speed but potentially worse at high speed. The airfoil in Figure 2.22 was run through FLUENT in a 

consistent manor with Figure 2.19. The results are shown in Figure 2.23. The dash lines indicate the 

results of the thin airfoil and are color consistent with the nominal blade run to the same turbulence 

model. The results are very similar with the thin blade overall slightly higher in loss. All three analyzes 

hint that low speed performance trends better than high speed performance. Based on this study there is 

no compelling evidence to depart from normal design philosophy (i.e., smooth channel convergence). 

2.12 Third Stage Combined Incidence Study

The third Stage combined study was conducted in similar fashion as the third blade only study. The 

simulation was composed of the second blade, the third vane and the third blade. (Figure 2.24) The inlet 

conditions into the second blade were held fixed in the absolute frame of reference simulating the exit 

conditions of the second vane. The exit condition of the third blade was a free vortex boundary with the 

average static pressure iterated to match the proper exit corrected flow. In order to assess the third stage 

performance, the efficiency of the second blade was ignored and the third stage was calculated based on 

its inlet and exit conditions in the converged solution. The meanline analysis was performed in exactly the 

same manor so that the CFD and meanline results may be compared directly. The speed was varied in a 

similar way as was done in the blade only study. There was no tip clearance, leakage or cooling modeled. 

In this calculation both the third vane and third blade experience the incidence swing associated with the 

speed change, therefore the efficiency impact with speed is higher than the previous study. Figure 2.25 

compares the resulting meanline efficiency to the CFD prediction. The conclusions are generally the same 

80

82

84

86

88

90

92

94

30 40 50 60 70 80 90 100 110 120

%Speed

3rd Stage Efficiency

MeanLine

Std, K-Epsilon Realizable

Std, K-Omega, Standard, Transitional

Flows

Std, K-Omega, SST

Thin, K-Epsilon Realizable

Thin, K-Omega, Standard, Transitional

Flows

Thin, K-Omega, SST Speed Range
NASA/CR—2012-217424 25

as the blade only calculations. The CFD prediction is more incidence tolerant than the meanline 

prediction and also indicates that negative incidence (high speed) is more forgiving than positive 

incidence. 

The third vane total pressure loss was extracted from the CFD and compared to the meanline 

prediction as well (Figure 2.26). 

The vane exhibits a similar trend as the blade in that it is more incidence tolerant at high speed 

(negative incidence) rather than low speed. The vane is exceptionally tolerant at negative incidence 

because the pressure side separation bubble is: 1) very small (less than 1⁄2 the thickness of the airfoil), and 

2) completely reattached at relatively low Mach number before the airfoil throat (Figure 2.27). Unlike the 

blade, the vane is not subject to the high centrifugal acceleration field and therefore the low momentum 

fluid trapped in the separation bubble is not transported radially.

Figure 2.24.—Third Stage Speed Study composed of Three airfoils

Figure 2.25.—Third Stage Performance

80

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86

88

90

92

94

30 40 50 60 70 80 90 100 110 120

%Speed

3rd Stage Efficiency

MeanLine

CFD-VORTEX

Speed Range
NASA/CR—2012-217424 26

Figure 2.26.—Third Vane Pressure Loss

Figure 2.27.—Vane Velocity Vectors

0

1

2

3

4

5

6

30 40 50 60 70 80 90 100 110 120

%Speed

3rd Vane Loss (dPT %)

MeanLine

CFD-VORTEX

Speed Range
NASA/CR—2012-217424 27

All the CFD work performed suggests that mission fuel burn is improved by designing for relatively 

low corrected speed. In this present work, the design speed chosen was 75 percent speed, or 

approximately half way between low speed cruise (54 percent) and high speed take-off (100 percent) 

based on meanline predictions. The CFD suggests that the turbine is: 1) more forgiving than the meanline 

predictions and 2) able to tolerate higher negative incidence. A lower design speed may further improve 

overall mission fuel burn. Figure 2.14 would suggest a design speed of 70 percent as a logical 

compromise or next design iteration. Designing for lower speed also results in airfoils with higher 

camber. This is an added benefit because higher camber airfoils are generally stiffer and more resilient to 

high cycle fatigue.

2.13 Airfoil Leading Edge Geometry

The aviation industry routinely designs wings for variation in loading and incidence. From the largest 

commercial aircraft to the private general aviation airplane, variable geometry (flaps and/or LE slats) are

employed to increase loading coefficient and wing area during take-off and landing. Zenith Aircraft 

Company uses a fixed LE slat (Figure 2.28) to make their STOL CH 701 stall resistant to very high 

angles of attack. The completely passive nature of their design is very attractive from a cost and 

complexity standpoint. Similarly, in this VSPT design, it would be very desirable to include features that 

improve tolerance while being completely passive. Turbine airfoils are relatively small and made from 

investment castings. It would be impractical to attempt to cast them with such intricate details. It would 

however be very advantageous to design turbine airfoils with a LE shape that was inherently incidence 

tolerant. One concept investigated in this study is to attempt to smooth the LE curvature distribution as 

much as possible in order to allow the air to smoothly transition from the LE to the airfoil pressure and 

suction sides. 

Turbine airfoils are typically designed with an elliptical LE connected to a curved pressure and 

suction side. See Figure 2.29. Although the intersection of the ellipse and airfoil curves is designed to 

match point and slope, it does not typically match curvature and can in fact be discontinuous. In order to 

assess the impact of this discontinuity, a smoothing algorithm was developed and applied to the third

blade from the previous studies. The algorithm calculates the curvature as a function of surface length (Sdistance) and calculates a local correction factor based on the gradient in curvature from one point to the 

next. Each point is moved normal to the surface in the direction to smooth the gradient by a small amount. 

The process was iterated 200 times until a smooth curvature distribution was obtained. See Figure 2.30. 

The actual change in the surface profile required to smooth the curvature distribution is well within any 

reasonable casting profile tolerance. As shown in Figure 2.30(b) it is nearly within the thickness of a line 

when plotted at a reasonable viewing size. Figure 2.30(c) clearly shows the discontinuity in curvature at 

the tangency points and the result of running the smoothing algorithm. Nonetheless, it is still desirable to 

establish the best possible design shape and apply manufacturing tolerance about that nominal shape 

rather than a less optimal design. In order to determine if the smooth shape is in fact better, the smoothed 

third blade was run through the same set of CFD calculations as in the blade incidence study.
NASA/CR—2012-217424 28

Figure 2.28.—Fixed geometry LE slats. Used with permission 

from Zenith Aircraft Company, Mexico, Missouri, 65265-0650. 

Figure 2.29.—Typical Turbine Airfoil Leading Edge Profile
NASA/CR—2012-217424 29

Figure 2.30.—Third Blade Mean, surface curvature smoothed

(b)

Suction Side

Pressure Side

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

-0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Before Smoothing

After Smoothing

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9

S Distance

Surface Curvature (1/inch)

Before Smoothing

After Smoothing

Suction Side Leading Edge Pressure Side 

(a)

(c)
NASA/CR—2012-217424 30

The changes to the geometry and CFD mesh were basically imperceivable to the eye. The global CFD 

results (i.e., efficiency and flow) for the third Blade at design speed (75 percent) were virtually unchanged 

relative to the non-smoothed blade. Figure 2.31 gives the mid-span surface static pressure loading also 

showing nearly identical results. Despite this disappointing result, the CFD was run at high and low speed 

to investigate off-incidence tolerance. The resulting efficiency trend with variation in speed was 

surprising. See Figure 2.32. Shown in green, the smoothed LE contour maintained better incidence 

tolerance at low speed relative the non-smoothed baseline configuration shown in pink. In order to 

understand this, a detailed investigation into the flow field was performed. At the design speed, no 

significant flow field changes were evident. This was also true at negative incidence (high speed), but at 

low speed, the smoothed LE resulted in an improved flow field. At approximately 80 percent span, the 

airfoil suction side loading is highest. As the airfoil loading is increased, this is the most likely location 

for the airfoil to separate. 

Figure 2.31.—Third Blade mid span static pressure distribution
NASA/CR—2012-217424 31

Figure 2.32.—Smoothed third Blade Efficiency Trend with Speed

Combing through the velocity vectors did reveal a separation in this location for the baseline 

(unsmoothed) blade. The easiest way to visualize this is to capture the separation bubble with a constant 

Mach number surface.

In Figure 2.33, the non-smoothed blade is compared to the smoothed blade. An iso-Mach number 

surface was generated for each calculation. The yellow-green surfaces shown are surfaces of Mach 

number equal to 0.15. Since the through-flow Mach numbers are all much higher than 0.15, all of the flow 

beneath the surfaces shown are boundary layers or separations. The non-smoothed blade has a separation 

bubble near the tip that is nearly completely removed after the blade is smoothed. The separation bubble 

is visually interacting with the secondary flow field near the shroud line. 

This result is based on a single solver and turbulence model. No further CFD modeling was 

performed within this study. It is not know how transition from laminar to turbulent flow may be 

impacted by curvature smoothing. Likewise, the impact of the unsteady flow field is not known. 

This work reinforces the importance of maintaining boundary layer health upstream of diffusing 

flowpaths. These results are encouraging: they suggest careful design of LE geometry can improve airfoil 

incidence tolerance. Additional, this completely passive design does not change the design point 

methodology. The design point analysis was completely unaffected by the incorporation of the smoothing 

algorithm. Addition research in this area may result in airfoil shapes that are inherently more incidence 

capable. 

80

82

84

86

88

90

92

94

30 40 50 60 70 80 90 100 110 120

%Speed

3rd Stage Efficiency

MeanLine

BaseLine Blade, no smoothing

Smoothed 3rd Blade LE 

Speed Range
NASA/CR—2012-217424 32

Figure 2.33.—Separation bubble visualization

3.0 VSPT LCTR Mission Performance Modeling

A thermodynamic cycle model was developed to study the performance impact of various power 

turbine designs. The basis of this study was the TS2-NPSS model provided by the NASA Glenn Research 

Center. The model was originally created March 5, 2010, and has description: “two-spool turboshaft 

about equal work for LPC/HPC, HPC is PR=1.3 axial + centrifugal - includes update for turbine cooling 

(best guess for number turbine stages)”. The model was updated from NPSSv1.6.5 to NPSSv2.3 and the 

output of the model was enhanced. A copy of the updated model was provided to NASA to assist in 

adopting the latest version of NPSS consistent with NASA’s overall goals. The only performance feature 

of the cycle model that was modified was the Power Turbine maps. 

Three turbine designs were evaluated at the three critical mission points defined in the LCTR 

“Design” Mission Profile. These mission points define the design conditions for the overall cycle and 

present some challenges for the turbine design because of the wide range of shaft speeds. Table 3.1 

summarizes the flight conditions and shaft speeds.

TABLE 3.1.—CRITICAL MISSION POINTS

Mission Segment Takeoff hot Climb Cruise

Time, hr 0.07 1.00 3.00

Power, hp 7859 2646 2351

N3, rpm 15000 15000 8077

Ambient

Mach Number 0 0.51 0.51

Altitude, ft 0 28000 28000

Delta T from standard conditions, F 45 0 0

VTAS, knot 0 303 303

Smoothed

Nonsmoothed
NASA/CR—2012-217424 33

Figure 3.1.—VSPT Total Mission Fuel Burn for Three Williams International Designs

The Takeoff hot condition requires the maximum power at high rotor speed, but the amount of time at 

that condition is limited to 3 min for takeoff and 3 min for landing with an additional minute for taxi. The 

climb is represented by the top of climb condition at high rotor speed and represents 30 min to climb plus 

an additional 30 min to fly to an alternate destination. The cruise condition is represented by the same 

flight condition as the climb point, but at shaft rpm that is 54 percent of the full throttle condition and also 

at high power output for 3 hr. 

The power turbine map provided with the NASA model was run at the three flight conditions and the 

power output was used as the requirement for each flight condition. Three power turbines were designed 

to provide performance at the cruise condition and to meet the maximum shaft speed requirement. The 

turbine design points were set at 65, 75 and 85 percent corrected speed and are labeled accordingly. 

Figure 3.1 shows the total mission fuel burn for the three designs.

The three proposed designs have significantly reduced mission fuel burn compared to the baseline 

power turbine design. The 75 percent design has the lowest mission fuel burn and is the best design on 

this basis. The 75 percent design uses 1.6 percent less fuel than the 65 percent design and 0.6 percent less

fuel than the 85 percent design. The 75 percent design uses 12.1 percent less fuel than the baseline design 

and is the best overall design based on this preliminary design study. For each of the three turbine 

designs, the NPSS output for the three critical mission points is given in Appendix H. 

In the cycle detailed output, there are 6 points presented for each turbine design. The takeoff point 

(T/O) is the cycle design point at takeoff power on a standard day at 15,000 rpm power turbine speed. The 

second point is takeoff on a hot day. The third point is at the climb condition, 15,000 rpm at the same 

power setting as the NASA design climb condition; however the power setting condition logic does not 

result in the same power output for different turbine designs. The fourth point is at the climb condition at 

the same power output as the NASA design to allow fuel flow comparisons. The fifth point is at the 

Cruise condition at reduced shaft speed of 8,077 rpm at the NASA power setting. The sixth point is at the 

Cruise condition at the NASA power level and is used for the fuel flow comparison. 

NASA, 3610

65%, 3224

75%, 3172 85%, 3191

2900

3000

3100

3200

3300

3400

3500

3600

3700

1

VSPT Study Total Mission Fuel Burn
NASA/CR—2012-217424 34

4.0 Development of a Cost-Effective Approach to an LCTR-Relevant VSPT 

Component Experiment

Testing of a power turbine presents unique challenges in that it is not self-supporting. In order to test 

a power turbine, inlet compressed air is required that requires heating to at least several hundred degrees F 

to avoid ice formation on exhaust structures and instrumentation. A power sink is also required that has 

excellent control characteristics in order to set rpm and avoid overspeeds. Ideally, the power turbine 

should be tested at full scale to minimize Reynolds effects and so that key inter-stage instrumentation can 

be inserted without unduly affecting the flow conditions in the local area. Since the VSPT for the LCTR 

will be relatively large, full scale testing will require a test facility that can provide continuous flow of 

large volumes of heated inlet air with substantial power absorption capability. Use of an existing engine 

as a gas generator testbed for testing the VSPT was considered as an option, but ruled out because the 

engine operating line would severely limit the range of power turbine entrance conditions that could be 

achieved during test. The optimum approach appears to be to develop a dedicated VSPT rig to mate to the 

single-spool turbine test facility at NASA GRC. The capabilities and limits of the single-spool turbine 

facility, listed in Table 4.1, provide more than sufficient capability to produce the entrance and exit 

conditions needed to evaluate the LCTR VSPT design concept at full scale. 

There are two basic engine configurations that can provide power to the rotor system, and both have 

been used successfully in large numbers of turboshaft and turboprop systems. The gas generator can be 

mounted with the compressor facing in the direction of flight, or opposite to the direction of flight. The 

aft-facing compressor configuration, similar to that used by the Pratt & Whitney PT-6 turboprop, provides 

a very large advantage in that the power turbine shaft can be very short and large in diameter since the 

power turbine module is adjacent to the reduction drive gearbox, compared to the long, thin shaft needed 

by the forward-compressor configuration, which needs to pass the turbine shaft through the center of the 

gas generator shafts. This greatly reduces or eliminates the rotordynamics and torque limitations issues 

associated with the long, thin shaft. The disadvantage of this configuration is that the airflow must be 

turned 180° prior to entering the inlet, and once again in the exhaust duct. This is necessary to avoid 

having the inlets face the ground during VTOL operation. An advantage is that it provides a simple 

method for rejecting ice, birds, or other foreign matter before it can enter the gas generator. The forwardfacing compressor configuration requires an S-duct inlet and can use an axial exhaust, which have lower 

aerodynamic losses. The aft-facing compressor design also provides a much easier approach to an inertial 

separator design for ejecting ice and solid objects, another distinct advantage. Mostly because of the 

reduced rotordynamics concerns, the compressor-aft configuration is recommended for the LCTR 

application. Figure 4.1 is a schematic of this configuration for a twin-pack LCTR design. The spacing 

between the power turbine exhaust and the reduction drive gearbox is the minimum required to provide a 

low-loss turn in the exhaust duct. 

TABLE 4.1.—NASA GRC SINGLE-SPOOL 

TURBINE TEST FACILITY CAPABILITIES

• Maximum Turbine Inlet Pressure 50 psia

• Minimum Exhaust Pressure 2 psia

• Maximum Inlet Air Temperature 940°F

(from in-line vitiated natural gas combustors)

• Maximum Primary Air Flow Rate 27 pps

• Secondary Air (150 psig supply):

» 2 Legs – 1.5 pps each up to 550oF

» 4 Legs – 0.08 to 1.19 pps each up to 250oF

» 6 Legs – at 70oF

• Maximum Turbine Rotational Speed 14,000 rpm

(with maximum Gear Ratio, G.R., of 7.87)

• Maximum Turbine Torque 36,217 ft·lbf/G.R.

• Minimum Gear Ratio, G.R. = 1.51

(Nmax= 2,718 rpm; Torquemax= 24,000 ft∙lbf

)

• Maximum Test Article Diameter 52 inch
NASA/CR—2012-217424 35

Figure 4.1.—Schematic of Recommended Engine Configuration for LCTR

Rotordynamics of turboshaft machinery such as tilt rotors are generally divided up into two 

categories, lateral and torsional. Each has its own set of typical challenges. 

Lateral challenges typically involve long flexible drive shafts that operate above the first flexible 

critical mode, i.e., supercritical rotors. Inadequate damping at the bearings results in damaging vibrations 

when traversing the lateral critical modes of drive shaft. Controlling run-out and wall thickness variation 

of long hollow flexible shafts at reasonable cost is often challenging. Misalignment of drive shaft between 

gearbox and power-turbine adds further complexity that must be addressed. Last and perhaps most 

important the large overhung tilt rotor makes the system sensitive to rotating unbalance. 

Torsional challenges typically involve shock from start up and elevated transient loading through the 

drive shaft. Unloading of gear teeth during surge events, back lash, gear run out, random vibration due to 

gear inaccuracies and rolling element defects, and closed loop control system instabilities have all been 

known to lead to torsional failure modes. All of these issues need to be addressed as part of the full engine 

and test article designs. 

Figure 4.2 shows a layout of the proposed full scale VSPT test article mated to the NASA GRC single 

spool turbine test facility dynamometer drive frame. Locations are indicated for multi-element 

instrumentation rakes at the inlet and exit of the VSPT, and for cylindrical radially-translating flow angle 

sensors at each of the three interstage locations. The rig inner and outer flowpaths are a combination of 

formed sheet metal and machined details, with the inner flowpath and bearing support structures 

supported by an exit guide vane row set well behind the last stage rotor. The four-stage turbine is 

overhung on the front of the shaft, supported by an aft roller bearing and forward ball bearing to react 

thrust loads. As shown, the thrust loads are intended to be reacted through the front bearing and out into 

the outer frame structure through the exit guide vane row. The bearing cartridge in the SSTTF has 

sufficient load capacity to support the VSPT test article as an entirely overhung mass, so an alternative 

approach would be to eliminate the VSPT bearings altogether and hang the VSPT off the front of the 

drive spindle. If feasible, this arrangement would simplify the system and eliminate the bearing 

lubrication requirements, as well as reducing the cost of the design and hardware. It will be necessary to 

analyze the shaft system to ensure that critical speeds are not an issue and displacements do not drive 

excessive tip clearances in the test article. The preliminary aero and structural design tasks in the 

experimental program will determine if it will also be necessary to include one or more balance pistons to 

offset some of the thrust load. 

Reduction

Drive

Gearbox

VSPT1

VSPT2

Exhaust

Exhaust

GG1

GG2

Inlet

Inlet

Reduction

Drive

Gearbox

VSPT1

VSPT2

Exhaust

Exhaust

GG1

GG2

Inlet

Inlet
NASA/CR—2012-217424 36

Figure 4.2.—VSPT Test Article Mated to NASA-GC Single Spool Turbine Test Facility

The four-stage rotor is shown as a clamped assembly with the clamp loads applied at the hub through 

curvic couplings. This was done in order to make it possible to use the cylindrical wake angle sensors. 

This type of sensor has performed very well in past tests and has the advantage of being much smaller in 

diameter than traditional cobra probe sensors because it is supported at both ends of the flowpath rather 

than cantilevered from the outer wall. This greatly minimizes blockage but imposes some limitations on 

the design of the test component. Since the sensing position on the probe has to transit the entire span 

from the outer to the inner wall, provisions must be made for the probe body to penetrate an equal 

distance beneath the inner flowpath when the inlet holes are at the innermost radial position. This makes it 

impossible to use with a drum rotor configuration. A detailed rotordynamic analysis of the rotor/shaft 

system will be a key part of the experimental program and its results will determine whether this approach 

is feasible or if a drum rotor configuration with conventional probes is required to achieve sufficient 

speed and frequency margins relative to the operating speed range. The spacing between stages and 

between vane and blade rows shown in the figure is notional and would be optimized during the test 

article design process to provide access and routing for all of the planned instrumentation. 

4.1 Experimental Test Plan and Instrumentation List

The proposed operating conditions of the VSPT vary from 54 to 100 percent speed. Therefore, it 

would be beneficial to develop a turbine map that fully describes the turbine efficiency within this range. 

The proposed test plan to characterize this turbine would include a pressure ratio sweep from 3.0 to 7.0 

and a speed sweep of 40 to 120 percent (Table 4.2). Generally speaking, it is easier to change speed than 

PR in a test facility so the order of operations would be to set PR and then increment through the speed 

range to develop lines of constant PR. 

Temperature Probes

Tt/Pt Rakes

3 Circumferential

Locations

Radially-Translating

Gas Angle Sensors

NASA SSTTF Drive System

Tri-ax

Accelerometers

Static Pressure Taps on All Stages

Surrounding Vane Airfoils

On Inner and Outer Flowpaths

120 Total Taps

Bearing Load Sensor

Clearance Rub Pins

(May use Capacitance 

or Eddy Current NSMS)

Rig Bearing

Thermocouples

Mate Rig to

SSTTF Drive System

Mate Rig Exit Flowpath

to Facility Collector

Existing Facility Instrumentation

for Speed, Torque, Exit Gas

Conditions, and System Health

Temperature Probes

Tt/Pt Rakes

3 Circumferential

Locations

Radially-Translating

Gas Angle Sensors

NASA SSTTF Drive System

Tri-ax

Accelerometers

Static Pressure Taps on All Stages

Surrounding Vane Airfoils

On Inner and Outer Flowpaths

120 Total Taps

Bearing Load Sensor

Clearance Rub Pins

(May use Capacitance 

or Eddy Current NSMS)

Rig Bearing

Thermocouples

Mate Rig to

SSTTF Drive System

Mate Rig Exit Flowpath

to Facility Collector

Existing Facility Instrumentation

for Speed, Torque, Exit Gas

Conditions, and System Health
NASA/CR—2012-217424 37

TABLE 4.2.—PROPOSED MAP/TEST PLAN

The turbine map should be developed at both high and low Reynolds number where “high” is 

equivalent to a SLTO condition and “low” is equivalent to the cruise condition.

Low Reynolds number cruise at highest corrected speed is most challenging condition, and requires 

vacuum. For similitude in Reynolds number, PR, Corrected Flow and Corrected speed, the following 

table defines the 100 percent speed conditions for the turbine:

Engine Proposed Rig 

Inlet PT 31.01 psia 20.6 psia 

Inlet TT 1749.1°R 1260.°R (800 °F) 

Inlet Mass Flow 12.04 lbm/s 9.425 lbm/s 

Power 2740 hp 1525 hp 

Exit PT 5.35 psia 3.55 psia 

rpm 14898 12645 

First Vane Reynolds Number 178,000 172,000 

Last Blade Reynolds Number 61,000 61,000 

The SLTO (high Reynolds Number) condition requires the following parameters: 

Engine Proposed Rig 

Inlet PT 88.49 psia 45 psia

Inlet TT 2166.3°R 1260 °R (800 °F) 

Inlet Mass Flow 9.41 lbm/s 20.6 lbm/s 

Power 7500 hp 3350 hp 

Exit PT 15.43 psia 7.76 psia 

rpm 14898 12645 

First Vane Reynolds Number 395,000 377,000 

Last Blade Reynolds Number 130,000 134,000 

These rig conditions are within the advertised capability of the New Single Spool Turbine Facility 

proposed by NASA to replace W-6A Warm Core Turbine Facility. 

In order to simplify the rig as much as possible, the rig would be uncooled. The proposed warm inlet 

temperature of 800 °F should allow for nearly no cooling flow. This allows for simple turbine efficiency 

calculations based only on measured inlet and exit total pressure and total temperatures. The Turbine 

efficiency can be calculated as follows:

0.1(T PR )

T

0.1

in

γ

γ−

−

∆

=η

PR

Speed% 3 3.5 4 4.5 5 5.5 6 6.5 7

40

50

60

70

80

90

100

110

120
NASA/CR—2012-217424 38

where γ is the ratio of specific heats calculated at the average of the inlet and exit temperatures.

The corrected speed is calculated as:

in

corr T

67.518

rpm = rpm 

where 100 percent is defined as rpmcorr = 8113. 

Of great interest is the turbines performance at the two design conditions (54 and 100 percent) speed.

At these conditions, inter stage gas swirl angle and total pressure profiles will be measured and compared 

back to predictions. The use of a cylindrical probe between the stages is proposed to measure gas angles 

behind rotors with minimal blockage. It is significantly more difficult to measure the gas angles behind 

stators because the circumferential variation in angle and pressure complicates the measurement and 

therefore it is not recommended.

Table 4.3 comprises an initial recommendation for instrumentation required to collect the desired test 

data.

TABLE 4.3.—PROPOSED INSTRUMENTATION LIST FOR VSPT COMPONENT EXPERIMENT

Sensor type Objective Location Quantity Required 

accuracy

Radially translating cylindrical gas 

angle sensor

Measure flow angles exiting each 

turbine stage Nozzle vane Leading Edge 1 per stage, 3 total ± 1° 

Six-element total pressure rake Measure total pressure at entrance 

and exit of VSPT Inlet and exit 6 ±0.5%

Static pressure taps Determine pressure distribution 

around vanes

Outer and inner wall, at root of 

nozzle vane

20 OD, 20 ID, 3 

locations, 120 total ± 0.5%

Six-element total temperature rake Determine stage temperature drop Inlet and exit 6 ± 1 °F

Bearing Thermocouple, type K Monitor bearing health Outer race 2 per bearing, 4 total ± 10 °F

NSMS or capacitance probe Actively monitor tip clearance At tip of each blade row 4 ± 0.001 in.

Rub Pins Verify min tip clearance At tip of each blade row 2 per row, 8 total ± 0.001 in.

Triax accelerometer Monitor vibes for rig health On fwd and aft bearing housing 2 ± 1g

Real Time Spectrum Analyzer Monitor vibes and frequencies for rig 

health Accelerometer output 1 N/A

Oil sump thermocouple, type K Monitor oil temperature Oil sump 1 ±10 °F

Strain gage thrust ring Monitor bearing thrust load Fwd bearing 2 ± 10 lbf

Facility Speed pickup Monitor speed facility 2 ±10 rpm

4.2 VSPT Component Experiment Program Plan, Schedule, and ROM Cost

A program to provide experimental validation of the proposed LCTR VSPT using the NASA GRC

Single Spool Turbine Facility can be accomplished in 36 months, of which 33 months are required for the 

technical effort and 3 months for reporting. Figure 4.3 shows a notional program schedule to accomplish 

this effort. During the preliminary design task, the concept for the VSPT will be refined to the point 

where all key aspects of the component and rig designs have been defined in sufficient detail to ensure 

that no key risk items are likely to force substantive design changes during detailed design. This requires 

that a comprehensive layout be produced, from which a bill of materials and parts list can be generated. 

Preliminary aerodynamics will be defined for each blade and vane row, from which structural models will 

be prepared. The aerodynamic, structural, and dynamic design of the blades, vanes, and other flowpath 

elements needs to take into consideration the actual operating conditions the VSPT would see in operation 

behind the gas generator, not just the relatively cold rig operating conditions, since it would do no good to 

test a component design which has no chance of surviving the actual operating conditions in the real 

engine. Rotordynamic analyses will be required as a part of the preliminary design in order to ensure that 

sufficient speed and frequency margins can be obtained with the proposed configuration. For a power 

turbine module that interfaces with the reduction gearbox directly rather than by extending a shaft through 
NASA/CR—2012-217424 39

Figure 4.3.—Proposed Schedule for VSPT Experiment

the gas generator (e.g., PT-6 configuration) there is substantial freedom in the design and opportunity to 

vary shaft characteristics and bearing spacing to achieve sufficient margins, so the risk of not achieving 

acceptable margins is fairly low. To reduce risk, a Design Failure Modes and Effects Analysis (DFMEA) 

will be conducted during preliminary design. This will help identify any potential failure modes and 

define mitigation approaches early enough in the program so they can be incorporated into the design and 

test plan. 

The rig configuration will be driven by the requirements to obtain the key data for validating the 

design, and by the interfaces with NASA’s single spool turbine facility. At the outset of the preliminary 

design task, Substantial coordination with the NASA technical team will be required to define the 

rig/facility interface requirements, as well as routing for instrumentation and secondary systems plumbing 

and rig and facility safety requirements.

The lubrication and secondary air systems will also be defined in the preliminary design. For the rig, a

conventional jetted recirculating oil lubrication system will be used. Facility pumps will provide motive 

flow and scavenge and these will be sized according to the predicted requirements of the rig across its 

operating range of speed and power output. Purge air flow and pressure requirements for bearing 

compartments and to prevent flowpath air ingestion will also be defined. The preliminary design effort is 

expected to require 7 months to complete. At the conclusion of the preliminary design efforts, a 

preliminary design review with the NASA technical team is planned.

Since all of the key characteristics of the VSPT component and rig design will have been defined in 

Preliminary Design, the detailed design efforts will focus on substantiating the preliminary design 

configuration via detailed modeling and analysis. The instrumentation and test plan will be finalized and 

will be provided to NASA along with a 3-D external model of the test rig and all its secondary systems 

and plumbing. Component aerodynamics will be finalized via detailed CFD, structural, and dynamics 

1 2 3

1 2 3 4 5 6 7 8 91011121 2 3 4 5 6 7 8 91011121 2 3 4 5 6 7 8 9101112

VSPT Test Article Design

Preliminary Design

Layout Design

Facility Interface Defn

Prelim Instr/Test Plan

Aero Design/CFD

Structural/Rotordynamic Design

Bearing/Lube Systems

PDR

Detailed Design

Final Instr/Test Plan

Final Aero/CFD

Thermal/Structural/Dynamics

Detailed Component Design

Facility Adaptive Hdw Design

Detailed Instr/Test Plan Review

Design Release Packages

DDR

Hardware Mfg

Long Lead Release

Component Fab/Procurement

Facilty Adaptive Hdw Fab

Rig Assembly/Instrumentation

Hdw Delivery to Test Site Testing Install Rig at Test Facility

Test Readiness Review

Rig/Facility Checkout

Testing

Data Reduction/Analysis

Program Management

Project Management

Reviews/Gates

Travel to Test Facility

Reporting
NASA/CR—2012-217424 40

analyses, including transient analyses to define final operating and build tip clearances. If necessary due 

to design changes, the rotordynamics model will be updated and exercised to finalize the design of the 

rotary group and bearing system. Design release packages will be produced, comprising all the design and 

manufacturing information needed to produce or procure the component and rig hardware. At the 

completion of the detailed design task, a detailed design review will be held with the NASA technical 

team. The DDR will include a review of the updated DFMEA based on the completed state of the design. 

Once the DDR is approved, long lead hardware will be ordered and hardware fabrication will begin. 

Since the rig and component hardware is primarily to be made of steel and aluminum, it is likely the only 

long lead hardware may be the bearings. As a risk reduction approach, the rig can be designed around 

bearings that are already in hand and available, or are known to be available on short lead. Fabrication of 

rig and component hardware, as well as facility adaptive hardware, can be completed in 8 months, at 

which time instrumentation and assembly of the rig will begin. The milestone for delivery of the 

completed instrumented rig to the NASA test facility occurs at month 24. 

A detailed test readiness and safety review will be conducted once the rig is installed at the test 

facility. This review will address all aspects of rig operation and data collection, including a review of the 

DFMEA.

Testing will begin at month 28 and will follow the approved test plan. Ideally, two sets of hardware 

with slightly different aerodynamics will be tested back-to-back to bracket the design and provide data for 

a sensitivity analysis. At completion of the test program, the rig and component hardware will be torn 

down and assessed to determine if any conditions exist that may have affected the test data, such as tip 

rubs or damage to any of the hardware or instrumentation. The test data will be reduced and analyzed and 

compared to pre-test predicted maps. The maps used in the cycle model will be updated to reflect actual 

performance and the mission analysis will be re-run to determine the effects of the status updates on the 

overall mission performance.

The program schedule shows milestones for major reviews and on-site meetings at the test facility. A 

final report will be compiled and submitted at month 36. 

A ROM cost estimate for the proposed 36-month VSPT experiment program shown in Figure 4.3 is 

$4.5M, broken down as follows: 

• Preliminary Design: $800,000 

• Detailed Design: $1,400,000 

• Component and rig hardware: $1,200,000 

• Testing: $300,000 

• Program management: $800,000 

This ROM represents an estimate of contractor cost to perform the design, build the hardware, 

conduct testing, and manage the effort. It does not include an estimate of costs for use of the test facility 

and support from NASA and government service contractors. If it is determined that the VSPT test 

components can be overhung directly from the facility bearing cartridge, eliminating the need for the 

dedicated component bearings and lube system, the cost to design and build the components would be 

reduced, and the total cost of the program could potentially be lower by as much as $200,000. 

5.0 Conclusions

In this study, a variable speed power turbine design was executed for a proposed Large Civil 

Tiltrotor. This application is unique in that it requires a turbine with far greater off-design capability than 

traditional propulsion related gas turbines. Airfoil incidence can change as much as 60° between the high 

speed and low speed rotor settings. These large changes in incidence cause airfoil separations and large 

loading changes resulting in reduced efficiency. In order to address these large loading swings, a study 

was performed in which a methodical multiple design-point process was used to arrive at a flowpath that 
NASA/CR—2012-217424 41

is fundamentally speed insensitive. This is in direct contrast to other techniques such as variable geometry 

or a variable gear ratio transmission. The figure of merit used in this study was to minimize the fuel burn 

throughout the mission by weighting various performance conditions in such a way as to mimic a typical 

flight. Various designs were analyzed and traded against each other with a turbine meanline code and 

CFD calculations were used to validate the results. CFD consistently showed better negative incidence 

tolerance (high speed) than the 1–D meanline loss systems. This finding would suggest moving the design 

point selection to lower speed than the 1–D prediction. Any further research would require testing. 

A component experiment program plan was proposed that can be accomplished within a 36-month 

period. This program would design and fabricate a stand-alone rig to mate to the NASA GRC Single 

Spool Turbine Test Facility and take advantage of its capabilities to run the testing at full scale for the 

proposed LCTR application in an economical manner. A notional component test article design was 

proposed that emulates the configuration recommended for the LCTR engine, and which greatly 

minimizes rotordynamic issues that would be major concerns for alternative configurations. 

The design methodology and technology investigated in this study can provide benefits to other 

systems beyond the LCTR. Any system that can benefit from improved off-design performance, whether 

turbofan, turboshaft, or turboprop, may be able to take advantage of the proposed approach to avoid the 

complexity and cost associated with traditionally variable geometry approaches. This includes not only 

aviation engines, but also ground power and automotive engines. 

Appendix A.—NPSS Outputs

TABLE A.1.—SEA LEVEL STATIC (MRP) 100 PERCENT NPT

NASA/CR—2012-217424 43
TABLE A.1.—Concluded.

NASA/CR—2012-217424 44
TABLE A.2.—2,000 ALTITUDE, +45 °F DAY, HOVER (NOT AT MAXIMUM POWER) 100 PERCENT NPR

NASA/CR—2012-217424 45
TABLE A.2.—Concluded.

NASA/CR—2012-217424 46
— -

TABLE A.3.—CRUISE MISSION 1, 303.4 kn, 28,000 ALTITUDE, +0 °F DAY, INITIAL CRUISE POWER LEVEL, 100 PERCENT NPR rpm/

NASA/CR—2012-217424 47
TABLE A.3.—Concluded.

NASA/CR—2012-217424 48
TABLE A.4.—CRUISE MISSION 1, 303.4 kn, 28,000 ALTITUDE, +0 °F DAY, INITIAL CRUISE POWER LEVEL,

54 PERCENT NPR rpm/350 ROTOR TIP SPEED—NO MULTISPEED GEARBOX 

NASA/CR—2012-217424 49
TABLE A.4.—Concluded.

NASA/CR—2012-217424 50
NASA/CR—2012-217424 51

Appendix B.—Definitions

AN2 is an indicator of blade pull stress. This stems from the fact that the pull stress of a spinning 

radial cylinder is proportional to AN2

. A good rule of thumb is that blade stress will be proportional to 

AN2 at the rate of 10 ksi per 10E9 AN2

. For example, a well designed turbine blade with nickel based 

alloys operating at 50E9 AN2 will have an average pull stress of about 50 ksi. 

AN2 ≡ (Flowpath Annulus area in.2

) X (rpm2) 

Rim speed combined with AN2 is an indicator of disk loading. Rim speed is calculated using the TE hub 

radius. 

Rim Speed(ft/s) = Radius Hub (in.)/12. * rpm *π / 30.

Figure B.1.—Turbine AN2 and Rim Speed Definitions

rpm

Annulus area calculated at TE

Radius Hub

Center Line

NASA/CR—2012-217424 53

Appendix C.—FlowPath Details

Figure C.1.—High Cx/U Four Stage 

High Cx/U

4 Stage

High CX/U

% Speed Design RPM Fuel Burn% ETA 1 ETA 2 ETA 3 ETA 4

53.8 8045 -3.29 73.34 68.62 69.34 91.39

69.2 10343 -7.88 88.33 84.71 84.12 88.62

84.6 12642 1.41 92.95 90.84 90.63 74.87

100.0 14941 23.20 91.25 91.58 92.80 57.42

%Speed Work Coeff. Flow Coeff.

54 1.68 0.813

100 0.5 0.448
NASA/CR—2012-217424 54

Figure C.2.—Low Cx/U Four Stage 

Low Cx/U

4 Stage

Low CX/U

% Speed Design RPM Fuel Burn% ETA 1 ETA 2 ETA 3 ETA 4

53.8 8045 -2.22 69.98 66.62 69.30 90.20

69.2 10343 -7.80 87.58 83.60 82.85 89.14

84.6 12642 -1.84 92.00 89.60 89.44 78.75

100.0 14941 24.30 89.29 89.78 91.43 57.00

%Speed Work Coeff. Flow Coeff.

54 1.66 0.532

100 0.49 0.3
NASA/CR—2012-217424 55

Figure C.3.—Three Stage

3 Stage

3 Stg

% Speed Design RPM Fuel Burn% ETA 1 ETA 2 ETA 3 ETA 4

53.8 8045 -1.11 70.57 66.14 67.52 89.72

69.2 10343 -4.51 78.24 74.89 74.04 89.63

84.6 12642 -7.19 93.53 91.76 91.60 84.44

100.0 14941 -6.36 92.35 92.49 93.53 66.26

%Speed Work Coeff. Flow Coeff.

54 2.11 0.722

100 0.63 0.368
NASA/CR—2012-217424 56

Figure C.4.—Four Stage High Loading (1) 

4 Stage

High Loading (1)

%Speed Work Coeff. Flow Coeff.

54 2.826 1.008

100 0.828 0.467

4 Stg Hi Loading (1)

% Speed Design RPM Fuel Burn% ETA 1 ETA 2 ETA 3 ETA 4

53.8 8045 -0.84 78.77 71.42 69.10 87.45

69.2 10343 -7.98 90.15 87.28 87.13 87.37

84.6 12642 -8.31 93.67 92.32 92.37 85.64

100.0 14941 -3.68 93.96 93.59 94.26 79.31
NASA/CR—2012-217424 57

Figure C.5.—Four Stage High Loading (2) 

4 Stage

High Loading (2)

4 Stg Hi Loading (2)

% Speed Design RPM Fuel Burn% ETA 1 ETA 2 ETA 3 ETA 4

54.0 7000 3.62 76.30 65.58 63.81 85.34

69.3 8988 -6.27 89.07 85.79 86.38 85.44

84.7 10975 -8.11 92.90 91.62 92.32 85.12

100.0 12963 -7.29 93.67 93.29 94.31 83.67

%Speed Work Coeff. Flow Coeff.

54 3.116 0.832

100 0.919 0.377
NASA/CR—2012-217424 58

Figure C.6.—SixStage High Cx/U 

6 Stage, High Cx/U

6 Stage A

% Speed Design RPM Fuel Burn% ETA 1 ETA 2 ETA 3 ETA 4

54.0 7000 1.01 69.66 63.25 64.03 89.39

69.3 8988 -6.27 87.12 83.61 82.71 87.05

84.7 10975 0.50 92.74 90.47 90.61 75.84

100.0 12963 20.42 92.19 92.22 93.34 59.02

%Speed Work Coeff. Flow Coeff.

54 2.031 1.037

100 0.611 0.541
NASA/CR—2012-217424 59

Figure C.7.—Three Stage B

3 Stage, B

3 Stage B

% Speed Design RPM Fuel Burn% ETA 1 ETA 2 ETA 3 ETA 4

54.0 6790 4.91 65.66 61.47 62.07 85.80

69.3 8718 -5.68 87.75 83.89 83.69 85.81

84.7 10646 -8.02 92.48 91.06 91.67 85.58

100.0 12574 -7.45 93.23 92.82 93.98 84.00

%Speed Work Coeff. Flow Coeff.

54 2.991 0.8423

100 0.966 0.4147
NASA/CR—2012-217424 60

Figure C.8.—Four Stage C

4 Stage, C

4 Stage C

% Speed Design RPM Fuel Burn% ETA 1 ETA 2 ETA 3 ETA 4

54.0 6200 4.41 68.91 60.48 62.16 86.31

69.3 7960 -5.84 87.29 83.39 83.22 86.26

84.7 9721 -6.21 92.48 90.80 91.14 83.40

100.0 11482 0.60 93.00 92.65 93.82 74.85

%Speed Work Coeff. Flow Coeff.

54 2.925 1.09025

100 0.864 0.507
NASA/CR—2012-217424 61

Figure C.9.—Smith Curve of All Turbines

Figure C.10.—Design Speed Comparison: All Turbines

0

0.5

1

1.5

2

2.5

3

3.5

0.2 0.4 0.6 0.8 1 1.2 1.4

Flow Coefficient

Work Coefficient

94% Efficiency

93% Efficiency

92% Efficiency

91% Efficiency

90% Efficiency

89% Efficiency

88% Efficiency

87% Efficiency

86% Efficiency

4 stg Hi Cx/U

4 stg Low Cx/U

3 Stage

4 Stage Hi Loading (1)

4 Stage Hi Loading (2)

6 Stage A

3 Stage B

4 Stage C

 

-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

50.0 55.0 60.0 65.0 70.0 75.0 80.0 85.0 90.0 95.0 100.0

Design RPM

Mission Fuel Burn Impact %

High CX/U

Low CX/U

3 Stg

4 Stg Hi Loading (1)

4 Stg Hi Loading (2)

6 Stage A

3 Stage B

4 Stage C

Cruise RPM

Max(SLTO) RPM

NASA/CR—2012-217424 63

Appendix D.—Four Stage CFD Analysis 

The Four Stage power turbine presented in this study was analyzed using a Williams International 

proprietary CFD code called VORTEX. VORTEX is a 3–D, finite volume, explicit time marching flow 

solver. The solution assumes steady-state, time averaged flow. Each blade row is analyzed in the relative 

frame using mixing planes to jump from rotating to stationary blade rows. The mixing planes assure 

conservation of mass, momentum and energy. The performance used to analyze the turbine was based on 

the mission point 4 (see Table 2.1 and Table A.4) with small modifications. Point 4 corresponds to a 

54 percent speed cruise condition. The CFD uses a fictitious design point. To execute the design, point 4 

is used for the thermodynamics, but the speed is increased to 75 percent. The pressure ratio was also 

modified. The NPSS model had an efficiency at point 4 of 78.6 percent and an efficiency at point 3 

(100 percent speed) of 84.9 percent. The predicted efficiency of this four stage is 86.54 and 90.74 percent

respectively which requires less PR in order to meet the power requirement. This would be a significant 

rematch to the engine and would require additional cycle work, possible including a reduction in engine 

core size. Below is a summary of the parameters used in the CFD as well as the cycle targets. The inlet 

temperature and pressures shown are mass averaged values taken from the converged solution and differ 

slightly from the targets. Typically the inlet profiles can be adjusted as the simulation/design matures to 

hone in on the target values. The inlet mass flow is approximately 2.7 percent high which would require 

closing airfoil throat areas to assure proper engine matching. 

Cycle CFD

• PT 31.0 psia 30.93 psia

• TT 1749 °R 1696 °R

• Mdot 12.04 lbm/s 12.37 lbm/s

• rpm 11174 (75 percent speed)

• PR 6.18 5.6

• ETA 78.6 - 84.9 percent 92.9 percent 1

1 No leakage, cooling or tip clearance: MeanLine prediction = 93.55 percent @ PR = 5.78

The geometry used in the CFD did not have fillets between the airfoil and endwall intersection. The 

following are surface static pressure loading plots of each stage. The vane and blade are plotted together: 

Hub, Mean and Tip. 
NASA/CR—2012-217424 64

D.1 Stage 1 

50% Span

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 60 70 80 90 100

Percent Chord

Ps/Pt

Vane1

Blade1

10% Span

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 60 70 80 90 100

Percent Chord

Ps/Pt

Vane1

Blade1
NASA/CR—2012-217424 65

D.2 Stage 2 

90% Span

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 60 70 80 90 100

Percent Chord

Ps/Pt

Vane1

Blade1

10% Span

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 60 70 80 90 100

Percent Chord

Ps/Pt

Vane1

Blade1
NASA/CR—2012-217424 66

50% Span

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 60 70 80 90 100

Percent Chord

Ps/Pt

Vane1

Blade1

90% Span

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 60 70 80 90 100

Percent Chord

Ps/Pt

Vane1

Blade1
NASA/CR—2012-217424 67

D.3 Stage 3 

10% Span

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 60 70 80 90 100

Percent Chord

Ps/Pt

Vane1

Blade1

50% Span

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 60 70 80 90 100

Percent Chord

Ps/Pt

Vane1

Blade1
NASA/CR—2012-217424 68

D.4 Stage 4 

90% Span

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 60 70 80 90 100

Percent Chord

Ps/Pt

Vane1

Blade1

10% Span

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 60 70 80 90 100

Percent Chord

Ps/Pt

Vane1

Blade1
NASA/CR—2012-217424 69

50% Span

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 60 70 80 90 100

Percent Chord

Ps/Pt

Vane1

Blade1

90% Span

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 60 70 80 90 100

Percent Chord

Ps/Pt

Vane1

Blade1
NASA/CR—2012-217424 70

Meanline Analysis of Design Point

75% Speed (11174 rpm) 

Flow Parm. (Inlet) : 16.240

Mass Flow : 12.040

Efficiency : 92.8662%

Flow Parm. (Exit) : 76.472

Power(hp) : 2684.958

Pressure Ratio (Total/Total) : 5.769

Pressure Ratio (Total/Static) : 6.330

Inlet Temp. (degrees R / F) : 1749.080 / 1289.410

TRIT (degrees R / F) : 1749.080 / 1289.410

Exit TT (degrees R / F) : 1165.389 / 705.719

Enthalpy Drop (BTU/lbm) : 39.608

Ratio Specific Heats (Gamma) : 1.340

Gas Constant (ft-lbf/degR/lbm): 53.374

Avg. Work Coefficient : 1.459

Core Flow (lbm/s) : 12.040

Nozzle Cooling : 0.000%

Rotor Cooling : 0.000%

Rotor Summary:

Title Reaction WorkCoef Cm/U AN^2 RimSpeed

ROTOR: STAGE 1 48.000% 1.470 0.726 11.390 689.720

ROTOR: STAGE 2 47.000% 1.490 0.563 18.720 671.266

ROTOR: STAGE 3 45.000% 1.496 0.551 27.121 617.638

ROTOR: STAGE 4 40.000% 1.384 0.702 32.240 567.395

Corrected Speed (rpm) : 6085.02 

(based on TRIT & 1st rpm found)

=======================================================================

 Vane Blade

 

Turning 58.1564 78.4812

 85.9121 90.6473

92.4592 93.8363

88.4801 81.7638

RVR 2.0792 1.9532

 2.0969 2.2366

2.4743 2.4077

2.4598 2.0300

Convergence Ratio 1.8046 1.6902

 1.7790 1.8930

2.0383 1.9791

1.9660 1.6718

Reynolds #, SS/1000. 179.2235 152.0635

 145.1666 126.1129

118.1032 93.2357

 80.7626 59.2618

LE Mach # (relative) 0.2733 0.2985

 0.2872 0.2673

0.2553 0.2647

0.2783 0.3262

TE Mach # (relative) 0.5824 0.5983

 0.6181 0.6148

0.6509 0.6579

0.7092 0.6836

LE Swirl (relative) 0.0000 17.9747

 -22.1197 24.7990

-25.4011 27.7528

-24.2202 23.9420

TE Swirl (relative) 58.1564 -60.3947

 63.7159 -65.7272
NASA/CR—2012-217424 71

 66.9995 -65.9808

64.2247 -57.7576

Total Loss % 1.4064 1.9212

 2.0358 2.1632

2.1774 2.3416

2.1681 2.2357

Zweifel 1.0569 1.0284

 1.0437 1.0370

1.0391 1.0437

1.0225 1.0499

Throat Area 37.6309 -42.5160 

 49.0312 -59.0217

69.3542 -85.1203

 102.2492 -131.8714

Number of Airfoils 52 65

 62 62 

59 65

67 76

Exit Mach/Swirl (Absolute) 0.3718 -9.3783

NASA/CR—2012-217424 73

Appendix E.—Meanline Results for Four Stage: High Loading 1

Rotor Summary at Design Speed of 54 percent: 

Title Reaction WorkCoef Cm/U AN2

 RimSpeed

ROTOR: STAGE 1 48.000% 2.826 1.072 5.902 496.707 

ROTOR: STAGE 2 45.000% 2.840 0.857 9.700 483.381 

ROTOR: STAGE 3 45.000% 2.863 0.880 14.081 444.190 

ROTOR: STAGE 4 39.992% 2.774 1.224 16.650 410.626 

Overall Efficiency = 87.5% 

Rotor Summary @ Design Speed 100%: 

Title Reaction WorkCoef Cm/U AN2

 RimSpeed

ROTOR: STAGE 1 48.000% 0.834 0.539 20.240 919.819 

ROTOR: STAGE 2 45.000% 0.848 0.416 33.265 895.143 

ROTOR: STAGE 3 45.000% 0.851 0.402 48.287 822.569 

ROTOR: STAGE 4 40.000% 0.778 0.512 57.098 760.413 

Overall Efficiency = 94%

Airfoil Summary 

 54% Speed 100% Speed

 Vane Blade Vane Blade

 

Turning 59.3261 101.7896 57.7106 51.4604

 110.8252 114.7838 58.0856 58.7734

 115.4375 116.0826 53.8484 56.6190

 110.8802 100.6000 52.2701 50.9701

Vexit/Vinlet 2.2231 1.7296 2.0611 2.0179

 1.6517 1.6362 2.2851 2.4019

 1.8324 1.7477 2.6784 2.6977

 1.7983 1.5571 2.6875 2.2304

Reynolds #, SS/1000. 192.2316 162.2900 176.8202 166.8413

 147.8500 121.7398 160.8162 137.0289

 112.3183 87.5698 136.1440 106.9008

 73.1437 53.5719 94.8810 66.7247

LE Mach # (relative) 0.2730 0.3809 0.2730 0.2876

 0.4105 0.4037 0.2644 0.2426

 0.3843 0.4147 0.2332 0.2325

 0.4390 0.5105 0.2532 0.2931

 54% Speed 100% Speed
NASA/CR—2012-217424 74

 Vane Blade Vane Blade

TE Mach # (relative) 0.6244 0.6770 0.5764 0.5956

 0.6956 0.6769 0.6213 0.5993

 0.7258 0.7479 0.6439 0.6480

 0.8204 0.8226 0.7056 0.6759

LE Swirl (relative) 0.0000 39.4746 0.0000 -9.0460

 -46.1872 48.9328 5.9468 -6.6781

 -48.6347 50.4989 13.3548 -9.6122

 -47.9455 44.9543 12.4835 -7.2519

TE Swirl (relative) 59.3261 -62.1228 57.7106 -60.5652

 64.5339 -65.7028 64.0554 -65.4882

 66.7344 -65.4703 67.2378 -66.2728

 62.8947 -55.5671 64.7740 -58.2441

Total Loss % 1.6196 3.4411 1.3734 1.4617

3.8016 3.8811 1.5134 1.5536

 3.8187 4.4511 1.6540 1.6506

 4.1192 5.0666 1.6129 1.5247

Zweifel 1.0550 1.0259 1.0649 1.0237

 1.0657 1.0499 1.0140 1.0355

 1.0641 1.0576 1.0127 1.0284

 1.0377 1.0356 1.0124 1.0190

Number of Airfoils 51 76 52 50

 74 77 50 49

 72 82 45 49

 88 105 49 56

Exit Mach/Swirl 0.5549 -32.7647 0.3768 18.4055

(Absolute) 
NASA/CR—2012-217424 75

Appendix F.—Disk Sizing

A 2–D disk sizing tool was used to approximate disk mass and structural feasibility. Below is a screen 

shot of disks that were designed based on achieving 25 percent over speed capability with typical disk 

alloys. The resulting weight and mass moment of inertia of each disk plus the blades is shown.

Figure F.1.—Approximate Disk Size

29 lbm

960 lbm*in2

33 lbm

1120 lbm*in2

34 lbm

11680 lbm*in2

35 lbm

1250 lbm*in2

NASA/CR—2012-217424 77

Appendix G.—Efficiency and Reaction Definitions 

The scope of this work is concentrated on understanding speed variations and the impact to turbine 

efficiency. In order to simplify this understanding, the analysis presented in this report does not consider 

cooling flows. This simplifies the efficiency definition. The efficiency numbers presented in this report 

are calculated assuming ideal gas as follows.















 −

∆

≡η =

γ

1 γ−

1*Tin Pr

Tt

IdealPower

ActualPower

where:

Pr = Total Pressure at inlet / Total Pressure at outlet

ΔTt = Total Temperature at inlet – Total Temperature at outlet

Tin = Total temperature at inlet

γ is the ratio of specific heats taken at the average of the inlet and exit Total Temperatures.

In this work, stage reaction refers to pressure reaction defined as the static pressure drop across the 

rotor normalized by the static pressure drop across the whole stage.

















−

− ≡ NozzleLE RotorTE

RotorLE RotorTE

Ps Ps

Ps Ps Re action

NASA/CR—2012-217424 79

Appendix H.—NPSS Output for Critical Mission Point
TABLE H.1.—65 PERCENT DESIGN SPEED TAKE OFF 

*********************************************************************************************************************************

Date:05/24/11 Time:13:01:28 Model: AHS 2010 Govt turboshaft engine - 65% speed turbine - Takeoff converge = 1 CASE: 

Version: NPSS_2.3 Gas Package: Janaf iter/pass/Jacb/Broy7= 7/ 18/ 1/ 5 Run by: tm1862 PC: 

 SUMMARY OUTPUT DATA MN alt dTs W Fn Power BSFC Wfuel VTAS OPR T4 T41 T47 Dy

0.000 0.0 45.00 28.17 464.6 7890.5 0.3305 2668.99 0.00 42.231 3769.2 3471.0 2884.2 

 FLOW STATION DATA W Pt Tt ht FAR Wc Ps Ts Aphy MN gamt g

FL1 InletStart.Fl_O 28.17 14.696 563.67 4.62 0.0000 29.36 14.696 563.67 ----.-- 0.000 1.3995 1.3

FL2 Inlet.Fl_O 28.17 14.696 563.67 4.62 0.0000 29.36 13.162 546.20 136.07 0.400 1.3995 1.3

FL22 Duct1.Fl_O 28.17 14.696 563.67 4.62 0.0000 29.36 14.292 559.20 253.60 0.200 1.3995 1.3

FL23 LPC.Fl_O 28.17 213.118 1302.21 187.46 0.0000 3.08 191.446 1265.56 14.45 0.399 1.3617 1.3

FL24 ICduct.Fl_O 28.17 212.692 1302.21 187.46 0.0000 3.08 191.063 1265.56 14.48 0.399 1.3617 1.3

FL25 HPC_axi.Fl_O 28.17 239.929 1349.79 199.78 0.0000 2.78 225.836 1328.37 16.76 0.300 1.3589 1.3

FL26 Bld25.Fl_O 26.23 239.929 1349.79 199.78 0.0000 2.59 215.589 1312.11 12.18 0.399 1.3589 1.3

FL27 HPC_centri.Fl_O 26.23 620.620 1786.31 315.94 0.0000 1.15 584.548 1759.54 6.98 0.300 1.3367 1.3

FL28 Bld3.Fl_O 19.87 620.620 1786.31 315.94 0.0000 0.87 595.290 1767.65 6.24 0.250 1.3367 1.3

FL3 Duct6.Fl_O 19.87 620.620 1786.31 315.94 0.0000 0.87 604.261 1774.33 7.70 0.200 1.3367 1.3

FL4 Burner.Fl_O 20.61 608.208 3769.16 260.95 0.0373 1.34 552.163 3694.08 6.50 0.401 1.2520 1.2

FL42 HPT.Fl_O 26.97 291.135 2956.47 148.09 0.0283 3.25 275.130 2919.73 20.07 0.300 1.2786 1.2

FL43 Duct43.Fl_O 26.97 291.135 2956.47 148.09 0.0283 3.25 263.408 2891.67 15.65 0.400 1.2786 1.2

FL44 LPT.Fl_O 28.91 84.443 2274.77 -26.60 0.0263 10.54 82.257 2260.99 93.61 0.202 1.2998 1.3

FL45 ITduct.Fl_O 28.91 84.443 2274.82 -26.60 0.0263 10.54 76.075 2220.41 50.08 0.404 1.2998 1.3

FL6 PowerT.Fl_O 28.91 15.430 1605.77 -219.51 0.0263 48.45 14.537 1582.30 293.77 0.301 1.3269 1.3

FL7 Duct12.Fl_O 28.91 15.430 1605.82 -219.51 0.0263 48.45 14.537 1582.36 293.78 0.301 1.3269 1.3

FL9 Nozzle.Fl_O 28.91 15.430 1605.88 -219.51 0.0263 48.45 14.696 1586.69 322.12 0.272 1.3269 1.3

TURBOMACHINERY PERFORMANCE DATA 

 Wc PR eff Nc TR efPoly pwr SMN SMW LPC 29.36 14.502 0.8439 12000.000 2.3102 0.8889 -7286.8 19.91 19.50 HPC_axi 3.08 1.128 0.8875 9681.203 1.0365 0.8892 -490.9 19.92 12.44 HPC_cen> 2.59 2.587 0.8591 9509.053 1.3234 0.8748 -4311.1 20.24 18.65 HPT 1.34 2.089 0.8503 249.863 1.1353 0.8159 4802.0 

LPT 3.25 3.448 0.8504 230.071 1.2582 0.8239 7286.7 PowerT 10.54 5.472 0.8835 314.498 1.4168 0.8587 7890.5 

TURBOMACHINERY MAP DATA 

 WcMap PRmap effMap NcMap R/Parm s_WcDes s_PRdes s_effDes s_NcDes LPC 30.00 9.006 0.8510 100.000 1.9970 0.978860 1.6865 0.9916 0.8333

HPC_axi 29.90 1.200 0.8519 0.997 1.9839 0.103125 0.6398 1.0418 0.0001

HPC_cen> 29.89 3.182 0.8517 0.997 1.9961 0.086701 0.7273 1.0086 0.0001 HPT 30.15 5.972 0.9291 100.188 5.9722 0.044531 4.5654 0.9152 0.0176

LPT 149.72 6.032 0.9280 100.511 6.0322 0.021712 2.0559 0.9163 0.0192

PowerT 10.03 5.473 0.8835 7162.562 5.4727 1.050286 1.0001 1.0001 1.0000

===INLETS==== eRam Afs Fram Inlet 1.0000 -----.-- 0.0 BLEEDS - output Wb/Win hscale Pscale W Tt ht 

 C_LPTCharg Bl> 0.0182 1.0000 1.0000 0.5126 1349.79 199.78 239.

====DUCTS==== dPnorm MN Aphy C_LPTUncharg Bl> 0.0506 1.0000 1.0000 1.4241 1349.79 199.78 239.

Duct1 0.0000 0.4001 136.07 C_HPTCharg Bl> 0.0823 1.0000 1.0000 2.1597 1786.31 315.94 620.

ICduct 0.0020 0.3994 14.45 C_HPTUncharg Bl> 0.1602 1.0000 1.0000 4.2020 1786.31 315.94 620.

Duct6 0.0000 0.2503 6.24 Duct43 0.0000 0.3004 20.07 ITduct 0.0000 0.2016 93.61 Duct12 0.0000 0.3009 293.77 

===SHAFTS==== Nmech trq in pwr in HP_Shaft 15340.0 1644.1 4802.0 IP_Shaft 12509.7 3059.3 7286.7 LP_Shaft 15000.0 2762.8 7890.5 

===BURNERS=== TtOut eff dPnorm Wfuel FAR EINOx ppm 

Burner 3769.16 1.0000 0.0200 0.74138 0.03731 

 

===NOZZLES=== PR Cfg CdTh Cv Ath MNth Vact Fg

Nozzle 1.050 1.0000 1.0000 1.0000 321.89 0.272 517.0 464.6

NASA/CR—2012-217424 80
TABLE H.2.—65 PERCENT DESIGN SPEED CLIMB 

*********************************************************************************************************************************

Date:05/24/11 Time:13:01:28 Model: AHS 2010 Govt turboshaft engine - 65% speed turbine - Climb converge = 1 CASE: 

Version: NPSS_2.3 Gas Package: Janaf iter/pass/Jacb/Broy= 20/ 31/ 1/18 Run by: tm1862 PC: 

 

 SUMMARY OUTPUT DATA MN alt dTs W Fn Power BSFC Wfuel VTAS OPR T4 T41 T47 Dy

0.000 0.0 0.00 19.98 304.1 2646.3 0.4551 1259.82 0.00 25.976 2903.4 2674.3 2203.1 

 FLOW STATION DATA W Pt Tt ht FAR Wc Ps Ts Aphy MN gamt g

FL1 InletStart.Fl_O 19.98 14.696 518.67 -6.18 0.0000 19.98 14.696 518.67 ----.-- 0.000 1.4002 1.4

FL2 Inlet.Fl_O 19.98 14.696 518.67 -6.18 0.0000 19.98 14.033 511.87 136.07 0.258 1.4002 1.4

FL22 Duct1.Fl_O 19.98 14.696 518.67 -6.18 0.0000 19.98 14.512 516.80 253.60 0.134 1.4002 1.4

FL23 LPC.Fl_O 19.98 139.757 1062.08 126.40 0.0000 3.01 126.302 1033.00 14.45 0.386 1.3769 1.3

FL24 ICduct.Fl_O 19.98 139.478 1062.08 126.40 0.0000 3.01 126.049 1033.00 14.48 0.386 1.3769 1.3

FL25 HPC_axi.Fl_O 19.98 157.365 1101.89 136.40 0.0000 2.72 148.577 1084.76 16.76 0.290 1.3743 1.3

FL26 Bld25.Fl_O 18.61 157.365 1101.89 136.40 0.0000 2.53 142.244 1071.93 12.18 0.386 1.3743 1.3

FL27 HPC_centri.Fl_O 18.61 381.746 1444.24 224.44 0.0000 1.20 357.780 1419.95 6.98 0.311 1.3535 1.3

FL28 Bld3.Fl_O 14.09 381.746 1444.24 224.44 0.0000 0.91 364.944 1427.34 6.24 0.259 1.3535 1.3

FL3 Duct6.Fl_O 14.09 381.746 1444.24 224.44 0.0000 0.91 370.907 1433.41 7.70 0.207 1.3535 1.3

FL4 Burner.Fl_O 14.44 374.111 2903.39 191.13 0.0248 1.34 338.989 2840.14 6.50 0.397 1.2820 1.2

FL42 HPT.Fl_O 18.96 178.418 2256.84 102.11 0.0188 3.26 168.470 2226.61 20.07 0.298 1.3052 1.3

FL43 Duct43.Fl_O 18.96 178.418 2256.89 102.11 0.0188 3.26 161.186 2203.61 15.65 0.397 1.3052 1.3

FL44 LPT.Fl_O 20.33 54.478 1727.90 -25.88 0.0175 10.01 53.204 1717.84 93.61 0.189 1.3266 1.3

FL45 ITduct.Fl_O 20.33 54.478 1727.95 -25.88 0.0175 10.01 49.665 1688.94 50.08 0.375 1.3266 1.3

FL6 PowerT.Fl_O 20.33 15.431 1391.41 -117.88 0.0175 31.71 15.063 1382.83 293.77 0.190 1.3443 1.3

FL7 Duct12.Fl_O 20.33 15.431 1391.47 -117.88 0.0175 31.71 15.063 1382.90 293.78 0.190 1.3443 1.3

FL9 Nozzle.Fl_O 20.33 15.431 1391.54 -117.88 0.0175 31.71 14.696 1374.25 210.76 0.270 1.3443 1.3

TURBOMACHINERY PERFORMANCE DATA 

 Wc PR eff Nc TR efPoly pwr SMN SMW LPC 19.98 9.510 0.8460 10818.559 2.0477 0.8853 -3747.7 17.84 19.09 HPC_axi 3.01 1.128 0.8936 9456.518 1.0375 0.8953 -282.6 19.37 11.28 HPC_cen> 2.53 2.426 0.8588 9284.124 1.3107 0.8741 -2317.5 26.03 25.07 HPT 1.34 2.097 0.8502 251.138 1.1488 0.8303 2599.9 

LPT 3.26 3.275 0.8520 227.727 1.2662 0.8307 3748.0 

PowerT 10.01 3.531 0.7181 360.849 1.2420 0.6839 2646.2 

TURBOMACHINERY MAP DATA 

 WcMap PRmap effMap NcMap R/Parm s_WcDes s_PRdes s_effDes s_NcDes LPC 20.41 6.046 0.8532 90.155 1.6982 0.978860 1.6865 0.9916 0.8333

HPC_axi 29.21 1.200 0.8577 0.974 1.8760 0.103125 0.6398 1.0418 0.0001

HPC_cen> 29.21 2.961 0.8514 0.973 2.0487 0.086701 0.7273 1.0086 0.0001

HPT 30.14 6.007 0.9290 100.699 6.0075 0.044531 4.5654 0.9152 0.0176

LPT 149.99 5.677 0.9298 99.487 5.6772 0.021712 2.0559 0.9163 0.0192 PowerT 9.53 3.531 0.7181 8218.192 3.5307 1.050286 1.0001 1.0001 1.0000

===INLETS==== eRam Afs Fram Inlet 1.0000 -----.-- 0.0 BLEEDS - output Wb/Win hscale Pscale W Tt ht 

 C_LPTCharg Bl> 0.0182 1.0000 1.0000 0.3636 1101.89 136.40 157.

====DUCTS==== dPnorm MN Aphy C_LPTUncharg Bl> 0.0506 1.0000 1.0000 1.0101 1101.89 136.40 157.

Duct1 0.0000 0.2576 136.07 C_HPTCharg Bl> 0.0823 1.0000 1.0000 1.5318 1444.24 224.44 381.

ICduct 0.0020 0.3859 14.45 C_HPTUncharg Bl> 0.1602 1.0000 1.0000 2.9804 1444.24 224.44 381.

Duct6 0.0000 0.2586 6.24 Duct43 0.0000 0.2980 20.07 ITduct 0.0000 0.1891 93.61 Duct12 0.0000 0.1897 293.77 

===SHAFTS==== Nmech trq in pwr in HP_Shaft 13532.1 1009.1 2599.9 IP_Shaft 10818.6 1819.5 3748.0 LP_Shaft 15000.0 926.5 2646.2 

===BURNERS=== TtOut eff dPnorm Wfuel FAR EINOx ppm 

Burner 2903.39 1.0000 0.0200 0.34995 0.02483 

 

===NOZZLES=== PR Cfg CdTh Cv Ath MNth Vact Fg Nozzle 1.050 1.0000 1.0000 1.0000 321.89 0.270 481.3 304.1 

 

NASA/CR—2012-217424 81
TABLE H.3.—65 PERCENT DESIGN SPEED CRUISE *********************************************************************************************************************************

Date:05/24/11 Time:13:01:29 Model: AHS 2010 Govt turboshaft engine - 65% speed turbine - Cruise converge = 1 CASE: 

Version: NPSS_2.3 Gas Package: Janaf iter/pass/Jacb/Broy= 28/ 50/ 2/25 Run by: tm1862 PC: 

 

 SUMMARY OUTPUT DATA MN alt dTs W Fn Power BSFC Wfuel VTAS OPR T4 T41 T47 Dy

0.510 28000.0 0.00 11.80 -25.9 2351.0 0.3141 735.13 511.85 39.130 2847.0 2619.0 2155.0 

 FLOW STATION DATA W Pt Tt ht FAR Wc Ps Ts Aphy MN gamt g

FL1 InletStart.Fl_O 11.80 5.705 440.66 -24.88 0.0000 28.03 4.776 418.82 107.88 0.510 1.4010 1.4

FL2 Inlet.Fl_O 11.80 5.705 440.66 -24.88 0.0000 28.03 5.169 428.40 136.07 0.378 1.4010 1.4

FL22 Duct1.Fl_O 11.80 5.705 440.66 -24.88 0.0000 28.03 5.562 437.48 253.60 0.190 1.4010 1.4

FL23 LPC.Fl_O 11.80 80.640 1019.99 115.89 0.0000 3.02 72.819 991.72 14.45 0.387 1.3795 1.3

FL24 ICduct.Fl_O 11.80 80.479 1019.99 115.89 0.0000 3.02 72.673 991.72 14.48 0.387 1.3795 1.3

FL25 HPC_axi.Fl_O 11.80 90.847 1058.62 125.54 0.0000 2.73 85.741 1041.97 16.76 0.291 1.3771 1.3

FL26 Bld25.Fl_O 10.99 90.847 1058.62 125.54 0.0000 2.54 82.059 1029.49 12.18 0.387 1.3771 1.3

FL27 HPC_centri.Fl_O 10.99 223.217 1394.60 211.44 0.0000 1.19 209.421 1371.40 6.98 0.308 1.3563 1.3

FL28 Bld3.Fl_O 8.33 223.217 1394.60 211.44 0.0000 0.90 213.541 1378.44 6.24 0.256 1.3563 1.3

FL3 Duct6.Fl_O 8.33 223.217 1394.60 211.44 0.0000 0.90 216.973 1384.23 7.70 0.205 1.3563 1.3

FL4 Burner.Fl_O 8.53 218.753 2847.03 178.94 0.0245 1.34 198.185 2784.66 6.50 0.397 1.2837 1.2

FL42 HPT.Fl_O 11.20 104.659 2208.49 92.17 0.0186 3.24 98.870 2179.03 20.07 0.296 1.3070 1.3

FL43 Duct43.Fl_O 11.20 104.659 2208.54 92.17 0.0186 3.24 94.637 2156.67 15.65 0.395 1.3070 1.3

FL44 LPT.Fl_O 12.01 28.056 1648.42 -43.94 0.0173 11.21 27.227 1636.16 93.61 0.213 1.3306 1.3

FL45 ITduct.Fl_O 12.01 28.056 1648.48 -43.94 0.0173 11.21 24.842 1599.24 50.08 0.431 1.3306 1.3

FL6 PowerT.Fl_O 12.01 5.015 1131.40 -182.32 0.0173 51.97 4.677 1110.67 293.77 0.321 1.3606 1.3

FL7 Duct12.Fl_O 12.01 5.015 1131.47 -182.32 0.0173 51.97 4.677 1110.73 293.78 0.321 1.3606 1.3

FL9 Nozzle.Fl_O 12.01 5.015 1131.53 -182.32 0.0173 51.98 4.776 1117.01 345.52 0.268 1.3606 1.3

TURBOMACHINERY PERFORMANCE DATA 

 Wc PR eff Nc TR efPoly pwr SMN SMW LPC 28.03 14.136 0.8489 11830.394 2.3147 0.8929 -2350.7 17.22 17.26 HPC_axi 3.02 1.129 0.8930 9493.110 1.0379 0.8947 -161.2 19.31 11.36 HPC_cen> 2.54 2.457 0.8599 9318.289 1.3174 0.8753 -1336.0 24.66 23.60 HPT 1.34 2.090 0.8502 249.497 1.1488 0.8311 1497.1 

LPT 3.24 3.730 0.8467 232.035 1.2982 0.8226 2350.7 

PowerT 11.21 5.595 0.8783 198.934 1.4572 0.8513 2350.9 

TURBOMACHINERY MAP DATA 

 WcMap PRmap effMap NcMap R/Parm s_WcDes s_PRdes s_effDes s_NcDes LPC 28.63 8.789 0.8560 98.587 1.8497 0.978860 1.6865 0.9916 0.8333

HPC_axi 29.31 1.201 0.8571 0.977 1.8849 0.103125 0.6398 1.0418 0.0001

HPC_cen> 29.30 3.003 0.8525 0.977 2.0338 0.086701 0.7273 1.0086 0.0001

HPT 30.15 5.977 0.9290 100.041 5.9770 0.044531 4.5654 0.9152 0.0176 LPT 149.41 6.613 0.9240 101.369 6.6132 0.021712 2.0559 0.9163 0.0192

PowerT 10.68 5.595 0.8783 4530.633 5.5951 1.050286 1.0001 1.0001 1.0000

===INLETS==== eRam Afs Fram Inlet 1.0000 107.88 187.8 BLEEDS - output Wb/Win hscale Pscale W Tt ht 

 C_LPTCharg Bl> 0.0182 1.0000 1.0000 0.2148 1058.62 125.54 90.

====DUCTS==== dPnorm MN Aphy C_LPTUncharg Bl> 0.0506 1.0000 1.0000 0.5968 1058.62 125.54 90.

Duct1 0.0000 0.3779 136.07 C_HPTCharg Bl> 0.0823 1.0000 1.0000 0.9050 1394.60 211.44 223.

ICduct 0.0020 0.3871 14.45 C_HPTUncharg Bl> 0.1602 1.0000 1.0000 1.7608 1394.60 211.44 223.

Duct6 0.0000 0.2563 6.24 Duct43 0.0000 0.2965 20.07 ITduct 0.0000 0.2127 93.61 Duct12 0.0000 0.3214 293.77 

===SHAFTS==== Nmech trq in pwr in 

HP_Shaft 13312.5 590.7 1497.1 IP_Shaft 10904.5 1132.2 2350.7 

LP_Shaft 8077.0 1528.7 2350.9 

===BURNERS=== TtOut eff dPnorm Wfuel FAR EINOx ppm 

Burner 2847.03 1.0000 0.0200 0.20420 0.02453 

===NOZZLES=== PR Cfg CdTh Cv Ath MNth Vact Fg Nozzle 1.050 1.0000 1.0000 1.0000 321.89 0.268 433.7 161.8 

NASA/CR—2012-217424 82
TABLE H.4.—75 PERCENT DESIGN SPEED TAKE OFF 

*********************************************************************************************************************************

Date:05/24/11 Time:12:57:33 Model: AHS 2010 Govt turboshaft engine - 75% speed turbine - Takeoff converge = 1 CASE: 

Version: NPSS_2.3 Gas Package: Janaf iter/pass/Jacb/Broy= 7/ 18/ 1/ 5 Run by: tm1862 PC: 

 SUMMARY OUTPUT DATA MN alt dTs W Fn Power BSFC Wfuel VTAS OPR T4 T41 T47 Dy

0.000 0.0 45.00 27.02 441.8 7866.9 0.3182 2559.60 0.00 42.270 3766.5 3470.5 2884.1 

 FLOW STATION DATA W Pt Tt ht FAR Wc Ps Ts Aphy MN gamt g

FL1 InletStart.Fl_O 27.02 14.696 563.67 4.62 0.0000 28.16 14.696 563.67 ----.-- 0.000 1.3995 1.3

FL2 Inlet.Fl_O 27.02 14.696 563.67 4.62 0.0000 28.16 13.161 546.20 130.50 0.400 1.3995 1.3

FL22 Duct1.Fl_O 27.02 14.696 563.67 4.62 0.0000 28.16 14.292 559.20 243.22 0.200 1.3995 1.3

FL23 LPC.Fl_O 27.02 213.138 1302.67 187.58 0.0000 2.95 191.426 1265.94 13.85 0.400 1.3617 1.3

FL24 ICduct.Fl_O 27.02 212.712 1302.67 187.58 0.0000 2.96 191.044 1265.94 13.88 0.400 1.3617 1.3

FL25 HPC_axi.Fl_O 27.02 239.729 1349.92 199.81 0.0000 2.67 225.624 1328.46 16.07 0.300 1.3589 1.3

FL26 Bld25.Fl_O 25.17 239.729 1349.92 199.81 0.0000 2.49 215.366 1312.16 11.69 0.400 1.3589 1.3

FL27 HPC_centri.Fl_O 25.17 621.191 1787.86 316.36 0.0000 1.11 585.141 1761.11 6.70 0.300 1.3367 1.3

FL28 Bld3.Fl_O 19.10 621.191 1787.86 316.36 0.0000 0.84 595.875 1769.21 6.00 0.250 1.3367 1.3

FL3 Duct6.Fl_O 19.10 621.191 1787.86 316.36 0.0000 0.84 604.840 1775.88 7.41 0.200 1.3367 1.3

FL4 Burner.Fl_O 19.81 608.767 3766.50 261.47 0.0372 1.29 552.655 3691.42 6.24 0.401 1.2521 1.2

FL42 HPT.Fl_O 25.89 290.964 2955.80 148.24 0.0282 3.12 274.959 2919.04 19.27 0.301 1.2786 1.2

FL43 Duct43.Fl_O 25.89 290.964 2955.80 148.24 0.0282 3.12 263.238 2890.96 15.02 0.401 1.2786 1.2

FL44 LPT.Fl_O 27.73 84.350 2274.58 -26.60 0.0263 10.12 82.177 2260.87 90.09 0.201 1.2998 1.3

FL45 ITduct.Fl_O 27.73 84.350 2274.63 -26.60 0.0263 10.12 76.035 2220.53 48.19 0.402 1.2998 1.3

FL6 PowerT.Fl_O 27.73 15.431 1578.15 -227.13 0.0263 46.06 14.531 1554.84 278.41 0.302 1.3283 1.3

FL7 Duct12.Fl_O 27.73 15.431 1578.21 -227.13 0.0263 46.06 14.531 1554.90 278.42 0.302 1.3283 1.3

FL9 Nozzle.Fl_O 27.73 15.431 1578.27 -227.13 0.0263 46.06 14.696 1559.32 306.20 0.272 1.3283 1.3

TURBOMACHINERY PERFORMANCE DATA 

 Wc PR eff Nc TR efPoly pwr SMN SMW LPC 28.16 14.503 0.8434 12000.000 2.3110 0.8886 -6993.4 20.01 19.60 HPC_axi 2.96 1.127 0.8869 9686.004 1.0363 0.8887 -467.6 19.94 12.48 HPC_cen> 2.49 2.591 0.8581 9514.980 1.3244 0.8740 -4151.3 20.11 18.46 HPT 1.29 2.092 0.8503 250.119 1.1356 0.8159 4618.9 

LPT 3.12 3.450 0.8505 230.097 1.2584 0.8240 6993.4 PowerT 10.12 5.466 0.9190 314.511 1.4414 0.9005 7866.9 

TURBOMACHINERY MAP DATA 

 WcMap PRmap effMap NcMap R/Parm s_WcDes s_PRdes s_effDes s_NcDes LPC 30.00 8.999 0.8510 100.000 2.0005 0.938796 1.6881 0.9911 0.8333

HPC_axi 29.93 1.200 0.8517 0.997 1.9877 0.098842 0.6347 1.0414 0.0001

HPC_cen> 29.92 3.188 0.8515 0.998 1.9949 0.083218 0.7273 1.0077 0.0001 HPT 30.15 5.974 0.9291 100.177 5.9744 0.042746 4.5543 0.9152 0.0176

LPT 149.74 6.012 0.9281 100.436 6.0116 0.020843 2.0460 0.9163 0.0192

PowerT 10.32 5.466 0.9190 7162.784 5.4664 0.980704 1.0000 1.0000 1.0000

===INLETS==== eRam Afs Fram Inlet 1.0000 -----.-- 0.0 BLEEDS - output Wb/Win hscale Pscale W Tt ht 

 C_LPTCharg Bl> 0.0180 1.0000 1.0000 0.4859 1349.92 199.81 239.

====DUCTS==== dPnorm MN Aphy C_LPTUncharg Bl> 0.0502 1.0000 1.0000 1.3558 1349.92 199.81 239.

Duct1 0.0000 0.4001 130.50 C_HPTCharg Bl> 0.0819 1.0000 1.0000 2.0613 1787.86 316.36 621.

ICduct 0.0020 0.3998 13.85 C_HPTUncharg Bl> 0.1595 1.0000 1.0000 4.0143 1787.86 316.36 621.

Duct6 0.0000 0.2501 6.00 Duct43 0.0000 0.3005 19.27 ITduct 0.0000 0.2011 90.09 Duct12 0.0000 0.3018 278.41 

===SHAFTS==== Nmech trq in pwr in HP_Shaft 15350.3 1580.4 4618.9 IP_Shaft 12509.7 2936.1 6993.4 LP_Shaft 15000.0 2754.5 7866.9 

===BURNERS=== TtOut eff dPnorm Wfuel FAR EINOx ppm Burner 3766.50 1.0000 0.0200 0.71100 0.03723 

 

===NOZZLES=== PR Cfg CdTh Cv Ath MNth Vact Fg

Nozzle 1.050 1.0000 1.0000 1.0000 305.32 0.272 512.7 441.8 

NASA/CR—2012-217424 83
TABLE H.5.—75 PERCENT DESIGN SPEED CLIMB 

*********************************************************************************************************************************

Date:05/24/11 Time:12:57:33 Model: AHS 2010 Govt turboshaft engine - 75% speed turbine - Climb converge = 1 CASE: 

Version: NPSS_2.3 Gas Package: Janaf iter/pass/Jacb/Broy= 18/ 29/ 1/16 Run by: tm1862 PC: 

 

 SUMMARY OUTPUT DATA MN alt dTs W Fn Power BSFC Wfuel VTAS OPR T4 T41 T47 Dy

0.000 0.0 0.00 18.92 281.5 2646.3 0.4171 1150.64 0.00 25.419 2849.1 2627.8 2165.6 

 FLOW STATION DATA W Pt Tt ht FAR Wc Ps Ts Aphy MN gamt g

FL1 InletStart.Fl_O 18.92 14.696 518.67 -6.18 0.0000 18.92 14.696 518.67 ----.-- 0.000 1.4002 1.4

FL2 Inlet.Fl_O 18.92 14.696 518.67 -6.18 0.0000 18.92 14.051 512.05 130.50 0.254 1.4002 1.4

FL22 Duct1.Fl_O 18.92 14.696 518.67 -6.18 0.0000 18.92 14.517 516.85 243.22 0.133 1.4002 1.4

FL23 LPC.Fl_O 18.92 138.843 1061.32 126.21 0.0000 2.86 125.656 1032.67 13.85 0.383 1.3769 1.3

FL24 ICduct.Fl_O 18.92 138.566 1061.32 126.21 0.0000 2.87 125.404 1032.67 13.88 0.383 1.3769 1.3

FL25 HPC_axi.Fl_O 18.92 156.159 1100.69 136.09 0.0000 2.59 147.546 1083.79 16.07 0.288 1.3744 1.3

FL26 Bld25.Fl_O 17.63 156.159 1100.69 136.09 0.0000 2.42 141.350 1071.15 11.69 0.383 1.3744 1.3

FL27 HPC_centri.Fl_O 17.63 373.551 1437.05 222.55 0.0000 1.15 349.784 1412.53 6.70 0.313 1.3539 1.3

FL28 Bld3.Fl_O 13.37 373.551 1437.05 222.55 0.0000 0.88 356.894 1419.99 6.00 0.260 1.3539 1.3

FL3 Duct6.Fl_O 13.37 373.551 1437.05 222.55 0.0000 0.88 362.809 1426.12 7.41 0.208 1.3539 1.3

FL4 Burner.Fl_O 13.69 366.080 2849.07 190.55 0.0239 1.29 331.678 2786.62 6.24 0.396 1.2841 1.2

FL42 HPT.Fl_O 17.95 174.554 2217.28 102.80 0.0181 3.12 164.832 2187.48 19.27 0.298 1.3070 1.3

FL43 Duct43.Fl_O 17.95 174.554 2217.33 102.80 0.0181 3.12 157.716 2164.84 15.02 0.397 1.3070 1.3

FL44 LPT.Fl_O 19.24 52.057 1689.29 -25.16 0.0169 9.80 50.796 1679.04 90.09 0.192 1.3289 1.3

FL45 ITduct.Fl_O 19.24 52.057 1689.35 -25.16 0.0169 9.80 47.276 1649.44 48.19 0.383 1.3289 1.3

FL6 PowerT.Fl_O 19.24 15.430 1331.28 -122.38 0.0169 29.35 15.080 1323.39 278.41 0.185 1.3483 1.3

FL7 Duct12.Fl_O 19.24 15.430 1331.35 -122.38 0.0169 29.35 15.080 1323.46 278.42 0.185 1.3483 1.3

FL9 Nozzle.Fl_O 19.24 15.430 1331.41 -122.38 0.0169 29.36 14.696 1314.71 195.08 0.270 1.3483 1.3

TURBOMACHINERY PERFORMANCE DATA Wc PR eff Nc TR efPoly pwr SMN SMW LPC 18.92 9.448 0.8439 10789.426 2.0462 0.8837 -3543.7 16.97 18.19 HPC_axi 2.87 1.127 0.8946 9399.682 1.0371 0.8963 -264.5 19.28 11.03 HPC_cen> 2.42 2.392 0.8581 9230.074 1.3056 0.8733 -2156.3 27.26 26.47 HPT 1.29 2.097 0.8504 251.907 1.1497 0.8311 2420.8 

LPT 3.12 3.353 0.8517 229.131 1.2734 0.8304 3543.8 PowerT 9.80 3.374 0.8014 364.949 1.2691 0.7748 2646.4 

TURBOMACHINERY MAP DATA WcMap PRmap effMap NcMap R/Parm s_WcDes s_PRdes s_effDes s_NcDes LPC 20.15 6.004 0.8515 89.912 1.6735 0.938796 1.6881 0.9911 0.8333

HPC_axi 29.04 1.200 0.8590 0.968 1.8534 0.098842 0.6347 1.0414 0.0001

HPC_cen> 29.04 2.914 0.8516 0.968 2.0536 0.083218 0.7273 1.0077 0.0001

HPT 30.14 5.997 0.9292 100.892 5.9971 0.042746 4.5543 0.9152 0.0176

LPT 149.89 5.814 0.9295 100.014 5.8144 0.020843 2.0460 0.9163 0.0192 PowerT 9.99 3.374 0.8014 8311.469 3.3737 0.980704 1.0000 1.0000 1.0000

===INLETS==== eRam Afs Fram Inlet 1.0000 -----.-- 0.0 BLEEDS - output Wb/Win hscale Pscale W Tt ht 

 C_LPTCharg Bl> 0.0180 1.0000 1.0000 0.3403 1100.69 136.09 156.

====DUCTS==== dPnorm MN Aphy C_LPTUncharg Bl> 0.0502 1.0000 1.0000 0.9494 1100.69 136.09 156.

Duct1 0.0000 0.2541 130.50 C_HPTCharg Bl> 0.0819 1.0000 1.0000 1.4434 1437.05 222.55 373.

ICduct 0.0020 0.3831 13.85 C_HPTUncharg Bl> 0.1595 1.0000 1.0000 2.8110 1437.05 222.55 373.

Duct6 0.0000 0.2603 6.00 

Duct43 0.0000 0.2976 19.27 ITduct 0.0000 0.1924 90.09 

Duct12 0.0000 0.1848 278.41 

===SHAFTS==== Nmech trq in pwr in HP_Shaft 13445.9 945.6 2420.8 IP_Shaft 10789.4 1725.1 3543.8 LP_Shaft 15000.0 926.6 2646.4 

===BURNERS=== TtOut eff dPnorm Wfuel FAR EINOx ppm 

Burner 2849.06 1.0000 0.0200 0.31962 0.02390 

 

===NOZZLES=== PR Cfg CdTh Cv Ath MNth Vact Fg

Nozzle 1.050 1.0000 1.0000 1.0000 305.32 0.270 470.7 281.5 

NASA/CR—2012-217424 84
TABLE H.6.—75 PERCENT DESIGN SPEED CRUISE 

*********************************************************************************************************************************

Date:05/24/11 Time:12:57:35 Model: AHS 2010 Govt turboshaft engine - 75% speed turbine - Cruise converge = 1 CASE: 

Version: NPSS_2.3 Gas Package: Janaf iter/pass/Jacb/Broy= 53/ 75/ 2/50 Run by: tm1862 PC: 

 

 SUMMARY OUTPUT DATA MN alt dTs W Fn Power BSFC Wfuel VTAS OPR T4 T41 T47 Dy

0.510 28000.0 0.00 11.45 -23.4 2351.3 0.3147 736.90 511.85 39.986 2895.8 2663.6 2191.6 

 FLOW STATION DATA W Pt Tt ht FAR Wc Ps Ts Aphy MN gamt g

FL1 InletStart.Fl_O 11.45 5.705 440.66 -24.88 0.0000 27.18 4.776 418.82 104.63 0.510 1.4010 1.4

FL2 Inlet.Fl_O 11.45 5.705 440.66 -24.88 0.0000 27.18 5.155 428.07 130.50 0.383 1.4010 1.4

FL22 Duct1.Fl_O 11.45 5.705 440.66 -24.88 0.0000 27.18 5.559 437.41 243.22 0.193 1.4010 1.4

FL23 LPC.Fl_O 11.45 81.120 1022.86 116.60 0.0000 2.91 73.121 994.03 13.85 0.391 1.3793 1.3

FL24 ICduct.Fl_O 11.45 80.957 1022.86 116.60 0.0000 2.92 72.975 994.03 13.88 0.391 1.3793 1.3

FL25 HPC_axi.Fl_O 11.45 91.306 1061.40 126.23 0.0000 2.64 86.095 1044.44 16.07 0.293 1.3769 1.3

FL26 Bld25.Fl_O 10.67 91.306 1061.40 126.23 0.0000 2.46 82.327 1031.69 11.69 0.390 1.3769 1.3

FL27 HPC_centri.Fl_O 10.67 228.102 1405.52 214.29 0.0000 1.13 214.211 1382.50 6.70 0.306 1.3556 1.3

FL28 Bld3.Fl_O 8.09 228.102 1405.52 214.29 0.0000 0.86 218.356 1389.48 6.00 0.254 1.3556 1.3

FL3 Duct6.Fl_O 8.09 228.102 1405.52 214.29 0.0000 0.86 221.811 1395.23 7.41 0.203 1.3556 1.3

FL4 Burner.Fl_O 8.30 223.540 2895.77 180.69 0.0253 1.29 202.534 2832.65 6.24 0.397 1.2819 1.2

FL42 HPT.Fl_O 10.87 106.607 2246.15 92.10 0.0192 3.12 100.693 2216.24 19.27 0.297 1.3053 1.3

FL43 Duct43.Fl_O 10.87 106.607 2246.20 92.10 0.0192 3.12 96.367 2193.47 15.02 0.396 1.3053 1.3

FL44 LPT.Fl_O 11.65 29.200 1684.67 -44.60 0.0179 10.57 28.373 1672.74 90.09 0.208 1.3284 1.3

FL45 ITduct.Fl_O 11.65 29.200 1684.74 -44.60 0.0179 10.57 26.013 1637.12 48.19 0.420 1.3284 1.3

FL6 PowerT.Fl_O 11.65 5.015 1154.21 -187.21 0.0179 50.93 4.652 1131.49 278.41 0.334 1.3588 1.3

FL7 Duct12.Fl_O 11.65 5.015 1154.28 -187.21 0.0179 50.94 4.652 1131.56 278.42 0.334 1.3588 1.3

FL9 Nozzle.Fl_O 11.65 5.015 1154.35 -187.21 0.0179 50.94 4.776 1139.55 338.39 0.269 1.3588 1.3

TURBOMACHINERY PERFORMANCE DATA 

 Wc PR eff Nc TR efPoly pwr SMN SMW LPC 27.18 14.220 0.8472 11869.667 2.3212 0.8918 -2291.4 17.98 18.02 HPC_axi 2.92 1.128 0.8908 9558.476 1.0377 0.8926 -155.9 19.48 11.70 HPC_cen> 2.46 2.498 0.8585 9383.356 1.3242 0.8744 -1329.0 23.31 22.04 HPT 1.29 2.097 0.8499 249.442 1.1487 0.8301 1485.0 

LPT 3.12 3.651 0.8474 230.845 1.2917 0.8238 2291.3 

PowerT 10.57 5.823 0.8690 196.781 1.4598 0.8397 2351.1 

TURBOMACHINERY MAP DATA 

 WcMap PRmap effMap NcMap R/Parm s_WcDes s_PRdes s_effDes s_NcDes LPC 28.95 8.831 0.8549 98.914 1.8864 0.938796 1.6881 0.9911 0.8333

HPC_axi 29.52 1.201 0.8554 0.984 1.9166 0.098842 0.6347 1.0414 0.0001

HPC_cen> 29.51 3.060 0.8520 0.984 2.0277 0.083218 0.7273 1.0077 0.0001

HPT 30.15 5.995 0.9287 99.905 5.9954 0.042746 4.5543 0.9152 0.0176

LPT 149.63 6.424 0.9247 100.763 6.4237 0.020843 2.0460 0.9163 0.0192 PowerT 10.78 5.823 0.8690 4481.571 5.8226 0.980704 1.0000 1.0000 1.0000

===INLETS==== eRam Afs Fram Inlet 1.0000 104.63 182.1 BLEEDS - output Wb/Win hscale Pscale W Tt ht 

 C_LPTCharg Bl> 0.0180 1.0000 1.0000 0.2059 1061.40 126.23 91.

====DUCTS==== dPnorm MN Aphy C_LPTUncharg Bl> 0.0502 1.0000 1.0000 0.5744 1061.40 126.23 91.

Duct1 0.0000 0.3830 130.50 C_HPTCharg Bl> 0.0819 1.0000 1.0000 0.8734 1405.52 214.29 228.

ICduct 0.0020 0.3905 13.85 C_HPTUncharg Bl> 0.1595 1.0000 1.0000 1.7009 1405.52 214.29 228.

Duct6 0.0000 0.2545 6.00 Duct43 0.0000 0.2972 19.27 ITduct 0.0000 0.2083 90.09 Duct12 0.0000 0.3341 278.41 

===SHAFTS==== Nmech trq in pwr in HP_Shaft 13423.1 581.1 1485.0 IP_Shaft 10940.7 1099.9 2291.3 LP_Shaft 8077.0 1528.8 2351.1 

===BURNERS=== TtOut eff dPnorm Wfuel FAR EINOx ppm 

Burner 2895.77 1.0000 0.0200 0.20469 0.02529 

 

===NOZZLES=== PR Cfg CdTh Cv Ath MNth Vact Fg

Nozzle 1.050 1.0000 1.0000 1.0000 305.32 0.269 438.3 158.7 

NASA/CR—2012-217424 85
TABLE H.7.—85 PERCENT DESIGN SPEED TAKE OFF 

*********************************************************************************************************************************

Date:05/24/11 Time:13:47:18 Model: AHS 2010 Govt turboshaft engine - 65% speed turbine - Takeoff converge = 1 CASE: 

Version: NPSS_2.3 Gas Package: Janaf iter/pass/Jacb/Broy= 7/ 29/ 2/ 4 Run by: tm1862 PC: 

 

 SUMMARY OUTPUT DATA MN alt dTs W Fn Power BSFC Wfuel VTAS OPR T4 T41 T47 Dy

0.000 0.0 45.00 26.67 433.8 7859.4 0.3130 2513.91 0.00 42.293 3748.4 3459.4 2876.7 

 FLOW STATION DATA W Pt Tt ht FAR Wc Ps Ts Aphy MN gamt g

FL1 InletStart.Fl_O 26.67 14.696 563.67 4.62 0.0000 27.80 14.696 563.67 ----.-- 0.000 1.3995 1.3

FL2 Inlet.Fl_O 26.67 14.696 563.67 4.62 0.0000 27.80 13.161 546.19 128.83 0.400 1.3995 1.3

FL22 Duct1.Fl_O 26.67 14.696 563.67 4.62 0.0000 27.80 14.292 559.20 240.10 0.200 1.3995 1.3

FL23 LPC.Fl_O 26.67 213.240 1303.06 187.68 0.0000 2.91 191.489 1266.28 13.66 0.400 1.3617 1.3

FL24 ICduct.Fl_O 26.67 212.813 1303.06 187.68 0.0000 2.92 191.106 1266.28 13.69 0.400 1.3617 1.3

FL25 HPC_axi.Fl_O 26.67 239.578 1349.89 199.81 0.0000 2.64 225.463 1328.41 15.87 0.300 1.3589 1.3

FL26 Bld25.Fl_O 24.89 239.578 1349.89 199.81 0.0000 2.46 215.196 1312.09 11.56 0.400 1.3589 1.3

FL27 HPC_centri.Fl_O 24.89 621.533 1788.60 316.56 0.0000 1.09 585.493 1761.87 6.62 0.300 1.3366 1.3

FL28 Bld3.Fl_O 18.97 621.533 1788.60 316.56 0.0000 0.83 596.224 1769.96 5.96 0.250 1.3366 1.3

FL3 Duct6.Fl_O 18.97 621.533 1788.60 316.56 0.0000 0.83 605.186 1776.63 7.36 0.200 1.3366 1.3

FL4 Burner.Fl_O 19.67 609.102 3748.43 262.28 0.0368 1.28 552.900 3673.49 6.18 0.401 1.2528 1.2

FL42 HPT.Fl_O 25.59 290.574 2946.75 148.62 0.0281 3.08 274.578 2910.05 19.04 0.301 1.2789 1.2

FL43 Duct43.Fl_O 25.59 290.574 2946.75 148.62 0.0281 3.08 262.861 2882.00 14.84 0.401 1.2789 1.2

FL44 LPT.Fl_O 27.37 83.903 2267.24 -26.44 0.0262 10.02 81.746 2253.58 89.36 0.201 1.3001 1.3

FL45 ITduct.Fl_O 27.37 83.903 2267.29 -26.44 0.0262 10.02 75.655 2213.48 47.81 0.402 1.3001 1.3

FL6 PowerT.Fl_O 27.37 15.431 1561.57 -229.40 0.0262 45.23 14.527 1538.35 272.81 0.302 1.3292 1.3

FL7 Duct12.Fl_O 27.37 15.431 1561.63 -229.40 0.0262 45.23 14.527 1538.41 272.82 0.302 1.3292 1.3

FL9 Nozzle.Fl_O 27.37 15.431 1561.69 -229.40 0.0262 45.23 14.696 1542.91 300.63 0.272 1.3292 1.3

TURBOMACHINERY PERFORMANCE DATA 

 Wc PR eff Nc TR efPoly pwr SMN SMW LPC 27.80 14.510 0.8431 12000.000 2.3118 0.8884 -6907.8 20.09 19.67 HPC_axi 2.92 1.126 0.8867 9689.199 1.0359 0.8884 -457.5 19.95 12.51 HPC_cen> 2.46 2.594 0.8577 9519.646 1.3250 0.8737 -4111.6 20.02 18.35 HPT 1.28 2.096 0.8503 250.842 1.1363 0.8162 4569.1 

LPT 3.08 3.463 0.8505 230.450 1.2595 0.8238 6908.0 

PowerT 10.02 5.437 0.9357 315.020 1.4520 0.9200 7859.2 

TURBOMACHINERY MAP DATA 

 WcMap PRmap effMap NcMap R/Parm s_WcDes s_PRdes s_effDes s_NcDes LPC 30.00 8.994 0.8509 100.000 2.0028 0.926742 1.6901 0.9909 0.8333

HPC_axi 29.94 1.200 0.8515 0.998 1.9904 0.097488 0.6285 1.0413 0.0001

HPC_cen> 29.93 3.192 0.8514 0.998 1.9942 0.082277 0.7273 1.0074 0.0001 HPT 30.15 5.976 0.9291 100.172 5.9760 0.042317 4.5393 0.9152 0.0175

LPT 149.76 5.999 0.9281 100.389 5.9991 0.020596 2.0295 0.9163 0.0191 PowerT 10.44 5.437 0.9357 7174.453 5.4374 0.959975 1.0000 1.0000 1.0000

===INLETS==== eRam Afs Fram Inlet 1.0000 -----.-- 0.0 BLEEDS - output Wb/Win hscale Pscale W Tt ht 

 C_LPTCharg Bl> 0.0175 1.0000 1.0000 0.4665 1349.89 199.81 239.

====DUCTS==== dPnorm MN Aphy C_LPTUncharg Bl> 0.0493 1.0000 1.0000 1.3145 1349.89 199.81 239.

Duct1 0.0000 0.4001 128.83 C_HPTCharg Bl> 0.0805 1.0000 1.0000 2.0039 1788.60 316.56 621.

ICduct 0.0020 0.4001 13.66 C_HPTUncharg Bl> 0.1572 1.0000 1.0000 3.9136 1788.60 316.56 621.

Duct6 0.0000 0.2500 5.96 Duct43 0.0000 0.3006 19.04 ITduct 0.0000 0.2008 89.36 Duct12 0.0000 0.3024 272.81 

===SHAFTS==== Nmech trq in pwr in HP_Shaft 15357.7 1562.6 4569.1 IP_Shaft 12509.7 2900.2 6908.0 LP_Shaft 15000.0 2751.8 7859.2 

===BURNERS=== TtOut eff dPnorm Wfuel FAR EINOx ppm Burner 3748.43 1.0000 0.0200 0.69831 0.03681 

 

===NOZZLES=== PR Cfg CdTh Cv Ath MNth Vact Fg

Nozzle 1.050 1.0000 1.0000 1.0000 299.10 0.272 510.0 433.8 

NASA/CR—2012-217424 86
TABLE H.8.—85 PERCENT DESIGN SPEED CLIMB 

*********************************************************************************************************************************

Date:05/24/11 Time:13:47:19 Model: AHS 2010 Govt turboshaft engine - 65% speed turbine - Climb converge = 1 CASE: 

Version: NPSS_2.3 Gas Package: Janaf iter/pass/Jacb/Broy= 19/ 30/ 1/17 Run by: tm1862 PC: 

 

 SUMMARY OUTPUT DATA MN alt dTs W Fn Power BSFC Wfuel VTAS OPR T4 T41 T47 Dy

0.000 0.0 0.00 18.51 271.5 2646.3 0.3984 1097.54 0.00 25.069 2806.6 2594.1 2139.6 

 FLOW STATION DATA W Pt Tt ht FAR Wc Ps Ts Aphy MN gamt g

FL1 InletStart.Fl_O 18.51 14.696 518.67 -6.18 0.0000 18.51 14.696 518.67 ----.-- 0.000 1.4002 1.4

FL2 Inlet.Fl_O 18.51 14.696 518.67 -6.18 0.0000 18.51 14.063 512.18 128.83 0.252 1.4002 1.4

FL22 Duct1.Fl_O 18.51 14.696 518.67 -6.18 0.0000 18.51 14.520 516.89 240.10 0.131 1.4002 1.4

FL23 LPC.Fl_O 18.51 138.096 1060.67 126.05 0.0000 2.82 125.070 1032.24 13.66 0.382 1.3769 1.3

FL24 ICduct.Fl_O 18.51 137.820 1060.67 126.05 0.0000 2.82 124.820 1032.24 13.69 0.382 1.3769 1.3

FL25 HPC_axi.Fl_O 18.51 155.129 1099.58 135.82 0.0000 2.55 146.627 1082.81 15.87 0.287 1.3745 1.3

FL26 Bld25.Fl_O 17.27 155.129 1099.58 135.82 0.0000 2.38 140.516 1070.28 11.56 0.382 1.3745 1.3

FL27 HPC_centri.Fl_O 17.27 368.418 1432.65 221.40 0.0000 1.15 344.817 1408.03 6.62 0.314 1.3541 1.3

FL28 Bld3.Fl_O 13.17 368.418 1432.65 221.40 0.0000 0.87 351.880 1415.53 5.96 0.261 1.3541 1.3

FL3 Duct6.Fl_O 13.17 368.418 1432.65 221.40 0.0000 0.87 357.754 1421.68 7.36 0.209 1.3541 1.3

FL4 Burner.Fl_O 13.47 361.050 2806.62 190.42 0.0232 1.28 327.083 2744.81 6.18 0.396 1.2857 1.2

FL42 HPT.Fl_O 17.58 171.977 2189.18 103.28 0.0177 3.09 162.404 2159.73 19.04 0.297 1.3082 1.3

FL43 Duct43.Fl_O 17.58 171.977 2189.23 103.28 0.0177 3.09 155.399 2137.29 14.84 0.396 1.3082 1.3

FL44 LPT.Fl_O 18.81 50.451 1663.08 -24.67 0.0165 9.81 49.206 1652.78 89.36 0.194 1.3304 1.3

FL45 ITduct.Fl_O 18.81 50.451 1663.15 -24.67 0.0165 9.81 45.721 1622.87 47.81 0.387 1.3304 1.3

FL6 PowerT.Fl_O 18.81 15.430 1295.39 -124.09 0.0165 28.32 15.091 1287.93 272.81 0.182 1.3508 1.3

FL7 Duct12.Fl_O 18.81 15.430 1295.46 -124.09 0.0165 28.32 15.091 1287.99 272.82 0.182 1.3507 1.3

FL9 Nozzle.Fl_O 18.81 15.430 1295.52 -124.09 0.0165 28.32 14.696 1279.21 188.20 0.269 1.3507 1.3

TURBOMACHINERY PERFORMANCE DATA Wc PR eff Nc TR efPoly pwr SMN SMW LPC 18.51 9.397 0.8422 10765.075 2.0450 0.8823 -3462.5 16.53 17.69 HPC_axi 2.82 1.126 0.8952 9369.305 1.0367 0.8968 -255.8 19.23 10.91 HPC_cen> 2.38 2.375 0.8580 9202.035 1.3029 0.8731 -2091.3 27.88 27.19 HPT 1.28 2.099 0.8505 252.907 1.1507 0.8317 2347.0 

LPT 3.09 3.409 0.8513 230.076 1.2783 0.8295 3462.6 

PowerT 9.81 3.270 0.8516 367.812 1.2840 0.8307 2646.3 

TURBOMACHINERY MAP DATA 

 WcMap PRmap effMap NcMap R/Parm s_WcDes s_PRdes s_effDes s_NcDes LPC 19.97 5.968 0.8500 89.709 1.6619 0.926742 1.6901 0.9909 0.8333

HPC_axi 28.95 1.200 0.8597 0.965 1.8417 0.097488 0.6285 1.0413 0.0001 HPC_cen> 28.95 2.891 0.8517 0.965 2.0555 0.082277 0.7273 1.0074 0.0001

HPT 30.14 5.991 0.9293 100.996 5.9905 0.042317 4.5393 0.9152 0.0175

LPT 149.82 5.889 0.9290 100.226 5.8886 0.020596 2.0295 0.9163 0.0191

PowerT 10.22 3.270 0.8516 8376.780 3.2697 0.959975 1.0000 1.0000 1.0000

===INLETS==== eRam Afs Fram Inlet 1.0000 -----.-- 0.0 BLEEDS - output Wb/Win hscale Pscale W Tt ht 

 C_LPTCharg Bl> 0.0175 1.0000 1.0000 0.3237 1099.58 135.82 155.

====DUCTS==== dPnorm MN Aphy C_LPTUncharg Bl> 0.0493 1.0000 1.0000 0.9122 1099.58 135.82 155.

Duct1 0.0000 0.2516 128.83 C_HPTCharg Bl> 0.0805 1.0000 1.0000 1.3906 1432.65 221.40 368.

ICduct 0.0020 0.3817 13.66 C_HPTUncharg Bl> 0.1572 1.0000 1.0000 2.7158 1432.65 221.40 368.

Duct6 0.0000 0.2611 5.96 Duct43 0.0000 0.2973 19.04 ITduct 0.0000 0.1942 89.36 Duct12 0.0000 0.1817 272.81 

===SHAFTS==== Nmech trq in pwr in HP_Shaft 13398.4 920.0 2347.0 

IP_Shaft 10765.1 1689.3 3462.6 LP_Shaft 15000.0 926.6 2646.3 

 

===BURNERS=== TtOut eff dPnorm Wfuel FAR EINOx ppm 

Burner 2806.61 1.0000 0.0200 0.30487 0.02316 

 

===NOZZLES=== PR Cfg CdTh Cv Ath MNth Vact Fg

Nozzle 1.050 1.0000 1.0000 1.0000 299.10 0.269 464.2 271.5 

 

NASA/CR—2012-217424 87
TABLE H.9.—85 PERCENT DESIGN SPEED CRUISE *********************************************************************************************************************************

Date:05/24/11 Time:13:47:20 Model: AHS 2010 Govt turboshaft engine - 65% speed turbine - Cruise converge = 1 CASE: 

Version: NPSS_2.3 Gas Package: Janaf iter/pass/Jacb/Broy= 41/ 74/ 3/37 Run by: tm1862 PC: 

 

 SUMMARY OUTPUT DATA MN alt dTs W Fn Power BSFC Wfuel VTAS OPR T4 T41 T47 Dy

0.510 28000.0 0.00 11.38 -21.3 2351.0 0.3207 751.16 511.85 40.624 2927.6 2695.8 2218.6 

 FLOW STATION DATA W Pt Tt ht FAR Wc Ps Ts Aphy MN gamt g

FL1 InletStart.Fl_O 11.38 5.705 440.66 -24.88 0.0000 27.01 4.776 418.82 103.97 0.510 1.4010 1.4

FL2 Inlet.Fl_O 11.38 5.705 440.66 -24.88 0.0000 27.01 5.147 427.87 128.83 0.386 1.4010 1.4

FL22 Duct1.Fl_O 11.38 5.705 440.66 -24.88 0.0000 27.01 5.557 437.36 240.10 0.194 1.4010 1.4

FL23 LPC.Fl_O 11.38 81.168 1023.71 116.81 0.0000 2.89 73.031 994.35 13.66 0.394 1.3793 1.3

FL24 ICduct.Fl_O 11.38 81.005 1023.71 116.81 0.0000 2.90 72.885 994.35 13.69 0.394 1.3793 1.3

FL25 HPC_axi.Fl_O 11.38 91.249 1061.96 126.37 0.0000 2.62 85.957 1044.72 15.87 0.296 1.3769 1.3

FL26 Bld25.Fl_O 10.62 91.249 1061.96 126.37 0.0000 2.45 82.122 1031.71 11.56 0.394 1.3769 1.3

FL27 HPC_centri.Fl_O 10.62 231.744 1413.48 216.37 0.0000 1.11 217.828 1390.69 6.62 0.303 1.3552 1.3

FL28 Bld3.Fl_O 8.09 231.744 1413.48 216.37 0.0000 0.85 221.977 1397.60 5.96 0.253 1.3552 1.3

FL3 Duct6.Fl_O 8.09 231.744 1413.48 216.37 0.0000 0.85 225.438 1403.30 7.36 0.202 1.3552 1.3

FL4 Burner.Fl_O 8.30 227.109 2927.61 182.05 0.0258 1.28 205.767 2863.94 6.18 0.397 1.2807 1.2

FL42 HPT.Fl_O 10.82 107.897 2273.17 91.74 0.0197 3.09 101.892 2242.85 19.04 0.298 1.3041 1.3

FL43 Duct43.Fl_O 10.82 107.897 2273.22 91.74 0.0197 3.09 97.496 2219.80 14.84 0.397 1.3041 1.3

FL44 LPT.Fl_O 11.58 30.139 1712.78 -45.12 0.0183 10.26 29.322 1701.22 89.36 0.204 1.3268 1.3

FL45 ITduct.Fl_O 11.58 30.139 1712.83 -45.12 0.0183 10.26 27.005 1667.01 47.81 0.409 1.3268 1.3

FL6 PowerT.Fl_O 11.58 5.015 1181.37 -188.56 0.0183 51.23 4.630 1156.80 272.81 0.345 1.3567 1.3

FL7 Duct12.Fl_O 11.58 5.015 1181.43 -188.56 0.0183 51.23 4.630 1156.86 272.82 0.345 1.3567 1.3

FL9 Nozzle.Fl_O 11.58 5.015 1181.50 -188.56 0.0183 51.23 4.776 1166.42 340.30 0.269 1.3567 1.3

TURBOMACHINERY PERFORMANCE DATA 

 Wc PR eff Nc TR efPoly pwr SMN SMW LPC 27.01 14.229 0.8463 11892.165 2.3231 0.8911 -2280.3 18.83 18.78 HPC_axi 2.90 1.126 0.8888 9626.512 1.0374 0.8906 -153.8 19.67 12.08 HPC_cen> 2.45 2.540 0.8575 9451.543 1.3310 0.8737 -1351.8 22.03 20.55 HPT 1.28 2.105 0.8497 249.951 1.1489 0.8294 1505.6 

LPT 3.09 3.580 0.8481 229.904 1.2862 0.8251 2280.3 

PowerT 10.26 6.010 0.8471 195.161 1.4500 0.8136 2351.0 

TURBOMACHINERY MAP DATA WcMap PRmap effMap NcMap R/Parm s_WcDes s_PRdes s_effDes s_NcDes LPC 29.15 8.827 0.8540 99.101 1.9218 0.926742 1.6901 0.9909 0.8333

HPC_axi 29.74 1.201 0.8535 0.992 1.9515 0.097488 0.6285 1.0413 0.0001

HPC_cen> 29.74 3.117 0.8512 0.991 2.0221 0.082277 0.7273 1.0074 0.0001

HPT 30.15 6.015 0.9284 99.816 6.0153 0.042317 4.5393 0.9152 0.0175 LPT 149.85 6.236 0.9256 100.151 6.2361 0.020596 2.0295 0.9163 0.0191

PowerT 10.69 6.010 0.8471 4444.712 6.0097 0.959975 1.0000 1.0000 1.0000

===INLETS==== eRam Afs Fram Inlet 1.0000 103.97 181.0 BLEEDS - output Wb/Win hscale Pscale W Tt ht 

 C_LPTCharg Bl> 0.0175 1.0000 1.0000 0.1990 1061.96 126.37 91.

====DUCTS==== dPnorm MN Aphy C_LPTUncharg Bl> 0.0493 1.0000 1.0000 0.5606 1061.96 126.37 91.

Duct1 0.0000 0.3861 128.83 C_HPTCharg Bl> 0.0805 1.0000 1.0000 0.8547 1413.48 216.37 231.

ICduct 0.0020 0.3940 13.66 C_HPTUncharg Bl> 0.1572 1.0000 1.0000 1.6692 1413.48 216.37 231.

Duct6 0.0000 0.2527 5.96 Duct43 0.0000 0.2979 19.04 ITduct 0.0000 0.2038 89.36 Duct12 0.0000 0.3446 272.81 

===SHAFTS==== Nmech trq in pwr in HP_Shaft 13524.2 584.7 1505.6 IP_Shaft 10961.4 1092.6 2280.3 LP_Shaft 8077.0 1528.8 2351.0 

===BURNERS=== TtOut eff dPnorm Wfuel FAR EINOx ppm 

Burner 2927.61 1.0000 0.0200 0.20866 0.02579 

===NOZZLES=== PR Cfg CdTh Cv Ath MNth Vact Fg Nozzle 1.050 1.0000 1.0000 1.0000 299.10 0.269 443.6 159.7 

NASA/CR—2012-217424 88
NASA/CR—2012-217424 89

References

1. Snyder, C. A. and Thurman, D. R., “Gas Turbine Characteristics for a Large Civil Tilt-Rotor 

(LCTR),” NASA/TM—2010-216089, February 2010. 

2. D’Angelo, M., “Wide Speed Range Turboshaft Study,” NASA CR-198380, August 1995. 

3. Welch, G.E., “Assessment of Aerodynamic Challenges of a Variable-Speed Power Turbine for Large 

Civil Tilt-Rotor Application,” Proc. American Helicopter Society 66th Annual Forum, Phoenix, AZ, 

May 11-13, 2010. 

4. Kacker, S. C., and Okapuu, U., “A Mean Line Prediction Method for Axial Flow Turbine Efficiency,” 

ASME 81-GT-58, 1981. 

5. Moustapha, S.H., Kacker, S. C., and Tremblay, B., “Improved Incidence Losses Prediction Method 

for Turbine Airfoils,” ASME 89-GT284, 1989. 

6. Smith, S. F., “A Simple Correlation of Turbine Efficiency,” J. Royal Aero. Soc., 69, 1965, p. 467–

470. 
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1. REPORT DATE (DD-MM-YYYY)

01-02-2012 

2. REPORT TYPE

Final Contractor Report 

3. DATES COVERED (From - To)

October 2010 to March 2011 

4. TITLE AND SUBTITLE

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

5a. CONTRACT NUMBER

NNC10BA15B 

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Suchezky, Mark; Cruzen, G., Scott 

5d. PROJECT NUMBER

5e. TASK NUMBER

NNC10TA76T 

5f. WORK UNIT NUMBER

WBS 877868.02.07.03.01.02.01 

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

Williams International Co. LLC 

2280 E. West Maple Road 

Walled Lake, Michigan 48390-0200 

8. PERFORMING ORGANIZATION

 REPORT NUMBER

E-18111 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

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 ACRONYM(S)

NASA 

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 REPORT NUMBER

NASA/CR-2012-217424 

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Unclassified-Unlimited 

Subject Categories: 01, 02, 03, and 07 

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

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

Turbine design concepts were studied for application to a large civil tiltrotor transport aircraft. The concepts addressed the need for high 

turbine efficiency across the broad 2:1 turbine operating speed range representative of the notional mission for the aircraft. The study 

focused on tailoring basic turbine aerodynamic design design parameters to avoid the need for complex, heavy, and expensive variable 

geometry features. The results of the study showed that good turbine performance can be achieved across the design speed range if the 

design focuses on tailoring the aerodynamics for good tolerance to large swings in incidence, as opposed to optimizing for best performance 

at the long range cruise design point. A rig design configuration and program plan are suggested for a dedicated experiment to validate the 

proposed approach. 

15. SUBJECT TERMS

Variable-speed power turbine; Turbine aerodynamics; Low pressure turbines; turbomachinery design; Rotordynamics; Turbine 

performance; Large civil tilt-rotor 

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 ABSTRACT

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100 

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