Gerard E. Welch

Glenn Research Center, Cleveland, Ohio

Computational Study of the Impact of Unsteadiness 

on the Aerodynamic Performance of a VariableSpeed Power Turbine

NASA/TM—2012-217425

April 2012

AIAA–2012–0937
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Gerard E. Welch

Glenn Research Center, Cleveland, Ohio

Computational Study of the Impact of Unsteadiness 

on the Aerodynamic Performance of a VariableSpeed Power Turbine

NASA/TM—2012-217425

April 2012

AIAA–2012–0937

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

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

This report contains preliminary fi ndings, 

subject to revision as analysis proceeds.

Acknowledgments

The author thanks Dr. Rodrick V. Chima (NASA) for expert assistance with his RANS tools, Michael Ni and Ron-Ho Ni

of AeroDynamic Solutions, Inc. for technical assistance with the ADS tools, and Dr. John P. Clark (AFRL) for facilitating

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

NASA Fundamental Aeronautics Program (FAP), Subsonic Rotary Wing (SRW) Project.
NASA/TM—2012-217425 1 

Computational Study of the Impact of Unsteadiness 

on the Aerodynamic Performance of a 

Variable-Speed Power Turbine 

Gerard E. Welch 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44130 

Abstract 

The design-point and off-design performance of an embedded 1.5-stage portion of a variable-speed 

power turbine (VSPT) was assessed using Reynolds-Averaged Navier-Stokes (RANS) analyses with 

mixing-planes and sector-periodic, unsteady RANS analyses. The VSPT provides one means by which to 

effect the nearly 50 percent main-rotor speed change required for the NASA Large Civil Tilt-Rotor 

(LCTR) application. The change in VSPT shaft-speed during the LCTR mission results in blade-row 

incidence angle changes of as high as 55. Negative incidence levels of this magnitude at takeoff 

operation give rise to a vortical flow structure in the pressure-side cove of a high-turn rotor that transports 

low-momentum flow toward the casing endwall. The intent of the effort was to assess the impact of 

unsteadiness of blade-row interaction on the time-mean flow and, specifically, to identify potential 

departure from the predicted trend of efficiency with shaft-speed change of meanline and 3-D 

RANS/mixing-plane analyses used for design. 

Nomenclature 

AN2 product of annulus area and shaft-speed squared 

cx axial chord 

h0, h total and static specific enthalpy 

i, iopt incidence, incidence at minimum loss 

N, N*

 power-turbine shaft speed (rpm), N/N100%, fraction of 100% (takeoff) speed 

PRTT overall total-pressure ratio 

p0, p total and static pressure 

Re, Recx Reynolds number, Re based on axial chord 

s blade pitch, or specific entropy 

T0 total temperature 

TRTT overall total-temperature ratio 

Tu turbulence intensity 

u (ux, u, ur), absolute velocity 

U rotor speed at pitchline 

Y 

0 1 2

0 1 0 2

p p

p p

,

, ,



 loss coefficient 

 absolute and relative flow angles 

TT adiabatic efficiency (total-to-total) 

 density 

ψ h0/U2

, work factor 

φ ux/U, flow coefficient 
NASA/TM—2012-217425 2 

Subscripts: 

c corrected to standard day 

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

4.5 power turbine inlet 

1.0 Introduction 

A key challenge of the NASA Large Civil Tilt-Rotor (LCTR, see Fig. 1) mission is a required 

variation of main (prop) rotor tip-speed from 650 ft/s at takeoff to 350 ft/s at cruise (Ref. 1). The speed 

variation (54%  N/N100%  100%), needed to manage main rotor prop efficiency at cruise flight speeds, 

can be accomplished by utilizing either a two-gear-ratio transmission (Ref. 2) (shifting) with a fixedspeed power-turbine or a variable-speed power turbine (Refs. 3 and 4) (VSPT) with a non-shifting 

transmission of fixed gear-ratio. A research effort is underway at NASA to address key aerodynamic 

(Refs. 4 to 7) and rotordynamic (Refs. 7 and 8) challenges of the VSPT approach. Progress related to 

prediction of the aerodynamic performance of the VSPT as shaft-speed is varied (54%  N/N100%  100%) 

is reported herein. 

1.1 Background and Motivation 

Power turbines of turboshaft engines for helicopter applications are typically controlled to a fixed 

operating speed. While limited speed variation is accommodated in some rotorcraft applications—for 

example, the AE1107 engine of the V-22 tilt-rotor operates in the range 82%  N*  100% (Ref. 9)—the 

nearly 50 percent speed power-turbine shaft-speed variation of the NASA LCTR application constitutes 

an significant departure from the nominal operation of a rotorcraft power turbine. In such operation, 

incidence angle swings with speed change can be as high as 55 in the VSPT blade and vane rows. 

VSPT conceptual and 3-D aero-designs for the LCTR application conducted recently highlight the 

need to optimize the turbine design for the required incidence tolerance while achieving cruise efficiency 

for acceptable fuel burn (Refs. 5 to 9). In the study by NASA (Ref. 5) and Rolls-Royce North American 

Technologies (Ref. 7), the design-intent air angles were set near the cruise operating VSPT shaft speed 

(N*

 = 54%) leading to the high (40 to 55) negative incidence at takeoff (N* = 100%). In the studies of 

General Electric (Ref. 3) and Williams International (Ref. 6), the optimum design speed was argued to be 

higher (e.g., N*

 = 70%) than the cruise speed based on a sensitivity study of mission fuel burn versus 

VSPT design speed. In all cases, the turbines had to operate with acceptable efficiency over an extensive 

(40 to 55) incidence angle range between takeoff (high negative incidence operation) and cruise (less 

than 5 to 10 positive incidence). 

Figure 1.—NASA Large Civil Tilt-Rotor notional vehicle (Ref. 1). 
NASA/TM—2012-217425 3 

Figure 2.—(a) Loss bucket for high-lift L1M rotor blading (Ref. 10) showing cruise (design air angles) and takeoff 

(–50 incidence) operation (Ref. 4); and, (b) vortical flow structure of pressure-side cove separation in Rotor 2 of 

embedded 1.5-stage of LCTR VSPT at takeoff (Ref. 5). 

A computed loss bucket for a 2-D section of representative modern, highly loaded, LPT rotor blading 

(L1M blading) of Clark (Ref. 10) is shown in Figure 2(a). The 2-D RANS computation (Ref. 4) was 

conducted using the RVCQ3D (Ref. 11) code with the low-Re turbulence model (Ref. 12). The 

range of the useful incidence (i.e., acceptable loss level) of the highly loaded blade was found to be about 

70 and was typical of LPT blading analyzed in this effort for which the loss buckets collapse well on the 

canonical off-design loss correlation of Ainley-Mathieson (Ref. 13) (Ref. 4). Note that at negative 55

incidence, typical of the VSPT incidence levels at LCTR takeoff, the loss levels (Fig. 2(a)) are nearly 

equal to those of the design air angles (e.g., 0 incidence) representative of cruise operation. Computed 

contours of Mach number for 2-D flow fields for cruise (0 incidence) and takeoff (–50 incidence) were 

shown in the insets. A pressure-side cove separation was admitted at the high negative incidence levels of 

takeoff. Because the separation was closed, and the blade-row was largely unloaded at this condition, the 

2-D loss levels associated with this condition were found acceptable. The acceptable loss level at high 

negative incidence was reflected in the efficiency versus speed trends reported earlier (Refs. 3 to 6)

whereby the VSPT efficiency was predicted to be 1.5 to 2 points higher at the unloaded off-design takeoff 

point (N*

 = 100%) than at the cruise point. There is thus strong impetus for the VSPT designer to set the 

turbine design speed close to the cruise shaft-speed (N*

 = 54%), and there concentrate aerodynamic 

design effort on maximizing the VSPT cruise efficiency, while accepting the off-design efficiency levels 

at the relatively shorter duration takeoff/hover mission points. 

The variation of VSPT efficiency with shaft speed was verified at the 3-D RANS mixing-plane level 

in an earlier study of an embedded 1.5-stages (R1/S2/R2) (Ref. 5). The efficiency-speed trend of 

RANS/mixing-plane and meanline efficiency levels were found to be the same (Fig. 3). Performance level 

differences were explained in terms of the 3-D flow effects at design and off-design which are not 

captured in the meanline loss correlations. In particular, it was noted that the apparent 2-D pressure-side 

cove separation (–50 in Fig. 2(a)), if admitted in a rotor, was in fact a portion of a large vortical, tornadolike, structure (Rotor 2 in Fig. 2(b)) that transports low-momentum fluid outward in radius toward the 

outer-span regions along the cove region. This structure was induced by the radial acceleration fields in 

the rotors acting on the low-momentum cove separation. 

a. Loss as a function of incidence.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-80 -60 -40 -20 0 20 40

Profile loss coefficient

i - iopt

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

L1M, Re_cx,2 = 62k, Tu = 3%

a. 2-D mid-span loss bucket. b. Vortical flow structure of pressure-side cove 

separation admitted in VSPT Rotor 2 at N* = 100% 

(takeoff operation).

R1

R2

S2 Takeoff Cruise

+

-
NASA/TM—2012-217425 4 

Figure 3.—Variation of embedded 1.5 stage (R1/S2/R2) 

adiabatic efficiency with speed from cruise (54% N*

) to take-off 

(100% N*

), showing comparison between results from 3-D 

mixing-planes analyses with low-Re  and fully turbulent 

Baldwin-Lomax turbulence models with design-intent meanline 

design/analysis. 

The present effort extends the computational analysis from the 3-D RANS/mixing-plane level 

(Refs. 5 and 6) to 3-D unsteady RANS (URANS) in an effort to assess the influence of unsteadiness 

associated with blade-row interaction on the design- and off-design aerodynamic performance of a VSPT 

for the NASA LCTR. The extension is motivated by the potential impact on performance of flow physics 

not accounted for in mixing-plane analyses. Firstly, a particular concern in the VSPT takeoff conditions is 

additional entropy production associated with the unsteady forcing of the vortical structure (Fig. 2(b)) in 

the pressure-side cove, which might degrade VSPT efficiency levels and modify the efficiency-speed 

trend relative to the meanline and steady 3-D RANS/mixing-plane used in the turbine design process. The 

unsteady computations will simulate, to some degree of accuracy, the influence of blade-row interaction 

associated with potential fields and wakes (and pitchwise nonuniformity) passing between multistage 

blade rows. In regions of vortical flow—for example, in the pressure-side cove region of rotors at high 

negative incidence (Fig. 2(b))—periodic unsteadiness associated with blade row interaction will lead to 

deterministic stress (Ref. 14) and heat flux fields that redistribute momentum and energy in the time-mean 

flow field. Secondly, the unsteady computations eliminate the need for the mixing-plane between blade 

rows, and accommodate transport of streamwise vorticity to/from blade rows, thereby admitting proper 

influence of vorticity associated with secondary flow field of one blade row on the instantaneous and 

time-mean flow fields of downstream blade rows (Ref. 14). Thirdly, the unsteady computations simulate 

spatiotemporal loss production associated with wake transport and stretching (Ref. 15) to some degree of 

accuracy (grid dependent). Lastly, Haselbach et al. (Ref. 16) and others have highlighted the impact of 

vortical unsteadiness in wakes from upstream blade rows on the design-point loss levels of transitional, 

low-Re LPT blade rows. The interaction of a passing wake with a transitional LPT boundary-layer at lowRe conditions has been studied in great detail (Ref. 17). At a given aerodynamic loading level, the loss 

levels in steady flows were found to be substantially (e.g., 20 percent) higher than when subjected to 

wake passing; further, the loss increase with Reynolds number lapse (sensitivity) was mitigated to some 

degree (Ref. 16). The impact of wake vorticity on the transitional blade and endwall flows was beyond 

the scope of the low-Re  turbulence models used in the present study work (Ref. 18). 

0.87

0.88

0.89

0.9

0.91

0.92

0.93

0.94

0.95

0 0.2 0.4 0.6 0.8 1 1.2

Adiabatic efficiency of R1/S2/R2

N / N100%

CFD B-L

CFD k-w

Meanline

Cruise

Take-off
NASA/TM—2012-217425 5 

1.2 Approach 

As in earlier mixing-plane analyses (Ref. 5), an embedded 1.5-stage (R1/S2/R2) of a 4-stage VSPT 

(Fig. 4) for the LCTR application was considered in the present study. The intent of the 3-D design was to 

create a representative embedded 1.5 stage (R1/S2/R2) with design-point stage efficiencies consistent 

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

performance of a stator (R1/S2), and vice-versa (S2/R2). Stator 1 (S1) was not included in the simulations 

because the S1 inlet and exit flow angles would not change appreciably with speed change; therefore, the 

S1 design was assumed achievable, and the S1 exit conditions at design and off-design exit flow 

conditions were set to those of the meanline analyses. For the case of the URANS simulations herein, the 

impact of the unsteadiness and streamwise vorticity of the S1 secondary flow field transported from S1 to 

R1, and subsequently through the 1.5-stage, was evidently neglected. Stage 2 stator (S2) was the first 

embedded blade row of the simulation, and R2 was the first rotor with forcing from an upstream stage 

(R1/S2). The impact the influence of the downstream stator row, S3, on the R2 flow field was neglected 

in the present study. 

The assessment of the impact of unsteadiness due to blade-row interaction documented in this paper 

relied on results from RANS/mixing-plane and sector-periodic URANS simulations conducted using a 

commercial code (described below); therefore, a portion of the effort was first concentrated on verifying 

that the mixing-plane solutions obtain the commercial software were in qualitative agreement—

particularly with respect to flow field structures and the trend of efficiency with speed change—with 

results from a validated in-house NASA code used in the earlier VSPT mixing-plane analysis (Ref. 5) 

before embarking on the URANS analyses. 

The paper is organized in the following manner. The VSPT operating requirements and conceptual 

and 3-D blade design approaches are reviewed. Results from a NASA in-house RANS/mixing-plane 

solver are then compared to steady and time-averaged, average-passage results from a commercially 

available code with both RANS/mixing-plane and sector-periodic URANS capabilities. Conclusions 

regarding the impact of unsteadiness on VSPT efficiency and the trend of efficiency with shaft-speed 

change are then provided. 

Figure 4.—Four-stage VSPT flow path from 

meanline design code, showing embedded 

1.5-stage of computational analysis (Ref. 5). 

5 10

5

10

R1/S2/R2

X, in.

r, in.

R1 S1

S2

R2

S3

R3 S4 R4

0

0
NASA/TM—2012-217425 6 

2.0 VSPT Requirements and Aerodynamic Design 

2.1 Turbine Requirements 

The NASA LCTR notional vehicle (Fig. 1) is envisaged to be a 90 passenger aircraft with 100,000 lbf

takeoff gross weight. There are two engines per nacelle (and main rotor), currently conceived to be of the 

7,500 shp-class level. Two key LCTR mission points are 2,000 ft takeoff/hover and 28,000 ft, Mach 0.5 

cruise. At takeoff, the main rotor and VSPT operate at 100% N*

, while at cruise the rotors and VSPT are 

slowed to 54% N*

. Specific VSPT requirements of an LCTR engine cycle study (Ref. 19) were provided 

in Table 1. 

2.2 Conceptual Design 

The conceptual and 3-D aero-design approach for a 4-stage VPST of the LCTR application was 

described in detail earlier (Ref. 5). The design air-angles were set at the cruise operating condition 

(54 percent N*

) where Reynolds numbers were lowest and work factors (h0/U2) were highest. The VSPT 

flow path from the free-vortex meanline1

 analysis was provided in Figure 4. Key turbine parameters, 

including blade row incidence levels at off-design, were provided in Table 2, and the design flow angles, 

some (see R2) with turning as high as 110, were provided in Table 3. 

TABLE 1.—VSPT REQUIREMENTS AT KEY FLIGHT 

POINTS OF LCTR MISSION (REF. 5) 

Flight point 

Altitude 

VSPT shaft-speed (N/N100%)

Main-rotor tip-speed 

Takeoff 

2k-ft 

100% 

650 ft/s 

Cruise 

28 k-ft 

54% 

350 ft/s 

Power, SHP 4593 2328 

Mass flow rate, lbm/s 22.03 12.22 

Specific power (BTU/lbm) 147 135 

Inlet temperature (T0,4.5), R 2204 1812 

Inlet pressure (p0,4.5), psia 58.0 26.76 

PRTT 4.04 5.34 

Corrected flow, lbm/s 11.51 12.54 

Corrected speed (Nc/Nc,100%), % 102.3 60.8 

Aft-stage unit-Re (in.–1)* 50,000/in. 30,000/in. a

Based on static conditions at last stage rotor with exit 

relative Mach number of 0.7. 

TABLE 2.—FOUR-STAGE DESIGN FOR LCTR VSPT 

REQUIREMENTS OF TABLE 1 (REF. 5) 

 Takeoff Cruise 

Speed (N/N100%) 100% 54% 

VSPT efficiency 0.9294 0.9154 

PRTT 4.04 5.34 

N, rpm 15,000 8,100 

Average ψ 0.75 2.36 

Average φ 0.493 0.957 

Average h0, BTU/lbm 41.8 39.1 

Max. AN2

, rpm2∙in2 47.7109

 13.9109

Stage efficiency 

(Stg 1, 2, 3, 4) 

0.9371, 0.9219, 

0.9229, 0.9068 

0.9105, 0.8887, 

0.9050, 0.9251 

Rotor incidence, deg. 

(R1, R2, R3, R4) 

–38, –42, 

–50, –54 0 

Stator incidence, deg 

(S2, S3, S4, EGV) 

–34, –40, 

–48, –35 0 

 

1

The Turbine Design and Analysis System (Ref. 10) of Dr. J.P. Clark, AFRL, includes design and offdesign meanline codes and blade profile generator of F. Huber, Florida Turbine Technologies, Inc. 
NASA/TM—2012-217425 7 

TABLE 3.—DESIGN-POINT AIR ANGLES OF 

4-STAGE VSPT (AN2

 = 47.7 109 rpm2·in.2) (REF. 5) 

Stage Stator vane Rotor blade 

1 2 Turn 1 2 Turn 

1 0 62 62 42 –56 99 

2 –39 64 104 50 –60 110 

3 –42 62 104 42 –56 98 

4 –31 54 85 27 –47 74 

2.3 3-D Aerodynamic Blade Design of Embedded 1.5-Stage 

The 3-D aero-design of the blading for the 1.5-stage (R1/S2/R2) of the present study was described in 

detail earlier (Ref. 5). R1 and R2 were shrouded, and leakage flows were neglected. With design air 

angles from the meanline design code, the AFRL Turbine Design and Analysis System (TDAAS 

(Ref. 10)) was used to design, optimize, and stack 2-D airfoil sections, at hub, mid-span, and tip, into a 

3-D blade geometry. The chordwise-location of maximum loading was influenced by the findings of Gier 

et al. (Ref. 20) concerning efficiency, Re-lapse, and sensitivity to incidence in low pressure turbines 

designed for low-Re operation. The 2-D sections (provided in Ref. 5) were stacked on their center of 

gravity along a radial stacking axis. No dihedral was considered in the present study, although the benefits 

of 3-D aerodynamic design (Ref. 21) might well prove of benefit in managing the secondary flow fields 

discussed in Section 4.0. 

3.0 Computational Tools 

3.1 SWIFT 3-D RANS/Mixing-Plane Solver 

In the previous study (Ref. 5), design- and off-design conditions were analyzed using the 3-D RANS 

turbomachinery flow solver, SWIFT (Ref. 22). The finite-difference form of the thin-layer Navier-Stokes 

equations in Cartesian coordinates were marched with local time-stepping using a multi-stage explicit 

Runge-Kutta integration with implicit residual smoothing. Inviscid flux vector differences were calculated 

using central-differencing with artificial dissipation, or with the H-CUSP (used herein) or AUSM+

upwind schemes. The viscous terms were central differenced. 3-D C-grids without clearance blocks were 

used in all blade rows and were generated using the TCGRID code (Ref. 23). The fully turbulent variant 

of the Baldwin-Lomax (Ref. 24) (B-L) and Wilcox’s low-Re  turbulence model for transitional flows 

(Ref. 12) were used. The results from the low-Re  turbulence model were considered in the present 

study. The SWIFT code has been validated against a number of turbomachinery data sets (Ref. 25). 

The mixing-plane interface condition was used between blade rows in RANS/mixing-plane 

computations (SWIFT and LEO below). In addition to neglecting unsteady blade-row interaction, the 

mixing-plane approach does not conserve streamwise vorticity between blade rows. The mixing-plane 

assumption was, therefore, expected to degrade accuracy at high load (design) and off-design conditions 

with attendant strong secondary flow fields and blade-row interaction levels. 

3.2 LEO 3-D RANS/Mixing-Plane and URANS Solver 

The WAND grid generator and LEO RANS/URANS flow solver of AeroDynamic Solutions, Inc

(ADS) were used for both 3-D RANS/mixing-plane and URANS computations (Ref. 26). The ADS 

software was selected for the URANS analyses because it was available to the author due to its utilization 

by the AFRL design system (TDAAS). The WAND code was used to generate structured grids (O-H-H-H 

multi-blocks) suitable for turbulent flow with integration to the wall (near-wall y+

 near unity). No 

clearance blocks were used. LEO was used for both 3-D RANS single-passage, multistage, mixing-plane 

calculations; and, 3-D, time-accurate, sector-periodic URANS computations with sliding interfaces 

between blade rows. The Navier-Stokes equations, in finite-volume form and in cylindrical coordinates, 
NASA/TM—2012-217425 8 

were marched in time: local time stepping and multi-grid were used for the mixing-plane computations; 

and, implicit dual-time-stepping (Ref. 27) was used for time-accurate simulations. The LEO code is 

density based. Flux vectors were discretized using central-differencing with artificial dissipation. The 

low-Re  turbulence model (Ref. 12) was used. 

The multistage LEO/URANS computations of the present study utilized an implicit scaling2

algorithm to set flux vectors at the sliding interfaces. The implicit scaling algorithm allows arbitrary blade 

counts (e.g., 87/73/81 for R1/S2/R2 of the LCTR VSPT) to be approximated by specified reduced-count 

periodic sectors (e.g., 9/7/8 herein) for the sake of computational efficiency. The blade geometry of the 

baseline turbine was not modified; rather, for each blade row, the physical -extent swept-out by the 

periodic sector of the reduced blade-count description, was mapped to a nondimensional unit extent. The 

scaling factors for this unit mapping were subsequently used at each time-step to establish the 

interpolation appropriate to the baseline physical geometry, given the interpolation effected at the 

interface of the nondimensional periodic sectors of extent unity. 

After converging the URANS simulations to time-periodicity, the time-averaged flow field in each 

passage of the simulation was obtained by an arithmetic average (for constant time steps) of the q-vectors 

at each node over a user specified number of time-steps (1350 time steps herein, corresponding to rotor 

traverse of the periodic sector); similarly, attainment of an average passage in each blade row was 

accomplished by obtaining an arithmetic average of the time-averaged q-vectors at each node over the 

number of passages in the periodic sectors of that blade row. The time- and average-passage averaging 

were accomplished by using utilities available from ADS. 

3.3 Grid Topologies 

The SWIFT computations were conducted using a C-grid generated using the TCGRID (Ref. 23) 

code while the LEO solver utilized an O-H-H-H grid (no clearance block) generated using the WAND 

(Ref. 26) code. The grids for R1 are shown in Figure 5. The SWIFT grids (Fig. 5(a)) have 565 k grid cells 

per blade while the LEO grids have approximately 665 k grid cells per blade. The LEO grid was 

purposely generated using the ADS recommended WAND input values for fine turbomachinery grids. 

Figure 5.—Rotor 1 grids used in RANS/mixing-plane and URANS computations. 

 

2

Summarized in an unpublished write-up, Ni, R-H, Ni, M., and Fan, G., “Unsteady Analysis of a Multi 

Stage Axial Turbine Using Implicit Scaling,” May, 2011. 

a. C-grid from TCGRID b. O-H-H-H grid from WAND
NASA/TM—2012-217425 9 

3.4 Boundary Conditions 

Boundary conditions were obtained from the design and off-design meanline analyses. Inlet total 

conditions and swirl angles at mid-span were prescribed along with an assumption of free-vortex flow. 

The free vortex flow is consistent with the spanwise flow distributions of the meanline code and the 2-D 

airfoil design. Radial equilibrium, with a prescribed static pressure (at hub for SWIFT and mid-span for 

LEO) was enforced at the exit boundary. 

4.0 RANS/Mixing-Plane Results and Comparison 

Comparisons of the RANS/mixing-plane results of SWIFT and LEO, for the embedded 1.5-stage 

turbine (R1/S2/R2) at the design (54% N*, 28 k-ft cruise) and off-design (100% N*, 2 k-ft take-off) 

conditions, are presented in this section. First computed design and off-design spanwise profiles are 

compared to meanline predictions. At both design (54% N*

) and off-design (100% N*), the 3-D structures 

associated with secondary flow transport and rotor acceleration fields are then discussed. Comparison of 

design- and off-design performance levels at the blade row, stage, and overall 1.5-stage performance 

levels is deferred to Section 6.0. 

4.1 Spanwise Profiles 

Spanwise profiles of pitchwise-averaged (mixed-out) normalized total-temperature and total-pressure 

(referenced to S1 inlet conditions) and absolute flow angles were provided below (Figs. 6 to 8) for the 

design-point (cruise, N*

 = 54%) and off-design (takeoff, N* = 100%) conditions. The computed R1 inlet 

total-temperature is unity (not plotted in Fig. 6), as specified by the meanline analysis. The inlet 

boundary-layer thickness is evident in the R1 inlet total-pressure profile (black) in Figure 7. The R1-inlet 

absolute flow angles computed using both the SWIFT and LEO codes absolute flow matched the freevortex profile of the meanline (black) shown in Figure 8. 

In general, the agreement between the RANS/mixing-plane solver (SWIFT and LEO) and the 

meanline tool for total-temperature (Fig. 6), an indication of work, and total-pressure (Fig. 7) were 

acceptable, with the exception of the LEO mixing-plane results near the casing endwall, where 

nonphysical T0 distributions were evident. After investigation, it was noted that the region of non-physical 

T0 (negative entropy) was introduced by the LEO mixing-plane algorithm at spanwise sections containing 

negative axial velocity at the mixing-plane. Resolution of the issue associated with reverse-flow at the 

LEO mixing plane remains for future work. 

Figure 6.—Spanwise profiles of normalized total-temperature, T0, at R1 and R2 exits, showing comparison with 

meanline at design point (54% N*

, 28 k-ft cruise) and off-design (100% N*, 2 k-ft takeoff). 

0

10

20

30

40

50

60

70

80

90

100

0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98

Percent span from hub, %

Normalized absolute T0

R1 exit meanline

R1 exit SWIFT

R1 exit LEO

R2 exit SWIFT

R2 exit LEO

R2 exit meanline

0

10

20

30

40

50

60

70

80

90

100

0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98

Percent span from hub, %

Normalized absolute T0

R1 exit meanline

R1 exit SWIFT

R1 exit LEO

R2 exit meanline

R2 exit SWIFT

R2 exit LEO

a. Design-point (cruise, N* = 54%) b. Off-design (takeoff, N* = 100%)
NASA/TM—2012-217425 10 

Figure 7.—Spanwise profiles of normalized total-pressure, p0, at R1 inlet and R1, S2, and R2 exits, showing 

comparison with meanline at design point (54% N*

, 28 k-ft cruise) and off-design (100% N*, 2 k-ft takeoff). 

Figure 8.—Spanwise profiles of absolute flow angle at R1 inlet and R1, S2, and R2 exits, showing comparison with 

meanline at design point (54% N*

, 28 k-ft cruise) and off-design (100% N*, 2 k-ft takeoff). 

For the design- and off-design conditions, both solvers predicted a deficit in pitchwise-averaged totalpressure at the exit of S2 (from 60 to 95 percent of span at design and 70 to 95 percent at off-design). The 

R2 discharge was weak from hub to 20 percent of span at design. The magnitude and spanwise-location 

of the p0-deficits were consistent with the cross-passage contours of entropy shown in Figures 9 and 10. 

Low enthalpy extraction (Fig. 6 and turning Fig. 8) was predicted by both solvers for the prescribed 

pressure ratio (Fig. 7), though LEO was generally closer to design-intent (meanline). The axial rating 

planes for the CFD and meanline were not coincident, which might have contributed to the disparity in 

CFD and meanline flow angles (Fig. 8). In general, the LEO and SWIFT flow angles tracked one another 

qualitatively, though inflection points in the R1 and R2 exit profiles (e.g., Fig. 8) were shifted spanwise 

relative to each other, indicating differences in the transport of low momentum flow by the secondary 

flow fields. 

0

10

20

30

40

50

60

70

80

90

100

0.4 0.5 0.6 0.7 0.8 0.9 1

Percent span from hub, %

Normalized absolute p0

R1 inlet meanline

R1 inlet SWIFT

R1 inlet LEO

R1 exit meanline

R1 exit SWIFT

R1 exit LEO

S2 exit meanline

S2 exit SWIFT

S2 exit LEO

R2 exit meanline

R2 exit SWIFT

R2 exit LEO

0

10

20

30

40

50

60

70

80

90

100

0.4 0.5 0.6 0.7 0.8 0.9 1

Percent span from hub, %

Normalized absolute p0

R1 inlet meanline

R1 inlet SWIFT

R1 inlet LEO

R1 exit meanline

R1 exit SWIFT

R1 exit LEO

S2 exit meanline

S2 exit SWIFT

S2 exit LEO

R2 exit meanline

R2 exit SWIFT

R2 exit LEO

a. Design-point (cruise, N* = 54%) b. Off-design (takeoff, N* = 100%)

0

10

20

30

40

50

60

70

80

90

100

-60 -40 -20 0 20 40 60 80

Percent span from hub, %

Absolute flow angle, deg.

R1 inlet meanline

R1 exit meanline

R1 exit SWIFT

R1 exit LEO

S2 exit meanline

S2 exit SWIFT

S2 exit LEO

R2 exit meanline

R2 exit SWIFT

R2 exit LEO

0

10

20

30

40

50

60

70

80

90

100

-20 0 20 40 60 80

Percent span from hub, %

Absolute flow angle, deg.

R1 inlet

R1 exit meanline

R1 exit SWIFT

R1 exit LEO

S2 exit meanline

S2 exit SWIFT

S2 exit LEO

R2 exit meanline

R2 exit SWIFT

R2 exit LEO

a. Design-point (cruise, N* = 54%) b. Off-design (takeoff, N* = 100%)
NASA/TM—2012-217425 11 

Figure 9.—Computed contours of entropy at the blade-row exit planes from RANS/mixing-plane calculations at 

design point (54% N*

, 28 k-ft cruise). 

Figure 10.—Computed contours of entropy at the blade-row exit planes from RANS/mixing-plane calculations at 

off-design point (100% N*

, 2 k-ft takeoff). 

4.2 Cross-Passage Contours at Blade-Row Exits 

4.2.1 Design-Point (28 k-ft, 54% N*) 

Design-point (28 k-ft, 54% N*

) entropy contours at the exit plane of blade rows R1, S2, and R2, 

computed using SWIFT and LEO RANS/mixing-plane, were provided in Figure 9. The low momentum 

flow, transported by the secondary flow field, accumulated preferentially at the hub/suction-side corners 

of the rotors and at the case/suction-side corner of the stator. With the mixing-plane approximation, these 

regions of low relative total-pressure were mixed-out between blade rows, and were manifested as 

axisymmetric bands (not shown) of high entropy flow downstream of each mixing plane. In practice, the 

regions of high aerodynamic-blockage would be strong sources of unsteadiness and induce spanwise 

mixing in the downstream blade row. In general, the contours from the RANS/mixing-plane 

calculations—SWIFT and LEO—were in good agreement. 

R1

exit

R2

exit

S2

exit

R1

exit

R2

exit

S2

exit

a. SWIFT b. LEO

R1

exit

R2

exit

S2

exit

R1

exit

R2

exit

S2

exit

a. SWIFT b. LEO
NASA/TM—2012-217425 12 

Figure 11.—Contours of axial velocity and streamlines in R1 and R2 at the 100% N* off-design takeoff point from 

mixing-plane computations of (a) SWIFT (Ref. 5) and (b) LEO. 

4.2.2 Off-Design (2 k-ft, 100% N*) 

The off-design (2 k-ft, 100% N*

) entropy contours at the exit plane of blade rows R1, S2, and R2 

were provided in Figure 10. Again, the two RANS/mixing-plane solvers were in good agreement. As at 

the design point (Fig. 9), the secondary flow fields transported flow to the rotor hub/suction-side corners 

and stator case/suction-side corner. Compared to the design-point flow, the regions of lower total-pressure 

were more diffuse, particularly in the high-turning second rotor, R2, due to the redistribution of low 

momentum flow from the hub regions to the casing via the pressure-side cove separation/vortex (Fig. 11). 

As shown in Figure 11, both RANS/mixing-plane solvers showed little reverse flow in the pressureside cove region of R1 at the off-design (negative incidence) condition. In R2, the strong vortical structure 

in the pressure-side cove was predicted by both solvers. The low-momentum flow was transported 

radially outward and discharged from the rotor at about 75 percent of span from hub. S2 had significant 

regions of reverse flow in the pressure-side cove as well at the off-design point; however, without the 

strong radial acceleration fields, no comparable 3-D structure was formed in the stator. 

5.0 URANS Comparison With RANS/Mixing-Plane 

As noted in the previous section, the results from the SWIFT and LEO RANS/mixing-plane solvers 

agreed well. In this section, the LEO RANS/mixing-plane results were compared with time-averaged, 

averaged-passage results from LEO sector-periodic URANS simulations at the VSPT design- and offdesign operating conditions. 

5.1 Spanwise Profiles 

Neglecting differences in the R1 exit profile (Fig. 12) in the first 5 percent immersion from case 

(associated with the LEO mixing-plane issue described earlier), the time-averaged, averaged-passage 

URANS results were in substantial agreement with the mixing-plane results. R1 and S2 exit profiles of T0

(Fig. 12) and p0 (Fig. 13) reflected negligible impact of unsteadiness in R1 and S2. Differences were 

noted in the R2-exit temperature profile (Fig. 12) where the greatest impact of unsteadiness associated 

with blade rows R1 and S2 was anticipated. At design-point operation the URANS T0 and p0 distributions 

(Figs. 12(a) and 13(a)) reflected lower R2 work extraction (and efficiency) from 0 to 60 percent span 

R1

R2

S2

a. SWIFT b. LEO

R1

R2

S2
NASA/TM—2012-217425 13 

from hub. At the extreme negative incidence point of off-design operation, the unsteadiness due to bladerow interaction was most expected to impact the time-mean flow in the pressure-side cove. The R2 work 

(Fig. 12(b)) of the URANS simulation was lower at 75 percent span from hub, perhaps reflecting the 

impact of unsteadiness on the tornado structure discharged at about this spanwise location (Fig. 11). 

5.2 Cross-Passage Contours at Blade-Row Exits 

Consistent with the agreement in the spanwise distributions, RANS/mixing-plane and URANS timeaveraged, average passage (URANS TA/AP) results for the design- (Fig. 15) and off-design (Fig. 16) 

operating points agreed well. The URANS TA/AP results are generally more diffuse than the mixingplane, reflective of the spatial envelope of time-dependent motion of vortical structures; nonetheless, the 

RANS/mixing plane results have evidently captured the key blade row flow physics quite well, in spite of 

the recognized modeling limitations introduced by the mixing-plane assumption (Section 1.1). The offdesign results (Fig. 16), at which the blade-rows were most unloaded (low turning) and negativeincidence levels into all blade rows were highest, were in particularly good agreement. 

Figure 12.—Spanwise profiles of normalized total-temperature, T0, at R1 and R2 exits, showing comparison with 

meanline at design point (54% N*

, 28 k-ft cruise) and off-design (100% N*, 2 k-ft takeoff). 

Figure 13.—Spanwise profiles of normalized total-pressure, p0, at R1 inlet and R1, S2, and R2 exits, showing 

comparison with meanline at design point (54% N*

, 28 k-ft cruise) and off-design (100% N*, 2 k-ft takeoff). 

0

10

20

30

40

50

60

70

80

90

100

0.8 0.85 0.9 0.95

Percent span from hub, %

Normalized absolute T0

R1 exit meanline

R1 exit LEO URANS

R1 exit LEO

R2 exit meanline

R2 exit LEO URANS

R2 exit LEO

0

10

20

30

40

50

60

70

80

90

100

0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96

Percent span from hub, %

Normalized absolute T0

R1 exit meanline

R1 exit LEO URANS

R1 exit LEO

R2 exit meanline

R2 exit LEO URANS

R2 exit LEO

a. Design-point (cruise, N* = 54%) b. Off-design (takeoff, N* = 100%)

0

10

20

30

40

50

60

70

80

90

100

0.4 0.5 0.6 0.7 0.8 0.9 1

Percent span from hub, %

Normalized absolute p0

R1 inlet meanline

R1 inlet LEO URANS

R1 inlet LEO

R1 exit meanline

R1 exit LEO URANS

R1 exit LEO

S2 exit meanline

S2 exit LEO URANS

S2 exit LEO

R2 exit meanline

R2 exit LEO URANS

R2 exit LEO

0

10

20

30

40

50

60

70

80

90

100

0.4 0.5 0.6 0.7 0.8

Percent span from hub, %

Normalized absolute p0

R1 exit meanline

R1 exit LEO URANS

R1 exit LEO

S2 exit meanline

S2 exit LEO URANS

S2 exit LEO

R2 exit meanline

R2 exit LEO URANS

R2 exit LEO

a. Design-point (cruise, N* = 54%) b. Off-design (takeoff, N* = 100%)
NASA/TM—2012-217425 14 

Figure 14.—Spanwise profiles of absolute flow angle at R1 inlet and R1, S2, and R2 exits, showing comparison 

with meanline at design point (54% N*

, 28 k-ft cruise) and off-design (100% N*, 2 k-ft takeoff). 

Figure 15.—Computed contours of entropy at the blade-row exit planes from LEO RANS/mixing-plane timeaveraged, average passage URANS calculations at design point (54% N*

, 28 k-ft cruise). 

0

10

20

30

40

50

60

70

80

90

100

-20 0 20 40 60 80

Percent span from hub, %

Absolute flow angle, deg.

R1 inlet

R1 exit meanline

R1 exit LEO URANS

R1 exit LEO

S2 exit meanline

S2 exit LEO URANS

S2 exit LEO

R2 exit meanline

R2 exit LEO URANS

R2 exit LEO

0

10

20

30

40

50

60

70

80

90

100

-60 -40 -20 0 20 40 60 80

Percent span from hub, %

Absolute flow angle, deg.

R1 exit meanline

R1 exit LEO URANS

R1 exit LEO

S2 exit meanline

S2 exit LEO URANS

S2 exit LEO

R2 exit meanline

R2 exit LEO URANS

R2 exit LEO

a. Design-point (cruise, N* = 54%) b. Off-design (takeoff, N* = 100%)

0

10

20

30

40

50

60

70

80

90

100

-60 -40 -20 0 20 40 60 80

Percent span from hub, %

Absolute flow angle, deg.

R1 exit meanline

R1 exit LEO URANS

R1 exit LEO

S2 exit meanline

S2 exit LEO URANS

S2 exit LEO

R2 exit meanline

R2 exit LEO URANS

R2 exit LEO

0

10

20

30

40

50

60

70

80

90

100

-60 -40 -20 0 20 40 60 80

Percent span from hub, %

Absolute flow angle, deg.

R1 exit meanline

R1 exit LEO URANS

R1 exit LEO

S2 exit meanline

S2 exit LEO URANS

S2 exit LEO

R2 exit meanline

R2 exit LEO URANS

R2 exit LEO

R1

exit

R2

exit

S2

exit

R1

exit

R2

exit

S2

exit

a. LEO mixing-plane b. LEO URANS TA/AP
NASA/TM—2012-217425 15 

Figure 16.—Computed contours of entropy at the blade-row exit planes at off-design point from LEO 

RANS/mixing-plane time-averaged, average passage URANS calculations at takeoff (2 k-ft, 100% N*

). 

6.0 Overall VSPT Performance 

The performance levels of the individual blade-rows and embedded stages, as predicted by the two 

RANS/mixing-plane solvers (SWIFT and LEO) and the LEO sector-periodic URANS solver, are 

compared to the meanline code levels in this section. Key blade-row and stage level metrics are reported 

in Table 4. The change in embedded 1.5-stage (R1/S2/R2) efficiency with speed is provided in Figure 17. 

The reported efficiencies and loss levels are based a spanwise mass-average of the pitchwise-averaged 

(mixed-out) flow at each section (k-plane). The performance levels of the mixing-plane codes are 

discussed first and the time-averaged, average-passage URANS levels follow. The trend of efficiency 

versus shaft-speed from the various solvers is presented in the final section. 

As a preface to discussion on performance levels, it is noted that the rotor efficiencies of the LEO 

RANS/mixing-plane solution reported in Table 4 are considered high as a result of the non-physical flow 

(mixing-plane issue) introduced at the R1 and R2 exit rating planes. The potential impact on performance 

rating was substantiated by plotting the axial distribution of passage-averaged p0 upstream and 

downstream of the rotor blade rows, whereby it was evident which axial stations were impacted by the 

non-physical flow. The contaminated R1 exit may have similarly caused high S2 loss levels to be reported 

for the LEO RANS/mixing-plane solution. The mixing-plane issue unfortunately limited the 

understanding that was to have been derived through the comparison of the predicted performance levels 

of the two mixing-plane solvers; and, more importantly, through comparison of the mixing-plane and 

URANS TA/AP results obtained on the same grid with the same flow solver. The SWIFT mixing-plane 

and the LEO URANS results did not suffer from the non-physical mixing-plane issue. 

6.1 RANS/Mixing-Plane Blade-Row Performance Levels 

Compared to the design- and off-design values from the meanline codes, the SWIFT mixing-plane 

predicted significantly lower R1 and S2 performance levels (Table 4). This was attributed to the 

difference in the computed work split in R1 and R2 by SWIFT as compared to meanline design-intent 

(Ref. 5). Unlike the meanline, the R2 efficiency of SWIFT decreased as shaft-speed was increased from 

N* = 54 to 100%, a difference attributed to loss production induced at off-design by the pressure-side cove 

vortex that was not captured by the meanline model (Ref. 5). The S2 loss levels, though almost two times 

higher than the meanline levels, trended correctly with VSPT shaft-speed change. 

R1

exit

R2

exit

S2

exit

R1

exit

R2

exit

S2

exit

a. LEO mixing-plane b. LEO URANS TA/AP
NASA/TM—2012-217425 16 

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

Design (54% N*

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

Model 

SWIFT 

RANS 

LEO 

RANS 

LEO 

URANS MEANLINE 

SWIFT 

RANS 

LEO 

RANS 

LEO 

URANS MEANLINE 

R1 tt 0.9152 0.9414 0.9349 0.9275 0.9481 0.9597 0.9525 0.9530 

R2 tt 0.9329 0.9281 0.9121 0.9453 0.9258 0.9326 0.9219 0.9692 

R1/S2tt 0.8100 0.8454 0.8454 0.8682 0.8679 0.8912 0.8822 0.9080 

S2/R2 tt 0.8444 0.8563 0.8463 0.9005 0.8269 0.8501 0.8383 0.9042 

R1/S2/R2 tt 0.8792 0.8952 0.8868 0.9152 0.9013 0.9170 0.9073 0.9448 

S2 Y 0.1414 0.1117 0.1157 0.0718 0.1326 0.1040 0.1088 0.0666 

S2 p0/p0 0.0436 0.0361 0.0368 0.0222 0.0329 0.0266 0.0278 0.0165 

PRTT R1/S2/R2 2.1375 2.1355 2.1434 2.1454 2.1307 2.1301 2.1323 2.1555 

TRTT

R1/S2/R2 

1.1779 1.1815 1.1804 1.1875 1.1756 1.1791 1.1772 1.1887 

Wc, lbm/s 12.942 12.874 12.797 12.868 12.423 12.224 12.169 12.060 

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

speed from cruise (54% N*

) to takeoff (100% N*) for SWIFT mixing-plane (BaldwinLomax and low-Re ), LEO mixing-plane (low-Re ), and LEO URANS TA/AP 

(low-Re . 

As noted in Section 4.0, the spanwise distributions of T0 and p0 from LEO mixing-plane were 

generally in better agreement with the meanline design-intent than those of SWIFT. The LEO 

RANS/mixing-plane predicted higher efficiency in R1 than in R2, in disagreement with the meanline 

design-intent where R1 efficiency is lower than R2 efficiency. The trends of increased R1 and R2 

efficiency, and decreased S2 loss levels, with increased VSPT shaft-speed were in agreement with the 

meanline (Table 4). 

6.2 URANS Blade-Row Performance Levels 

The time-averaged, averaged-passage URANS results (Table 4) were generally in excellent 

agreement with results from the meanline codes, with the exception of the R2 efficiency, which was lower 

than design-intent. The trends of R1 and R2 efficiency and S2 loss levels with shaft-speed change were in 

agreement with the meanline. 

0.87

0.88

0.89

0.9

0.91

0.92

0.93

0.94

0.95

0 0.2 0.4 0.6 0.8 1 1.2

Adiabatic efficiency of R1/S2/R2

N / N100%

Meanline

SWIFT RANS/mixing-plane/B-L

SWIFT RANS/mixing-plane/k-w

LEO RANS/mixing-plane/k-w

LEO URANS TA/AP/k-w
NASA/TM—2012-217425 17 

Arguably, a comparison of the LEO RANS/mixing-plane and LEO URANS results of Table 4 might 

suggest that the blade-row interaction effects have degraded R2 efficiency by one point relative to the 

mixing-plane, and hence the overall embedded 1.5-stage performance. At off-design, the efficiency 

difference might be attributed, in part, to the impact of unsteadiness on vortical flows—particularly the 

tornado of the pressure-side-cove at off-design—manifested as increased entropy production and reduced 

work in the time-mean, average-passage flow. Similarly, a constituent of the efficiency-delta 

(RANS/mixing-plane versus URANS) at off-design (N*

 = 100%) might arguably be attributed to the 

impact of unsteadiness on the S2 loss levels at the high negative incidence conditions of off-design 

operation. Unfortunately, the deleterious impact of the non-physical endwall flow in the LEO mixingplane solution makes the inferences tenuous. 

6.3 Efficiency Versus Shaft-Speed Trend of Embedded 1.5-Stage 

The predicted variation of embedded 1.5-stage (R1/S2/R1) efficiency with speed change for the 

various modeling approaches was provided in Figure 17. The difference in the embedded stage 

efficiencies of the SWIFT and LEO RANS/mixing plane solutions of the present study was largely 

attributed to the significantly different R1 efficiency levels and S2 loss levels. As shown, the results for 

both mixing-plane solvers agreed in terms of the predicted trend of efficiency versus speed. The fully 

turbulent SWIFT/mixing-plane with Baldwin-Lomax (fully turbulent option) from Reference 5 was 

repeated for reference. The slope of the efficiency-speed trend of the fully turbulent B-L solutions most 

closely agrees with the slope of the meanline. As in the earlier study (Ref. 5), the solutions using the lowRe RANS and URANS) have different slopes than the fully turbulent result, but nonetheless trend 

the same as the meanline. 

As evident by comparing the time-averaged, average-passage URANS results with the mixing-plane 

results (Fig. 17), the unsteadiness due to blade-row interaction did not impact the qualitative trend of 

efficiency versus shaft-speed change. The VSPT, which was designed at the cruise shaft speed N*

 = 54%, 

showed increased efficiency at N*

 = 100%, in spite of the potential for performance degradation by 

unsteady forcing at this operating condition. As mentioned, an attribution of the difference between the 

LEO RANS/mixing-plane and URANS TA/AP efficiency levels (Fig. 17) to the effects of unsteadiness 

was unfortunately not substantiated herein. 

7.0 Conclusion 

RANS/mixing-plane and the time-averaged, averaged-passage URANS simulation results were 

compared at the design- and off-design operating points of a variable-speed power turbine (VSPT) for the 

NASA Large Civil Tilt-Rotor application. The impact of unsteadiness associated with blade-row interaction 

was assessed in term of its impact on efficiency and the trend of efficiency with shaft-speed change. 

The unsteadiness was found to degrade work and efficiency levels in Rotor 2, which was most 

impacted by the upstream blade rows of the embedded R1/S2/R2 1.5-stage simulation. Quantification of 

the efficiency degradation (approximately 1 point) associated with unsteadiness, vis-à-vis comparison of 

efficiency predicted using the RANS/mixing-plane and sector-periodic URANS computations, was 

unfortunately rendered inconclusive. Introduction of non-physical flow at the rotor mixing-planes 

precluded a definitive back-to-back comparison of results from RANS/mixing-plane and URANS 

computations on the same grid, by the same flow solver (LEO). 

The trend of efficiency with changing VSPT shaft speed from the URANS simulation, from N*

 = 54% 

(28 k-ft, cruise) to N*

 = 100% (2 k-ft, takeoff), agreed with the corresponding trends from the two 

RANS/mixing plane codes (SWIFT and LEO) and meanline codes used for turbine design. This key 

finding gives confidence to the turbine designer in their selection of optimum turbine design speed for 

minimizing mission fuel burn. 
NASA/TM—2012-217425 18 

References 

1. Acree, C.W., Hyeonsoo, Y., and Sinsay, J.D., “Performance Optimization of the NASA Large Civil 

Tiltrotor,” Proc. Int. Powered Lift Conf., London, UK, July 22–24, 2008. 

2. Stevens, M.A., Handschuh, R.F., Lewicki, D.G., “Variable/Multispeed Rotorcraft Drive System 

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

3. D′Angelo, M., “Wide Speed Range Turboshaft Study,” NASA/CR—1995–198380, Aug, 1995. 

4. Welch, G.E., “Assessment of Aerodynamic Challenges of a Variable-Speed Power Turbine for 

Large Civil Tilt-Rotor Application,” Proc. AHS Int. 66th Ann. Forum, TX, May, 2010; also 

NASA/TM—2010-216758, Aug, 2010. 

5. Welch, G.E., “Computational Assessment of the Aerodynamic Performance of a Variable-Speed 

Power Turbine for Large Civil Tilt-Rotor Application,” Proc. AHS Int. 67th Ann. Forum, May, 

2011; also NASA/TM—2011-217124, Nov., 2011. 

6. Suchezky, M. and Cruzen, G.S., “Variable-Speed Power Turbine for the Large Civil Tilt Rotor,” 

NASA/CR—2012-217424, Feb. 2012. 

7. Ford, A., Turner, E., Bloxham, M., Gegg, S., King, B., Harris, C., Bell, M. and Eames, D., 

“Variable-Speed Power-Turbine Component Research Plan,” NASA/CR—2012-217423, 

Feb. 2012. 

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Propulsion system for Large Civil Tilt-Rotor Applications,” Proc. AHS Int. Forum 68, May, 2012; 

also NASA/TM—2012-217134, 2012. 

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Transport Rotorcraft,” NASA/CR—2009-214594, Jun, 2009. 

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Johnson, P.D., “Design of Turbine Components to Answer Research Questions in Unsteady 

Aerodynamics and Heat Transfer,” AFRL-RZ-WP-TR-2009-2180, Sep, 2009. 

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Turbomachinery using an Implicit Dual Time-Step Approach,” AIAA-1996-2565, Jul, 1996. 
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4. TITLE AND SUBTITLE

Computational Study of the Impact of Unsteadiness on the Aerodynamic Performance of a 

Variable-Speed Power Turbine 

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6. AUTHOR(S)

Welch, Gerard, E. 

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WBS 877868.02.07.03.01.02.01 

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National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

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14. ABSTRACT

The design-point and off-design performance of an embedded 1.5-stage portion of a variable-speed power turbine (VSPT) was assessed 

using Reynolds-Averaged Navier-Stokes (RANS) analyses with mixing-planes and sector-periodic, unsteady RANS analyses. The VSPT 

provides one means by which to effect the nearly 50 percent main-rotor speed change required for the NASA Large Civil Tilt-Rotor (LCTR) 

application. The change in VSPT shaft-speed during the LCTR mission results in blade-row incidence angle changes of as high as 55°. 

Negative incidence levels of this magnitude at takeoff operation give rise to a vortical flow structure in the pressure-side cove of a high-turn 

rotor that transports low-momentum flow toward the casing endwall. The intent of the effort was to assess the impact of unsteadiness of 

blade-row interaction on the time-mean flow and, specifically, to identify potential departure from the predicted trend of efficiency with 

shaft-speed change of meanline and 3-D RANS/mixing-plane analyses used for design.

15. SUBJECT TERMS

Axial flow turbine; Low pressure turbine; Rotary wing; Tilt-rotor; Aerodynamics 

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